SoSe 25  
 Mathematics and...  
 Master's progra...  
 Course

Computer Science

Master's programme in Computer Science (2014 study regulations)

0089c_MA120

  • Software Project: Applied Computer Science A

    0089cA1.23
    • 19308412 Project Seminar
      Software Project: Data Management (Agnès Voisard)
      Schedule: Mo 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-02-05)
      Location: T9/137 Konferenzraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group

      Students in the Master's or Bachelor's programme

       

      Prerequisites

      Good programming skills, introduction to database systems.

      Comments

      Subject of the project: either development of software together with a company (in this case: 4­ weeks fulltime August/September) or we build a so called NoSQL system. Decision in March. Further information are published in the KVV.

      Suggested reading

      Wird bekannt gegeben. / To be announced.
    • 19314012 Project Seminar
      Software Project: Semantic Technologies (Adrian Paschke)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A7/SR 031 (Arnimallee 7)

      Additional information / Pre-requisites

      Corporate Semantic Web

      Further information can be found on the course website

      Comments

      Mixed groups of master and bachelor students will either implement an independent project or are part of a larger project in the area of semantic technologies. They will gain in-depth programming knowledge about applications of semantic technologies and artificial intelligence techniques in the Corporate Semantic Web. They will practice teamwork and best practices in software development of large distributed systems and Semantic Web applications. The software project can be done in collaboration with an external partner from industry or standardization. It is possible to continue the project as bachelor or master thesis.

      Suggested reading

      Corporate Semantic Web
    • 19323612 Project Seminar
      The AMOS Project (Lutz Prechelt)
      Schedule: -
      Location: keine Angabe

      Additional information / Pre-requisites

      Educational objectives and competencies

      • Students learn about software products and software development in an industry context
      • Students learn about agile methods, in particular Scrum and Extreme Programming
      • Students learn about open source software development and its underlying principles
      • Students gain practical hands-on experience with a Scrum process and XP technical practices

      Target group

      Students of computer science (and related fields). If you want to play the software developer role, you should have had practical programming experience. This is not a course to learn programming.

      Language

      English (lectures in English, team meeting German or English by choice of student team)

      Grading

      • Software developer
        • 10% of grade: 5 class quizzes, each consisting of 5 questions at 2 points each
        • 90% of grade: Weekly project work

      Other

      • SWS: 4 SWS (2 SWS lecture, 2 SWS team meeting)
      • Semester: Every semester
      • Modality: Online, across multiple universities
      • Tags: Scrum

       

      Comments

      This course teaches agile methods (Scrum and XP) and open source tools using a single semester-long project. It takes place online and across multiple universities. Topics covered are:

      • Agile methods and related software development processes
      • Scrum roles, process practices, including product and engineering management
      • Technical practices like refactoring, continuous integration, and test-driven development
      • Principles and best practices of open source software development

      The project is a software development project in which each student team works with an industry partner who provides the idea for the project. This is a practical hands-on experience.

      Students play the role of a software developer. In this role, students estimate the effort for requirements and implement them. Students must have prior software development experience.

      Students will be organized into teams of 7-9 people, combining one Scrum master with two product owners with six software developers.

      An industry partner will provide requirements to be worked out in detail by the product owners and to be realized by the software developers. The available projects will be presented in the run-up to the course.

      Class consists of a 90 min. lecture followed by a 90 min. team meeting. Rooms and times for team meetings are assigned at the beginning of the semester. You must be able to regularly participate in the team meetings. If you can't, do not sign up for this course.

      Attention: this course is organized externally and additional sign-up steps are required. Sign-up and further course information are available through a Google spreadsheet at https://amos.uni1.de – please declare your interest by filling out the course interest declaration survey as soon as it opens.

      Suggested reading

      http://goo.gl/5Wqnr7
    • 19329912 Project Seminar
      Software Project: Secure Identity (Volker Roth)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A7/SR 031 (Arnimallee 7)

      Comments

      Die Aufgabe wird die Entwicklung einer Software sein. Es wird um sichere Softwareentwicklung gehen. Die Aufgabe wird in Gruppenarbeit gelöst.
    • 19334212 Project Seminar
      Softwareproject: Machine Learning and Explainability for Improved (Cancer) Treatment (Pauline Hiort)
      Schedule: Di 15:00-17:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-02-26)
      Location: T9/K40 Multimediaraum (Takustr. 9)

      Comments

      In the software project, we will implement, train, and evaluate various machine learning (ML) methods. The focus of the project is on neural networks (NN) and their explainability. We will compare the methods with different baseline models, such as regression models. The various ML methods will be applied to a specific dataset, e.g., for predicting drug combinations for cancer treatment, and evaluated accordingly. The dataset will be prepared by us and analyzed using the implemented methods. Additionally, we will focus on explainability to ensure that the predictions of the ML models are understandable and interpretable. For this purpose, we will integrate appropriate explainability techniques to better understand and visualize the decision-making processes of the models.

      The programming language is Python, and we plan to use modern Python modules for ML like scikit-learn, and PyTorch. Good Python skills are required. The goal is to create a Python package that provides reusable code for preprocessing, training ML models, and evaluating results with documentation (e.g., using Sphinx) for the specific use case. The software project takes place throughout the semester and can also be conducted in English.
    • 19334412 Project Seminar
      SWP: Szenario-Management in the Future Security Lab (Larissa Groth)
      Schedule: Mi 23.04. 14:00-16:00 (Class starts on: 2025-04-23)
      Location: T9/K63 Hardwarepraktikum (Takustr. 9)

      Comments

      The BeLIFE project, part of the working group Telematics & Computer Systems, focuses on improving knowledge transfer and communication in civil security research. A central component of the project is the Future Security Lab, located at the Einstein Center Digital Future (ECDF) in Mitte. The lab welcomes politicians from federal and state levels, as well as representatives from authorities and organizations with security responsibilities.

      Within the software project, students develop concepts to optimize and creatively enhance the existing technical infrastructure of the space. The goal is to increase the usability of the space for scientists and improve the user experience for visitors. To achieve this, the software project consists of several sub-areas, either arising from a specific problem to be solved or requiring creative approaches and ingenuity. Tasks include system administration, interface development, as well as light/sound installation and orchestration. Examples of challenges include the parallel startup of all computers in a network via WakeOn LAN from a web app or optimizing the existing web app for scenario presentation.

      The tasks are exclusively addressed in small groups (3-5 students). Collaboration and code availability are facilitated through the department's own GitLab or a public GitHub. Results should be well-documented, for example, through README files in Git and a well-structured wiki. Modularity and expandability of the developed code, along with thorough documentation, are crucial for the success of this software project!

      Regarding the process, this software project takes place throughout the semester. There are a few mandatory large group meetings with all participants. In addition, there are short weekly meetings where at least one group member reports on the current status. The first date (23.04.25, 14h, K63) will take place at Takustraße 9. At this event, the solutions already implemented will be presented in theory and the problems addressed. A live demo will then take place one week later, on 30.04.2025, in Berlin Mitte at the Future Security Lab, Wilhelmstr. 67, 10117 Berlin. Afterwards, there are a total of three presentation dates: the presentation of an initial approach to problem-solving (14.04.2025), a brief interim presentation (11.06.2025), and the final presentation (16.07.2025).

      Students also regularly have the opportunity to work in the Future Security Lab premises, familiarize themselves with the equipment, and conduct tests.

  • Software Project: Applied Computer Science B

    0089cA1.24
    • 19308412 Project Seminar
      Software Project: Data Management (Agnès Voisard)
      Schedule: Mo 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-02-05)
      Location: T9/137 Konferenzraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group

      Students in the Master's or Bachelor's programme

       

      Prerequisites

      Good programming skills, introduction to database systems.

      Comments

      Subject of the project: either development of software together with a company (in this case: 4­ weeks fulltime August/September) or we build a so called NoSQL system. Decision in March. Further information are published in the KVV.

      Suggested reading

      Wird bekannt gegeben. / To be announced.
    • 19314012 Project Seminar
      Software Project: Semantic Technologies (Adrian Paschke)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A7/SR 031 (Arnimallee 7)

      Additional information / Pre-requisites

      Corporate Semantic Web

      Further information can be found on the course website

      Comments

      Mixed groups of master and bachelor students will either implement an independent project or are part of a larger project in the area of semantic technologies. They will gain in-depth programming knowledge about applications of semantic technologies and artificial intelligence techniques in the Corporate Semantic Web. They will practice teamwork and best practices in software development of large distributed systems and Semantic Web applications. The software project can be done in collaboration with an external partner from industry or standardization. It is possible to continue the project as bachelor or master thesis.

      Suggested reading

      Corporate Semantic Web
    • 19323612 Project Seminar
      The AMOS Project (Lutz Prechelt)
      Schedule: -
      Location: keine Angabe

      Additional information / Pre-requisites

      Educational objectives and competencies

      • Students learn about software products and software development in an industry context
      • Students learn about agile methods, in particular Scrum and Extreme Programming
      • Students learn about open source software development and its underlying principles
      • Students gain practical hands-on experience with a Scrum process and XP technical practices

      Target group

      Students of computer science (and related fields). If you want to play the software developer role, you should have had practical programming experience. This is not a course to learn programming.

      Language

      English (lectures in English, team meeting German or English by choice of student team)

      Grading

      • Software developer
        • 10% of grade: 5 class quizzes, each consisting of 5 questions at 2 points each
        • 90% of grade: Weekly project work

      Other

      • SWS: 4 SWS (2 SWS lecture, 2 SWS team meeting)
      • Semester: Every semester
      • Modality: Online, across multiple universities
      • Tags: Scrum

       

      Comments

      This course teaches agile methods (Scrum and XP) and open source tools using a single semester-long project. It takes place online and across multiple universities. Topics covered are:

      • Agile methods and related software development processes
      • Scrum roles, process practices, including product and engineering management
      • Technical practices like refactoring, continuous integration, and test-driven development
      • Principles and best practices of open source software development

      The project is a software development project in which each student team works with an industry partner who provides the idea for the project. This is a practical hands-on experience.

      Students play the role of a software developer. In this role, students estimate the effort for requirements and implement them. Students must have prior software development experience.

      Students will be organized into teams of 7-9 people, combining one Scrum master with two product owners with six software developers.

      An industry partner will provide requirements to be worked out in detail by the product owners and to be realized by the software developers. The available projects will be presented in the run-up to the course.

      Class consists of a 90 min. lecture followed by a 90 min. team meeting. Rooms and times for team meetings are assigned at the beginning of the semester. You must be able to regularly participate in the team meetings. If you can't, do not sign up for this course.

      Attention: this course is organized externally and additional sign-up steps are required. Sign-up and further course information are available through a Google spreadsheet at https://amos.uni1.de – please declare your interest by filling out the course interest declaration survey as soon as it opens.

      Suggested reading

      http://goo.gl/5Wqnr7
    • 19329912 Project Seminar
      Software Project: Secure Identity (Volker Roth)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A7/SR 031 (Arnimallee 7)

      Comments

      Die Aufgabe wird die Entwicklung einer Software sein. Es wird um sichere Softwareentwicklung gehen. Die Aufgabe wird in Gruppenarbeit gelöst.
    • 19334212 Project Seminar
      Softwareproject: Machine Learning and Explainability for Improved (Cancer) Treatment (Pauline Hiort)
      Schedule: Di 15:00-17:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-02-26)
      Location: T9/K40 Multimediaraum (Takustr. 9)

      Comments

      In the software project, we will implement, train, and evaluate various machine learning (ML) methods. The focus of the project is on neural networks (NN) and their explainability. We will compare the methods with different baseline models, such as regression models. The various ML methods will be applied to a specific dataset, e.g., for predicting drug combinations for cancer treatment, and evaluated accordingly. The dataset will be prepared by us and analyzed using the implemented methods. Additionally, we will focus on explainability to ensure that the predictions of the ML models are understandable and interpretable. For this purpose, we will integrate appropriate explainability techniques to better understand and visualize the decision-making processes of the models.

      The programming language is Python, and we plan to use modern Python modules for ML like scikit-learn, and PyTorch. Good Python skills are required. The goal is to create a Python package that provides reusable code for preprocessing, training ML models, and evaluating results with documentation (e.g., using Sphinx) for the specific use case. The software project takes place throughout the semester and can also be conducted in English.
    • 19334412 Project Seminar
      SWP: Szenario-Management in the Future Security Lab (Larissa Groth)
      Schedule: Mi 23.04. 14:00-16:00 (Class starts on: 2025-04-23)
      Location: T9/K63 Hardwarepraktikum (Takustr. 9)

      Comments

      The BeLIFE project, part of the working group Telematics & Computer Systems, focuses on improving knowledge transfer and communication in civil security research. A central component of the project is the Future Security Lab, located at the Einstein Center Digital Future (ECDF) in Mitte. The lab welcomes politicians from federal and state levels, as well as representatives from authorities and organizations with security responsibilities.

      Within the software project, students develop concepts to optimize and creatively enhance the existing technical infrastructure of the space. The goal is to increase the usability of the space for scientists and improve the user experience for visitors. To achieve this, the software project consists of several sub-areas, either arising from a specific problem to be solved or requiring creative approaches and ingenuity. Tasks include system administration, interface development, as well as light/sound installation and orchestration. Examples of challenges include the parallel startup of all computers in a network via WakeOn LAN from a web app or optimizing the existing web app for scenario presentation.

      The tasks are exclusively addressed in small groups (3-5 students). Collaboration and code availability are facilitated through the department's own GitLab or a public GitHub. Results should be well-documented, for example, through README files in Git and a well-structured wiki. Modularity and expandability of the developed code, along with thorough documentation, are crucial for the success of this software project!

      Regarding the process, this software project takes place throughout the semester. There are a few mandatory large group meetings with all participants. In addition, there are short weekly meetings where at least one group member reports on the current status. The first date (23.04.25, 14h, K63) will take place at Takustraße 9. At this event, the solutions already implemented will be presented in theory and the problems addressed. A live demo will then take place one week later, on 30.04.2025, in Berlin Mitte at the Future Security Lab, Wilhelmstr. 67, 10117 Berlin. Afterwards, there are a total of three presentation dates: the presentation of an initial approach to problem-solving (14.04.2025), a brief interim presentation (11.06.2025), and the final presentation (16.07.2025).

      Students also regularly have the opportunity to work in the Future Security Lab premises, familiarize themselves with the equipment, and conduct tests.

  • Academic Work in Applied Computer Science A

    0089cA1.25
    • 19303811 Seminar
      Project Seminar: Data Management (Muhammed-Ugur Karagülle)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: T9/137 Konferenzraum (Takustr. 9)

      Additional information / Pre-requisites

      Requirement

      ALP I-III, Foundations of Datenbase Systems, good programming knowledge.

      Comments

      Content

      A project seminar serves as preparation of a thesis (bachelor or master) in the AGDB. The focus of this project seminar lies on the analysis and visualization of medical data. Additionally, we will realize a small software project.

      Suggested reading

      Wird bekannt gegeben.
    • 19305811 Seminar
      Seminar: Contributions to Software Engineering (Lutz Prechelt)
      Schedule: Do 16:00-18:00 (Class starts on: 2025-04-17)
      Location: T9/049 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group

      Students of Computer Science (also Minor).

      In case you are interested, please contact an adecuate group member with a topic suggestion or request.

      As this lecture is offered continuously, attendance may also start any time during the semester.

      Requirements

      Any computer science student having attended the lecture Software Engineering (Softwaretechnik).

      It may become necessary to deal with materials from the lecture Empirical Evaluation in Informatics (Empirische Bewertung in der Informatik).

      Homepage

      http://www.inf.fu-berlin.de/w/SE/SeminarBeitraegeZumSE

      Comments

      Content

      This is a reseach seminar: normally the presentations are supposed to advance current research projects. Thus, there are, generally speaking, three possible types of topics:

      • published or current research projects from one of the areas in which our software engineering group works
      • especially good specific research projects (or other knowledge) from other areas of software engineering or adjacent areas of computer science
      • basis topics from important areas of software engineering or adjacent disciplines such as psychology, sociology, pedagogics, economics as well as their methods.

      There is no exact restriction of topics though; almost anything is possible.

      Suggested reading

      Je nach Wahl des Vortragsthemas
    • 19307117 Seminar / Undergraduate Course
      Seminar/Proseminar: Smart Homes and the World of IoT (Marius Max Wawerek)
      Schedule: Mo 14:00-16:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-14)
      Location: T9/K63 Hardwarepraktikum (Takustr. 9)

      Comments

      This seminar focuses on various aspects of modern “Internet of Things” (IoT) systems. The main component will be applications and publications related to the area of the “Smart Home”. At the beginning of the seminar, suggested topics will be given, which will mainly deal with data analysis (both “normal” statistics and machine learning), security aspects and the usefulness of the Internet of Things or the “Smart Home”. You are also welcome to suggest your own topics, but they must be related to IoT systems. The topics should be worked on alone.

      About the procedure: This seminar takes place throughout the semester. There are few meetings, but these are mandatory. On the first date (14.04.2025) the list of topics will be handed out and discussed. In the next week (21.04.2025) there will be another opportunity to discuss topic suggestions. If you are interested in your own topic, please prepare a short (2-3 minutes) outline of your proposal. As in the third week (28.04.2025) the topics will be assigned.


      There will then be 3 presentation dates per person: the presentation of the literature research (19.05.2025), a short interim presentation (16.06.2025) and the final presentation on one of the dates in the period from 30.06.2025 - 14.07.2025. There will be no further meetings beyond this.

      This means that, depending on the number of participants, the following meetings are mandatory:

      • 14.04.2025
      • 21.04.2025
      • 19.05.2025
      • 16.06.2025
      • 30.06.2025
      • 07.07.2025
      • 14.07.2025
    • 19328217 Seminar / Undergraduate Course
      Seminar/Proseminar: New Trends in Information Systems (Agnès Voisard)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A3/SR 119 (Arnimallee 3-5)

      Comments

      This seminar aims at studying recent trends in data management. Among others, we will look at two emerging topics, namely Location-Based Services (LBS) and Event-Based Services (EBS).

      Event-based Systems (EBS) are part of many current applications such as business activity monitoring, stock tickers, facility management, data streaming, or security. In the past years, the topic has gained increasing attention from both the industrial and the academic community. Current research concentrates of diverse aspects that range from event capture (incoming data) to response triggering. This seminar aims at studying some of the current trends in Event-based Systems with a strong focus on models and design. Location-based services are now often part of every day's life through applications such as navigation assistants in the public or private transportation domain. The underlying technology deals with many different aspects, such as location detection, information retrieval, or privacy. More recently, aspects such as user context and preferences were considered in order to send users more personalized information.

      A solid background in databases is required, typically a database course at a bachelor level.

      Suggested reading

      Wird bekannt gegeben.
    • 19333311 Seminar
      Seminar: Continual Learning (Manuel Heurich)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      This seminar focuses on recent advances in ‘Continual Learning’, an increasingly important field within machine learning. Continual Learning tackles the problem of drifting data in input space and changes between input and target distribution. Static models drop significantly in performance when data distributions are subject to change over time. We will cover recent approaches that tackle this problem from different angles. This seminar explores the training of adaptive models that can perform strongly in highly volatile domains.
    • 19334617 Seminar / Undergraduate Course
      Seminar/Proseminar: How to Startup (Tim Landgraf)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: T9/046 Seminarraum (Takustr. 9)

      Comments

      This seminar explores the multifaceted world of startups, providing students with a comprehensive understanding of what it takes to succeed in a dynamic and competitive environment. Topics covered include team composition, market analysis, investment logic, emerging trends (such as AI), and common pitfalls faced by startups.
      Unlike traditional seminars, this course emphasizes practical engagement. Students will work on preparing concise "Impulsvorträge" (short, 15-minute talks) on specific startup-related topics. These presentations will draw from a variety of sources, including:

      * Web Research: Gathering insights from industry reports, blogs, and articles.
      * Interviews: Engaging with actual startups to gain firsthand knowledge and perspectives.
      * Trend Analysis: Examining current innovations and disruptions in the startup ecosystem.


      Each talk will serve as the starting point for an interactive discussion, stimulating deeper understanding and diverse viewpoints among participants.
      This seminar is ideal for students who are curious about entrepreneurship and eager to explore how startups operate, grow, and navigate challenges in today's fast-paced world.

       
    • 19335011 Seminar
      Seminar: Networks, dynamic models and ML for data integration in the life sciences (Katharina Baum)
      Schedule: Di 12:00-14:00 (Class starts on: 2025-04-15)
      Location: T9/137 Konferenzraum (Takustr. 9)

      Comments

      Research seminar of the group Data Integration in the Life Sciences (DILiS). Also open for seminar participation in the Master's program, online participation possible. Please refer to the current schedule on the whiteboard!

      The seminar offers space for the discussion of advanced and integrative data analysis techniques, in particular presentations and discussion of ongoing or planned research projects, news from conferences, review and discussion of current literature and discussion of possible future teaching formats and content, and presentations, as well as final presentations on theses or project seminars. The seminar language is mostly English. Interested students are welcome to attend and drop in without obligation or present a topic of their own choice of interest to the working group as in a usual seminar. Please note: Individual dates may be canceled or postponed. Please contact me in case of questions (katharina.baum@fu-berlin.de)!
    • 19336717 Seminar / Undergraduate Course
      Active learning, uncertainty and XAI with applications in biomedicine (Katharina Baum)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: T9/051 Seminarraum (Takustr. 9)

      Comments

      In this advanced seminar, we will discuss a variety of methods for machine learning. The focus will be on approaches to active learning, uncertainty estimation and its utilization, as well as methods for explaining models. The application and development of these methods for biomedical research questions will be explored using current research papers.

      Examples of approaches covered include:

      • selective sampling
      • SHAP values
      • Gaussian ensemble models
      • Bayesian neural networks

      The seminar will primarily be conducted in English, but of course, you are welcome to ask questions in German.

  • Academic Work in Applied Computer Science B

    0089cA1.26
    • 19303811 Seminar
      Project Seminar: Data Management (Muhammed-Ugur Karagülle)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: T9/137 Konferenzraum (Takustr. 9)

      Additional information / Pre-requisites

      Requirement

      ALP I-III, Foundations of Datenbase Systems, good programming knowledge.

      Comments

      Content

      A project seminar serves as preparation of a thesis (bachelor or master) in the AGDB. The focus of this project seminar lies on the analysis and visualization of medical data. Additionally, we will realize a small software project.

      Suggested reading

      Wird bekannt gegeben.
    • 19305811 Seminar
      Seminar: Contributions to Software Engineering (Lutz Prechelt)
      Schedule: Do 16:00-18:00 (Class starts on: 2025-04-17)
      Location: T9/049 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group

      Students of Computer Science (also Minor).

      In case you are interested, please contact an adecuate group member with a topic suggestion or request.

      As this lecture is offered continuously, attendance may also start any time during the semester.

      Requirements

      Any computer science student having attended the lecture Software Engineering (Softwaretechnik).

      It may become necessary to deal with materials from the lecture Empirical Evaluation in Informatics (Empirische Bewertung in der Informatik).

      Homepage

      http://www.inf.fu-berlin.de/w/SE/SeminarBeitraegeZumSE

      Comments

      Content

      This is a reseach seminar: normally the presentations are supposed to advance current research projects. Thus, there are, generally speaking, three possible types of topics:

      • published or current research projects from one of the areas in which our software engineering group works
      • especially good specific research projects (or other knowledge) from other areas of software engineering or adjacent areas of computer science
      • basis topics from important areas of software engineering or adjacent disciplines such as psychology, sociology, pedagogics, economics as well as their methods.

      There is no exact restriction of topics though; almost anything is possible.

      Suggested reading

      Je nach Wahl des Vortragsthemas
    • 19307117 Seminar / Undergraduate Course
      Seminar/Proseminar: Smart Homes and the World of IoT (Marius Max Wawerek)
      Schedule: Mo 14:00-16:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-14)
      Location: T9/K63 Hardwarepraktikum (Takustr. 9)

      Comments

      This seminar focuses on various aspects of modern “Internet of Things” (IoT) systems. The main component will be applications and publications related to the area of the “Smart Home”. At the beginning of the seminar, suggested topics will be given, which will mainly deal with data analysis (both “normal” statistics and machine learning), security aspects and the usefulness of the Internet of Things or the “Smart Home”. You are also welcome to suggest your own topics, but they must be related to IoT systems. The topics should be worked on alone.

      About the procedure: This seminar takes place throughout the semester. There are few meetings, but these are mandatory. On the first date (14.04.2025) the list of topics will be handed out and discussed. In the next week (21.04.2025) there will be another opportunity to discuss topic suggestions. If you are interested in your own topic, please prepare a short (2-3 minutes) outline of your proposal. As in the third week (28.04.2025) the topics will be assigned.


      There will then be 3 presentation dates per person: the presentation of the literature research (19.05.2025), a short interim presentation (16.06.2025) and the final presentation on one of the dates in the period from 30.06.2025 - 14.07.2025. There will be no further meetings beyond this.

      This means that, depending on the number of participants, the following meetings are mandatory:

      • 14.04.2025
      • 21.04.2025
      • 19.05.2025
      • 16.06.2025
      • 30.06.2025
      • 07.07.2025
      • 14.07.2025
    • 19328217 Seminar / Undergraduate Course
      Seminar/Proseminar: New Trends in Information Systems (Agnès Voisard)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A3/SR 119 (Arnimallee 3-5)

      Comments

      This seminar aims at studying recent trends in data management. Among others, we will look at two emerging topics, namely Location-Based Services (LBS) and Event-Based Services (EBS).

      Event-based Systems (EBS) are part of many current applications such as business activity monitoring, stock tickers, facility management, data streaming, or security. In the past years, the topic has gained increasing attention from both the industrial and the academic community. Current research concentrates of diverse aspects that range from event capture (incoming data) to response triggering. This seminar aims at studying some of the current trends in Event-based Systems with a strong focus on models and design. Location-based services are now often part of every day's life through applications such as navigation assistants in the public or private transportation domain. The underlying technology deals with many different aspects, such as location detection, information retrieval, or privacy. More recently, aspects such as user context and preferences were considered in order to send users more personalized information.

      A solid background in databases is required, typically a database course at a bachelor level.

      Suggested reading

      Wird bekannt gegeben.
    • 19333311 Seminar
      Seminar: Continual Learning (Manuel Heurich)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      This seminar focuses on recent advances in ‘Continual Learning’, an increasingly important field within machine learning. Continual Learning tackles the problem of drifting data in input space and changes between input and target distribution. Static models drop significantly in performance when data distributions are subject to change over time. We will cover recent approaches that tackle this problem from different angles. This seminar explores the training of adaptive models that can perform strongly in highly volatile domains.
    • 19334617 Seminar / Undergraduate Course
      Seminar/Proseminar: How to Startup (Tim Landgraf)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: T9/046 Seminarraum (Takustr. 9)

      Comments

      This seminar explores the multifaceted world of startups, providing students with a comprehensive understanding of what it takes to succeed in a dynamic and competitive environment. Topics covered include team composition, market analysis, investment logic, emerging trends (such as AI), and common pitfalls faced by startups.
      Unlike traditional seminars, this course emphasizes practical engagement. Students will work on preparing concise "Impulsvorträge" (short, 15-minute talks) on specific startup-related topics. These presentations will draw from a variety of sources, including:

      * Web Research: Gathering insights from industry reports, blogs, and articles.
      * Interviews: Engaging with actual startups to gain firsthand knowledge and perspectives.
      * Trend Analysis: Examining current innovations and disruptions in the startup ecosystem.


      Each talk will serve as the starting point for an interactive discussion, stimulating deeper understanding and diverse viewpoints among participants.
      This seminar is ideal for students who are curious about entrepreneurship and eager to explore how startups operate, grow, and navigate challenges in today's fast-paced world.

       
    • 19335011 Seminar
      Seminar: Networks, dynamic models and ML for data integration in the life sciences (Katharina Baum)
      Schedule: Di 12:00-14:00 (Class starts on: 2025-04-15)
      Location: T9/137 Konferenzraum (Takustr. 9)

      Comments

      Research seminar of the group Data Integration in the Life Sciences (DILiS). Also open for seminar participation in the Master's program, online participation possible. Please refer to the current schedule on the whiteboard!

      The seminar offers space for the discussion of advanced and integrative data analysis techniques, in particular presentations and discussion of ongoing or planned research projects, news from conferences, review and discussion of current literature and discussion of possible future teaching formats and content, and presentations, as well as final presentations on theses or project seminars. The seminar language is mostly English. Interested students are welcome to attend and drop in without obligation or present a topic of their own choice of interest to the working group as in a usual seminar. Please note: Individual dates may be canceled or postponed. Please contact me in case of questions (katharina.baum@fu-berlin.de)!
    • 19336717 Seminar / Undergraduate Course
      Active learning, uncertainty and XAI with applications in biomedicine (Katharina Baum)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: T9/051 Seminarraum (Takustr. 9)

      Comments

      In this advanced seminar, we will discuss a variety of methods for machine learning. The focus will be on approaches to active learning, uncertainty estimation and its utilization, as well as methods for explaining models. The application and development of these methods for biomedical research questions will be explored using current research papers.

      Examples of approaches covered include:

      • selective sampling
      • SHAP values
      • Gaussian ensemble models
      • Bayesian neural networks

      The seminar will primarily be conducted in English, but of course, you are welcome to ask questions in German.
    • 19337517 Seminar / Undergraduate Course
      Seminar/Proseminar: Time Series Learning (Manuel Heurich)
      Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      This seminar focuses on Machine Learning approaches that specialize in sequential data. Most real-world data is acquired over time. Moreover, most of the available data is not image data. We will discuss works before the Transformer era (e.g., RNNs, LSTMs) and highlight their strengths and weaknesses outside the Computer Vision domain. More recently, transformer-based approaches have outperformed earlier methods. We selectively pick works that highlight their strength in knowledge discovery on sequential data. With the strong trend towards powerful multi-modal models, the seminar aims to introduce state-of-the-art methods to produce robust embeddings based on Time Series data.

  • Current research topics in Applied Computer Science

    0089cA1.27
    • 19302801 Lecture
      Applied Biometrics (Andreas Wolf)
      Schedule: Mo 08:00-10:00 (Class starts on: 2025-04-14)
      Location: T9/K40 Multimediaraum (Takustr. 9)

      Additional information / Pre-requisites

      Die Lehrveranstaltung soll am Freitag den 12. April beginnen.

      Das Vorlesungsskript liegt unter

      https://drive.google.com/drive/folders/0B7NhYbv9QewkRkk2WVRuM2Rqd00?usp=sharing

      Webex Link zu der Veranstaltung:

      Meeting-Link: https://fu-berlin.webex.com/fu-berlin/j.php?MTID=m2cc50d96918fcaeb09f3c36a264f4f29

      Meeting-ID: 121 079 7504

      Meeting-Password: mCwDw274PS8

      Comments

      The lecture held by Dr. Andreas Wolf (from the Bundesdruckerei) He will give a broad overview of biometric processes and applications. He will also address the current issues with ePassports and new electronic identity cards.

      The course aims to include:

      • General structure of biometric systems
      • Features of biometric modalities
      • IT security and risk assessment
      • Errors in biometric processes
      • Fingerprinting
      • Facial and iris recognition
      • Speaker recognition and other modalities
      • Standards
      • ePassport

      Next to the theoretical foundations of biometric modalities, the students are to develop the ability to assess the applicability of biometrics in various scenarios.
    • 19325301 Lecture
      Cluster Computing (Barry Linnert)
      Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/055 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group

      • Computer Science Master students

      Requirements

      • Experience with computers and software as well as programing skills.

      Language

      • The course language is German (or English if requested).
      • The exam will be formulated in German, but answers may be given in English, too.

      Credits & Exams

      The criteria for gaining credits are

      • active participation in the tutorials: regular preparation of assignements & presentation of results in the tutorials
      • passing of the exam

      Website

      https://www.mi.fu-berlin.de/w/SE/VorlesungClusterComputing

       

      Comments

      Cluster computer are the prevailing type of high performance computers. They are built of custom off-the-shelf processor boards that are connected by a high speed interconnection network. Although usually locally integrated, they are conceptually distributed systems with local operating system images. Their enormous potential, however, can only be exploited, if program code and data are optimally distributed across the nodes. Cluster management mechanisms also need to be scalable to be employed in systems with thousands of nodes. The lecture course gives an overview of the architecture of cluster computers and the related management problems for which algorithmic solutions are presented.

      Suggested reading

      • Heiss, H.-U.: Prozessorzuteilung in Parallelrechnern, BI-Verlag, Mannheim, 1996
      • Andrews, G. A.: Foundations of Multithreaded, Parallel and Distributed Programming, Addison-Wesley, 2000
      • Pfister, G.: In Search of Clusters 2nd ed., Prentice Hall, 1998
      • Zomaya, A.: Parallel and distributed computing handbook, McGraw Gill, 1995
      • Buyya, R.: High Performance Cluster Computing, Vol. 1+2, Prentice Hall, 1999
    • 19327401 Lecture
      Image- and video coding (Heiko Schwarz)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
      Location: T9/053 Seminarraum (Takustr. 9)

      Comments

      This course introduces the most important concepts and algorithms that are used in modern image and video coding approaches. We will particularly focus on techniques that are found in current international video coding standards.

      In a short first part, we introduce the so-called raw data formats, which are used as input and output formats of image and video codecs. This part covers the following topics:

      • Colour spaces and their relation to human visual perception
      • Transfer functions (gamma encoding)
      • Why do we use the YCbCr format?

      The second part of the course deals with still image coding and includes the following topics:

      • The start: How does JPEG work?
      • Why do we use the Discrete Cosine Transform?
      • Efficient coding of transform coefficients
      • Prediction of image blocks
      • Adaptive block partitioning
      • How do we take decisions in an encoder?
      • Optimized quantization

      In the third part, we discuss approaches that make video coding much more efficient than coding all pictures using still image coding techniques:

      • Motion-compensated prediction
      • Coding of motion vectors
      • Algorithms for motion estimation
      • Sub-sample accurate motion vectors and interpolation filters
      • Usage of multiple reference pictures
      • What are B pictures and why do we use them?
      • Deblocking and deringing filters
      • Efficient temporal coding structures

      In the exercises, we will implement our own image codec (in a gradual manner). We may extend it to a simple video codec.

       

      Suggested reading

      • Bull, D. R., “Communicating Pictures: A Course in Image and Video Coding,” Elsevier, 2014.
      • Ohm, J.-R., “Multimedia Signal Coding and Transmission,” Springer, 2015.
      • Wien, M., “High Efficiency Video Coding — Coding Tools and Specifications,” Springer 2014.
      • Sze, V., Budagavi, M., and Sullivan, G. J. (eds.), “High Efficiency Video Coding (HEVC): Algorithm and Architectures,” Springer, 2014.
      • Wiegand, T. and Schwarz, H., "Source Coding: Part I of Fundamentals of Source and Video Coding,” Foundations and Trends in Signal Processing, Now Publishers, vol. 4, no. 1–2, 2011.
      • Schwarz, H. and Wiegand, T., “Video Coding: Part II of Fundamentals of Source and Video Coding,” Foundations and Trends in Signal Processing, Now Publishers, vol. 10, no. 1–3, 2016.
    • 19331101 Lecture
      Human Centered Data Science (Claudia Müller-Birn)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: T9/SR 006 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      [link HCC-Webseite aktuelles Semester]

      Comments

      In recent years, data science has developed rapidly, primarily due to the progress in machine learning. This development has opened up new opportunities in a variety of social, scientific, and technological areas. From the experience of recent years, however, it is becoming increasingly clear that the concentration on purely statistical and numerical aspects in data science fails to capture social nuances or take ethical criteria into account. The research area Human-Centered Data Science closes this gap at the intersection of Human-Computer Interaction (HCI), Computer-Supported Cooperative Work (CSCW), Human Computation, and the statistical and numerical techniques of Data Science.

      Human-Centered Data Science (HCDS) focuses on fundamental principles of data science and its human implications, including research ethics; data privacy; legal frameworks; algorithmic bias, transparency, fairness, and accountability; data provenance, curation, preservation, and reproducibility; user experience design and research for big data; human computation; effective oral, written, and visual scientific communication; and societal impacts of data science.

      At the end of this course, students will understand the main concepts, theories, practices, and different perspectives on which data can be collected and manipulated. Furthermore, students will be able to realize the impact of current technological developments may have on society.

      This course curriculum was initially developed by Jonathan T. Morgan, Cecilia Aragon, Os Keyes, and Brock Craft. We have adapted the curriculum for the European context and our specific understanding of the field.

      Suggested reading

      Aragon, C. M., Hutto, C., Echenique, A., Fiore-Gartland, B., Huang, Y., Kim, J., et al. (2016). Developing a Research Agenda for Human-Centered Data Science. (pp. 529–535). Presented at the CSCW Companion, New York, New York, USA: ACM Press. http://doi.org/10.1145/2818052.2855518

      Baumer, E. P. (2017). Toward human-centered algorithm design:. Big Data & Society, 4(2), 205395171771885. http://doi.org/10.1177/2053951717718854

      Kogan, M., Halfaker, A., Guha, S., Aragon, C., Muller, M., & Geiger, S. (2020, January). Mapping Out Human-Centered Data Science: Methods, Approaches, and Best Practices. In Companion of the 2020 ACM International Conference on Supporting Group Work (pp. 151-156).
    • 19333101 Lecture
      Cybersecurity and AI II: Explainability (Gerhard Wunder)
      Schedule: Mo 12:00-14:00, Di 10:00-12:00, Fr 12:00-14:00 (Class starts on: 2025-04-15)
      Location: 1.3.21 Seminarraum T1 (Arnimallee 14)
    • 19333701 Lecture
      Ethics and Epistemology of AI (Christoph Benzmüller)
      Schedule: -
      Location: keine Angabe

      Comments

      The course Ethics and Epistemology of AI will be offered again in summer 2025 in cooperation with the TU Berlin (Prof. Sabine Ammon) and U Bamberg. It will bring together an interdisciplinary mix of students from different institutions, including BUA Berlin and Erasmus students.

      Innovative. Experimental. Interdisciplinary.

      More Information: https://www.tu.berlin/en/philtech/study-and-teaching/courses/ethics-and-epistemology-of-ai

      Information for interested students:

      • The course primarily targets masters students with interest in assessing critical aspects of latest artificial intelligence technology and to explore possible solutions and improvements; the course is also part of the Berlin Ethics certificate.
      • Online on-boarding meetings are offered on April 16 (14:15) and April 23 (14:15). The link will be communicated.
      • The course starts immediately after easter with a small pre-exercise to be conducted by each participant individually.
      • Very important is that students then meet for one week in person in Berlin from 28. April to 2. Mai. Participation in this intensive (but also great fun) daily event at TU Berlin is crucial, since it is here where the interdisciplinary and interinstitutional working teams are formed and where the working topics are defined in interaction with the supervisors.
      • After the intensive meeting in Berlin the teams work independently  via the internet; the group typically meets online with their supervisors each Wednesday (early afternoon).
      • Group project presentations are scheduled for June 11; after this date the groups then work on their joint final report.
      • This course is challenging but also fun, and you can expect to build an international network of other students who are interested in assessing critical aspects of AI.

      Contact for administrational questions at TU Berlin: Leon Dirmeier (dirmeier@campus.tu-berlin.de)
    • 19302802 Practice seminar
      Practice seminar for Applied Biometrics (Andreas Wolf)
      Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
      Location: T9/K40 Multimediaraum (Takustr. 9)
    • 19325302 Practice seminar
      Practice seminar for Cluster Computing (Barry Linnert)
      Schedule: Do 10:00-12:00 (Class starts on: 2025-04-17)
      Location: T9/K44 Rechnerpoolraum (Takustr. 9)
    • 19327402 Practice seminar
      Practice seminar for image- und video coding (Heiko Schwarz)
      Schedule: Mo 12:00-14:00 (Class starts on: 2025-04-14)
      Location: T9/053 Seminarraum (Takustr. 9)
    • 19331102 Practice seminar
      Practice Session on Human Centered Data Science (Claudia Müller-Birn)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
      Location: T9/SR 006 Seminarraum (Takustr. 9)
    • 19333102 Practice seminar
      Practice seminar for Cybersecurity and AI II (Gerhard Wunder)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-28)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)
    • 19333702 Practice seminar
      Ethics and Epistemology of AI (Christoph Benzmüller)
      Schedule: -
      Location: keine Angabe

  • Special Aspects of Applied Computer Science

    0089cA1.28
    • 19302801 Lecture
      Applied Biometrics (Andreas Wolf)
      Schedule: Mo 08:00-10:00 (Class starts on: 2025-04-14)
      Location: T9/K40 Multimediaraum (Takustr. 9)

      Additional information / Pre-requisites

      Die Lehrveranstaltung soll am Freitag den 12. April beginnen.

      Das Vorlesungsskript liegt unter

      https://drive.google.com/drive/folders/0B7NhYbv9QewkRkk2WVRuM2Rqd00?usp=sharing

      Webex Link zu der Veranstaltung:

      Meeting-Link: https://fu-berlin.webex.com/fu-berlin/j.php?MTID=m2cc50d96918fcaeb09f3c36a264f4f29

      Meeting-ID: 121 079 7504

      Meeting-Password: mCwDw274PS8

      Comments

      The lecture held by Dr. Andreas Wolf (from the Bundesdruckerei) He will give a broad overview of biometric processes and applications. He will also address the current issues with ePassports and new electronic identity cards.

      The course aims to include:

      • General structure of biometric systems
      • Features of biometric modalities
      • IT security and risk assessment
      • Errors in biometric processes
      • Fingerprinting
      • Facial and iris recognition
      • Speaker recognition and other modalities
      • Standards
      • ePassport

      Next to the theoretical foundations of biometric modalities, the students are to develop the ability to assess the applicability of biometrics in various scenarios.
    • 19325301 Lecture
      Cluster Computing (Barry Linnert)
      Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/055 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group

      • Computer Science Master students

      Requirements

      • Experience with computers and software as well as programing skills.

      Language

      • The course language is German (or English if requested).
      • The exam will be formulated in German, but answers may be given in English, too.

      Credits & Exams

      The criteria for gaining credits are

      • active participation in the tutorials: regular preparation of assignements & presentation of results in the tutorials
      • passing of the exam

      Website

      https://www.mi.fu-berlin.de/w/SE/VorlesungClusterComputing

       

      Comments

      Cluster computer are the prevailing type of high performance computers. They are built of custom off-the-shelf processor boards that are connected by a high speed interconnection network. Although usually locally integrated, they are conceptually distributed systems with local operating system images. Their enormous potential, however, can only be exploited, if program code and data are optimally distributed across the nodes. Cluster management mechanisms also need to be scalable to be employed in systems with thousands of nodes. The lecture course gives an overview of the architecture of cluster computers and the related management problems for which algorithmic solutions are presented.

      Suggested reading

      • Heiss, H.-U.: Prozessorzuteilung in Parallelrechnern, BI-Verlag, Mannheim, 1996
      • Andrews, G. A.: Foundations of Multithreaded, Parallel and Distributed Programming, Addison-Wesley, 2000
      • Pfister, G.: In Search of Clusters 2nd ed., Prentice Hall, 1998
      • Zomaya, A.: Parallel and distributed computing handbook, McGraw Gill, 1995
      • Buyya, R.: High Performance Cluster Computing, Vol. 1+2, Prentice Hall, 1999
    • 19327401 Lecture
      Image- and video coding (Heiko Schwarz)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
      Location: T9/053 Seminarraum (Takustr. 9)

      Comments

      This course introduces the most important concepts and algorithms that are used in modern image and video coding approaches. We will particularly focus on techniques that are found in current international video coding standards.

      In a short first part, we introduce the so-called raw data formats, which are used as input and output formats of image and video codecs. This part covers the following topics:

      • Colour spaces and their relation to human visual perception
      • Transfer functions (gamma encoding)
      • Why do we use the YCbCr format?

      The second part of the course deals with still image coding and includes the following topics:

      • The start: How does JPEG work?
      • Why do we use the Discrete Cosine Transform?
      • Efficient coding of transform coefficients
      • Prediction of image blocks
      • Adaptive block partitioning
      • How do we take decisions in an encoder?
      • Optimized quantization

      In the third part, we discuss approaches that make video coding much more efficient than coding all pictures using still image coding techniques:

      • Motion-compensated prediction
      • Coding of motion vectors
      • Algorithms for motion estimation
      • Sub-sample accurate motion vectors and interpolation filters
      • Usage of multiple reference pictures
      • What are B pictures and why do we use them?
      • Deblocking and deringing filters
      • Efficient temporal coding structures

      In the exercises, we will implement our own image codec (in a gradual manner). We may extend it to a simple video codec.

       

      Suggested reading

      • Bull, D. R., “Communicating Pictures: A Course in Image and Video Coding,” Elsevier, 2014.
      • Ohm, J.-R., “Multimedia Signal Coding and Transmission,” Springer, 2015.
      • Wien, M., “High Efficiency Video Coding — Coding Tools and Specifications,” Springer 2014.
      • Sze, V., Budagavi, M., and Sullivan, G. J. (eds.), “High Efficiency Video Coding (HEVC): Algorithm and Architectures,” Springer, 2014.
      • Wiegand, T. and Schwarz, H., "Source Coding: Part I of Fundamentals of Source and Video Coding,” Foundations and Trends in Signal Processing, Now Publishers, vol. 4, no. 1–2, 2011.
      • Schwarz, H. and Wiegand, T., “Video Coding: Part II of Fundamentals of Source and Video Coding,” Foundations and Trends in Signal Processing, Now Publishers, vol. 10, no. 1–3, 2016.
    • 19331101 Lecture
      Human Centered Data Science (Claudia Müller-Birn)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: T9/SR 006 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      [link HCC-Webseite aktuelles Semester]

      Comments

      In recent years, data science has developed rapidly, primarily due to the progress in machine learning. This development has opened up new opportunities in a variety of social, scientific, and technological areas. From the experience of recent years, however, it is becoming increasingly clear that the concentration on purely statistical and numerical aspects in data science fails to capture social nuances or take ethical criteria into account. The research area Human-Centered Data Science closes this gap at the intersection of Human-Computer Interaction (HCI), Computer-Supported Cooperative Work (CSCW), Human Computation, and the statistical and numerical techniques of Data Science.

      Human-Centered Data Science (HCDS) focuses on fundamental principles of data science and its human implications, including research ethics; data privacy; legal frameworks; algorithmic bias, transparency, fairness, and accountability; data provenance, curation, preservation, and reproducibility; user experience design and research for big data; human computation; effective oral, written, and visual scientific communication; and societal impacts of data science.

      At the end of this course, students will understand the main concepts, theories, practices, and different perspectives on which data can be collected and manipulated. Furthermore, students will be able to realize the impact of current technological developments may have on society.

      This course curriculum was initially developed by Jonathan T. Morgan, Cecilia Aragon, Os Keyes, and Brock Craft. We have adapted the curriculum for the European context and our specific understanding of the field.

      Suggested reading

      Aragon, C. M., Hutto, C., Echenique, A., Fiore-Gartland, B., Huang, Y., Kim, J., et al. (2016). Developing a Research Agenda for Human-Centered Data Science. (pp. 529–535). Presented at the CSCW Companion, New York, New York, USA: ACM Press. http://doi.org/10.1145/2818052.2855518

      Baumer, E. P. (2017). Toward human-centered algorithm design:. Big Data & Society, 4(2), 205395171771885. http://doi.org/10.1177/2053951717718854

      Kogan, M., Halfaker, A., Guha, S., Aragon, C., Muller, M., & Geiger, S. (2020, January). Mapping Out Human-Centered Data Science: Methods, Approaches, and Best Practices. In Companion of the 2020 ACM International Conference on Supporting Group Work (pp. 151-156).
    • 19333101 Lecture
      Cybersecurity and AI II: Explainability (Gerhard Wunder)
      Schedule: Mo 12:00-14:00, Di 10:00-12:00, Fr 12:00-14:00 (Class starts on: 2025-04-15)
      Location: 1.3.21 Seminarraum T1 (Arnimallee 14)
    • 19333701 Lecture
      Ethics and Epistemology of AI (Christoph Benzmüller)
      Schedule: -
      Location: keine Angabe

      Comments

      The course Ethics and Epistemology of AI will be offered again in summer 2025 in cooperation with the TU Berlin (Prof. Sabine Ammon) and U Bamberg. It will bring together an interdisciplinary mix of students from different institutions, including BUA Berlin and Erasmus students.

      Innovative. Experimental. Interdisciplinary.

      More Information: https://www.tu.berlin/en/philtech/study-and-teaching/courses/ethics-and-epistemology-of-ai

      Information for interested students:

      • The course primarily targets masters students with interest in assessing critical aspects of latest artificial intelligence technology and to explore possible solutions and improvements; the course is also part of the Berlin Ethics certificate.
      • Online on-boarding meetings are offered on April 16 (14:15) and April 23 (14:15). The link will be communicated.
      • The course starts immediately after easter with a small pre-exercise to be conducted by each participant individually.
      • Very important is that students then meet for one week in person in Berlin from 28. April to 2. Mai. Participation in this intensive (but also great fun) daily event at TU Berlin is crucial, since it is here where the interdisciplinary and interinstitutional working teams are formed and where the working topics are defined in interaction with the supervisors.
      • After the intensive meeting in Berlin the teams work independently  via the internet; the group typically meets online with their supervisors each Wednesday (early afternoon).
      • Group project presentations are scheduled for June 11; after this date the groups then work on their joint final report.
      • This course is challenging but also fun, and you can expect to build an international network of other students who are interested in assessing critical aspects of AI.

      Contact for administrational questions at TU Berlin: Leon Dirmeier (dirmeier@campus.tu-berlin.de)
    • 19336901 Lecture
      Advanced Data Visualization for Artificial Intelligence (Georges Hattab)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A6/SR 007/008 Seminarraum (Arnimallee 6)

      Comments

      The lecture on Advanced Data Visualization for Artificial Intelligence is a comprehensive exploration of state-of-the-art techniques and tools to create and validate complex visualizations for communicating data insights and stories, with a specific focus on applications in Natural Language Processing (NLP) and Explainable AI. The lecture will introduce participants to the nested model of visualization, which encompasses four layers: characterizing the task and data, abstracting into operations and data types, designing visual encoding and interaction techniques, and creating algorithms to execute techniques efficiently. This model will serve as a framework for designing and validating data visualizations.

      Furthermore, the lecture will delve into the application of data visualization in NLP, emphasizing the visualization of word embeddings and language models to aid in the exploration of semantic relationships between words and the interpretation of language model behavior. In the context of Explainable AI, the focus will be on using visualizations to explain model predictions and feature importance, thereby enhancing the interpretability of AI models. By leveraging the nested model of visualization and focusing on NLP and Explainable AI, the lecture aims to empower participants with the essential skills to design and validate advanced data visualizations tailored to these specific applications, ultimately enabling them to effectively communicate complex data patterns and gain deeper insights from their data.
    • 19302802 Practice seminar
      Practice seminar for Applied Biometrics (Andreas Wolf)
      Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
      Location: T9/K40 Multimediaraum (Takustr. 9)
    • 19325302 Practice seminar
      Practice seminar for Cluster Computing (Barry Linnert)
      Schedule: Do 10:00-12:00 (Class starts on: 2025-04-17)
      Location: T9/K44 Rechnerpoolraum (Takustr. 9)
    • 19327402 Practice seminar
      Practice seminar for image- und video coding (Heiko Schwarz)
      Schedule: Mo 12:00-14:00 (Class starts on: 2025-04-14)
      Location: T9/053 Seminarraum (Takustr. 9)
    • 19331102 Practice seminar
      Practice Session on Human Centered Data Science (Claudia Müller-Birn)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
      Location: T9/SR 006 Seminarraum (Takustr. 9)
    • 19333102 Practice seminar
      Practice seminar for Cybersecurity and AI II (Gerhard Wunder)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-28)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)
    • 19333702 Practice seminar
      Ethics and Epistemology of AI (Christoph Benzmüller)
      Schedule: -
      Location: keine Angabe
    • 19336902 Practice seminar
      Ü: Advanced Data Visualization for Artificial Intelligence (Georges Hattab)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A6/SR 007/008 Seminarraum (Arnimallee 6)

  • Special Aspects of Software Development

    0089cA1.30
    • 19336901 Lecture
      Advanced Data Visualization for Artificial Intelligence (Georges Hattab)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A6/SR 007/008 Seminarraum (Arnimallee 6)

      Comments

      The lecture on Advanced Data Visualization for Artificial Intelligence is a comprehensive exploration of state-of-the-art techniques and tools to create and validate complex visualizations for communicating data insights and stories, with a specific focus on applications in Natural Language Processing (NLP) and Explainable AI. The lecture will introduce participants to the nested model of visualization, which encompasses four layers: characterizing the task and data, abstracting into operations and data types, designing visual encoding and interaction techniques, and creating algorithms to execute techniques efficiently. This model will serve as a framework for designing and validating data visualizations.

      Furthermore, the lecture will delve into the application of data visualization in NLP, emphasizing the visualization of word embeddings and language models to aid in the exploration of semantic relationships between words and the interpretation of language model behavior. In the context of Explainable AI, the focus will be on using visualizations to explain model predictions and feature importance, thereby enhancing the interpretability of AI models. By leveraging the nested model of visualization and focusing on NLP and Explainable AI, the lecture aims to empower participants with the essential skills to design and validate advanced data visualizations tailored to these specific applications, ultimately enabling them to effectively communicate complex data patterns and gain deeper insights from their data.
    • 19336902 Practice seminar
      Ü: Advanced Data Visualization for Artificial Intelligence (Georges Hattab)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A6/SR 007/008 Seminarraum (Arnimallee 6)

  • Selected Topics in Applied Computer Science

    0089cA1.31
    • 19326601 Lecture
      Markov Chains (Katinka Wolter)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/Gr. Hörsaal (Takustr. 9)

      Comments

      In this course we will study stochastic models commonly used to analyse the performance of dynamic systems. Markov models and queues are used to study the behaviour over time of a wide range of systems, from computer hardware, communication systems, biological systems, epidemics, traffic networks to crypto-currencies. We will take a tour of the basics of Markov modelling, starting from birth-death processes, the Poisson process to general Markov and semi-Markov processes and solution methods for those processes. Then we will look at queueing models and queueing networks with exact and approximate solution algorithms. If time allows we will finally study some of the foundations of discrete event simulation.

      Suggested reading

      William Stewart. Probability, Markov Chains, Queues and Simulation. Princeton University Press 2009.
    • 19326602 Practice seminar
      Practice seminar for Markov Chains (Justus Purat)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A6/SR 007/008 Seminarraum (Arnimallee 6)

  • Empirical Evaluation in Computer Science

    0089cA1.5
    • 19303401 Lecture
      Empirical Methods in Software Engineering (Lutz Prechelt)
      Schedule: Mo 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-14)
      Location: T9/049 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      The course language is German, but the actual slides and practice sheets are in English.

      The exam will be formulated in German, but answers may be given in English, too.

      Homepage: http://www.inf.fu-berlin.de/w/SE/VorlesungEmpirie

      Comments

      Software Engineering is a field of so-high socio-technical complexity that the properties (let alone the usefulness) of proposed methods and tools are not at all obvious. We need to evaluate them empirically.

      This course introduces two different manners in which one can think about this situation and approach evaluations:

      1. A quantitative perspective. This aims at quantified statements about the tools and methods and is based on a positivist epistemological stance and corresponding culture.
      2. A qualitative perspective. This aims at making sense of the things that are going on to create the phenomena that give rise to the quantitative outcomes. This perspective is based on an interpretivist epistemological stance and has a culture that values different things.

      Both perspectives have different strengths and weaknesses and are suitable for different types of research interest. In this course, we will learn to think in both of these perspectives and to appreciate the different benefits they provide. We will learn what it means that a study has high quality: it has high credibility and high relevance. We will train diagnosing the various quality problems that often reduce credibility or relevance.

       

      We will work through the most common research methods and will discuss real examples (interesting published studies) of each, along with their strengths and weaknesses.

      Participants will understand how and when to apply each method and for one of them develop some practical skills by doing so.

      Suggested reading

      • Jacob Cohen: The Earth Is Round (p > .05). American Psychologist 49(12): 997003, 1994. Darrell Huff: How to lie with statistics, Penguin 1991.
      • John C. Knight, Nancy G. Leveson: An Experimental Evaluation of the Assumption of Independence in Multi-Version Programming. IEEE Transactions on Software Engineering 12(1):9609, January 1986.
      • John C. Knight, Nancy G. Leveson: A Reply to the Criticisms of the Knight and Leveson Experiment. Software Engineering Notes 15(1):24-35, January 1990.
      • Audris Mockus, Roy T. Fielding, James D. Herbsleb: Two Case Studies of Open Source Software Development: Apache and Mozilla. ACM Transactions of Software Engineering and Methodology 11(3):309-346, July 2002.
      • Timothy Lethbridge: What Knowledge Is Important to a Software Professional? IEEE Computer 33(5):44-50, May 2000.
      • David A. Scanlan: Structured Flowcharts Outperform Pseudocode: An Experimental Comparison. IEEE Software 6(5):28-36, September 1989.
      • Ben Shneiderman, Richard Mayer, Don McKay, Peter Heller: Experimental investigations of the utility of detailed flowcharts in programming. Commun. ACM 20(6):373-381, 1977.
      • Lutz Prechelt, Barbara Unger-Lamprecht, Michael Philippsen, Walter F. Tichy: Two Controlled Experiments Assessing the Usefulness of Design Pattern Documentation in Program Maintenance. IEEE Transactions on Software Engineering 28(6):595-606, 2002.
      • Lutz Prechelt. An Empirical Comparison of Seven Programming Languages: Computer 33(10):23-29, October 2000.
      • Lutz Prechelt: An empirical comparison of C, C++, Java, Perl, Python, Rexx, and Tcl for a search/string-processing program. Technical Report 2000-5, March 2000.
      • Tom DeMarco, Tim Lister: Programmer performance and the effects of the workplace. Proceedings of the 8th international conference on Software engineering. IEEE Computer Society Press, 268-272, 1985.
      • John L. Henning: SPEC CPU2000: Measuring CPU Performance in the New Millennium. Computer 33(7):28-35, July 2000.
      • Susan Elliot Sim, Steve Easterbrook, Richard C. Holt: Using Benchmarking to Advance Research: A Challenge to Software Engineering. Proceedings of the 25th International Conference on Software Engineering (ICSE'03). 2003.
      • Ellen M. Voorhees, Donna Harman: Overview of the Eighth Text REtrieval Conference (TREC-8).
      • Susan Elliott Sim, Richard C. Holt: The Ramp-Up Problem in Software Projects: A case Study of How Software Immigrants Naturalize. Proceedings of the 20th international conference on Software engineering, April 19-25, 1998, Kyoto, Japan: 361-370.
      • Oliver Laitenberger, Thomas Beil, Thilo Schwinn: An Industrial Case Study to Examine a Non-Traditional Inspection Implementation for Requirements Specifications. Empirical Software Engineering 7(4): 345-374, 2002.
      • Yatin Chawathe, Sylvia Ratnasamy, Lee Breslau, Nick Lanham, Scott Shenker: Making Gnutella-like P2P Systems Scalable. Proceedings of ACM SIGCOMM 2003. April 2003.
      • Stephen G. Eick, Todd L. Graves, Alan F. Karr, J.S. Marron, Audris Mockus: Does Code Decay? Assessing the Evidence from Change Management Data. IEEE Transactions of Software Engineering 27(1):12, 2001.
      • Chris Sauer, D. Ross Jeffrey, Lesley Land, Philip Yetton: The Effectiveness of Software Development Technical Reviews: A Behaviorally Motivated Program of Research. IEEE Transactions on Software Engineering 26(1):14, January 2000.
    • 19303402 Practice seminar
      Practice seminar for Empirical Methods in Software Engineering (Lutz Prechelt)
      Schedule: Mi 08:00-10:00 (Class starts on: 2025-04-16)
      Location: T9/046 Seminarraum (Takustr. 9)

  • Fundamentals of IT Project Management

    0159cA2.6
    • 19335406 Seminar-style instruction
      Project management in agile environments part 2 (Lutz Prechelt)
      Schedule: Mo 08:00-10:00, Fr 16:00-18:00 (Class starts on: 2025-04-14)
      Location: T9/SR 006 Seminarraum (Takustr. 9)

      Comments

      Goals

      The students understand several different models of scaled agile software development, that is, agile development encompassing multiple cooperating teams. They understand basic and intermediate methods of hybrid, predictive, and adaptive project management in such agile environments and are able to apply them. They can design a project plan and validate it with suitable methods. They can participate in the project management team of such a hybrid effort and take responsibility for substantial parts of the project management, including managing staff. They can lead a simple project alone.

      Contents

      Students learn the principles, methods and procedures of scaled agile software production using established models (e.g. Scaled Agile Framework) and project management using a recognized methodology (e.g. “Project Management Body of Knowledge” (PMBoK)) and practice their practical application. They develop agile principles and values as well as Scrum and practise both. In addition, they discuss and practise planning the scope of the product and coordinating several teams working together on it, the necessary processes and the roles involved. They also learn about all areas of project management, discuss their application and practise some of their implementation:

      •     Project creation, definition and project scope planning,
      •     project planning,
      •     project process control, status determination and reporting,
      •     Project organization and embedding a project in the executing organization,
      •     Management without formal power,
      •     project communication,
      •     Leading a project team and quality management

  • Software Project: Theoretical Computer Science A

    0089cA2.10
    • 19308312 Project Seminar
      Implementation Project: Applications of Algorithms (Mahmoud Elashmawi)
      Schedule: Do 08:30-10:00 (Class starts on: 2025-04-10)
      Location: T9/053 Seminarraum (Takustr. 9)

      Comments

      Contents

      We choose a typical application area of algorithms, usually for geometric problems, and develop software solutions for it, e.g., computer graphics (representation of objects in a computer, projections, hidden edge and surface removal, lighting, raytracing), computer vision (image processing, filtering, projections, camera calibration, stereo-vision) or pattern recognition (classification, searching).

      Prerequsitions

      Basic knowledge in design and anaylsis of algorithms.

      Suggested reading

      je nach Anwendungsgebiet

  • Software Project: Theoretical Computer Science B

    0089cA2.11
    • 19308312 Project Seminar
      Implementation Project: Applications of Algorithms (Mahmoud Elashmawi)
      Schedule: Do 08:30-10:00 (Class starts on: 2025-04-10)
      Location: T9/053 Seminarraum (Takustr. 9)

      Comments

      Contents

      We choose a typical application area of algorithms, usually for geometric problems, and develop software solutions for it, e.g., computer graphics (representation of objects in a computer, projections, hidden edge and surface removal, lighting, raytracing), computer vision (image processing, filtering, projections, camera calibration, stereo-vision) or pattern recognition (classification, searching).

      Prerequsitions

      Basic knowledge in design and anaylsis of algorithms.

      Suggested reading

      je nach Anwendungsgebiet

  • Academic Work in Theoretical Computer Science A

    0089cA2.12
    • 19306711 Seminar
      Seminar on Algorithms (László Kozma)
      Schedule: Do 14:00-16:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
      Location: T9/049 Seminarraum (Takustr. 9)

      Comments

      Contents

      Advanced topics in algorithm design with a changing focus. The topic is determined in each semester.

      This semester we plan a reading-group-style seminar on recent breakthrough results (2020-2025) in shortest paths algorithms.

      Target audience

      Masters students in computer science and mathematics.

      Recommended prerequisites

      "Advanced algorithms" or a similar class.

      Suggested reading

      Spezialliteratur aus Zeitschriften
    • 19331617 Seminar / Undergraduate Course
      Seminar/Proseminar: Information-theoretical principles of ML (Gerhard Wunder)
      Schedule: Fr 14:00-16:00 (Class starts on: 2025-04-25)
      Location: T9/K40 Multimediaraum (Takustr. 9)

      Comments

      Recently, artificial intelligence and machine learning (AI/ML) has emerged as a valuable tool in the field of communication and signal processing. It is therefore natural to extend the investigations to the field of physical layer security and privacy. This field is still in its infancy with some very preliminary results on wiretap channel code design, feature extraction of wireless channels and a growing part of contributions to privacy-preserving, distributed AI/ML. This seminar will teach the latest advances and synergies between the broad fields of AI/ML and secure communications.

      Keywords: ML overview, basic tools, universal approximation, deep learning, stochastic gradient, acceleration strategies, deep convolutional networks, feature extraction, classification, mutual information neural network estimation, structured sparsity in convolutional neural networks, matrix decompositions

       
    • 19335011 Seminar
      Seminar: Networks, dynamic models and ML for data integration in the life sciences (Katharina Baum)
      Schedule: Di 12:00-14:00 (Class starts on: 2025-04-15)
      Location: T9/137 Konferenzraum (Takustr. 9)

      Comments

      Research seminar of the group Data Integration in the Life Sciences (DILiS). Also open for seminar participation in the Master's program, online participation possible. Please refer to the current schedule on the whiteboard!

      The seminar offers space for the discussion of advanced and integrative data analysis techniques, in particular presentations and discussion of ongoing or planned research projects, news from conferences, review and discussion of current literature and discussion of possible future teaching formats and content, and presentations, as well as final presentations on theses or project seminars. The seminar language is mostly English. Interested students are welcome to attend and drop in without obligation or present a topic of their own choice of interest to the working group as in a usual seminar. Please note: Individual dates may be canceled or postponed. Please contact me in case of questions (katharina.baum@fu-berlin.de)!

  • Academic Work in Theoretical Computer Science B

    0089cA2.13
    • 19306711 Seminar
      Seminar on Algorithms (László Kozma)
      Schedule: Do 14:00-16:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
      Location: T9/049 Seminarraum (Takustr. 9)

      Comments

      Contents

      Advanced topics in algorithm design with a changing focus. The topic is determined in each semester.

      This semester we plan a reading-group-style seminar on recent breakthrough results (2020-2025) in shortest paths algorithms.

      Target audience

      Masters students in computer science and mathematics.

      Recommended prerequisites

      "Advanced algorithms" or a similar class.

      Suggested reading

      Spezialliteratur aus Zeitschriften
    • 19331617 Seminar / Undergraduate Course
      Seminar/Proseminar: Information-theoretical principles of ML (Gerhard Wunder)
      Schedule: Fr 14:00-16:00 (Class starts on: 2025-04-25)
      Location: T9/K40 Multimediaraum (Takustr. 9)

      Comments

      Recently, artificial intelligence and machine learning (AI/ML) has emerged as a valuable tool in the field of communication and signal processing. It is therefore natural to extend the investigations to the field of physical layer security and privacy. This field is still in its infancy with some very preliminary results on wiretap channel code design, feature extraction of wireless channels and a growing part of contributions to privacy-preserving, distributed AI/ML. This seminar will teach the latest advances and synergies between the broad fields of AI/ML and secure communications.

      Keywords: ML overview, basic tools, universal approximation, deep learning, stochastic gradient, acceleration strategies, deep convolutional networks, feature extraction, classification, mutual information neural network estimation, structured sparsity in convolutional neural networks, matrix decompositions

       
    • 19335011 Seminar
      Seminar: Networks, dynamic models and ML for data integration in the life sciences (Katharina Baum)
      Schedule: Di 12:00-14:00 (Class starts on: 2025-04-15)
      Location: T9/137 Konferenzraum (Takustr. 9)

      Comments

      Research seminar of the group Data Integration in the Life Sciences (DILiS). Also open for seminar participation in the Master's program, online participation possible. Please refer to the current schedule on the whiteboard!

      The seminar offers space for the discussion of advanced and integrative data analysis techniques, in particular presentations and discussion of ongoing or planned research projects, news from conferences, review and discussion of current literature and discussion of possible future teaching formats and content, and presentations, as well as final presentations on theses or project seminars. The seminar language is mostly English. Interested students are welcome to attend and drop in without obligation or present a topic of their own choice of interest to the working group as in a usual seminar. Please note: Individual dates may be canceled or postponed. Please contact me in case of questions (katharina.baum@fu-berlin.de)!

  • Current Research Topics in Theoretical Computer Science

    0089cA2.3
    • 19320501 Lecture
      Cryptanalysis of Symmetrical Schemes (Marian Margraf)
      Schedule: Di 12:00-14:00 (Class starts on: 2025-04-15)
      Location: 1.4.03 Seminarraum T2 (Arnimallee 14)

      Comments

      The lecture aims at a deeper understanding of cryptographic algorithms, especially which design criteria have to be considered for the development of secure encryption algorithms. For that purpose we will get to know and evaluate different cryptanalytic methods for symmetrical and asymmetrical encryption techniques – e.g. linear and differential cryptanalysis on block ciphers, correlation attacks on stream ciphers and algorithms to solve the factorization problem and the discrete logarithm problem. Weaknesses in the implementation, e.g. to exploit side-channel attacks, will be discussed only peripherally.
    • 19321101 Lecture
      Advanced Data Structures (László Kozma)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

      Efficient data structures are important components of all nontrivial algorithms, and are basic building blocks of the modern computing infrastructure. Besides their practical importance, the design and analysis of data structures has revealed a rich mathematical theory. The ultimate theoretical limits of data structures are the subject of deep open questions.

      The topic of this course is the design and analysis of advanced data structures (including both classical and recent results).
      An earlier course with a similar selection of topics can be seen here:
      https://page.mi.fu-berlin.de/lkozma/ds2020

      Familiarity with algorithmic and relevant mathematical concepts is assumed (e.g., the course "Advanced algorithms" or similar as a prerequisite).

       

      Suggested reading

      D. E. Knuth, The Art of Computer Programming, Volume 4A: Combinatorial Algorithms, Part 1. (Addison-Wesley, 2011), xv+883pp. ISBN 0-201-03804-8
    • 19322701 Lecture
      Cryptoanalysis of Asymmetrical Schemes (Marian Margraf)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Comments

      Cryptoanalysis of asymmetrical schemes

      The lecture deals with different asymmetrical cryptanalytics, in particular with the supposed hard problems of these processes. Some of the contents are

      • RSA and the problem of factorization
      • DSA and the discrete logarithm problem
      • Merkel-Hellman and the knapsack and grid problem
      • McEliece and the problem of decoding
      • Matsumoto-Imai and the multivariate Polynomial System

      Knowledge in the areas of IT security and cryptography is obligatory.
    • 19337401 Lecture
      Elliptic Curve Cryptography (Marian Margraf)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: T9/SR 005 Übungsraum (Takustr. 9)
    • 19320502 Practice seminar
      Practice seminar for Cryptanalysis (Marian Margraf)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: T9/SR 005 Übungsraum (Takustr. 9)
    • 19321102 Practice seminar
      Practice seminar for Advanced Data Structures (N.N.)
      Schedule: Do 10:00-12:00 (Class starts on: 2025-04-17)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      Comments

      Übungen
    • 19322702 Practice seminar
      Practice seminar for Cryptoanalysis of Asymmetrical Schemes (Marian Margraf)
      Schedule: Mi 16:00-18:00 (Class starts on: 2025-04-16)
      Location: T9/K40 Multimediaraum (Takustr. 9)
    • 19337402 Practice seminar
      Tutorials for Elliptic Curve Cryptography (Marian Margraf)
      Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
      Location: T9/K40 Multimediaraum (Takustr. 9)

  • Computational Geometry

    0089cA2.4
    • 19313801 Lecture
      Computational Geometry (Günther Rothe)
      Schedule: Mo 10:00-12:00, Do 14:00-16:00 (Class starts on: 2025-04-14)
      Location: T9/051 Seminarraum (Takustr. 9)
    • 19313802 Practice seminar
      Practice seminar for Computational Geometry (Günther Rothe)
      Schedule: Fr 14:00-16:00 (Class starts on: 2025-04-25)
      Location: T9/SR 006 Seminarraum (Takustr. 9)

  • Selected Topics in Theoretical Computer Science

    0089cA2.5
    • 19315401 Lecture
      Multiplicative Weights - A Popular Algorithmic Technique with Countless Applications (Wolfgang Mulzer)
      Schedule: Di 14:00-16:00, Fr 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/055 Seminarraum (Takustr. 9)

      Comments

      Just like greedy algorithms, dynamic programming, or divide-and-conquer, the multiplicative weights method is a fundamental algorithmic technique with countless applications across disciplines. However, it is taught only rarely in basic classes.



      In this class, we will study the multiplicative weights method in detail. We will learn about the basic technique and its variations, explore connections to other fields such as online convex optimization and machine learning, and see the beautiful mathematics that lies behind it.



      We will also see many applications of the technique, with examples from combinatorial optimization, machine learning, algorithmic game theory, computational geometry, information theory, online algorithms, and many more. For some of the applications, we will have invited speakers who have applied the technique in their respective fields.



      The class is jointly attended by students at Sorbonne Paris Nord in Paris and will be given in a hybrid format.



      The course website can be found here: https://www.inf.fu-berlin.de/lehre/SS25/mwu/


      Suggested reading

      Wird noch bekannt gegeben.
    • 19326601 Lecture
      Markov Chains (Katinka Wolter)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/Gr. Hörsaal (Takustr. 9)

      Comments

      In this course we will study stochastic models commonly used to analyse the performance of dynamic systems. Markov models and queues are used to study the behaviour over time of a wide range of systems, from computer hardware, communication systems, biological systems, epidemics, traffic networks to crypto-currencies. We will take a tour of the basics of Markov modelling, starting from birth-death processes, the Poisson process to general Markov and semi-Markov processes and solution methods for those processes. Then we will look at queueing models and queueing networks with exact and approximate solution algorithms. If time allows we will finally study some of the foundations of discrete event simulation.

      Suggested reading

      William Stewart. Probability, Markov Chains, Queues and Simulation. Princeton University Press 2009.
    • 19315402 Practice seminar
      Practice seminar for Multiplicative Weights (Michaela Krüger)
      Schedule: Do 10:00-12:00 (Class starts on: 2025-04-17)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    • 19326602 Practice seminar
      Practice seminar for Markov Chains (Justus Purat)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A6/SR 007/008 Seminarraum (Arnimallee 6)

  • Advanced topics in Theoretical Computer Science

    0089cA2.6
    • 19315401 Lecture
      Multiplicative Weights - A Popular Algorithmic Technique with Countless Applications (Wolfgang Mulzer)
      Schedule: Di 14:00-16:00, Fr 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/055 Seminarraum (Takustr. 9)

      Comments

      Just like greedy algorithms, dynamic programming, or divide-and-conquer, the multiplicative weights method is a fundamental algorithmic technique with countless applications across disciplines. However, it is taught only rarely in basic classes.



      In this class, we will study the multiplicative weights method in detail. We will learn about the basic technique and its variations, explore connections to other fields such as online convex optimization and machine learning, and see the beautiful mathematics that lies behind it.



      We will also see many applications of the technique, with examples from combinatorial optimization, machine learning, algorithmic game theory, computational geometry, information theory, online algorithms, and many more. For some of the applications, we will have invited speakers who have applied the technique in their respective fields.



      The class is jointly attended by students at Sorbonne Paris Nord in Paris and will be given in a hybrid format.



      The course website can be found here: https://www.inf.fu-berlin.de/lehre/SS25/mwu/


      Suggested reading

      Wird noch bekannt gegeben.
    • 19326601 Lecture
      Markov Chains (Katinka Wolter)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/Gr. Hörsaal (Takustr. 9)

      Comments

      In this course we will study stochastic models commonly used to analyse the performance of dynamic systems. Markov models and queues are used to study the behaviour over time of a wide range of systems, from computer hardware, communication systems, biological systems, epidemics, traffic networks to crypto-currencies. We will take a tour of the basics of Markov modelling, starting from birth-death processes, the Poisson process to general Markov and semi-Markov processes and solution methods for those processes. Then we will look at queueing models and queueing networks with exact and approximate solution algorithms. If time allows we will finally study some of the foundations of discrete event simulation.

      Suggested reading

      William Stewart. Probability, Markov Chains, Queues and Simulation. Princeton University Press 2009.
    • 19315402 Practice seminar
      Practice seminar for Multiplicative Weights (Michaela Krüger)
      Schedule: Do 10:00-12:00 (Class starts on: 2025-04-17)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)
    • 19326602 Practice seminar
      Practice seminar for Markov Chains (Justus Purat)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A6/SR 007/008 Seminarraum (Arnimallee 6)

  • Special aspects of Theoretical Computer Science

    0089cA2.7
    • 19320501 Lecture
      Cryptanalysis of Symmetrical Schemes (Marian Margraf)
      Schedule: Di 12:00-14:00 (Class starts on: 2025-04-15)
      Location: 1.4.03 Seminarraum T2 (Arnimallee 14)

      Comments

      The lecture aims at a deeper understanding of cryptographic algorithms, especially which design criteria have to be considered for the development of secure encryption algorithms. For that purpose we will get to know and evaluate different cryptanalytic methods for symmetrical and asymmetrical encryption techniques – e.g. linear and differential cryptanalysis on block ciphers, correlation attacks on stream ciphers and algorithms to solve the factorization problem and the discrete logarithm problem. Weaknesses in the implementation, e.g. to exploit side-channel attacks, will be discussed only peripherally.
    • 19321101 Lecture
      Advanced Data Structures (László Kozma)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

      Efficient data structures are important components of all nontrivial algorithms, and are basic building blocks of the modern computing infrastructure. Besides their practical importance, the design and analysis of data structures has revealed a rich mathematical theory. The ultimate theoretical limits of data structures are the subject of deep open questions.

      The topic of this course is the design and analysis of advanced data structures (including both classical and recent results).
      An earlier course with a similar selection of topics can be seen here:
      https://page.mi.fu-berlin.de/lkozma/ds2020

      Familiarity with algorithmic and relevant mathematical concepts is assumed (e.g., the course "Advanced algorithms" or similar as a prerequisite).

       

      Suggested reading

      D. E. Knuth, The Art of Computer Programming, Volume 4A: Combinatorial Algorithms, Part 1. (Addison-Wesley, 2011), xv+883pp. ISBN 0-201-03804-8
    • 19322701 Lecture
      Cryptoanalysis of Asymmetrical Schemes (Marian Margraf)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Comments

      Cryptoanalysis of asymmetrical schemes

      The lecture deals with different asymmetrical cryptanalytics, in particular with the supposed hard problems of these processes. Some of the contents are

      • RSA and the problem of factorization
      • DSA and the discrete logarithm problem
      • Merkel-Hellman and the knapsack and grid problem
      • McEliece and the problem of decoding
      • Matsumoto-Imai and the multivariate Polynomial System

      Knowledge in the areas of IT security and cryptography is obligatory.
    • 19337401 Lecture
      Elliptic Curve Cryptography (Marian Margraf)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: T9/SR 005 Übungsraum (Takustr. 9)
    • 19320502 Practice seminar
      Practice seminar for Cryptanalysis (Marian Margraf)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: T9/SR 005 Übungsraum (Takustr. 9)
    • 19321102 Practice seminar
      Practice seminar for Advanced Data Structures (N.N.)
      Schedule: Do 10:00-12:00 (Class starts on: 2025-04-17)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      Comments

      Übungen
    • 19322702 Practice seminar
      Practice seminar for Cryptoanalysis of Asymmetrical Schemes (Marian Margraf)
      Schedule: Mi 16:00-18:00 (Class starts on: 2025-04-16)
      Location: T9/K40 Multimediaraum (Takustr. 9)
    • 19337402 Practice seminar
      Tutorials for Elliptic Curve Cryptography (Marian Margraf)
      Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
      Location: T9/K40 Multimediaraum (Takustr. 9)

  • Current Research Topics in Computer Systems

    0089cA3.10
    • 19325301 Lecture
      Cluster Computing (Barry Linnert)
      Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/055 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group

      • Computer Science Master students

      Requirements

      • Experience with computers and software as well as programing skills.

      Language

      • The course language is German (or English if requested).
      • The exam will be formulated in German, but answers may be given in English, too.

      Credits & Exams

      The criteria for gaining credits are

      • active participation in the tutorials: regular preparation of assignements & presentation of results in the tutorials
      • passing of the exam

      Website

      https://www.mi.fu-berlin.de/w/SE/VorlesungClusterComputing

       

      Comments

      Cluster computer are the prevailing type of high performance computers. They are built of custom off-the-shelf processor boards that are connected by a high speed interconnection network. Although usually locally integrated, they are conceptually distributed systems with local operating system images. Their enormous potential, however, can only be exploited, if program code and data are optimally distributed across the nodes. Cluster management mechanisms also need to be scalable to be employed in systems with thousands of nodes. The lecture course gives an overview of the architecture of cluster computers and the related management problems for which algorithmic solutions are presented.

      Suggested reading

      • Heiss, H.-U.: Prozessorzuteilung in Parallelrechnern, BI-Verlag, Mannheim, 1996
      • Andrews, G. A.: Foundations of Multithreaded, Parallel and Distributed Programming, Addison-Wesley, 2000
      • Pfister, G.: In Search of Clusters 2nd ed., Prentice Hall, 1998
      • Zomaya, A.: Parallel and distributed computing handbook, McGraw Gill, 1995
      • Buyya, R.: High Performance Cluster Computing, Vol. 1+2, Prentice Hall, 1999
    • 19327401 Lecture
      Image- and video coding (Heiko Schwarz)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
      Location: T9/053 Seminarraum (Takustr. 9)

      Comments

      This course introduces the most important concepts and algorithms that are used in modern image and video coding approaches. We will particularly focus on techniques that are found in current international video coding standards.

      In a short first part, we introduce the so-called raw data formats, which are used as input and output formats of image and video codecs. This part covers the following topics:

      • Colour spaces and their relation to human visual perception
      • Transfer functions (gamma encoding)
      • Why do we use the YCbCr format?

      The second part of the course deals with still image coding and includes the following topics:

      • The start: How does JPEG work?
      • Why do we use the Discrete Cosine Transform?
      • Efficient coding of transform coefficients
      • Prediction of image blocks
      • Adaptive block partitioning
      • How do we take decisions in an encoder?
      • Optimized quantization

      In the third part, we discuss approaches that make video coding much more efficient than coding all pictures using still image coding techniques:

      • Motion-compensated prediction
      • Coding of motion vectors
      • Algorithms for motion estimation
      • Sub-sample accurate motion vectors and interpolation filters
      • Usage of multiple reference pictures
      • What are B pictures and why do we use them?
      • Deblocking and deringing filters
      • Efficient temporal coding structures

      In the exercises, we will implement our own image codec (in a gradual manner). We may extend it to a simple video codec.

       

      Suggested reading

      • Bull, D. R., “Communicating Pictures: A Course in Image and Video Coding,” Elsevier, 2014.
      • Ohm, J.-R., “Multimedia Signal Coding and Transmission,” Springer, 2015.
      • Wien, M., “High Efficiency Video Coding — Coding Tools and Specifications,” Springer 2014.
      • Sze, V., Budagavi, M., and Sullivan, G. J. (eds.), “High Efficiency Video Coding (HEVC): Algorithm and Architectures,” Springer, 2014.
      • Wiegand, T. and Schwarz, H., "Source Coding: Part I of Fundamentals of Source and Video Coding,” Foundations and Trends in Signal Processing, Now Publishers, vol. 4, no. 1–2, 2011.
      • Schwarz, H. and Wiegand, T., “Video Coding: Part II of Fundamentals of Source and Video Coding,” Foundations and Trends in Signal Processing, Now Publishers, vol. 10, no. 1–3, 2016.
    • 19325302 Practice seminar
      Practice seminar for Cluster Computing (Barry Linnert)
      Schedule: Do 10:00-12:00 (Class starts on: 2025-04-17)
      Location: T9/K44 Rechnerpoolraum (Takustr. 9)
    • 19327402 Practice seminar
      Practice seminar for image- und video coding (Heiko Schwarz)
      Schedule: Mo 12:00-14:00 (Class starts on: 2025-04-14)
      Location: T9/053 Seminarraum (Takustr. 9)

  • Special Aspects of Computer Systems

    0089cA3.11
    • 19325301 Lecture
      Cluster Computing (Barry Linnert)
      Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/055 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group

      • Computer Science Master students

      Requirements

      • Experience with computers and software as well as programing skills.

      Language

      • The course language is German (or English if requested).
      • The exam will be formulated in German, but answers may be given in English, too.

      Credits & Exams

      The criteria for gaining credits are

      • active participation in the tutorials: regular preparation of assignements & presentation of results in the tutorials
      • passing of the exam

      Website

      https://www.mi.fu-berlin.de/w/SE/VorlesungClusterComputing

       

      Comments

      Cluster computer are the prevailing type of high performance computers. They are built of custom off-the-shelf processor boards that are connected by a high speed interconnection network. Although usually locally integrated, they are conceptually distributed systems with local operating system images. Their enormous potential, however, can only be exploited, if program code and data are optimally distributed across the nodes. Cluster management mechanisms also need to be scalable to be employed in systems with thousands of nodes. The lecture course gives an overview of the architecture of cluster computers and the related management problems for which algorithmic solutions are presented.

      Suggested reading

      • Heiss, H.-U.: Prozessorzuteilung in Parallelrechnern, BI-Verlag, Mannheim, 1996
      • Andrews, G. A.: Foundations of Multithreaded, Parallel and Distributed Programming, Addison-Wesley, 2000
      • Pfister, G.: In Search of Clusters 2nd ed., Prentice Hall, 1998
      • Zomaya, A.: Parallel and distributed computing handbook, McGraw Gill, 1995
      • Buyya, R.: High Performance Cluster Computing, Vol. 1+2, Prentice Hall, 1999
    • 19327401 Lecture
      Image- and video coding (Heiko Schwarz)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
      Location: T9/053 Seminarraum (Takustr. 9)

      Comments

      This course introduces the most important concepts and algorithms that are used in modern image and video coding approaches. We will particularly focus on techniques that are found in current international video coding standards.

      In a short first part, we introduce the so-called raw data formats, which are used as input and output formats of image and video codecs. This part covers the following topics:

      • Colour spaces and their relation to human visual perception
      • Transfer functions (gamma encoding)
      • Why do we use the YCbCr format?

      The second part of the course deals with still image coding and includes the following topics:

      • The start: How does JPEG work?
      • Why do we use the Discrete Cosine Transform?
      • Efficient coding of transform coefficients
      • Prediction of image blocks
      • Adaptive block partitioning
      • How do we take decisions in an encoder?
      • Optimized quantization

      In the third part, we discuss approaches that make video coding much more efficient than coding all pictures using still image coding techniques:

      • Motion-compensated prediction
      • Coding of motion vectors
      • Algorithms for motion estimation
      • Sub-sample accurate motion vectors and interpolation filters
      • Usage of multiple reference pictures
      • What are B pictures and why do we use them?
      • Deblocking and deringing filters
      • Efficient temporal coding structures

      In the exercises, we will implement our own image codec (in a gradual manner). We may extend it to a simple video codec.

       

      Suggested reading

      • Bull, D. R., “Communicating Pictures: A Course in Image and Video Coding,” Elsevier, 2014.
      • Ohm, J.-R., “Multimedia Signal Coding and Transmission,” Springer, 2015.
      • Wien, M., “High Efficiency Video Coding — Coding Tools and Specifications,” Springer 2014.
      • Sze, V., Budagavi, M., and Sullivan, G. J. (eds.), “High Efficiency Video Coding (HEVC): Algorithm and Architectures,” Springer, 2014.
      • Wiegand, T. and Schwarz, H., "Source Coding: Part I of Fundamentals of Source and Video Coding,” Foundations and Trends in Signal Processing, Now Publishers, vol. 4, no. 1–2, 2011.
      • Schwarz, H. and Wiegand, T., “Video Coding: Part II of Fundamentals of Source and Video Coding,” Foundations and Trends in Signal Processing, Now Publishers, vol. 10, no. 1–3, 2016.
    • 19325302 Practice seminar
      Practice seminar for Cluster Computing (Barry Linnert)
      Schedule: Do 10:00-12:00 (Class starts on: 2025-04-17)
      Location: T9/K44 Rechnerpoolraum (Takustr. 9)
    • 19327402 Practice seminar
      Practice seminar for image- und video coding (Heiko Schwarz)
      Schedule: Mo 12:00-14:00 (Class starts on: 2025-04-14)
      Location: T9/053 Seminarraum (Takustr. 9)

  • Microprocessor Lab

    0089cA3.2
    • 19310030 Internship
      Practical Project: Microprocessors (Larissa Groth)
      Schedule: Mo 16:00-18:00, Di 14:00-16:00, Mi 12:00-14:00 (Class starts on: 2025-04-14)
      Location: T9/K63 Hardwarepraktikum (Takustr. 9)

      Additional information / Pre-requisites

      Important information about the course:
      The microprocessor practical course will be offered this semester with a joint theory session on Wednesdays, 12-14 o'clock, and two independent practical exercise sessions:

      • Group A, Mondays, 4-6 p.m. Takustraße 9, Room K63
      • Group B, Tuesdays, 2-4 p.m. Takustraße 9, Room K63

      One of these practice dates must be chosen.

      Comments

      ATTENTION: Contrary to the schedule in the course catalog, this course does not have 3 mandatory dates, but only 2! See below for further information!

      The overwhelming majority of future computer systems will be characterized by communicating, embedded systems. These are found in machine controls, household appliances, motor vehicles, airplanes, intelligent buildings, etc. and will in future be increasingly integrated into networks such as the Internet.

      The internship will address the architecture of embedded systems and demonstrate the differences to traditional PC architectures (e.g., real-time capability, interaction with the environment) with practical examples. The internship is based on 16- and 32-bit microcontroller systems.

      The main focus of the internship is the following:

          register structures
          memory organization
          Hardware assembler and high-language programming
          I / O system and timer programming
          Interrupt system
          Watchdog logic
          Analog interface
          Bus system connection of components
          Communication (serial, CAN bus, Ethernet, radio and USB)
          Control of models and use of different sensors

      Suggested reading

      • Brian W. Kernighan, Dennis M. Ritchie: The C Programming Language, Second Edition, Prentice Hall, 1988.

  • Mobile Communications

    0089cA3.3
    • 19303901 Lecture
      Mobile Communications (Jochen Schiller)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: T9/049 Seminarraum (Takustr. 9)

      Comments

      The module mobile communication presents major topics from mobile and wireless communications - the key drivers behind today's communication industry that influence everybody's daily life. 

      The whole lecture focuses on a system perspective giving many pointers to real systems, standardization and current research.

      The format of the lecture is the flipped classroom, i.e., you should watch the videos of a lecture BEFORE participating in the Q&A session. We will then discuss all open issues, answer questions etc. during the Q&A session.

      Main topics of the lecture are:

      • Basics of wireless transmission: frequencies, signals, antennas, multiplexing, modulation, spread spectrum
      • Medium access: SDMA, FDMA, TDMA, CDMA;
      • Wireless telecommunication systems: GSM, TETRA, IMT-2000, LTE, 5G
      • Wireless local area networks: infrastructure/ad-hoc, IEEE 802.11/15, Bluetooth, ZigBee
      • Mobile networking: Mobile IP, ad-hoc networks
      • Mobile transport layer: traditional TCP, additional mechanisms
      • Outlook: 5 to 6G, low power wireless networks

      Suggested reading

      Jochen Schiller, Mobilkommunikation, Addison-Wesley, 2.Auflage 2003

      Alle Unterlagen verfügbar unter http://www.mi.fu-berlin.de/inf/groups/ag-tech/teaching/resources/Mobile_Communications/course_Material/index.html

  • Robotics

    0089cA3.4
    • 19304701 Lecture
      Robotics (Daniel Göhring)
      Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
      Location: T9/Gr. Hörsaal (Takustr. 9)

      Additional information / Pre-requisites

      Students interested in robotics with application to autonomous vehicles. Voraussetzungen: As a prerequisite, student should have basic knowledge of maths, in particular linear algebra and a bit of optimization. Students will work with a real model car in the robotics lab.

      Comments

      Content

      This class will give an introduction to robotics. It will be structured into the following parts:

      • Generating motion and and dynamic control: This chapter will cover coordinate frames, non-holonomic constraints, Ackermann-drive (in analogy to street cars), PID.
      • Planning: Planning around obstacles, path finding, Dijkstra, A*, configuration space obstacles, RRTs, lattice planners, gradient methods, potential fields, splines.
      • Localization and mapping: state estimation problem, Bayesian filter, Odometry, Particle & Kalman filter, Extended and Unscented Kalman-Filter, simultaneous localization and mapping (SLAM).
      • Vision and perception: SIFT, HOG-features, Deformable parts models, hough transform, lane detection, 3d-point clouds, RANSAC .

      After these lectures, students will be able to design basic algorithms for motion, control and state estimation for robotics.

      The lecture will be in German, accompanying materials in English.

      Suggested reading

      Literatur:


      John J Craig: Introduction to Robotics: Mechanics and Control; Steven LaValle: Planning Algorithms; Sebastian Thrun, Wolfram Burgard, Dieter Fox: Probabilistic Robotics

       
    • 19304702 Practice seminar
      Practice seminar for Robotics (Daniel Göhring)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: T9/049 Seminarraum (Takustr. 9)

  • Software Project: Computer Systems A

    0089cA3.6
    • 19315312 Project Seminar
      Software Project: Distributed Systems (Justus Purat)
      Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
      Location: T9/K63 Hardwarepraktikum (Takustr. 9)
    • 19334412 Project Seminar
      SWP: Szenario-Management in the Future Security Lab (Larissa Groth)
      Schedule: Mi 23.04. 14:00-16:00 (Class starts on: 2025-04-23)
      Location: T9/K63 Hardwarepraktikum (Takustr. 9)

      Comments

      The BeLIFE project, part of the working group Telematics & Computer Systems, focuses on improving knowledge transfer and communication in civil security research. A central component of the project is the Future Security Lab, located at the Einstein Center Digital Future (ECDF) in Mitte. The lab welcomes politicians from federal and state levels, as well as representatives from authorities and organizations with security responsibilities.

      Within the software project, students develop concepts to optimize and creatively enhance the existing technical infrastructure of the space. The goal is to increase the usability of the space for scientists and improve the user experience for visitors. To achieve this, the software project consists of several sub-areas, either arising from a specific problem to be solved or requiring creative approaches and ingenuity. Tasks include system administration, interface development, as well as light/sound installation and orchestration. Examples of challenges include the parallel startup of all computers in a network via WakeOn LAN from a web app or optimizing the existing web app for scenario presentation.

      The tasks are exclusively addressed in small groups (3-5 students). Collaboration and code availability are facilitated through the department's own GitLab or a public GitHub. Results should be well-documented, for example, through README files in Git and a well-structured wiki. Modularity and expandability of the developed code, along with thorough documentation, are crucial for the success of this software project!

      Regarding the process, this software project takes place throughout the semester. There are a few mandatory large group meetings with all participants. In addition, there are short weekly meetings where at least one group member reports on the current status. The first date (23.04.25, 14h, K63) will take place at Takustraße 9. At this event, the solutions already implemented will be presented in theory and the problems addressed. A live demo will then take place one week later, on 30.04.2025, in Berlin Mitte at the Future Security Lab, Wilhelmstr. 67, 10117 Berlin. Afterwards, there are a total of three presentation dates: the presentation of an initial approach to problem-solving (14.04.2025), a brief interim presentation (11.06.2025), and the final presentation (16.07.2025).

      Students also regularly have the opportunity to work in the Future Security Lab premises, familiarize themselves with the equipment, and conduct tests.

  • Software Project: Computer Systems B

    0089cA3.7
    • 19315312 Project Seminar
      Software Project: Distributed Systems (Justus Purat)
      Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
      Location: T9/K63 Hardwarepraktikum (Takustr. 9)
    • 19334412 Project Seminar
      SWP: Szenario-Management in the Future Security Lab (Larissa Groth)
      Schedule: Mi 23.04. 14:00-16:00 (Class starts on: 2025-04-23)
      Location: T9/K63 Hardwarepraktikum (Takustr. 9)

      Comments

      The BeLIFE project, part of the working group Telematics & Computer Systems, focuses on improving knowledge transfer and communication in civil security research. A central component of the project is the Future Security Lab, located at the Einstein Center Digital Future (ECDF) in Mitte. The lab welcomes politicians from federal and state levels, as well as representatives from authorities and organizations with security responsibilities.

      Within the software project, students develop concepts to optimize and creatively enhance the existing technical infrastructure of the space. The goal is to increase the usability of the space for scientists and improve the user experience for visitors. To achieve this, the software project consists of several sub-areas, either arising from a specific problem to be solved or requiring creative approaches and ingenuity. Tasks include system administration, interface development, as well as light/sound installation and orchestration. Examples of challenges include the parallel startup of all computers in a network via WakeOn LAN from a web app or optimizing the existing web app for scenario presentation.

      The tasks are exclusively addressed in small groups (3-5 students). Collaboration and code availability are facilitated through the department's own GitLab or a public GitHub. Results should be well-documented, for example, through README files in Git and a well-structured wiki. Modularity and expandability of the developed code, along with thorough documentation, are crucial for the success of this software project!

      Regarding the process, this software project takes place throughout the semester. There are a few mandatory large group meetings with all participants. In addition, there are short weekly meetings where at least one group member reports on the current status. The first date (23.04.25, 14h, K63) will take place at Takustraße 9. At this event, the solutions already implemented will be presented in theory and the problems addressed. A live demo will then take place one week later, on 30.04.2025, in Berlin Mitte at the Future Security Lab, Wilhelmstr. 67, 10117 Berlin. Afterwards, there are a total of three presentation dates: the presentation of an initial approach to problem-solving (14.04.2025), a brief interim presentation (11.06.2025), and the final presentation (16.07.2025).

      Students also regularly have the opportunity to work in the Future Security Lab premises, familiarize themselves with the equipment, and conduct tests.

  • Academic Work in Computer Systems A

    0089cA3.8
    • 19307117 Seminar / Undergraduate Course
      Seminar/Proseminar: Smart Homes and the World of IoT (Marius Max Wawerek)
      Schedule: Mo 14:00-16:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-14)
      Location: T9/K63 Hardwarepraktikum (Takustr. 9)

      Comments

      This seminar focuses on various aspects of modern “Internet of Things” (IoT) systems. The main component will be applications and publications related to the area of the “Smart Home”. At the beginning of the seminar, suggested topics will be given, which will mainly deal with data analysis (both “normal” statistics and machine learning), security aspects and the usefulness of the Internet of Things or the “Smart Home”. You are also welcome to suggest your own topics, but they must be related to IoT systems. The topics should be worked on alone.

      About the procedure: This seminar takes place throughout the semester. There are few meetings, but these are mandatory. On the first date (14.04.2025) the list of topics will be handed out and discussed. In the next week (21.04.2025) there will be another opportunity to discuss topic suggestions. If you are interested in your own topic, please prepare a short (2-3 minutes) outline of your proposal. As in the third week (28.04.2025) the topics will be assigned.


      There will then be 3 presentation dates per person: the presentation of the literature research (19.05.2025), a short interim presentation (16.06.2025) and the final presentation on one of the dates in the period from 30.06.2025 - 14.07.2025. There will be no further meetings beyond this.

      This means that, depending on the number of participants, the following meetings are mandatory:

      • 14.04.2025
      • 21.04.2025
      • 19.05.2025
      • 16.06.2025
      • 30.06.2025
      • 07.07.2025
      • 14.07.2025
    • 19310817 Seminar / Undergraduate Course
      Seminar/Proseminar: High Performance and Cloud Computing (Barry Linnert)
      Schedule: Di 12:00-14:00 (Class starts on: 2025-04-22)
      Location: T9/K40 Multimediaraum (Takustr. 9)

      Comments

      When it comes to processing complex applications or large amounts of data within a reasonable time frame, the use of parallel programs is unavoidable. However, these can be very different due to the specific application framework or the technical environments. For example, high-performance computing (HPC) uses supercomputers that support applications with a high degree of interaction, while cloud computing focuses on the provision of data and computing capacity on demand.
      Both application areas have challenges both at the programming level and in the administration of the corresponding systems.
      In the seminar, we will focus on one aspect of this spectrum and summarize and evaluate current research in this area.

      Further information on the procedure will be provided at the first meeting on 22.04.2025.
    • 19329617 Seminar / Undergraduate Course
      Seminar/Proseminar: Telematics (Jochen Schiller)
      Schedule: Di 15.07. 10:00-16:00, Di 22.07. 10:00-18:00 (Class starts on: 2025-07-15)
      Location: T9/K40 Multimediaraum (Takustr. 9)

      Comments

      This seminar focuses on several aspects of technical Computer Science. At the start of the seminar you will receive a list of suggested topics that mainly deal with particular aspects of the so-called Trusted Computing and security issues in the Internet of Things. You are also very welcome to suggest your own research topic that is closely related to technical Computer Science. You can work on your topic exclusively or in a small group of 2-3 students. But then, it has to be apparent who contributed what part to the seminar paper.

       

      It is possible to combine this seminar with the software project Telematics. Then, the theoretical foundations of the topic are dealt with in the scientific seminar paper and implemented in practice in the software project. Please note that the seminar paper is not supposed to deal with details of the implementation and that you are still obliged to write an accurate documentation of the software project in written form. 

       

      Concerning the schedule: This seminar takes place during the semester. There are only a few meetings, but these are mandatory. On the first meeting (03.11.2020), the topic list will be handed out and discussed. Please prepare a short (2-3 minutes) overview of your own topic suggestion if you would like to include it in the seminar. On the next week (10.11.2020), the topics will be assigned. After that there will be 3 presentation dates in total: the topic presentation (01.12.2021), a short interim presentation (12.01.2021) and the final presentation (23.02.2021). There will be no further meetings beyond that. This semester, all meetings will take place as video conferences with Webex.

  • Academic Work in Computer Systems B

    0089cA3.9
    • 19307117 Seminar / Undergraduate Course
      Seminar/Proseminar: Smart Homes and the World of IoT (Marius Max Wawerek)
      Schedule: Mo 14:00-16:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-14)
      Location: T9/K63 Hardwarepraktikum (Takustr. 9)

      Comments

      This seminar focuses on various aspects of modern “Internet of Things” (IoT) systems. The main component will be applications and publications related to the area of the “Smart Home”. At the beginning of the seminar, suggested topics will be given, which will mainly deal with data analysis (both “normal” statistics and machine learning), security aspects and the usefulness of the Internet of Things or the “Smart Home”. You are also welcome to suggest your own topics, but they must be related to IoT systems. The topics should be worked on alone.

      About the procedure: This seminar takes place throughout the semester. There are few meetings, but these are mandatory. On the first date (14.04.2025) the list of topics will be handed out and discussed. In the next week (21.04.2025) there will be another opportunity to discuss topic suggestions. If you are interested in your own topic, please prepare a short (2-3 minutes) outline of your proposal. As in the third week (28.04.2025) the topics will be assigned.


      There will then be 3 presentation dates per person: the presentation of the literature research (19.05.2025), a short interim presentation (16.06.2025) and the final presentation on one of the dates in the period from 30.06.2025 - 14.07.2025. There will be no further meetings beyond this.

      This means that, depending on the number of participants, the following meetings are mandatory:

      • 14.04.2025
      • 21.04.2025
      • 19.05.2025
      • 16.06.2025
      • 30.06.2025
      • 07.07.2025
      • 14.07.2025
    • 19310817 Seminar / Undergraduate Course
      Seminar/Proseminar: High Performance and Cloud Computing (Barry Linnert)
      Schedule: Di 12:00-14:00 (Class starts on: 2025-04-22)
      Location: T9/K40 Multimediaraum (Takustr. 9)

      Comments

      When it comes to processing complex applications or large amounts of data within a reasonable time frame, the use of parallel programs is unavoidable. However, these can be very different due to the specific application framework or the technical environments. For example, high-performance computing (HPC) uses supercomputers that support applications with a high degree of interaction, while cloud computing focuses on the provision of data and computing capacity on demand.
      Both application areas have challenges both at the programming level and in the administration of the corresponding systems.
      In the seminar, we will focus on one aspect of this spectrum and summarize and evaluate current research in this area.

      Further information on the procedure will be provided at the first meeting on 22.04.2025.
    • 19329617 Seminar / Undergraduate Course
      Seminar/Proseminar: Telematics (Jochen Schiller)
      Schedule: Di 15.07. 10:00-16:00, Di 22.07. 10:00-18:00 (Class starts on: 2025-07-15)
      Location: T9/K40 Multimediaraum (Takustr. 9)

      Comments

      This seminar focuses on several aspects of technical Computer Science. At the start of the seminar you will receive a list of suggested topics that mainly deal with particular aspects of the so-called Trusted Computing and security issues in the Internet of Things. You are also very welcome to suggest your own research topic that is closely related to technical Computer Science. You can work on your topic exclusively or in a small group of 2-3 students. But then, it has to be apparent who contributed what part to the seminar paper.

       

      It is possible to combine this seminar with the software project Telematics. Then, the theoretical foundations of the topic are dealt with in the scientific seminar paper and implemented in practice in the software project. Please note that the seminar paper is not supposed to deal with details of the implementation and that you are still obliged to write an accurate documentation of the software project in written form. 

       

      Concerning the schedule: This seminar takes place during the semester. There are only a few meetings, but these are mandatory. On the first meeting (03.11.2020), the topic list will be handed out and discussed. Please prepare a short (2-3 minutes) overview of your own topic suggestion if you would like to include it in the seminar. On the next week (10.11.2020), the topics will be assigned. After that there will be 3 presentation dates in total: the topic presentation (01.12.2021), a short interim presentation (12.01.2021) and the final presentation (23.02.2021). There will be no further meetings beyond that. This semester, all meetings will take place as video conferences with Webex.

  • Analysis II

    0084dA1.2
    • 19211601 Lecture
      Analysis II (Marita Thomas)
      Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Comments

      Content

      This is the continuation of the Analysis I course taught in the previous winter term. Central topics of the course are integration in one space dimension and differential calculus of several variables. 

      Suggested reading

      • O. Forster: Analysis 1 und 2. Vieweg/Springer.
      • Königsberger, K: Analysis 1,2, Springer.
      • E. Behrends: Analysis Band 1 und 2, Vieweg/Springer.
      • H. Heuser: Lehrbuch der Analysis 1 und 2, Teubner/Springer.
    • 19211602 Practice seminar
      Practice seminar for Analysis II (Marita Thomas)
      Schedule: Mi 14:00-16:00, Do 16:00-18:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: 1.1.53 Seminarraum E2 (Arnimallee 14)

  • Linear Algebra II

    0084dA1.5
    • 19211701 Lecture
      Linear Algebra II (Alexander Schmitt)
      Schedule: Mo 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-04-14)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Comments

      Contents:

      • Determinants
      • Eigenvalues and eigenvectors: diagonalizability, trigonalizability, set of Cayley-Hamilton, Jordanian normal form
      • Bilinear forms
      • Vectorräume with scalar product: Euclidean, unitary vectorräume, orthogonal projection, isometries, self-adjusted images, Gram-Schmidt orthonormalization methods, major axis transformation

      Prerequisites:
      Linear Algebra I
      Literature:

      Will be mentioned in the lecture.
    • 19211702 Practice seminar
      Practice seminar for Linear Algebra II (Alexander Schmitt)
      Schedule: Do 08:00-10:00, Do 10:00-12:00, Do 16:00-18:00, Fr 08:00-10:00, Fr 10:00-12:00 (Class starts on: 2025-04-17)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

  • Computer-Oriented Mathematics II

    0084dA1.7
    • 19211901 Lecture
      Computer-oriented Mathematics II (Robert Gruhlke)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
      Location: T9/Gr. Hörsaal (Takustr. 9)

      Additional information / Pre-requisites

      Studierende der Mathematik (Monobachelor und Lehramt) und Bioinformatik, sowie Numerikinteressierte aus Physik, Informatik und anderen Natur- und Geisteswissenschaften.

      Comments

      Inhalt:

      Die Auswahl der behandelten numerischen Verfahren enthält Polynominterpolation, Newton-Cotes-Formeln zur numerische Integration und Euler-Verfahren für lineare Differentialgleichungen.
    • 19211902 Practice seminar
      Practice seminar for Computer-oriented Mathematics II (Robert Gruhlke)
      Schedule: Di 08:00-10:00, Di 16:00-18:00, Mi 16:00-18:00, Do 08:00-10:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

  • Numerical Mathematics I

    0084dA1.9
    • 19212001 Lecture
      Numerics I (Claudia Schillings)
      Schedule: Mo 10:00-12:00, Mi 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-14)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)

      Comments

      Numerical methods for: iterative solution of nonlinear systems of equations (fixpoint and Newton methods), curve fitting, interpolation, numerical quadrature, and numerics of ODE systems.

      Suggested reading

      Stoer, Josef und Roland Bulirsch: Numerische Mathematik - eine Einführung, Band 1. Springer, Berlin, 2005.

      Aus dem FU-Netz auch online verfügbar.

      Link
    • 19212002 Practice seminar
      Practice seminar for Numerics I (N.N.)
      Schedule: Di 08:00-10:00, Di 12:00-14:00 (Class starts on: 2025-04-15)
      Location: T9/049 Seminarraum (Takustr. 9)

  • Academic Work in Mathematics

    0084dB1.1
    • 19203611 Seminar
      Proseminar/Seminar: das Buch der Beweise (Giulia Codenotti)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A3/SR 115 (Arnimallee 3-5)

      Comments

      Inhalt: Vorträge zu Gitterproblemen in 2 (und 3) Dimensionen. Weitere Informationen finden Sie auf der Homepage des Proseminars.
    • 19213910 Proseminar
      Proseminar/Seminar on Number Theory: Geometry of Numbers (Niels Lindner)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
      Location: A3/SR 119 (Arnimallee 3-5)

      Additional information / Pre-requisites

      Nötige Vorkenntnisse: Lineare Algebra und eine gewisse Vertrautheit mit den Grundbegriffen der Algebra, etwa "Gruppe", "Ring", "Körper", "Ideal", "Normalteiler", etc.

      Comments

      This proseminar/seminar deals with Minkowski's "geometry of numbers", which does not only open up a geometric perspective on algebraic number theory, but also enables interesting applications in discrete geometry and combinatorial optimization. More precisely, we will dive into the following topics:

      * Minkowski's classical convex body theorems

      * Gaussian integers, Fermat's two-squares theorem, Legendre's four-squares theorem

      * Algebraic number fields, finiteness of the class number, Dirichlet's unit theorem

      * Linear equations over the integers: Hermite and Smith normal forms

      * Basics of lattice theory

      * Lattice basis reduction and the LLL algorithm

      * The shortest vector problem

      * Dense sphere packings

      * Khinchine's flatness theorem

      * Integer linear programming in fixed dimension

      The purpose of this list is to offer a coarse thematic overview. The precise seminar topics will be fixed later, together with the participants.

      Further information will be provided on the Whiteboard homepage of the seminar at the beginning of the lecture period.
    • 19226511 Seminar
      Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      Audience: At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

      Comments

      Content: The seminar will concern the discussion of state-of-art techniques in molecular simulation which allow for a simulation of several space (especially) and time scale within one computational approach.

      The discussion will concerns both, specific computational coding and conceptual developments.

      Suggested reading

      Related Basic Literature:

      (1) M.Praprotnik, L.Delle Site and K.Kremer, Ann.Rev.Phys.Chem.59, 545-571 (2008)

      (2) C.Peter, L.Delle Site and K.Kremer, Soft Matter 4, 859-869 (2008).

      (3) M.Praprotnik and L.Delle Site, in "Biomolecular Simulations: Methods and Protocols" L.Monticelli and E.Salonen Eds. Vol.924, 567-583 (2012) Methods Mol. Biol. Springer-Science
    • 19233511 Seminar
      Geometric Group Theory (Georg Lehner)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Additional information / Pre-requisites

      Aimed at: Bachelor and masters students

      Prerequisites: Group theory. Additionally either Geometry (especially elementary non-euclidean geometry) and/or Topology (point-set topology) can be helpful.

      Comments

      Groups are best understood as symmetries of mathematical objects. Whereas finite groups can often be completely understood by their actions on vector spaces, this approach will often fail with infinite groups, such as free groups or hyperbolic groups. Geometric group theory tries to construct natural geometric objects (topological spaces such as manifolds or graphs for example) that these groups act on and allows one to classify the complexity these groups can have.

      In this seminar, we will follow Clara Löh's book on the subject. Topics will include Cayley graphs, free groups and their subgroups, quasi-isometry classes of groups, growth types of groups, hyperbolic groups and the Banach-Tarski theorem.

      Suggested reading

      Clara Löh - Geometric Group Theory
    • 19239711 Seminar
      Advanced Dynamical Systems (Bernold Fiedler)
      Schedule: Do 16:00-18:00 (Class starts on: 2025-04-17)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Students present recent papers on topics in delay equations. Dates only by arrangement.
    • 19239911 Seminar
      Advanced Differential Equations (Bernold Fiedler)
      Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Students present recent papers on topics in dynamical systems. Dates only by arrangement.
    • 19247111 Seminar
      Variational methods & Gamma-convergence (Marita Thomas)
      Schedule: Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Comments

      This seminar addresses bachelor and master students interested in the analysis of partial differential equations (PDEs). It focuses on elliptic PDEs, where the direct method of the calculus of variations provides a powerful tool to handle linear as well as nonlinear problems by investigating the minimality properties of the functional associated with the PDE. Closely related to this is the method of Gamma-convergence, which allows it to study sequences of functionals and minimization problems. A background with courses in analysis, functional analysis, and introduction to PDEs is useful to attend the seminar, but the topics for the presentations will be adapted to the background of the participants.   The main part of the seminar will be held en block in the teaching-free period.

  • Special topics in Mathematics

    0084dB2.11
    • 19248101 Lecture
      Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
      Schedule: Mo 14:00-16:00, Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

      Terminhinweis: Die Veranstaltung findet regelmäßig Mo 12‒16 und Di 14‒16 Uhr statt, allerdings mit folgender Ausnahme: Aufgrund des Dies Academicus, den das Institut für Mathematik am ersten Tag des Semesters veranstaltet, gibt es in der ersten Woche abweichende Termine. Für die Einteilung in Kleingruppen, in denen man das Semester über arbeitet, ist es notwendig, beim ersten Treffen am Dienstag, 15. April von 14‒18 Uhr anwesend zu sein.
       

      Leitidee der Veranstaltung
      Ziel der Veranstaltung ist es, einen Überblick über die Bedeutung und Anwendbarkeit diverser mathematischer Gebiete im Kontext von Nachhaltigkeit zu bekommen. Ferner soll dies anhand kleinerer Probleme selbst angewendet werden können. Mathematik ist bekanntermaßen überall und besitzt eine hohe gesellschaftliche Relevanz. Insbesondere im Kontext Nachhaltigkeit sollten wir als mathematische Community Verantwortung übernehmen, einen lebenswerten Planeten zu erhalten und unsere Erkenntnisse, Methoden, Verfahren etc. gemeinwohlorientiert einzusetzen. Dies involviert auch die Aufbereitung und Kommunikation der behandelten mathematischen Themenbereiche.

      Inhaltliche Schwerpunkte
      Wir werden eine Einführung in die vier mathematischen Bereiche Optimierung, Spieltheorie, Statistik, Dynamische Systeme geben. Mittels mathematischer Modellierung werden wir identifizieren, wie diese Bereiche zum Verständnis und mit Lösungsansätzen zu Klimakrise, Verlust von Biodiversität, Ressourcenverknappung und sozialer Ungleichheit beitragen. 

      Methodische Konzeption
      Diese Veranstaltung wird durch ein zeitgemäßes didaktisches Konzept begleitet. Dazu gehören Elemente aus dem Design Thinking, New Work-Methoden wie agiles Arbeiten, aber auch der Ansatz der student agency. Dies bedeutet, dass Lernende Verantwortung für ihren Lernerfolg und Kompetenzzuwachs übernehmen, dabei aber natürlich nicht auf sich alleine gestellt sind, sondern auf diverse inhaltliche bzw. methodische Ressourcen zurückgreifen können. 

      Die inhaltliche Arbeit erfolgt in festen Kleingruppen, die zu jedem mathematischen Themenfeld ein Anwendungsszenario erarbeitet. Dazu werden kleinere reale Probleme bzw. entsprechende mathematische Forschungspaper als Aufhänger und Ausgangspunkt für die Gruppenarbeit ausgewählt. 
      Jeder dieser thematischen „eduSCRUM-Sprints“ besteht aus Planung, Durchführung, Präsentation und endet mit der Reflexion der Arbeitsweisen innerhalb des Teams.

      Zu jedem der vier mathematischen Bereiche gibt es einen Sprint von ca. drei Wochen. Zwischen den Sprints wird zu jedem Themengebiet eine kleine Challenge (zwei bis drei kurze Aufgaben) veröffentlicht, die in Gruppen bearbeitet abzugeben ist. Der Workload dieser Veranstaltung verteilt sich anteilig ungefähr wie folgt: 30% Präsenztermine (Montag & Dienstag) + 10% Challenges + 60% eduScrum-Projektarbeit
       

      Überblick über die wöchentliche Struktur der Veranstaltung 

      • Dienstag 14–16 Uhr: Die Vorlesungstermine dienen der kompakten Aufbereitung der benötigten mathematischen Gebiete und bilden damit die fundamentale  inhaltliche Grundlage für die Projektarbeit. Wir geben dabei einen Einblick in diverse mathematische Gebiete und ihren Anwendungsbezug. 
      • Projektarbeitsphase (zwischen Dienstag 16 Uhr und Montag 12 Uhr): Die Projektarbeitsphase dient dem agilen Arbeiten in Kleingruppen, welche über das Semester verteilt mehrere Anwendungen von Mathematik in SDG-Kontext erarbeiten und aufbereiten. Dabei wird sich an der Methode eduSCRUM orientiert, um über das Semester verteilt in mehreren agilen Sprints über jeweils 2-3 Wochen fokussiert zu arbeiten. Erfahrungen im agilen Arbeiten werden nicht vorausgesetzt. Die erarbeiteten Anwendungsszenarien sollen dabei jeweils passend zu den vier inhaltlichen Themenblöcken der Veranstaltung gestaltet werden, wobei die Kleingruppen durch den Einbau partizipativer Elemente an diversen Stellen Gestaltungsspielraum haben.
      • Montag 12–16 Uhr: Die „Übungstermine“ dienen dem Austausch zwischen den Gruppen, hier werden die in den Sprints erarbeiteten Themen untereinander vorgestellt und ausführlich diskutiert. Nach jedem Sprint werden innerhalb der Gruppen die Arbeitsweise reflektiert und Absprachen für den folgenden Sprint getroffen. Weiterhin können auch inhaltliche Fragen besprochen oder methodische Unterstützung bei eduScrum angeboten werden.

       

      Lernziele
      Die übergeordneten Lernziele dieser Veranstaltung verteilen sich auf fünf Bereiche: Mathematische Grundlagen verstehen und anwenden, Mathematische Modelle anwenden, Modelle beurteilen, Kommunikation von Mathematik im SDG-Kontext & Reflexion des eigenen Lernprozesses.

      Nach erfolgreicher Teilnahme an der Veranstaltung haben Teilnehmer*innen die folgenden Kompetenzen erlangt:

      • Sie verstehen die Bedeutung grundlegender mathematischer Konzepte und Verfahren (aus Optimierung, Spieltheorie, Statistik, Dynamische Systeme). Insbesondere können sie die Terminologie und mathematischen Aussagen präzise erklären und Anwendungsgebiete anhand ausgewählter inner- und außermathematischer Problemstellungen erläutern. 
      • Sie können mathematische Modelle nutzen, um reale Fragestellungen zu beschreiben und zu analysieren.  Dabei können sie verschiedene mathematische Werkzeuge und Techniken verwenden, um qualitative und quantitative Aussagen über die Auswirkungen von Entscheidungen und Maßnahmen zu treffen. 
      • Sie können die Gültigkeit, Angemessenheit und Grenzen mathematischer Modelle beurteilen, indem sie etwa Modellannahmen, verwendete Daten oder Sensitivität der Ergebnisse analysieren, um fundierte Entscheidungen über die Nutzung dieser Modelle im Bereich nachhaltiger Entwicklung zu treffen.
      • Die Ergebnisse mathematischer Analysen und Modelle können klar und prägnant an verschiedene Zielgruppen unter Nutzung verschiedener Medien und Formate kommuniziert werden. Dies geschieht mit dem Ziel, das gesellschaftliche Bewusstsein für die Bedeutung von Mathematik für BNE sowie transformative Prozesse zu fördern.
      • Sie können die eigenen Lernerfahrungen reflektieren, indem sie individuelle Stärken, Lernstrategien, Einstellungen zur Mathematik und ihr mathematisches Selbstkonzept analysieren, um ihre mathematischen Kompetenzen weiterzuentwickeln und so später ihre Rolle als mündige und verantwortungsvolle Bürger*innen in der Gesellschaft auszufüllen.

       

      Formalia & Organisatorisches
      a) Für die regelmäßige Teilnahme ist regelmäßig und in Person an den Terminen montags teilzunehmen. 
      b) Die aktive Teilnahme an der Projektarbeit besteht aus mehreren Aspekten, die über das Semester verteilt in Kleingruppen bearbeitet werden: 

      • Die im Rahmen der eduSCRUM-Sprints erarbeiteten Anwendungsszenarien werden zum Ende des Sprints präsentiert und zugleich durch ein passendes digitales Produkt gesichert. 
      • Die Challenges werden nicht differenziert bewertet, sollen aber bestanden werden.
      • Um das formale Aufschreiben von Mathematik zu lernen, ist eine kurze, nicht differenziert bewertete schriftliche Einzelleistung zu einem mathematischen Inhalt vorgesehen.

      c) Modulabschlussprüfung: Die Veranstaltung kann entweder im Modul „Spezialthemen der Mathematik“ (B.Sc. Mathematik Mono/Lehramt) oder im Modul „Ergänzungsmodul: Ausgewählte Themen A/B/C“ (M.Sc. Mathematik) belegt werden. Bitte beachten Sie, dass je nach Studiengang differenzierte inhaltliche Anforderungen gestellt werden. Beide Module entsprechen vom Workload-Umfang 10 LP. Als Modulabschlussprüfung werden vsl. mündliche Einzelprüfungen angeboten. Die Details werden in der ersten Sitzung bekanntgegeben. 
       
    • 19248102 Practice seminar
      Practice seminar for Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
      Schedule: Mo 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

  • Complex Analysis

    0084dB2.3
    • 19212801 Lecture
      Theory of Functions (Nicolas Perkowski)
      Schedule: Di 14:00-16:00, Do 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Comments

      Function theory is a classical field of mathematics, which deals with the properties of complex-differentiable functions on the complex number plane and has connections to algebra, analysis, number theory and geometry.

      The concept of complex differentiability restricts real-differentiable functions from R2 to R2 to angle-preserving images. We will discover that complex-differentiable functions are quite rigid objects, but they are endowed with many amazing analytical, geometric, and visual properties.

      A major result discussed in this lecture is Cauchy's integral theorem which states that the integral of any complexly differentiable function along a closed path in the complex plane is zero. We will see many nice consequences of this result, e.g. Cauchy's integral formula, the residual theorem and a proof of the fundamental theorem of algebra, as well as modern graphical representation methods.

      Suggested reading

      Literatur:

      E. Freitag and R. Busam 'Complex analysis', (Springer) 2nd Edition 2009 (the original German version is called 'Funktionentheorie')
    • 19212802 Practice seminar
      Practice seminar for Theory of Functions (Julian Kern)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

  • Geometry

    0084dB2.7
    • 19213101 Lecture
      Geometry (Giulia Codenotti)
      Schedule: Di 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-04-15)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Comments

      Inhalt

      Diese Vorlesung für das Bachelorstudium soll als natürliche Fortsetzung von Lineare Algebra I und II Fundamente legen für Vorlesungen/Zyklen wie Diskrete Geometrie, Algebraische Geometrie und Differenzialgeometrie.

      Sie behandelt grundlegende Modelle der Geometrie, insbesondere

      euklidische, affine, sphärische, projektive und hyperbolische Geometrie,Möbiusgeometrie, Polarität und Dualität Strukturgruppen, Messen (Längen, Winkel, Volumina), explizite Berechnungen und Anwendungen, Beispiele sowie Illustrationsthemen;

      Dabei werden weitere Bezüge hergestellt, zum Beispiel zur Funktionentheorie und zur Numerik.

      Suggested reading

      Literatur

      1. Marcel Berger. Geometry I
      2. David A. Brannan, Matthew F. Esplen, and Jeremy J. Gray. Geometry
      3. Gerd Fischer. Analytische Geometrie
      4. V.V. Prasolov und V.M. Tikhomirov. Geometry
    • 19213102 Practice seminar
      Practice seminar for Geometry (Giulia Codenotti)
      Schedule: Mo 10:00-12:00, Mo 16:00-18:00 (Class starts on: 2025-04-14)
      Location: A3/SR 119 (Arnimallee 3-5)

  • Mathematical Project

    0084dB2.9
    • 19246021 Projekt
      Mathematical modeling in discussions of societal challenges (Sarah Wolf, Anina Mischau, Joshua Wiebe)
      Schedule: Mi 13:00-17:00 (Class starts on: 2025-04-16)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Additional information / Pre-requisites

      Die Veranstaltungen mit Schüler*innen können ggf außerhalb der üblichen Veranstaltungszeit stattfinden.

      Voraussetzungen:

      • mindestens ein Interesse an Programmieren, grundlegende Programmierkenntnisse wären wünschenswert
      • Interesse an mathematischer Modellierung und gesellschaftlichen Diskursen

       

      Comments

      Dieses Projektseminar steht in Verbindung mit „Schule@DecisionTheatreLab“, einem Experimentallabor für Wissenschaftskommunikation gefördert von der Berlin University Alliance und dem Excellenzcluster MATH+. Das Projekt entwickelt ein innovatives Kommunikationsformat basierend auf mathematischen Modellen und führt dieses mit Gruppen von Schüler*innen durch. Decision Theatres sind Diskussionsveranstaltungen, in denen Teilnehmende eine gesellschaftliche Herausforderung mit Wissenschaftler*innen diskutieren und dabei mit einem mathematischen Modell experimentieren können.

      Das Projektseminar ist interdisziplinär ausgerichtet und verbindet mathematische Forschung mit didaktischen und sozialwissenschaftlichen Perspektiven. So werden z.B. einerseits Grundlagen des Kommunikationsformats vorgestellt (bspw. mathematische und agenten-basierte Modellierung oder die Arbeit mit empirischen Informationen), aber auch ein Bezug zum Mathematikunterricht an Schulen und damit zur Vermittlung von Mathematik erarbeitet. Andererseits arbeiten die Studierenden direkt an der Vorbereitung, Durchführung, Beobachtung und Auswertung von Decision Theatre Veranstaltungen mit.

      In dem Projektseminar ist ein intensiver Austausch zwischen Studierenden aus dem Monostudiengang und aus dem Lehramtsstudiengang der Mathematik intendiert. Über das Kennenlernen von und die Mitwirkung in einem aktuellen mathematischen wie didaktischen Forschungsprojekt und dessen Abläufe wie Methoden erhalten die Studierende die Chance jeweils ihren Blick über den Tellerand ihres Studiengangs hinaus zu erweitern.

      Schwerpunkte im Bereich Mathematik für Schulen:

      • Chancen der Einbettung des Kommunikationsformates im Mathematikunterricht
      • neue Perspektiven auf Modellieren im Unterricht
      • Interaktion mit Schüler*innengruppen

      Schwerpunkte im Bereich mathematische Forschung:

      • Agenten-basierte Modelle: Definition, Implementierung, Sensitivitätsanalyse, Kalibrierung und Validierung
      • synthetische Populationen: Daten, Algorithmen, Software Tools
      • Weiterentwicklung von mathematischen Modellen im Dialog mit Nicht-Wissenschaftler*innen (z.B. Schüler*innen)

      Suggested reading

      Wird in der ersten Sitzung bekannt gegeben.

  • Differential Equations I

    0084dB3.1
    • 19215601 Lecture Cancelled
      Basic Module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

      <p>Analysis I to III and Lineare Algebra I and II.</p>¶¶

      Comments

      Dynamical Systems are concerned with anything that moves. They are typically described by ordinary, functional, or partial differential equations, or, in the case of discrete time, by iterations. In this course, we will study flows and evolutions, first integrals, the existence and uniqueness of solutions, as well as ω-limit sets and Lyapunov functions. Dynamical systems have a vast range of applications, from physics and biology to economics and engineering.

      Requirements: Analysis 1 & 2, Linear Algebra 1 & 2. An interest in applications is advantageous.

      Suggested reading

      L.C. Evans, Partial Differential Equations. Gelegentlich: W. Strauss, Partial Differential Equation. Alle Exemplare beider Texte stehen im Handapparat Ecker.

      Vorausgesetztes Material zu Analysis II und III siehe z.B. Appendices in diesem Buch (vor allem Appendix C und E (Maß- und Integrationstheorie).
    • 19215602 Practice seminar Cancelled
      Practice seminar for Basis module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
      Location: 0.1.01 Hörsaal B (Arnimallee 14)

      Comments

      Am 23. April findet keine Übung statt.

  • Discrete Mathematics I

    0084dB3.2
    • 19214701 Lecture
      Discrete Mathematics I (Ralf Borndörfer)
      Schedule: Di 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group:

      BMS students, Master and Bachelor students

      Whiteboard:

      You need access to the whiteboard in order to receive information and participate in the exercises.

      Large tutorial:

      Participation is recommended, but non-mandatory.

      Exams:

      1st exam: Thurday July 17, 14:00-16:00, room tba, i.e., in the last lecture
      2nd exam: Thursday October 09, 10:00-12:00, room tba, i.e., in the last week before the lectures of the winter semester start

      Comments

      Content:

      Selection from the following topics:

      • Enumeration (twelvefold way, inclusion-exclusion, double counting, recursions, generating functions, inversion, Ramsey's Theorem, asymptotic counting)
      • Discrete Structures (graphs, set systems, designs, posets, matroids)
      • Graph Theory (trees, matchings, connectivity, planarity, colorings)

      Suggested reading

      • J. Matousek, J. Nesetril (2002/2007): An Invitation to Discrete Mathematics, Oxford University Press, Oxford/Diskrete Mathematik, Springer Verlag, Berlin, Heidelberg.
      • L. Lovasz, J. Pelikan, K. Vesztergombi (2003): Discrete Mathemtics - Elementary and Beyond/Diskrete Mathematik, Springer Verlag, New York.
      • N. Biggs (2004): Discrete Mathematics. Oxford University Press, Oxford.
      • M. Aigner (2004/2007): Diskrete Mathematik, Vieweg Verlag, Wiesbaden/Discrete Mathemattics, American Mathematical Society, USA.
      • D. West (2011): Introduction to Graph Theory. Pearson Education, New York.
    • 19214702 Practice seminar
      Practice seminar for Discrete Mathematics I (Silas Rathke)
      Schedule: Di 16:00-18:00, Do 14:00-16:00 (Class starts on: 2025-04-22)
      Location: A3/SR 119 (Arnimallee 3-5)

      Comments

      Content:

      Selection from the following topics:

      • Counting (basics, double counting, Pigeonhole Principle, recursions, generating functions, Inclusion-Exclusion, inversion, Polya theory)
      • Discrete Structures (graphs, set systems, designs, posets, matroids)
      • Graph Theory (trees, matchings, connectivity, planarity, colorings)
      • Algorithms (asymptotic running time, BFS, DFS, Dijkstra, Greedy, Kruskal, Hungarian, Ford-Fulkerson)

  • Topology I

    0084dB3.6
    • 19205401 Lecture
      Basic module: Topology I (Christian Haase)
      Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: 1.3.14 Hörsaal A (Arnimallee 14)

      Comments


      Course Overview This is a beginning course from the series of three courses Topology I—III:

      1. Basic notions: topological spaces, continuous maps, connectedness, compactness, products, coproducts, quotients.
      2. Groups acting on topological spaces
      3. Gluing constructions, simplicial complexes
      4. Homotopies between continuous maps, degree of a map, fundamental group.
      5. Seifert-van Kampen Theorem.
      6. Covering spaces.
      7. Simplicial homology
      8. Combinatorial applications

      Suggested reading

      Literature:

      1. M. A. Armstron: Basic Topology, Springer UTM
      2. Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website
      3. Jirí Matoušek: Using the Borsuk-Ulam Theorem, Springer UTX
      4. Mark de Longueville: A Course in Topological Combinatorics, Springer UTX
      5. Tammo tom Dieck: Topologie, De Gruyter Lehrbuch
      6. Klaus Jänich: Topologie, Springer-Verlag
      7. Gerd Laures, Markus Szymik: Grundkurs Topologie, Spektrum Akademischer Verlag
      8. James R. Munkres: Topology, Prentice Hall
    • 19205402 Practice seminar
      Exercise for Basic Module: Topology I (Sofia Garzón Mora)
      Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-28)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

  • Communicating about Mathematics

    0162bA1.1
    • 19200810 Proseminar
      Undergraduate Seminar: History + Contextualization of Mathematics (Anina Mischau)
      Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Comments

      This proseminar, specially designed for teacher training students, focuses on the discovery and development of mathematics as part of culture and society. From the point of view of "becoming mathematics", the main focus will be on the intra-mathematical development of selected mathematical topics and findings, their historical and cultural contextualisation and the actors involved in this development. In addition, some of these topics and findings will be examined as examples of where and to what extent they have found their way into other areas and contexts, e.g. in art, music, architecture or other scientific disciplines. In the second part of the proseminar, students will prepare small projects independently in group work on a mathematical topic of their choice and present them in the course.

      Suggested reading

      ... wird im Seminar bekannt gegeben.
    • 19203611 Seminar
      Proseminar/Seminar: das Buch der Beweise (Giulia Codenotti)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A3/SR 115 (Arnimallee 3-5)

      Comments

      Inhalt: Vorträge zu Gitterproblemen in 2 (und 3) Dimensionen. Weitere Informationen finden Sie auf der Homepage des Proseminars.
    • 19213910 Proseminar
      Proseminar/Seminar on Number Theory: Geometry of Numbers (Niels Lindner)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
      Location: A3/SR 119 (Arnimallee 3-5)

      Additional information / Pre-requisites

      Nötige Vorkenntnisse: Lineare Algebra und eine gewisse Vertrautheit mit den Grundbegriffen der Algebra, etwa "Gruppe", "Ring", "Körper", "Ideal", "Normalteiler", etc.

      Comments

      This proseminar/seminar deals with Minkowski's "geometry of numbers", which does not only open up a geometric perspective on algebraic number theory, but also enables interesting applications in discrete geometry and combinatorial optimization. More precisely, we will dive into the following topics:

      * Minkowski's classical convex body theorems

      * Gaussian integers, Fermat's two-squares theorem, Legendre's four-squares theorem

      * Algebraic number fields, finiteness of the class number, Dirichlet's unit theorem

      * Linear equations over the integers: Hermite and Smith normal forms

      * Basics of lattice theory

      * Lattice basis reduction and the LLL algorithm

      * The shortest vector problem

      * Dense sphere packings

      * Khinchine's flatness theorem

      * Integer linear programming in fixed dimension

      The purpose of this list is to offer a coarse thematic overview. The precise seminar topics will be fixed later, together with the participants.

      Further information will be provided on the Whiteboard homepage of the seminar at the beginning of the lecture period.
    • 19214210 Proseminar
      Proseminar Wissenschaftskommunikation der Mathematik (Anna Maria Hartkopf)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-28)
      Location: A6/030 Rechnerpoolraum (Arnimallee 6)
    • 19230410 Proseminar
      Proseminar: Exploring randomness (Julian Kern)
      Schedule: Fr 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-25)
      Location: A3/SR 115 (Arnimallee 3-5)

      Additional information / Pre-requisites

      The date in the first lecture week is cancelled. Instead, there will be an additional block date at the end of the semester on which all talks will be presented. The date will be discussed in the first meeting of the proseminar.

      Target group: Bachelor students (mono and combined)
      Prerequisites: None (topics will be adapted to previous knowledge)

      Comments

      Content: Students work independently and in groups on a project and present their results. The basis for assessment are not the research results, but the research process itself. At the end, the results are presented in the form of talks. A list of possible topics is discussed on the first date and adapted to the students' previous knowledge. All topics are from the field of probability theory.

      Suggested reading

      Keine
    • 19234810 Proseminar
      Women in the History of Mathematics and Computer Science (Anina Mischau)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      For mathematicians and computer scientists in a monobachelor's degree, creditable as ABV!

      Comments

      The seminar focuses on the development and rediscovery of the life stories and the work of some important mathematicians and computer scientists in the 19th and 20th centuries. The life and work of Sophie Germaine (1776-1831), Ada Lovelace (1815-1852), Sonja Kovalevskaya (1850-1891), Emmy Noether (1882-1935), Ruth Moufang (1905-1977), Grace Murray Hopper (1906-1992) and other female scientists are examined.

      The seminar is not about highlighting these women as an exception, because it would only set them on their exotic status. Rather, it is about a historical contextualization of their life and work. This not only enables an exemplary examination of social and cultural inclusion and exclusion processes along the gender category, but also the development of new perspectives on the traditional cultural history of both disciplines. The seminar is based on the approach of researching or discovering learning, i.e. the students will independently prepare and present individual seminar topics in group work. These presentations will then be discussed in the seminar. Through the use of observation sheets, a feedback culture is also to be tested that will be helpful in dealing with pupils and/or colleagues in later professional life.
    • 19241710 Proseminar
      Proseminar Mathematics Panorama (Anna Maria Hartkopf)
      Schedule: Termine siehe LV-Details (Class starts on: 2025-09-24)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Comments

      Detaillierte Informationen finden Sie auf der Webseite zum Seminar Panorama der Mathematik.

      Inhalt: Im Seminar Panorama der Mathematik sollen in Absprache mit den Teilnehmern ausgewählte Themen aus der älteren und jüngeren Geschichte der Mathematik herausgegriffen und untersucht werden. Denkbare Themen sind zum Beispiel die Entwicklung von Algorithmen wie Newton-Verfahren, Gauss-Elimination, Matrix-Multiplikation, Simplex-Verfahren etc., die Entwicklung von Bereichen der Mathematik wie Invariantentheorie, Mengenlehre, Topologie o.ä.. Dabei sollen auch moderne Aspekte berücksichtigt werden, etwa aktuelle Anwendungen, Forschungsstand, Ergebnisse aus der jüngeren Vergangenheit.

      Suggested reading

      1. Hans Wußing, 6000 Jahre Mathematik: Eine kulturgeschichtliche Zeitreise;
      2. Band 1: Von den Anfängen bis Leibniz und Newton, Band 2: Von Euler bis zur Gegenwart, Springer 2009
      3. Heinz-Wilhelm Alten et al., 4000 Jahre Algebra, Springer 2008
      4. Christoph J. Scriba, 5000 Jahre Geometrie, Springer 2009
      5. Heinz-Niels Jahnke, Geschichte der Analysis: Texte zur Didaktik der Mathematik, Spektrum 1999
      6. Richard Courant und Herbert Robbins, Was ist Mathematik?, Springer 2010
      7. Phillip J. Davis, Reuben Hersh, The Mathematical Experience, Mariner Books 1999
      8. Knoebel, Arthur; Laubenbacher, Reinhard; Lodder, Jerry; Pengelley, David
      9. Mathematical masterpieces, Springer 2007
      10. Laubenbacher, Reinhard; Pengelley, David, Mathematical expeditions. Chronicles by the explorers, Springer 1999
      11. sowie abhängig vom Thema
    • 19245610 Proseminar
      Proseminar Mathematik - Lehramt (Brigitte Lutz-Westphal)
      Schedule: Mo 08:00-10:00 (Class starts on: 2025-04-14)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Additional information / Pre-requisites

      Der Titel dieses Seminares ist „Was genau soll ich unterrichten? Schulmathematik neu entdeckt“.

      Dabei werden wir ausgewählte Lehrplanthemen gründlich durchdenken und das dafür benötigte Fachwissen genauer beleuchten. Eine solche „Sachanalyse“ ist die Basis für jegliche Unterrichtsplanung, wie sie in den späteren Fachdidaktik-Modulen Stück für Stück erarbeitet wird. Eine aktive Mitarbeit in den Seminarsitzungen wird erwartet. (Die Themen dieses Proseminars eigenen sich evtl. nicht als Themen für die in der Fachwissenschaft anzufertigende Bachelorarbeit!)

       

      Comments

      Dieses Proseminar richtet sich ausdrücklich an Lehramtsstudierende bereits ab dem 2. Fachsemester Mathematik.
      Es folgt einem neuen Konzept, das wir erproben wollen, um schon zu Beginn des Lehramtsstudiums bereits den Blick stärker in Richtung Schule und Unterricht wenden zu können. Auch höhere Semester sind willkommen.

      Achtung, das Seminar beginnt erst am Montag, den 28.04.! Am Montag 14.04. finden wegen des Dies Academicus keine Lehrveranstaltungen statt und am Montag 21.04. ist ein Feiertag.

      Suggested reading

      Literatur wird im Seminar bekannt gegeben.
    • 19245910 Proseminar
      Undergraduate Seminar: XSRG (Jan-Hendrik de Wiljes)
      Schedule: Do 09:00-12:00 (Class starts on: 2025-04-17)
      Location: Virtueller Raum 02

      Additional information / Pre-requisites

      Voraussetzungen: Mindestens 2-3 Anfangsvorlesungen in Mathematik, insbesondere Lineare Algebra, sollten besucht worden sein. Es wird nicht so sehr um die dort vermittelten Inhalte gehen, sondern vielmehr darum, mathematisches Arbeiten an der Hochschule (Definition, Satz, Beweis, Problemlösen) kennengelernt zu haben.

      Comments

      Hinweise

      • Wichtig: Dieses Proseminar dient nur als Platzhalter-Veranstaltung für die X-Student Research Group, die als Präsenzveranstaltung Do 9‒12 Uhr in Raum 024/A3 stattfindet. 
      • XSRGs sind studentische Forschungsgruppen, weitere Infos zu diesem Format unter: https://www.berlin-university-alliance.de/commitments/teaching-learning/sturop/research-groups/index.html 
      • Teilnahme: Insgesamt gibt es 15 Plätze. Um einen Platz zu erhalten, muss man am ersten Veranstatlungstermin physisch anwesend sein. Bei mehr als 15 Personen entscheidet das Los.
      • Die erfolgreiche Teilnahme an dem XSRG-Modul gibt 5 LP (unbenotet, nur pass/fail). Anschließend kann beim jeweiligen Prüfungsbüro ein Antrag gestellt werden, um dieses Modul im ABV-Bereich (alle Studiengänge) anzurechnen. Je nach Studiengang wurde die XSRG in der Vergangenheit beispielsweise auch schon als fachdidaktisches Wahlmodul oder mathematisches Proseminar angerechnet. 
      • Bei Fragen gerne im Vorfeld an weygandt@math.fu-berlin.de und jan.dewiljes@math.fu-berlin.de wenden.

       

      XSRG „Mathematiklehre bottom-up denken“

      Was passiert eigentlich, wenn Studierende Hochschullehre reflektieren und lernförderlich (um)gestalten?

      Es ist immer einfach, bestehende Konzepte zu kritisieren ‒ aber davon alleine ändert sich ja nichts! Daher wollen wir euch die einmalige Gelegenheit geben, eure Erfahrungen, Expertise und Perspektive als Lernende in die Weiterentwicklung guter Hochschullehre einzubringen. 

      Lassen wir uns dafür mal auf ein ‒ vielleicht verrücktes? ‒ Gedankenexperiment ein:

      • Was würde herauskommen, wenn Studierende eine für sie selbst sinnvolle und gute Mathe-Vorlesung gestalten? Oder gleich ein ganzes Modul?
      • Welche Art von Tutorien haltet ihr für sinnvoll? Welche Tätigkeiten (denken, nachrechnen, diskutieren ...) sollten in den jeweiligen Veranstaltungen (VL, Übung, Zentralübung...) in welchem Format (frontal, einzeln, Gruppe ...) passieren?
      • Und was ist mit dem Material: Wie sollten Übungsaufgaben aussehen? Skripte? Klausuren?

      Ablauf

      Zur Inspiration beginnen wir mit einer kurzen Einführung in die Hochschulmathematikdidaktik und u.a. auch einem Besuch beim University:Future Festival.

      Anschließend widmen wir uns in Kleingruppen unterschiedlichen Mathematik-Veranstaltungen aus euren Studiengängen. Infrage kommt alles von Mathematik entdecken über Analysis I, Mathematik für Physiker*innen I, die Nebenfachvorlesung im Medizinstudium bis hin zu Höherer Topologie VIII ‒ wichtig ist, dass ihr damit Erfahrungen gemacht habt!

      Die von euch erarbeiteten Ideen, Ansätze und Konzepte können wir anschließend auch mit Hochschullehrenden diskutieren und ausprobieren! 

       

      Suggested reading

      Die Literatur wird bei der Vorbesprechung bekanntgegeben. Zur Einstimmung kann man bereits etwas in einem der Bände der Reihe Winning Ways for Your Mathematical Plays von Berlekamp, Conway und Guy schmökern.

      Unbedingt zur Seminarvorbereitung lesen:

      M. Lehn: Wie halte ich einen Seminarvortrag?

  • Introductory Module: Algebra II

    0280bA2.2
    • 19214501 Lecture
      Basic Module: Algebra II (Holger Reich)
      Schedule: Mo 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-04)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisits: Comutitive algebra

      Comments

      The course deals with the fundamentals of homological algebra, sheaf theory, and the theory of ringed spaces and schemes.

      Possible topics include: 
      - categories and functors
      - additive and abelian categories
      - cohomology
      - sheaf theory
      - ringed spaces
      - schemes
      - separated and proper morphisms
      - blowing up
      - embeddings into projective spaces, divisors, invertible sheaves 
      - Riemann-Roch -Gröbner bases.

      Suggested reading

      For example: Introduction to Schemes, Geir Ellingsrud and John Christian Otten
    • 19214502 Practice seminar
      Practice seminar for Basic Module: Algebra II (Georg Lehner)
      Schedule: Mi 08:00-10:00, Do 14:00-16:00 (Class starts on: 2025-04-23)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

  • Introductory Module: Discrete Mathematics I

    0280bA3.1
    • 19214701 Lecture
      Discrete Mathematics I (Ralf Borndörfer)
      Schedule: Di 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group:

      BMS students, Master and Bachelor students

      Whiteboard:

      You need access to the whiteboard in order to receive information and participate in the exercises.

      Large tutorial:

      Participation is recommended, but non-mandatory.

      Exams:

      1st exam: Thurday July 17, 14:00-16:00, room tba, i.e., in the last lecture
      2nd exam: Thursday October 09, 10:00-12:00, room tba, i.e., in the last week before the lectures of the winter semester start

      Comments

      Content:

      Selection from the following topics:

      • Enumeration (twelvefold way, inclusion-exclusion, double counting, recursions, generating functions, inversion, Ramsey's Theorem, asymptotic counting)
      • Discrete Structures (graphs, set systems, designs, posets, matroids)
      • Graph Theory (trees, matchings, connectivity, planarity, colorings)

      Suggested reading

      • J. Matousek, J. Nesetril (2002/2007): An Invitation to Discrete Mathematics, Oxford University Press, Oxford/Diskrete Mathematik, Springer Verlag, Berlin, Heidelberg.
      • L. Lovasz, J. Pelikan, K. Vesztergombi (2003): Discrete Mathemtics - Elementary and Beyond/Diskrete Mathematik, Springer Verlag, New York.
      • N. Biggs (2004): Discrete Mathematics. Oxford University Press, Oxford.
      • M. Aigner (2004/2007): Diskrete Mathematik, Vieweg Verlag, Wiesbaden/Discrete Mathemattics, American Mathematical Society, USA.
      • D. West (2011): Introduction to Graph Theory. Pearson Education, New York.
    • 19214702 Practice seminar
      Practice seminar for Discrete Mathematics I (Silas Rathke)
      Schedule: Di 16:00-18:00, Do 14:00-16:00 (Class starts on: 2025-04-22)
      Location: A3/SR 119 (Arnimallee 3-5)

      Comments

      Content:

      Selection from the following topics:

      • Counting (basics, double counting, Pigeonhole Principle, recursions, generating functions, Inclusion-Exclusion, inversion, Polya theory)
      • Discrete Structures (graphs, set systems, designs, posets, matroids)
      • Graph Theory (trees, matchings, connectivity, planarity, colorings)
      • Algorithms (asymptotic running time, BFS, DFS, Dijkstra, Greedy, Kruskal, Hungarian, Ford-Fulkerson)

  • Introductory Module: Discrete Geometry II

    0280bA3.4
    • 19214901 Lecture
      Basic Module: Discrete Geometrie II (Georg Loho)
      Schedule: Di 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-04-15)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Solid background in linear algebra and some analysis. Basic knowledge and experience with polytopes and/or convexity (as from the course "Discrete Geometry I") will be helpful. .

      Comments

      Inhalt:

      This is the second in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures with an emphasis on metric and convex geometric properties. In the course we will develop central themes in metric and convex geometry including proof techniques and applications to other areas in mathematics.

      The material will be a selection of the following topics:
      Linear programming and some applications

       

      • Linear programming and duality
      • Pivot rules and the diameter of polytopes

      Subdivisions and triangulations

      • Delaunay and Voronoi
      • Delaunay triangulations and inscribable polytopes
      • Weighted Voronoi diagrams and optimal transport

      Basic structures in convex geometry

       

      • convexity and separation theorems
      • convex bodies and polytopes/polyhedra
      • polarity
      • Mahler’s conjecture
      • approximation by polytopes

      Volumes and roundness

      • Hilbert’s third problem
      • volumes and mixed volumes
      • volume computations and estimates
      • Löwner-John ellipsoids and roundness
      • valuations

      Geometric inequalities

      • Brunn-Minkowski and Alexandrov-Fenchel inequality
      • isoperimetric inequalities
      • measure concentration and phenomena in high-dimensions

      Geometry of numbers

      • lattices
      • Minkowski's (first) theorem
      • successive minima
      • lattice points in convex bodies and Ehrhart's theorem
      • Ehrhart-Macdonald reciprocity

      Sphere packings

      • lattice packings and coverings
      • the Theorem of Minkowski-Hlawka
      • analytic methods

      Applications in optimization, number theory, algebra, algebraic geometry, and functional analysis

      Suggested reading

      The course will use material from P. M. Gruber, " Convex and Discrete Geometry" (Springer 2007) and various other sources. There will be brief lecture notes available for course participants with detailed pointers to the literature.
    • 19214902 Practice seminar
      Practice seminar for BasicM: Discrete Geometry II (Georg Loho)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

  • Advanced Module: Discrete Mathematics III

    0280bA3.5
    • 19215001 Lecture
      Constructive Combinatorics (Tibor Szabo)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A3/SR 119 (Arnimallee 3-5)

      Additional information / Pre-requisites

      Basic Bachelor Algebra, Probability, and Disrete Mathematics.

      Comments

      Abstract:
      Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
      The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
      Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
      For further details please check Prof. Szabó's homepage.

      Suggested reading

      A script will be provided.
    • 19215002 Practice seminar
      Constructive Combinatorics exercises (Tibor Szabo)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Comments

      Abstract:
      Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
      The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
      Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
      For further details please check Prof. Szabó's homepage.

  • Research Module: Discrete Mathematics

    0280bA3.7
    • 19206011 Seminar
      Discrete Mathematics Masterseminar (Tibor Szabo)
      Schedule: Fr 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-11)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

       

       

      Comments

      Content:
      The seminar covers advanced topics in Extremal and Probabilistic Combinatorics.
      Target audience:
      BMS students, Master students, or advanced Bachelor students.
      Prerequisites:
      Prerequisite is the successful completion of the modul Discrete Mathematics II or III (or equivalent background: please contact the instructor).

       

  • Introductory Module: Topology I

    0280bA4.1
    • 19205401 Lecture
      Basic module: Topology I (Christian Haase)
      Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: 1.3.14 Hörsaal A (Arnimallee 14)

      Comments


      Course Overview This is a beginning course from the series of three courses Topology I—III:

      1. Basic notions: topological spaces, continuous maps, connectedness, compactness, products, coproducts, quotients.
      2. Groups acting on topological spaces
      3. Gluing constructions, simplicial complexes
      4. Homotopies between continuous maps, degree of a map, fundamental group.
      5. Seifert-van Kampen Theorem.
      6. Covering spaces.
      7. Simplicial homology
      8. Combinatorial applications

      Suggested reading

      Literature:

      1. M. A. Armstron: Basic Topology, Springer UTM
      2. Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website
      3. Jirí Matoušek: Using the Borsuk-Ulam Theorem, Springer UTX
      4. Mark de Longueville: A Course in Topological Combinatorics, Springer UTX
      5. Tammo tom Dieck: Topologie, De Gruyter Lehrbuch
      6. Klaus Jänich: Topologie, Springer-Verlag
      7. Gerd Laures, Markus Szymik: Grundkurs Topologie, Spektrum Akademischer Verlag
      8. James R. Munkres: Topology, Prentice Hall
    • 19205402 Practice seminar
      Exercise for Basic Module: Topology I (Sofia Garzón Mora)
      Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-28)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

  • Research Module: Topology

    0280bA4.5
    • 19233511 Seminar
      Geometric Group Theory (Georg Lehner)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Additional information / Pre-requisites

      Aimed at: Bachelor and masters students

      Prerequisites: Group theory. Additionally either Geometry (especially elementary non-euclidean geometry) and/or Topology (point-set topology) can be helpful.

      Comments

      Groups are best understood as symmetries of mathematical objects. Whereas finite groups can often be completely understood by their actions on vector spaces, this approach will often fail with infinite groups, such as free groups or hyperbolic groups. Geometric group theory tries to construct natural geometric objects (topological spaces such as manifolds or graphs for example) that these groups act on and allows one to classify the complexity these groups can have.

      In this seminar, we will follow Clara Löh's book on the subject. Topics will include Cayley graphs, free groups and their subgroups, quasi-isometry classes of groups, growth types of groups, hyperbolic groups and the Banach-Tarski theorem.

      Suggested reading

      Clara Löh - Geometric Group Theory

  • Introductory Module: Numerical Analysis III

    0280bA5.2
    • 19215201 Lecture
      Basic Module: Numerics III (Volker John)
      Schedule: Mo 10:00-12:00, Mo 14:00-16:00 (Class starts on: 2025-04-28)
      Location: A6/SR 031 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisites

      Prerequisites for this course are basic knowledge in calculus (Analysis I-III) and Numerical Analysis (Numerik I). Some knowledge in Functional Analysis will help a lot.

      Comments

      The mathematical modeling of many processes in nature and industry leads to partial differential equations. Generally, such equations cannot be solved analytically. It is only possible to compute numerical approximations to the solution on the basis of discretized equations. This course studies discretizations of elliptic partial differential equations. Major topics are finite difference methods and finite element methods.

       

      Suggested reading

      • D. Braess: Finite Elemente. Springer, 3. Auflage (2002)
      • A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements (2004)
    • 19215202 Practice seminar
      Practice seminar for Basic Module: Numerics III (André-Alexander Zepernick)
      Schedule: Fr 08:00-10:00 (Class starts on: 2025-04-25)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Comments

      Homepage:Wiki der Numerik II

  • Advanced Module: Numerical Mathematics IV

    0280bA5.3
    • 19215301 Lecture
      Mathematical Modelling in Climate Research (Rupert Klein)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)

      Comments

      Content:

      Mathematics plays a central role in the development and analysis of models for weather prediction. Controlled physical experiments are out of question, and the only way we can study Earth’s weather and climate system is through mathematical models, computational experiments, and data analysis.

      Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and consequently no general solutions to problems in turbulent flows are available. Instead, scientists rely on conceptual models and statistical descriptions to understand the essence of daily weather and how that feeds back on climate behavior.

       

      This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.

      The course will cover a selection from the following topics

      1. Conservation laws and governing equations,

      2. Numerical methods for geophysical flow simulations,

      3. Dynamical systems and bifurcation theory,

      4. Data-based characterization of atmospheric flows

       

      This course can be attended as the second part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered by the course 19235701 + 19235702 "Introduction to Mathematical Modeling with Partial Differential Equations" abgedeckt, which is offered at FU Berlin in winter terms. 

      Suggested reading

      Literaturhinweise werden anfangs des Semesters in Abhängigkeit von der Themenauswahl gegeben. Interessante Startpunkte, die einen ersten Einstieg in obige drei Hauptpunkte erlauben, sind Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., vol. 42, 249-274 (2010) D. Durran, Numerical Methods for Fluid Dynamics with Applications to Geophysics, Springer, Computational Science and Engineering Series, (2010) Metzner Ph., Putzig L., Horenko I., Analysis of persistent nonstationary time series and applications Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)

      Tennekes and Lumley, A first course in Turbulence, MIT Press (1974)

       
    • 19216201 Lecture
      Markov chains and markov models (Marcus Weber)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A3/SR 119 (Arnimallee 3-5)

      Additional information / Pre-requisites

      Master students of Mathematics and Physics

      Comments

      Markov chains are a universal tool to model real-world processes, including financial markets, reaction kinetics and molecular dynamics.

      Topics:

      • Introduction to the theory of Markov chains
      • Estimation of Markov chains from data
      • Estimation uncertainty
      • Transition path theory
      • Analysis of Markov chains
      • Spectral analysis
      • Discretization of continuous Markov processes
    • 19223901 Lecture
      Uncertainty Quantification and Quasi-Monte Carlo (Claudia Schillings)
      Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Comments

      High-dimensional numerical integration plays a central role in contemporary study of uncertainty quantification. The analysis of how uncertainties associated with material parameters or the measurement configuration propagate within mathematical models leads to challenging high-dimensional integration problems, fueling the need to develop efficient numerical methods for this task. Modern quasi-Monte Carlo (QMC) methods are based on tailoring specially designed cubature rules for high-dimensional integration problems. By leveraging the smoothness and anisotropy of an integrand, it is possible to achieve faster-than-Monte Carlo convergence rates. QMC methods have become a popular tool for solving partial differential equations (PDEs) involving random coefficients, a central topic within the field of uncertainty quantification. This course provides an introduction to uncertainty quantification and how QMC methods can be applied to solve problems arising within this field.

      Suggested reading

      The following books will be relevant:

      • O. P. Le Maître and O. M. Knio. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. Scientific Computation. Springer, New York, 2010.
      • R. C. Smith. Uncertainty Quantification: Theory, Implementation, and Applications, volume 12 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2014.
      • T. J. Sullivan. Introduction to Uncertainty Quantification. Springer, New York, in press.
      • D. Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton, NJ, 2010.
    • 19234501 Lecture
      Mathematical strategies for complex stochastic dynamics (Wei Zhang)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
      Location: T9/053 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Prerequisites: Basic knowledge of stochastics, and numerical methods

      Comments

      Content:

      Stochastic dynamics are widely studied in scientific fields such as physics, biology, and climate. Understanding these dynamics is often challenging due to their high dimensionality and multiscale characteristics. This lecture provides an introduction to theoretical and numerical techniques, including machine learning techniques, for studying such complex stochastic dynamics. The following topics will be covered:

      - Basic of stochastic processes:

      Langevin dynamics, overdamped Langevin dynamics, Markov chains, generators and Fokker-Planck equation, convergence to equilibrium, Ito’s formula

      - Model reduction techniques for stochastic dynamics:

      averaging technique, effective dynamics, Markov state modeling

      - Machine learning techniques using/for stochastic dynamics: 

      dynamics of stochastic gradient descent, autoencoders, solving eigenvalue problems by deep learning, generative modeling using diffusion models, continuous normalizing flow, or flow-matching

      Suggested reading

      1) Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. 5th. Springer, 2000

      2) Kevin P. Murphy. Probabilistic Machine Learning: An introduction. MIT Press, 2022. url: probml.ai

      3) J.-H. Prinz et al. “Markov models of molecular kinetics: Generation and validation”. In: J. Chem. Phys. 134.17, 174105 (2011), p. 174105

      4) W. Zhang, C. Hartmann, and C. Schütte. “Effective dynamics along given reaction coordinates and reaction rate theory”. In: Faraday Discuss. 195 (2016), pp. 365–394

      5) Mardt, A., Pasquali, L., Wu, H. et al. VAMPnets for deep learning of molecular kinetics. Nat Commun 9, 5 (2018).

      6)  Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole, ICLR 2021.
    • 19215302 Practice seminar
      Practice seminar for Mathematical Modelling in Climate Research (Rupert Klein)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    • 19216202 Practice seminar
      Practice seminar for Markov chains and markov models (Marcus Weber)
      Schedule: Di 12:00-14:00 (Class starts on: 2025-04-22)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Markov chains are a universal tool to model real-world processes, including financial markets, reaction kinetics and molecular dynamics.

      Topics:

      • Introduction to the theory of Markov chains
      • Estimation of Markov chains from data
      • Estimation uncertainty
      • Transition path theory
      • Analysis of Markov chains
      • Spectral analysis
      • Discretization of continuous Markov processes
    • 19223902 Practice seminar
      Übung zu UQ and QMC (Claudia Schillings)
      Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
      Location: A3/SR 120 (Arnimallee 3-5)
    • 19234502 Practice seminar
      Practice seminar for Mathematical strategies for complex stochastic dynamics (Wei Zhang)
      Schedule: Fr 10:00-12:00 (Class starts on: 2025-04-25)
      Location: T9/046 Seminarraum (Takustr. 9)

      Comments

      Concrete and simple stochastic dynamics will be studied to illustrate analytical and numerical techniques. Numerical methods will be demonstrated using Jupyter Notebook.

  • Introductory Module: Differential Equations I

    0280bA6.1
    • 19215601 Lecture Cancelled
      Basic Module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

      <p>Analysis I to III and Lineare Algebra I and II.</p>¶¶

      Comments

      Dynamical Systems are concerned with anything that moves. They are typically described by ordinary, functional, or partial differential equations, or, in the case of discrete time, by iterations. In this course, we will study flows and evolutions, first integrals, the existence and uniqueness of solutions, as well as ω-limit sets and Lyapunov functions. Dynamical systems have a vast range of applications, from physics and biology to economics and engineering.

      Requirements: Analysis 1 & 2, Linear Algebra 1 & 2. An interest in applications is advantageous.

      Suggested reading

      L.C. Evans, Partial Differential Equations. Gelegentlich: W. Strauss, Partial Differential Equation. Alle Exemplare beider Texte stehen im Handapparat Ecker.

      Vorausgesetztes Material zu Analysis II und III siehe z.B. Appendices in diesem Buch (vor allem Appendix C und E (Maß- und Integrationstheorie).
    • 19241301 Lecture
      Partial Differential Equations I (André Erhardt)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Comments

      • Basic differential equations (Laplace,- heat and wave equations)
      • Representation formulas
      • Solution methods
      • Introduction to Hilbert space methods

      This can serve as the basis for a BSc and/or MSc project.  

      Suggested reading

      L.C. Evans, Partial Differential Equations
       
    • 19215602 Practice seminar Cancelled
      Practice seminar for Basis module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
      Location: 0.1.01 Hörsaal B (Arnimallee 14)

      Comments

      Am 23. April findet keine Übung statt.
    • 19241302 Practice seminar
      Exercises to Partial Differential Equations I (Piotr Pawel Wozniak)
      Schedule: Di 16:00-18:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
      Location: 0.1.01 Hörsaal B (Arnimallee 14)

  • Advanced Module: Differential Equations III

    0280bA6.3
    • 19243001 Lecture
      Partial Differential Equations III (Erica Ipocoana)
      Schedule: Di 08:00-10:00 (Class starts on: 2025-04-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Voraussetzungen: Partielle Differentialgleichungen I und II

      Comments

      The course builds upon the the PDE II course offered in the previous winter term. Methods for boundary value problems of elliptic PDEs are deepend. A central aspect of the course are variational methods, in particular multi-dimensional calculus of variations. 

       

      Suggested reading

      Wird in der Vorlesung bekannt gegeben / to be announced.
    • 19243002 Practice seminar
      Tutorial Partial Differential Equations III (Erica Ipocoana)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-24)
      Location: A3/SR 119 (Arnimallee 3-5)

  • Complementary Module: Selected Topics

    0280bA7.1
    • 19241301 Lecture
      Partial Differential Equations I (André Erhardt)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Comments

      • Basic differential equations (Laplace,- heat and wave equations)
      • Representation formulas
      • Solution methods
      • Introduction to Hilbert space methods

      This can serve as the basis for a BSc and/or MSc project.  

      Suggested reading

      L.C. Evans, Partial Differential Equations
       
    • 19241302 Practice seminar
      Exercises to Partial Differential Equations I (Piotr Pawel Wozniak)
      Schedule: Di 16:00-18:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
      Location: 0.1.01 Hörsaal B (Arnimallee 14)

  • Complementary Module: Selected Research Topics

    0280bA7.2
    • 19207101 Lecture
      Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: 1.3.14 Hörsaal A (Arnimallee 14)

      Comments

      Many problems in the sciences are determined by processes on several scales. Such problems are denoted as multi-scale problems. One example for a multi-scale problem is the partial differential equations (PDEs), which govern geophysical fluid flows. Averaging methods can be used for the analytical description of the slow scales. These descriptions are beneficial for numerical time-stepping schemes, as they allow for taking bigger time-steps than the unaveraged problem. The focus of this course will be on averaging methods for PDEs describing fluid flows and the design of parallelisable numerical time stepping methods, which are versions of the Parareal method and incorporate averaging techniques.

      Requirements: basic courses in analysis, basic course numerical mathematics

      Literature:

      Wingate, B.A.; Rosemeier, J.; Haut, T., Mean Flow from Phase Averages in the 2D Boussinesq Equations. Atmosphere 2023, 14, 1523.
      https://doi.org/10.3390/atmos14101523

      T. Haut, B. Wingate,  An asymptotic parallel-in-time method for highly oscillatory pde's, SIAM Journal on Scientific Computing, 36 (2014), pp. A693-A713

      J.-L. Lions, G. Turinici, A "parareal" in time discretization of PDE's, Comptes Rendus de l'Academie des Sciences - Series I - Mathematics, 332 (2001), pp. 661-668

      Sanders, F. Verhulst, J. Murdock,  Averaging Methods in Nonlinear Dynamical Systems, Springer New York, NY, 2ed., 2000
    • 19222601 Lecture
      Numerical methods for stochastic differential equations (Ana Djurdjevac)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Zielgruppe: Students who are interested in stochastics and numerics
      Voraussetzungen: Stochastik I + II, Numerik I + II

      Comments

      Inhalt der Veranstaltung:
      The lecture will cover the following topics (not exhaustive)

      • Brownian motion 
      • Numerical discretization of stochastic differential equations
      • Monte Carlo methods
      • Representations of random fields
      • Modelling with stochastic differential equations
      • Applications

      Suggested reading

      Literatur:

      1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
      2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
      3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
      4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
      5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014
    • 19242101 Lecture
      Stochastics IV: (Guilherme de Lima Feltes, Nicolas Perkowski)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisite: Stochastics I, II, III. 
      Recommended: Functional Analysis.

      Comments

      Content: We will learn two different methods for solving stochastic partial differential equations. The classical method is based on Ito calculus, and we will use it to solve semilinear SPDEs with space-time white noise in one space dimension. But we will see that in higher dimensions this theory only works for linear equations, and motivated by that we will introduce "paracontrolled distributions“, which we developed in the last years based on ideas from harmonic analysis and rough paths, and which allow us to solve some interesting semilinear equations in higher dimensions. Along the way we will learn about regularity theory for semilinear PDEs, Gaussian Hilbert spaces, and much more.

      • Ito calculus for Gaussian random measures;
      • semilinear stochastic PDEs in one dimension;
      • Schauder estimates;
      • Gaussian hypercontractivity;
      • paraproducts and paracontrolled distributions;
      • local existence and uniqueness for semilinear SPDEs in higher dimensions;
      • properties of solutions

      Detailed Information can be found on the Homepage of 19246301 SPDEs: Classical and New.

      Suggested reading

      Literature
      There will be lecture notes.
    • 19320501 Lecture
      Cryptanalysis of Symmetrical Schemes (Marian Margraf)
      Schedule: Di 12:00-14:00 (Class starts on: 2025-04-15)
      Location: 1.4.03 Seminarraum T2 (Arnimallee 14)

      Comments

      The lecture aims at a deeper understanding of cryptographic algorithms, especially which design criteria have to be considered for the development of secure encryption algorithms. For that purpose we will get to know and evaluate different cryptanalytic methods for symmetrical and asymmetrical encryption techniques – e.g. linear and differential cryptanalysis on block ciphers, correlation attacks on stream ciphers and algorithms to solve the factorization problem and the discrete logarithm problem. Weaknesses in the implementation, e.g. to exploit side-channel attacks, will be discussed only peripherally.
    • 19207102 Practice seminar
      Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)
    • 19222602 Practice seminar
      Practice seminar for Numerical methods for stochastic differential equations (Ana Djurdjevac)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19240702 Practice seminar
      Practice seminar for Functional Analysis applied to modeling of molecular systems (Luigi Delle Site)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    • 19242102 Practice seminar
      Exercise: Stochastics IV (Guilherme de Lima Feltes)
      Schedule: Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)
    • 19320502 Practice seminar
      Practice seminar for Cryptanalysis (Marian Margraf)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

  • Complementary Module: Specific Aspects

    0280bA7.3
    • 19215001 Lecture
      Constructive Combinatorics (Tibor Szabo)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A3/SR 119 (Arnimallee 3-5)

      Additional information / Pre-requisites

      Basic Bachelor Algebra, Probability, and Disrete Mathematics.

      Comments

      Abstract:
      Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
      The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
      Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
      For further details please check Prof. Szabó's homepage.

      Suggested reading

      A script will be provided.
    • 19215301 Lecture
      Mathematical Modelling in Climate Research (Rupert Klein)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)

      Comments

      Content:

      Mathematics plays a central role in the development and analysis of models for weather prediction. Controlled physical experiments are out of question, and the only way we can study Earth’s weather and climate system is through mathematical models, computational experiments, and data analysis.

      Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and consequently no general solutions to problems in turbulent flows are available. Instead, scientists rely on conceptual models and statistical descriptions to understand the essence of daily weather and how that feeds back on climate behavior.

       

      This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.

      The course will cover a selection from the following topics

      1. Conservation laws and governing equations,

      2. Numerical methods for geophysical flow simulations,

      3. Dynamical systems and bifurcation theory,

      4. Data-based characterization of atmospheric flows

       

      This course can be attended as the second part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered by the course 19235701 + 19235702 "Introduction to Mathematical Modeling with Partial Differential Equations" abgedeckt, which is offered at FU Berlin in winter terms. 

      Suggested reading

      Literaturhinweise werden anfangs des Semesters in Abhängigkeit von der Themenauswahl gegeben. Interessante Startpunkte, die einen ersten Einstieg in obige drei Hauptpunkte erlauben, sind Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., vol. 42, 249-274 (2010) D. Durran, Numerical Methods for Fluid Dynamics with Applications to Geophysics, Springer, Computational Science and Engineering Series, (2010) Metzner Ph., Putzig L., Horenko I., Analysis of persistent nonstationary time series and applications Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)

      Tennekes and Lumley, A first course in Turbulence, MIT Press (1974)

       
    • 19216201 Lecture
      Markov chains and markov models (Marcus Weber)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A3/SR 119 (Arnimallee 3-5)

      Additional information / Pre-requisites

      Master students of Mathematics and Physics

      Comments

      Markov chains are a universal tool to model real-world processes, including financial markets, reaction kinetics and molecular dynamics.

      Topics:

      • Introduction to the theory of Markov chains
      • Estimation of Markov chains from data
      • Estimation uncertainty
      • Transition path theory
      • Analysis of Markov chains
      • Spectral analysis
      • Discretization of continuous Markov processes
    • 19229601 Lecture Cancelled
      Stochastic dynamics in fluids (Felix Höfling)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Additional information / Pre-requisites

      Target audience: M.Sc. Computational Sciences/Mathematik/Physik

      Requirements: some advanced course on either statistical physics or stochastic processes

      Comments

      The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond standard Brownian motion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

      The course is at the interface of probability theory and statistical mechanics. Noting that fluids constitute high-dimensional stochastic processes, I will give an introduction to the principles of liquid state theory, and we will derive the mathematical structure of the relevant correlation functions. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

      Keywords:

      • Brownian motion, diffusion, and stochastic processes in fluids
      • harmonic analysis of correlation functions
      • Zwanzig-Mori projection operator formalism
      • mode-coupling approximations, long-time tails
      • critical dynamics and transport anomalies

      Suggested reading

      • Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
      • Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

      Further literature will be given during the course.
    • 19234501 Lecture
      Mathematical strategies for complex stochastic dynamics (Wei Zhang)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
      Location: T9/053 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Prerequisites: Basic knowledge of stochastics, and numerical methods

      Comments

      Content:

      Stochastic dynamics are widely studied in scientific fields such as physics, biology, and climate. Understanding these dynamics is often challenging due to their high dimensionality and multiscale characteristics. This lecture provides an introduction to theoretical and numerical techniques, including machine learning techniques, for studying such complex stochastic dynamics. The following topics will be covered:

      - Basic of stochastic processes:

      Langevin dynamics, overdamped Langevin dynamics, Markov chains, generators and Fokker-Planck equation, convergence to equilibrium, Ito’s formula

      - Model reduction techniques for stochastic dynamics:

      averaging technique, effective dynamics, Markov state modeling

      - Machine learning techniques using/for stochastic dynamics: 

      dynamics of stochastic gradient descent, autoencoders, solving eigenvalue problems by deep learning, generative modeling using diffusion models, continuous normalizing flow, or flow-matching

      Suggested reading

      1) Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. 5th. Springer, 2000

      2) Kevin P. Murphy. Probabilistic Machine Learning: An introduction. MIT Press, 2022. url: probml.ai

      3) J.-H. Prinz et al. “Markov models of molecular kinetics: Generation and validation”. In: J. Chem. Phys. 134.17, 174105 (2011), p. 174105

      4) W. Zhang, C. Hartmann, and C. Schütte. “Effective dynamics along given reaction coordinates and reaction rate theory”. In: Faraday Discuss. 195 (2016), pp. 365–394

      5) Mardt, A., Pasquali, L., Wu, H. et al. VAMPnets for deep learning of molecular kinetics. Nat Commun 9, 5 (2018).

      6)  Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole, ICLR 2021.
    • 19240701 Lecture
      Functional Analysis Applied to Modeling of Molecular Systems (Luigi Delle Site)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      Die Vorlesung findet Dienstags von 14-16 Uhr in der Arnimallee 9 statt.

      Die Übung findet Montags von von 14-16 Uhr in der Arnimallee 9 statt.

      Comments

      Prpgram:

      -Existence of ordinary matter as a mathematical problem -the existence of the thermodynamic limit -One concrete way to model molecules: Density Functional theory and its mathematical structure -Existence/non-existence of relativistic matter, Dirac Operator on scalar fields -Spinors, Second Quantization and Fock space

    • 19215002 Practice seminar
      Constructive Combinatorics exercises (Tibor Szabo)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Comments

      Abstract:
      Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
      The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
      Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
      For further details please check Prof. Szabó's homepage.
    • 19215302 Practice seminar
      Practice seminar for Mathematical Modelling in Climate Research (Rupert Klein)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    • 19216202 Practice seminar
      Practice seminar for Markov chains and markov models (Marcus Weber)
      Schedule: Di 12:00-14:00 (Class starts on: 2025-04-22)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Markov chains are a universal tool to model real-world processes, including financial markets, reaction kinetics and molecular dynamics.

      Topics:

      • Introduction to the theory of Markov chains
      • Estimation of Markov chains from data
      • Estimation uncertainty
      • Transition path theory
      • Analysis of Markov chains
      • Spectral analysis
      • Discretization of continuous Markov processes
    • 19229602 Practice seminar Cancelled
      Exercises to Stochastic processes in fluids (Felix Höfling)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-29)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19234502 Practice seminar
      Practice seminar for Mathematical strategies for complex stochastic dynamics (Wei Zhang)
      Schedule: Fr 10:00-12:00 (Class starts on: 2025-04-25)
      Location: T9/046 Seminarraum (Takustr. 9)

      Comments

      Concrete and simple stochastic dynamics will be studied to illustrate analytical and numerical techniques. Numerical methods will be demonstrated using Jupyter Notebook.

  • Complementary Module: Specific Research Aspects

    0280bA7.4
    • 19219701 Lecture
      Algebra with Probability in Combinatorics (Tibor Szabo)
      Schedule: Do 08:00-10:00 (Class starts on: 2025-04-17)
      Location: T9/049 Seminarraum (Takustr. 9)

      Comments

      In this lecture specialized topics of Combinatorics and Graph Theory are presented.

  • Complementary Module: Research Seminar

    0280bA7.5
    • 19206011 Seminar
      Discrete Mathematics Masterseminar (Tibor Szabo)
      Schedule: Fr 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-11)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

       

       

      Comments

      Content:
      The seminar covers advanced topics in Extremal and Probabilistic Combinatorics.
      Target audience:
      BMS students, Master students, or advanced Bachelor students.
      Prerequisites:
      Prerequisite is the successful completion of the modul Discrete Mathematics II or III (or equivalent background: please contact the instructor).

       
    • 19226511 Seminar
      Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      Audience: At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

      Comments

      Content: The seminar will concern the discussion of state-of-art techniques in molecular simulation which allow for a simulation of several space (especially) and time scale within one computational approach.

      The discussion will concerns both, specific computational coding and conceptual developments.

      Suggested reading

      Related Basic Literature:

      (1) M.Praprotnik, L.Delle Site and K.Kremer, Ann.Rev.Phys.Chem.59, 545-571 (2008)

      (2) C.Peter, L.Delle Site and K.Kremer, Soft Matter 4, 859-869 (2008).

      (3) M.Praprotnik and L.Delle Site, in "Biomolecular Simulations: Methods and Protocols" L.Monticelli and E.Salonen Eds. Vol.924, 567-583 (2012) Methods Mol. Biol. Springer-Science
    • 19226611 Seminar
      Seminar Quantum Computational Methods (Luigi Delle Site)
      Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

      Die Veranstaltung findet Mittwochs von 12-14 Uhr in der Arnimallee 9 statt.

      Comments

      The seminar will focus on the literature related to the most popular molecular simulation methods for quantum mechanical systems.
      In particular we will read and discuss the paper at the foundation of Path Integral Molecular Dynamics, Quantum Monte Carlo techniques and Density Functional Theory. A new development became relevant in the last yeras, i.e. quantum calculations on quantum computers, part of the seminar will treat also such novel aspects.
      Moreover the reading and the discussion will be complemented by paper about the latest developments and applications of the methods.

      Suggested reading

      Related Basic Literature:
      (1) David M.Ceperley, Reviews of Modern Physics 67 279 (1995)
      (2) Miguel A. Morales, Raymond Clay, Carlo Pierleoni, and David M. Ceperley, Entropy 2014, 16(1), 287-321
      (3) P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864-B871
    • 19227611 Seminar
      Seminar Uncertainty Quantification & Inverse Problems (Claudia Schillings)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-24)
      Location: A3/SR 115 (Arnimallee 3-5)

      Comments

      The seminar covers advanced topics of uncertainty quantification and inverse problems.
    • 19233511 Seminar
      Geometric Group Theory (Georg Lehner)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Additional information / Pre-requisites

      Aimed at: Bachelor and masters students

      Prerequisites: Group theory. Additionally either Geometry (especially elementary non-euclidean geometry) and/or Topology (point-set topology) can be helpful.

      Comments

      Groups are best understood as symmetries of mathematical objects. Whereas finite groups can often be completely understood by their actions on vector spaces, this approach will often fail with infinite groups, such as free groups or hyperbolic groups. Geometric group theory tries to construct natural geometric objects (topological spaces such as manifolds or graphs for example) that these groups act on and allows one to classify the complexity these groups can have.

      In this seminar, we will follow Clara Löh's book on the subject. Topics will include Cayley graphs, free groups and their subgroups, quasi-isometry classes of groups, growth types of groups, hyperbolic groups and the Banach-Tarski theorem.

      Suggested reading

      Clara Löh - Geometric Group Theory
    • 19239711 Seminar
      Advanced Dynamical Systems (Bernold Fiedler)
      Schedule: Do 16:00-18:00 (Class starts on: 2025-04-17)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Students present recent papers on topics in delay equations. Dates only by arrangement.
    • 19239911 Seminar
      Advanced Differential Equations (Bernold Fiedler)
      Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Students present recent papers on topics in dynamical systems. Dates only by arrangement.

  • Complementary Module: BMS Fridays

    0280bA7.8
    • 19223111 Seminar
      BMS Fridays (Holger Reich)
      Schedule: Fr 14:00-17:00 (Class starts on: 2025-04-25)
      Location: T9/Gr. Hörsaal (Takustr. 9)

      Comments

      The Friday colloquia of BMS represent a common meeting point for Berlin mathematics at Urania Berlin: a colloquium with broad emanation that permits an overview of large-scale connections and insights. In thematic series, the conversation is about “mathematics as a whole,” and we hope to be able to witness some breakthroughs.

      Typically, there is a BMS colloquium every other Friday afternoon in the BMS Loft at Urania during term time. BMS Friday colloquia usually start at 2:15 pm. Tea and cookies are served before each talk at 1:00 pm.

      More details: https://www.math-berlin.de/academics/bms-fridays

  • Complementary Module: What is…?

    0280bA7.9
    • 19217311 Seminar
      PhD Seminar "What is...?" (Holger Reich)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-18)
      Location: A7/SR 031 (Arnimallee 7)

      Additional information / Pre-requisites

      The "What is ...?" seminars are usually held before the BMS Friday seminar to complement the topic of the talk.

      Audience: Anybody interested in mathematics is invited to attend the "What is ...?" seminars. This includes Bachelors, Masters, Diplom, and PhD students from any field, as well as researchers like Post-Docs.
      Requirements: The speakers assume that the audience has at least a general knowledge of graduate-level mathematics.

      Comments

      Content: The "What is ...?" seminar is a 30-minute weekly seminar that concisely introduces terms and ideas that are fundamental to certain fields of mathematics but may not be familiar in others.
      The vast mathematical landscape in Berlin welcomes mathematicians with diverse backgrounds to work side by side, yet their paths often only cross within their individual research groups. To encourage interdisciplinary cooperation and collaboration, the "What is ...?" seminar attempts to initiate contact by introducing essential vocabulary and foundational concepts of the numerous fields represented in Berlin. The casual atmosphere of the seminar invites the audience to ask many questions and the speakers to experiment with their presentation styles.
      The location of the seminar rotates among the Urania, FU, TU, and HU. On the weeks when a BMS Friday takes place, the "What is ...?" seminar topic is arranged to coincide with the Friday talk acting as an introductory talk for the BMS Friday Colloquium. For a schedule of the talks and their locations, check the website. The website is updated frequently throughout the semester.

      Talks and more detailed information can be found here
      Homepage: http://www.math.fu-berlin.de/w/Math/WhatIsSeminar

  • Introductory Module: Numerical Mathematics III

    0280cA1.12
    • 19215201 Lecture
      Basic Module: Numerics III (Volker John)
      Schedule: Mo 10:00-12:00, Mo 14:00-16:00 (Class starts on: 2025-04-28)
      Location: A6/SR 031 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisites

      Prerequisites for this course are basic knowledge in calculus (Analysis I-III) and Numerical Analysis (Numerik I). Some knowledge in Functional Analysis will help a lot.

      Comments

      The mathematical modeling of many processes in nature and industry leads to partial differential equations. Generally, such equations cannot be solved analytically. It is only possible to compute numerical approximations to the solution on the basis of discretized equations. This course studies discretizations of elliptic partial differential equations. Major topics are finite difference methods and finite element methods.

       

      Suggested reading

      • D. Braess: Finite Elemente. Springer, 3. Auflage (2002)
      • A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements (2004)
    • 19215202 Practice seminar
      Practice seminar for Basic Module: Numerics III (André-Alexander Zepernick)
      Schedule: Fr 08:00-10:00 (Class starts on: 2025-04-25)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Comments

      Homepage:Wiki der Numerik II

  • Introductory Module: Partial Differential Equations I

    0280cA1.13
    • 19241301 Lecture
      Partial Differential Equations I (André Erhardt)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Comments

      • Basic differential equations (Laplace,- heat and wave equations)
      • Representation formulas
      • Solution methods
      • Introduction to Hilbert space methods

      This can serve as the basis for a BSc and/or MSc project.  

      Suggested reading

      L.C. Evans, Partial Differential Equations
       
    • 19241302 Practice seminar
      Exercises to Partial Differential Equations I (Piotr Pawel Wozniak)
      Schedule: Di 16:00-18:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
      Location: 0.1.01 Hörsaal B (Arnimallee 14)

  • Introductory Module: Topology I

    0280cA1.17
    • 19205401 Lecture
      Basic module: Topology I (Christian Haase)
      Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: 1.3.14 Hörsaal A (Arnimallee 14)

      Comments


      Course Overview This is a beginning course from the series of three courses Topology I—III:

      1. Basic notions: topological spaces, continuous maps, connectedness, compactness, products, coproducts, quotients.
      2. Groups acting on topological spaces
      3. Gluing constructions, simplicial complexes
      4. Homotopies between continuous maps, degree of a map, fundamental group.
      5. Seifert-van Kampen Theorem.
      6. Covering spaces.
      7. Simplicial homology
      8. Combinatorial applications

      Suggested reading

      Literature:

      1. M. A. Armstron: Basic Topology, Springer UTM
      2. Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website
      3. Jirí Matoušek: Using the Borsuk-Ulam Theorem, Springer UTX
      4. Mark de Longueville: A Course in Topological Combinatorics, Springer UTX
      5. Tammo tom Dieck: Topologie, De Gruyter Lehrbuch
      6. Klaus Jänich: Topologie, Springer-Verlag
      7. Gerd Laures, Markus Szymik: Grundkurs Topologie, Spektrum Akademischer Verlag
      8. James R. Munkres: Topology, Prentice Hall
    • 19205402 Practice seminar
      Exercise for Basic Module: Topology I (Sofia Garzón Mora)
      Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-28)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

  • Introductory Module: Algebra II

    0280cA1.2
    • 19214501 Lecture
      Basic Module: Algebra II (Holger Reich)
      Schedule: Mo 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-04)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisits: Comutitive algebra

      Comments

      The course deals with the fundamentals of homological algebra, sheaf theory, and the theory of ringed spaces and schemes.

      Possible topics include: 
      - categories and functors
      - additive and abelian categories
      - cohomology
      - sheaf theory
      - ringed spaces
      - schemes
      - separated and proper morphisms
      - blowing up
      - embeddings into projective spaces, divisors, invertible sheaves 
      - Riemann-Roch -Gröbner bases.

      Suggested reading

      For example: Introduction to Schemes, Geir Ellingsrud and John Christian Otten
    • 19214502 Practice seminar
      Practice seminar for Basic Module: Algebra II (Georg Lehner)
      Schedule: Mi 08:00-10:00, Do 14:00-16:00 (Class starts on: 2025-04-23)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

  • Introductory Module: Discrete Geometry II

    0280cA1.6
    • 19214901 Lecture
      Basic Module: Discrete Geometrie II (Georg Loho)
      Schedule: Di 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-04-15)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Solid background in linear algebra and some analysis. Basic knowledge and experience with polytopes and/or convexity (as from the course "Discrete Geometry I") will be helpful. .

      Comments

      Inhalt:

      This is the second in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures with an emphasis on metric and convex geometric properties. In the course we will develop central themes in metric and convex geometry including proof techniques and applications to other areas in mathematics.

      The material will be a selection of the following topics:
      Linear programming and some applications

       

      • Linear programming and duality
      • Pivot rules and the diameter of polytopes

      Subdivisions and triangulations

      • Delaunay and Voronoi
      • Delaunay triangulations and inscribable polytopes
      • Weighted Voronoi diagrams and optimal transport

      Basic structures in convex geometry

       

      • convexity and separation theorems
      • convex bodies and polytopes/polyhedra
      • polarity
      • Mahler’s conjecture
      • approximation by polytopes

      Volumes and roundness

      • Hilbert’s third problem
      • volumes and mixed volumes
      • volume computations and estimates
      • Löwner-John ellipsoids and roundness
      • valuations

      Geometric inequalities

      • Brunn-Minkowski and Alexandrov-Fenchel inequality
      • isoperimetric inequalities
      • measure concentration and phenomena in high-dimensions

      Geometry of numbers

      • lattices
      • Minkowski's (first) theorem
      • successive minima
      • lattice points in convex bodies and Ehrhart's theorem
      • Ehrhart-Macdonald reciprocity

      Sphere packings

      • lattice packings and coverings
      • the Theorem of Minkowski-Hlawka
      • analytic methods

      Applications in optimization, number theory, algebra, algebraic geometry, and functional analysis

      Suggested reading

      The course will use material from P. M. Gruber, " Convex and Discrete Geometry" (Springer 2007) and various other sources. There will be brief lecture notes available for course participants with detailed pointers to the literature.
    • 19214902 Practice seminar
      Practice seminar for BasicM: Discrete Geometry II (Georg Loho)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

  • Introductory Module: Dynamical Systems I

    0280cA1.9
    • 19215601 Lecture Cancelled
      Basic Module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

      <p>Analysis I to III and Lineare Algebra I and II.</p>¶¶

      Comments

      Dynamical Systems are concerned with anything that moves. They are typically described by ordinary, functional, or partial differential equations, or, in the case of discrete time, by iterations. In this course, we will study flows and evolutions, first integrals, the existence and uniqueness of solutions, as well as ω-limit sets and Lyapunov functions. Dynamical systems have a vast range of applications, from physics and biology to economics and engineering.

      Requirements: Analysis 1 & 2, Linear Algebra 1 & 2. An interest in applications is advantageous.

      Suggested reading

      L.C. Evans, Partial Differential Equations. Gelegentlich: W. Strauss, Partial Differential Equation. Alle Exemplare beider Texte stehen im Handapparat Ecker.

      Vorausgesetztes Material zu Analysis II und III siehe z.B. Appendices in diesem Buch (vor allem Appendix C und E (Maß- und Integrationstheorie).
    • 19215602 Practice seminar Cancelled
      Practice seminar for Basis module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
      Location: 0.1.01 Hörsaal B (Arnimallee 14)

      Comments

      Am 23. April findet keine Übung statt.

  • Advanced Module: Discrete Mathematics III

    0280cA2.4
    • 19215001 Lecture
      Constructive Combinatorics (Tibor Szabo)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A3/SR 119 (Arnimallee 3-5)

      Additional information / Pre-requisites

      Basic Bachelor Algebra, Probability, and Disrete Mathematics.

      Comments

      Abstract:
      Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
      The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
      Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
      For further details please check Prof. Szabó's homepage.

      Suggested reading

      A script will be provided.
    • 19215002 Practice seminar
      Constructive Combinatorics exercises (Tibor Szabo)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Comments

      Abstract:
      Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
      The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
      Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
      For further details please check Prof. Szabó's homepage.

  • Advanced Module: Numerical Mathematics IV

    0280cA2.6
    • 19207101 Lecture
      Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: 1.3.14 Hörsaal A (Arnimallee 14)

      Comments

      Many problems in the sciences are determined by processes on several scales. Such problems are denoted as multi-scale problems. One example for a multi-scale problem is the partial differential equations (PDEs), which govern geophysical fluid flows. Averaging methods can be used for the analytical description of the slow scales. These descriptions are beneficial for numerical time-stepping schemes, as they allow for taking bigger time-steps than the unaveraged problem. The focus of this course will be on averaging methods for PDEs describing fluid flows and the design of parallelisable numerical time stepping methods, which are versions of the Parareal method and incorporate averaging techniques.

      Requirements: basic courses in analysis, basic course numerical mathematics

      Literature:

      Wingate, B.A.; Rosemeier, J.; Haut, T., Mean Flow from Phase Averages in the 2D Boussinesq Equations. Atmosphere 2023, 14, 1523.
      https://doi.org/10.3390/atmos14101523

      T. Haut, B. Wingate,  An asymptotic parallel-in-time method for highly oscillatory pde's, SIAM Journal on Scientific Computing, 36 (2014), pp. A693-A713

      J.-L. Lions, G. Turinici, A "parareal" in time discretization of PDE's, Comptes Rendus de l'Academie des Sciences - Series I - Mathematics, 332 (2001), pp. 661-668

      Sanders, F. Verhulst, J. Murdock,  Averaging Methods in Nonlinear Dynamical Systems, Springer New York, NY, 2ed., 2000
    • 19215301 Lecture
      Mathematical Modelling in Climate Research (Rupert Klein)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)

      Comments

      Content:

      Mathematics plays a central role in the development and analysis of models for weather prediction. Controlled physical experiments are out of question, and the only way we can study Earth’s weather and climate system is through mathematical models, computational experiments, and data analysis.

      Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and consequently no general solutions to problems in turbulent flows are available. Instead, scientists rely on conceptual models and statistical descriptions to understand the essence of daily weather and how that feeds back on climate behavior.

       

      This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.

      The course will cover a selection from the following topics

      1. Conservation laws and governing equations,

      2. Numerical methods for geophysical flow simulations,

      3. Dynamical systems and bifurcation theory,

      4. Data-based characterization of atmospheric flows

       

      This course can be attended as the second part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered by the course 19235701 + 19235702 "Introduction to Mathematical Modeling with Partial Differential Equations" abgedeckt, which is offered at FU Berlin in winter terms. 

      Suggested reading

      Literaturhinweise werden anfangs des Semesters in Abhängigkeit von der Themenauswahl gegeben. Interessante Startpunkte, die einen ersten Einstieg in obige drei Hauptpunkte erlauben, sind Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., vol. 42, 249-274 (2010) D. Durran, Numerical Methods for Fluid Dynamics with Applications to Geophysics, Springer, Computational Science and Engineering Series, (2010) Metzner Ph., Putzig L., Horenko I., Analysis of persistent nonstationary time series and applications Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)

      Tennekes and Lumley, A first course in Turbulence, MIT Press (1974)

       
    • 19222601 Lecture
      Numerical methods for stochastic differential equations (Ana Djurdjevac)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Zielgruppe: Students who are interested in stochastics and numerics
      Voraussetzungen: Stochastik I + II, Numerik I + II

      Comments

      Inhalt der Veranstaltung:
      The lecture will cover the following topics (not exhaustive)

      • Brownian motion 
      • Numerical discretization of stochastic differential equations
      • Monte Carlo methods
      • Representations of random fields
      • Modelling with stochastic differential equations
      • Applications

      Suggested reading

      Literatur:

      1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
      2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
      3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
      4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
      5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014
    • 19223901 Lecture
      Uncertainty Quantification and Quasi-Monte Carlo (Claudia Schillings)
      Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Comments

      High-dimensional numerical integration plays a central role in contemporary study of uncertainty quantification. The analysis of how uncertainties associated with material parameters or the measurement configuration propagate within mathematical models leads to challenging high-dimensional integration problems, fueling the need to develop efficient numerical methods for this task. Modern quasi-Monte Carlo (QMC) methods are based on tailoring specially designed cubature rules for high-dimensional integration problems. By leveraging the smoothness and anisotropy of an integrand, it is possible to achieve faster-than-Monte Carlo convergence rates. QMC methods have become a popular tool for solving partial differential equations (PDEs) involving random coefficients, a central topic within the field of uncertainty quantification. This course provides an introduction to uncertainty quantification and how QMC methods can be applied to solve problems arising within this field.

      Suggested reading

      The following books will be relevant:

      • O. P. Le Maître and O. M. Knio. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. Scientific Computation. Springer, New York, 2010.
      • R. C. Smith. Uncertainty Quantification: Theory, Implementation, and Applications, volume 12 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2014.
      • T. J. Sullivan. Introduction to Uncertainty Quantification. Springer, New York, in press.
      • D. Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton, NJ, 2010.
    • 19234501 Lecture
      Mathematical strategies for complex stochastic dynamics (Wei Zhang)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
      Location: T9/053 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Prerequisites: Basic knowledge of stochastics, and numerical methods

      Comments

      Content:

      Stochastic dynamics are widely studied in scientific fields such as physics, biology, and climate. Understanding these dynamics is often challenging due to their high dimensionality and multiscale characteristics. This lecture provides an introduction to theoretical and numerical techniques, including machine learning techniques, for studying such complex stochastic dynamics. The following topics will be covered:

      - Basic of stochastic processes:

      Langevin dynamics, overdamped Langevin dynamics, Markov chains, generators and Fokker-Planck equation, convergence to equilibrium, Ito’s formula

      - Model reduction techniques for stochastic dynamics:

      averaging technique, effective dynamics, Markov state modeling

      - Machine learning techniques using/for stochastic dynamics: 

      dynamics of stochastic gradient descent, autoencoders, solving eigenvalue problems by deep learning, generative modeling using diffusion models, continuous normalizing flow, or flow-matching

      Suggested reading

      1) Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. 5th. Springer, 2000

      2) Kevin P. Murphy. Probabilistic Machine Learning: An introduction. MIT Press, 2022. url: probml.ai

      3) J.-H. Prinz et al. “Markov models of molecular kinetics: Generation and validation”. In: J. Chem. Phys. 134.17, 174105 (2011), p. 174105

      4) W. Zhang, C. Hartmann, and C. Schütte. “Effective dynamics along given reaction coordinates and reaction rate theory”. In: Faraday Discuss. 195 (2016), pp. 365–394

      5) Mardt, A., Pasquali, L., Wu, H. et al. VAMPnets for deep learning of molecular kinetics. Nat Commun 9, 5 (2018).

      6)  Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole, ICLR 2021.
    • 19207102 Practice seminar
      Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)
    • 19215302 Practice seminar
      Practice seminar for Mathematical Modelling in Climate Research (Rupert Klein)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    • 19222602 Practice seminar
      Practice seminar for Numerical methods for stochastic differential equations (Ana Djurdjevac)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19223902 Practice seminar
      Übung zu UQ and QMC (Claudia Schillings)
      Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
      Location: A3/SR 120 (Arnimallee 3-5)
    • 19234502 Practice seminar
      Practice seminar for Mathematical strategies for complex stochastic dynamics (Wei Zhang)
      Schedule: Fr 10:00-12:00 (Class starts on: 2025-04-25)
      Location: T9/046 Seminarraum (Takustr. 9)

      Comments

      Concrete and simple stochastic dynamics will be studied to illustrate analytical and numerical techniques. Numerical methods will be demonstrated using Jupyter Notebook.

  • Advanced Module: Partial Differential Equations III

    0280cA2.7
    • 19243001 Lecture
      Partial Differential Equations III (Erica Ipocoana)
      Schedule: Di 08:00-10:00 (Class starts on: 2025-04-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Voraussetzungen: Partielle Differentialgleichungen I und II

      Comments

      The course builds upon the the PDE II course offered in the previous winter term. Methods for boundary value problems of elliptic PDEs are deepend. A central aspect of the course are variational methods, in particular multi-dimensional calculus of variations. 

       

      Suggested reading

      Wird in der Vorlesung bekannt gegeben / to be announced.
    • 19243002 Practice seminar
      Tutorial Partial Differential Equations III (Erica Ipocoana)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-24)
      Location: A3/SR 119 (Arnimallee 3-5)

  • Advanced Module: Probability and Statistics IV

    0280cA2.8
    • 19222601 Lecture
      Numerical methods for stochastic differential equations (Ana Djurdjevac)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Zielgruppe: Students who are interested in stochastics and numerics
      Voraussetzungen: Stochastik I + II, Numerik I + II

      Comments

      Inhalt der Veranstaltung:
      The lecture will cover the following topics (not exhaustive)

      • Brownian motion 
      • Numerical discretization of stochastic differential equations
      • Monte Carlo methods
      • Representations of random fields
      • Modelling with stochastic differential equations
      • Applications

      Suggested reading

      Literatur:

      1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
      2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
      3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
      4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
      5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014
    • 19229601 Lecture Cancelled
      Stochastic dynamics in fluids (Felix Höfling)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Additional information / Pre-requisites

      Target audience: M.Sc. Computational Sciences/Mathematik/Physik

      Requirements: some advanced course on either statistical physics or stochastic processes

      Comments

      The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond standard Brownian motion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

      The course is at the interface of probability theory and statistical mechanics. Noting that fluids constitute high-dimensional stochastic processes, I will give an introduction to the principles of liquid state theory, and we will derive the mathematical structure of the relevant correlation functions. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

      Keywords:

      • Brownian motion, diffusion, and stochastic processes in fluids
      • harmonic analysis of correlation functions
      • Zwanzig-Mori projection operator formalism
      • mode-coupling approximations, long-time tails
      • critical dynamics and transport anomalies

      Suggested reading

      • Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
      • Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

      Further literature will be given during the course.
    • 19242101 Lecture
      Stochastics IV: (Guilherme de Lima Feltes, Nicolas Perkowski)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisite: Stochastics I, II, III. 
      Recommended: Functional Analysis.

      Comments

      Content: We will learn two different methods for solving stochastic partial differential equations. The classical method is based on Ito calculus, and we will use it to solve semilinear SPDEs with space-time white noise in one space dimension. But we will see that in higher dimensions this theory only works for linear equations, and motivated by that we will introduce "paracontrolled distributions“, which we developed in the last years based on ideas from harmonic analysis and rough paths, and which allow us to solve some interesting semilinear equations in higher dimensions. Along the way we will learn about regularity theory for semilinear PDEs, Gaussian Hilbert spaces, and much more.

      • Ito calculus for Gaussian random measures;
      • semilinear stochastic PDEs in one dimension;
      • Schauder estimates;
      • Gaussian hypercontractivity;
      • paraproducts and paracontrolled distributions;
      • local existence and uniqueness for semilinear SPDEs in higher dimensions;
      • properties of solutions

      Detailed Information can be found on the Homepage of 19246301 SPDEs: Classical and New.

      Suggested reading

      Literature
      There will be lecture notes.
    • 19222602 Practice seminar
      Practice seminar for Numerical methods for stochastic differential equations (Ana Djurdjevac)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19229602 Practice seminar Cancelled
      Exercises to Stochastic processes in fluids (Felix Höfling)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-29)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19242102 Practice seminar
      Exercise: Stochastics IV (Guilherme de Lima Feltes)
      Schedule: Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

  • Specialization Module: Master's Seminar on Discrete Mathematics

    0280cA3.4
    • 19206011 Seminar
      Discrete Mathematics Masterseminar (Tibor Szabo)
      Schedule: Fr 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-11)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

       

       

      Comments

      Content:
      The seminar covers advanced topics in Extremal and Probabilistic Combinatorics.
      Target audience:
      BMS students, Master students, or advanced Bachelor students.
      Prerequisites:
      Prerequisite is the successful completion of the modul Discrete Mathematics II or III (or equivalent background: please contact the instructor).

       

  • Specialization Module: Master’s Seminar on Numerical Mathematics

    0280cA3.6
    • 19226611 Seminar
      Seminar Quantum Computational Methods (Luigi Delle Site)
      Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

      Die Veranstaltung findet Mittwochs von 12-14 Uhr in der Arnimallee 9 statt.

      Comments

      The seminar will focus on the literature related to the most popular molecular simulation methods for quantum mechanical systems.
      In particular we will read and discuss the paper at the foundation of Path Integral Molecular Dynamics, Quantum Monte Carlo techniques and Density Functional Theory. A new development became relevant in the last yeras, i.e. quantum calculations on quantum computers, part of the seminar will treat also such novel aspects.
      Moreover the reading and the discussion will be complemented by paper about the latest developments and applications of the methods.

      Suggested reading

      Related Basic Literature:
      (1) David M.Ceperley, Reviews of Modern Physics 67 279 (1995)
      (2) Miguel A. Morales, Raymond Clay, Carlo Pierleoni, and David M. Ceperley, Entropy 2014, 16(1), 287-321
      (3) P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864-B871
    • 19227611 Seminar
      Seminar Uncertainty Quantification & Inverse Problems (Claudia Schillings)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-24)
      Location: A3/SR 115 (Arnimallee 3-5)

      Comments

      The seminar covers advanced topics of uncertainty quantification and inverse problems.

  • Specialization Module: Master's Seminar on Partial Differential Equations

    0280cA3.7
    • 19247111 Seminar
      Variational methods & Gamma-convergence (Marita Thomas)
      Schedule: Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Comments

      This seminar addresses bachelor and master students interested in the analysis of partial differential equations (PDEs). It focuses on elliptic PDEs, where the direct method of the calculus of variations provides a powerful tool to handle linear as well as nonlinear problems by investigating the minimality properties of the functional associated with the PDE. Closely related to this is the method of Gamma-convergence, which allows it to study sequences of functionals and minimization problems. A background with courses in analysis, functional analysis, and introduction to PDEs is useful to attend the seminar, but the topics for the presentations will be adapted to the background of the participants.   The main part of the seminar will be held en block in the teaching-free period.

  • Specialization Module: Master’s Seminar on Topology

    0280cA3.9
    • 19233511 Seminar
      Geometric Group Theory (Georg Lehner)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Additional information / Pre-requisites

      Aimed at: Bachelor and masters students

      Prerequisites: Group theory. Additionally either Geometry (especially elementary non-euclidean geometry) and/or Topology (point-set topology) can be helpful.

      Comments

      Groups are best understood as symmetries of mathematical objects. Whereas finite groups can often be completely understood by their actions on vector spaces, this approach will often fail with infinite groups, such as free groups or hyperbolic groups. Geometric group theory tries to construct natural geometric objects (topological spaces such as manifolds or graphs for example) that these groups act on and allows one to classify the complexity these groups can have.

      In this seminar, we will follow Clara Löh's book on the subject. Topics will include Cayley graphs, free groups and their subgroups, quasi-isometry classes of groups, growth types of groups, hyperbolic groups and the Banach-Tarski theorem.

      Suggested reading

      Clara Löh - Geometric Group Theory

  • Complementary Module: Selected Topics A

    0280cA4.1
    • 19205401 Lecture
      Basic module: Topology I (Christian Haase)
      Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: 1.3.14 Hörsaal A (Arnimallee 14)

      Comments


      Course Overview This is a beginning course from the series of three courses Topology I—III:

      1. Basic notions: topological spaces, continuous maps, connectedness, compactness, products, coproducts, quotients.
      2. Groups acting on topological spaces
      3. Gluing constructions, simplicial complexes
      4. Homotopies between continuous maps, degree of a map, fundamental group.
      5. Seifert-van Kampen Theorem.
      6. Covering spaces.
      7. Simplicial homology
      8. Combinatorial applications

      Suggested reading

      Literature:

      1. M. A. Armstron: Basic Topology, Springer UTM
      2. Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website
      3. Jirí Matoušek: Using the Borsuk-Ulam Theorem, Springer UTX
      4. Mark de Longueville: A Course in Topological Combinatorics, Springer UTX
      5. Tammo tom Dieck: Topologie, De Gruyter Lehrbuch
      6. Klaus Jänich: Topologie, Springer-Verlag
      7. Gerd Laures, Markus Szymik: Grundkurs Topologie, Spektrum Akademischer Verlag
      8. James R. Munkres: Topology, Prentice Hall
    • 19214501 Lecture
      Basic Module: Algebra II (Holger Reich)
      Schedule: Mo 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-04)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisits: Comutitive algebra

      Comments

      The course deals with the fundamentals of homological algebra, sheaf theory, and the theory of ringed spaces and schemes.

      Possible topics include: 
      - categories and functors
      - additive and abelian categories
      - cohomology
      - sheaf theory
      - ringed spaces
      - schemes
      - separated and proper morphisms
      - blowing up
      - embeddings into projective spaces, divisors, invertible sheaves 
      - Riemann-Roch -Gröbner bases.

      Suggested reading

      For example: Introduction to Schemes, Geir Ellingsrud and John Christian Otten
    • 19214701 Lecture
      Discrete Mathematics I (Ralf Borndörfer)
      Schedule: Di 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group:

      BMS students, Master and Bachelor students

      Whiteboard:

      You need access to the whiteboard in order to receive information and participate in the exercises.

      Large tutorial:

      Participation is recommended, but non-mandatory.

      Exams:

      1st exam: Thurday July 17, 14:00-16:00, room tba, i.e., in the last lecture
      2nd exam: Thursday October 09, 10:00-12:00, room tba, i.e., in the last week before the lectures of the winter semester start

      Comments

      Content:

      Selection from the following topics:

      • Enumeration (twelvefold way, inclusion-exclusion, double counting, recursions, generating functions, inversion, Ramsey's Theorem, asymptotic counting)
      • Discrete Structures (graphs, set systems, designs, posets, matroids)
      • Graph Theory (trees, matchings, connectivity, planarity, colorings)

      Suggested reading

      • J. Matousek, J. Nesetril (2002/2007): An Invitation to Discrete Mathematics, Oxford University Press, Oxford/Diskrete Mathematik, Springer Verlag, Berlin, Heidelberg.
      • L. Lovasz, J. Pelikan, K. Vesztergombi (2003): Discrete Mathemtics - Elementary and Beyond/Diskrete Mathematik, Springer Verlag, New York.
      • N. Biggs (2004): Discrete Mathematics. Oxford University Press, Oxford.
      • M. Aigner (2004/2007): Diskrete Mathematik, Vieweg Verlag, Wiesbaden/Discrete Mathemattics, American Mathematical Society, USA.
      • D. West (2011): Introduction to Graph Theory. Pearson Education, New York.
    • 19214901 Lecture
      Basic Module: Discrete Geometrie II (Georg Loho)
      Schedule: Di 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-04-15)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Solid background in linear algebra and some analysis. Basic knowledge and experience with polytopes and/or convexity (as from the course "Discrete Geometry I") will be helpful. .

      Comments

      Inhalt:

      This is the second in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures with an emphasis on metric and convex geometric properties. In the course we will develop central themes in metric and convex geometry including proof techniques and applications to other areas in mathematics.

      The material will be a selection of the following topics:
      Linear programming and some applications

       

      • Linear programming and duality
      • Pivot rules and the diameter of polytopes

      Subdivisions and triangulations

      • Delaunay and Voronoi
      • Delaunay triangulations and inscribable polytopes
      • Weighted Voronoi diagrams and optimal transport

      Basic structures in convex geometry

       

      • convexity and separation theorems
      • convex bodies and polytopes/polyhedra
      • polarity
      • Mahler’s conjecture
      • approximation by polytopes

      Volumes and roundness

      • Hilbert’s third problem
      • volumes and mixed volumes
      • volume computations and estimates
      • Löwner-John ellipsoids and roundness
      • valuations

      Geometric inequalities

      • Brunn-Minkowski and Alexandrov-Fenchel inequality
      • isoperimetric inequalities
      • measure concentration and phenomena in high-dimensions

      Geometry of numbers

      • lattices
      • Minkowski's (first) theorem
      • successive minima
      • lattice points in convex bodies and Ehrhart's theorem
      • Ehrhart-Macdonald reciprocity

      Sphere packings

      • lattice packings and coverings
      • the Theorem of Minkowski-Hlawka
      • analytic methods

      Applications in optimization, number theory, algebra, algebraic geometry, and functional analysis

      Suggested reading

      The course will use material from P. M. Gruber, " Convex and Discrete Geometry" (Springer 2007) and various other sources. There will be brief lecture notes available for course participants with detailed pointers to the literature.
    • 19215201 Lecture
      Basic Module: Numerics III (Volker John)
      Schedule: Mo 10:00-12:00, Mo 14:00-16:00 (Class starts on: 2025-04-28)
      Location: A6/SR 031 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisites

      Prerequisites for this course are basic knowledge in calculus (Analysis I-III) and Numerical Analysis (Numerik I). Some knowledge in Functional Analysis will help a lot.

      Comments

      The mathematical modeling of many processes in nature and industry leads to partial differential equations. Generally, such equations cannot be solved analytically. It is only possible to compute numerical approximations to the solution on the basis of discretized equations. This course studies discretizations of elliptic partial differential equations. Major topics are finite difference methods and finite element methods.

       

      Suggested reading

      • D. Braess: Finite Elemente. Springer, 3. Auflage (2002)
      • A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements (2004)
    • 19215601 Lecture Cancelled
      Basic Module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

      <p>Analysis I to III and Lineare Algebra I and II.</p>¶¶

      Comments

      Dynamical Systems are concerned with anything that moves. They are typically described by ordinary, functional, or partial differential equations, or, in the case of discrete time, by iterations. In this course, we will study flows and evolutions, first integrals, the existence and uniqueness of solutions, as well as ω-limit sets and Lyapunov functions. Dynamical systems have a vast range of applications, from physics and biology to economics and engineering.

      Requirements: Analysis 1 & 2, Linear Algebra 1 & 2. An interest in applications is advantageous.

      Suggested reading

      L.C. Evans, Partial Differential Equations. Gelegentlich: W. Strauss, Partial Differential Equation. Alle Exemplare beider Texte stehen im Handapparat Ecker.

      Vorausgesetztes Material zu Analysis II und III siehe z.B. Appendices in diesem Buch (vor allem Appendix C und E (Maß- und Integrationstheorie).
    • 19241301 Lecture
      Partial Differential Equations I (André Erhardt)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Comments

      • Basic differential equations (Laplace,- heat and wave equations)
      • Representation formulas
      • Solution methods
      • Introduction to Hilbert space methods

      This can serve as the basis for a BSc and/or MSc project.  

      Suggested reading

      L.C. Evans, Partial Differential Equations
       
    • 19248101 Lecture
      Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
      Schedule: Mo 14:00-16:00, Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

      Terminhinweis: Die Veranstaltung findet regelmäßig Mo 12‒16 und Di 14‒16 Uhr statt, allerdings mit folgender Ausnahme: Aufgrund des Dies Academicus, den das Institut für Mathematik am ersten Tag des Semesters veranstaltet, gibt es in der ersten Woche abweichende Termine. Für die Einteilung in Kleingruppen, in denen man das Semester über arbeitet, ist es notwendig, beim ersten Treffen am Dienstag, 15. April von 14‒18 Uhr anwesend zu sein.
       

      Leitidee der Veranstaltung
      Ziel der Veranstaltung ist es, einen Überblick über die Bedeutung und Anwendbarkeit diverser mathematischer Gebiete im Kontext von Nachhaltigkeit zu bekommen. Ferner soll dies anhand kleinerer Probleme selbst angewendet werden können. Mathematik ist bekanntermaßen überall und besitzt eine hohe gesellschaftliche Relevanz. Insbesondere im Kontext Nachhaltigkeit sollten wir als mathematische Community Verantwortung übernehmen, einen lebenswerten Planeten zu erhalten und unsere Erkenntnisse, Methoden, Verfahren etc. gemeinwohlorientiert einzusetzen. Dies involviert auch die Aufbereitung und Kommunikation der behandelten mathematischen Themenbereiche.

      Inhaltliche Schwerpunkte
      Wir werden eine Einführung in die vier mathematischen Bereiche Optimierung, Spieltheorie, Statistik, Dynamische Systeme geben. Mittels mathematischer Modellierung werden wir identifizieren, wie diese Bereiche zum Verständnis und mit Lösungsansätzen zu Klimakrise, Verlust von Biodiversität, Ressourcenverknappung und sozialer Ungleichheit beitragen. 

      Methodische Konzeption
      Diese Veranstaltung wird durch ein zeitgemäßes didaktisches Konzept begleitet. Dazu gehören Elemente aus dem Design Thinking, New Work-Methoden wie agiles Arbeiten, aber auch der Ansatz der student agency. Dies bedeutet, dass Lernende Verantwortung für ihren Lernerfolg und Kompetenzzuwachs übernehmen, dabei aber natürlich nicht auf sich alleine gestellt sind, sondern auf diverse inhaltliche bzw. methodische Ressourcen zurückgreifen können. 

      Die inhaltliche Arbeit erfolgt in festen Kleingruppen, die zu jedem mathematischen Themenfeld ein Anwendungsszenario erarbeitet. Dazu werden kleinere reale Probleme bzw. entsprechende mathematische Forschungspaper als Aufhänger und Ausgangspunkt für die Gruppenarbeit ausgewählt. 
      Jeder dieser thematischen „eduSCRUM-Sprints“ besteht aus Planung, Durchführung, Präsentation und endet mit der Reflexion der Arbeitsweisen innerhalb des Teams.

      Zu jedem der vier mathematischen Bereiche gibt es einen Sprint von ca. drei Wochen. Zwischen den Sprints wird zu jedem Themengebiet eine kleine Challenge (zwei bis drei kurze Aufgaben) veröffentlicht, die in Gruppen bearbeitet abzugeben ist. Der Workload dieser Veranstaltung verteilt sich anteilig ungefähr wie folgt: 30% Präsenztermine (Montag & Dienstag) + 10% Challenges + 60% eduScrum-Projektarbeit
       

      Überblick über die wöchentliche Struktur der Veranstaltung 

      • Dienstag 14–16 Uhr: Die Vorlesungstermine dienen der kompakten Aufbereitung der benötigten mathematischen Gebiete und bilden damit die fundamentale  inhaltliche Grundlage für die Projektarbeit. Wir geben dabei einen Einblick in diverse mathematische Gebiete und ihren Anwendungsbezug. 
      • Projektarbeitsphase (zwischen Dienstag 16 Uhr und Montag 12 Uhr): Die Projektarbeitsphase dient dem agilen Arbeiten in Kleingruppen, welche über das Semester verteilt mehrere Anwendungen von Mathematik in SDG-Kontext erarbeiten und aufbereiten. Dabei wird sich an der Methode eduSCRUM orientiert, um über das Semester verteilt in mehreren agilen Sprints über jeweils 2-3 Wochen fokussiert zu arbeiten. Erfahrungen im agilen Arbeiten werden nicht vorausgesetzt. Die erarbeiteten Anwendungsszenarien sollen dabei jeweils passend zu den vier inhaltlichen Themenblöcken der Veranstaltung gestaltet werden, wobei die Kleingruppen durch den Einbau partizipativer Elemente an diversen Stellen Gestaltungsspielraum haben.
      • Montag 12–16 Uhr: Die „Übungstermine“ dienen dem Austausch zwischen den Gruppen, hier werden die in den Sprints erarbeiteten Themen untereinander vorgestellt und ausführlich diskutiert. Nach jedem Sprint werden innerhalb der Gruppen die Arbeitsweise reflektiert und Absprachen für den folgenden Sprint getroffen. Weiterhin können auch inhaltliche Fragen besprochen oder methodische Unterstützung bei eduScrum angeboten werden.

       

      Lernziele
      Die übergeordneten Lernziele dieser Veranstaltung verteilen sich auf fünf Bereiche: Mathematische Grundlagen verstehen und anwenden, Mathematische Modelle anwenden, Modelle beurteilen, Kommunikation von Mathematik im SDG-Kontext & Reflexion des eigenen Lernprozesses.

      Nach erfolgreicher Teilnahme an der Veranstaltung haben Teilnehmer*innen die folgenden Kompetenzen erlangt:

      • Sie verstehen die Bedeutung grundlegender mathematischer Konzepte und Verfahren (aus Optimierung, Spieltheorie, Statistik, Dynamische Systeme). Insbesondere können sie die Terminologie und mathematischen Aussagen präzise erklären und Anwendungsgebiete anhand ausgewählter inner- und außermathematischer Problemstellungen erläutern. 
      • Sie können mathematische Modelle nutzen, um reale Fragestellungen zu beschreiben und zu analysieren.  Dabei können sie verschiedene mathematische Werkzeuge und Techniken verwenden, um qualitative und quantitative Aussagen über die Auswirkungen von Entscheidungen und Maßnahmen zu treffen. 
      • Sie können die Gültigkeit, Angemessenheit und Grenzen mathematischer Modelle beurteilen, indem sie etwa Modellannahmen, verwendete Daten oder Sensitivität der Ergebnisse analysieren, um fundierte Entscheidungen über die Nutzung dieser Modelle im Bereich nachhaltiger Entwicklung zu treffen.
      • Die Ergebnisse mathematischer Analysen und Modelle können klar und prägnant an verschiedene Zielgruppen unter Nutzung verschiedener Medien und Formate kommuniziert werden. Dies geschieht mit dem Ziel, das gesellschaftliche Bewusstsein für die Bedeutung von Mathematik für BNE sowie transformative Prozesse zu fördern.
      • Sie können die eigenen Lernerfahrungen reflektieren, indem sie individuelle Stärken, Lernstrategien, Einstellungen zur Mathematik und ihr mathematisches Selbstkonzept analysieren, um ihre mathematischen Kompetenzen weiterzuentwickeln und so später ihre Rolle als mündige und verantwortungsvolle Bürger*innen in der Gesellschaft auszufüllen.

       

      Formalia & Organisatorisches
      a) Für die regelmäßige Teilnahme ist regelmäßig und in Person an den Terminen montags teilzunehmen. 
      b) Die aktive Teilnahme an der Projektarbeit besteht aus mehreren Aspekten, die über das Semester verteilt in Kleingruppen bearbeitet werden: 

      • Die im Rahmen der eduSCRUM-Sprints erarbeiteten Anwendungsszenarien werden zum Ende des Sprints präsentiert und zugleich durch ein passendes digitales Produkt gesichert. 
      • Die Challenges werden nicht differenziert bewertet, sollen aber bestanden werden.
      • Um das formale Aufschreiben von Mathematik zu lernen, ist eine kurze, nicht differenziert bewertete schriftliche Einzelleistung zu einem mathematischen Inhalt vorgesehen.

      c) Modulabschlussprüfung: Die Veranstaltung kann entweder im Modul „Spezialthemen der Mathematik“ (B.Sc. Mathematik Mono/Lehramt) oder im Modul „Ergänzungsmodul: Ausgewählte Themen A/B/C“ (M.Sc. Mathematik) belegt werden. Bitte beachten Sie, dass je nach Studiengang differenzierte inhaltliche Anforderungen gestellt werden. Beide Module entsprechen vom Workload-Umfang 10 LP. Als Modulabschlussprüfung werden vsl. mündliche Einzelprüfungen angeboten. Die Details werden in der ersten Sitzung bekanntgegeben. 
       
    • 20110401 Lecture
      Quantum information theory (Jens Eisert)
      Schedule: Di 08:00-10:00, Do 08:00-10:00 (Class starts on: 2025-04-15)
      Location: Di 0.1.01 Hörsaal B (Arnimallee 14), Do 0.1.01 Hörsaal B (Arnimallee 14)

      Comments

      Information theory usually abstracts from the underlying physical carriers of information: There is no "hard-drive information" any different from "newspaper information". This is because one type of information can be transformed into another one in a lossless fashion, and hence the actual physical carrier does not matter when it comes to thinking about what ways of processing of information are possible. Things change dramatically, however, if single quantum systems - such as trapped ions, cold atoms, or light quanta - are taken as elementary carriers of information. This course will give an introduction into what is possible pursuing this idea. We will discuss applications of quantum key distribution (allowing for the secure transmission of information), quantum computing (giving rise to computers that can solve some problems faster than conventional supercomputers), quantum simulation (allowing to simulate other complex quantum systems) and sensing devices. For this, we will develop the underlying quantum information theory, with notions of entanglement taking center stage. These applications are subsumed into what is now often called quantum technologies. Specific emphasis will finally be put onto elaborating on the intersection of quantum information theory on the one hand and condensed-matter physics on the other, where new perspectives arise.
    • 19205402 Practice seminar
      Exercise for Basic Module: Topology I (Sofia Garzón Mora)
      Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-28)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    • 19214502 Practice seminar
      Practice seminar for Basic Module: Algebra II (Georg Lehner)
      Schedule: Mi 08:00-10:00, Do 14:00-16:00 (Class starts on: 2025-04-23)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19214702 Practice seminar
      Practice seminar for Discrete Mathematics I (Silas Rathke)
      Schedule: Di 16:00-18:00, Do 14:00-16:00 (Class starts on: 2025-04-22)
      Location: A3/SR 119 (Arnimallee 3-5)

      Comments

      Content:

      Selection from the following topics:

      • Counting (basics, double counting, Pigeonhole Principle, recursions, generating functions, Inclusion-Exclusion, inversion, Polya theory)
      • Discrete Structures (graphs, set systems, designs, posets, matroids)
      • Graph Theory (trees, matchings, connectivity, planarity, colorings)
      • Algorithms (asymptotic running time, BFS, DFS, Dijkstra, Greedy, Kruskal, Hungarian, Ford-Fulkerson)
    • 19214902 Practice seminar
      Practice seminar for BasicM: Discrete Geometry II (Georg Loho)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19215202 Practice seminar
      Practice seminar for Basic Module: Numerics III (André-Alexander Zepernick)
      Schedule: Fr 08:00-10:00 (Class starts on: 2025-04-25)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Comments

      Homepage:Wiki der Numerik II
    • 19215602 Practice seminar Cancelled
      Practice seminar for Basis module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
      Location: 0.1.01 Hörsaal B (Arnimallee 14)

      Comments

      Am 23. April findet keine Übung statt.
    • 19241302 Practice seminar
      Exercises to Partial Differential Equations I (Piotr Pawel Wozniak)
      Schedule: Di 16:00-18:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
      Location: 0.1.01 Hörsaal B (Arnimallee 14)
    • 19248102 Practice seminar
      Practice seminar for Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
      Schedule: Mo 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: A3/019 Seminarraum (Arnimallee 3-5)
    • 20110402 Practice seminar
      Quantum information theory (Jens Eisert)
      Schedule: Mo 14:00-16:00, Mo 16:00-18:00, Di 16:00-18:00 (Class starts on: 2025-04-22)
      Location: Mo 1.1.53 Seminarraum E2 (Arnimallee 14), Mo 1.3.48 Seminarraum T3 (Arnimallee 14), Mo 1.4.31 Seminarraum E3 (Arnimallee 14), Di 1.1.16 FB-Raum (Arnimallee 14)

  • Complementary Module: Specific Research Aspects

    0280cA4.10
    • 19219701 Lecture
      Algebra with Probability in Combinatorics (Tibor Szabo)
      Schedule: Do 08:00-10:00 (Class starts on: 2025-04-17)
      Location: T9/049 Seminarraum (Takustr. 9)

      Comments

      In this lecture specialized topics of Combinatorics and Graph Theory are presented.

  • Complementary Module: Selected Topics B

    0280cA4.2
    • 19205401 Lecture
      Basic module: Topology I (Christian Haase)
      Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: 1.3.14 Hörsaal A (Arnimallee 14)

      Comments


      Course Overview This is a beginning course from the series of three courses Topology I—III:

      1. Basic notions: topological spaces, continuous maps, connectedness, compactness, products, coproducts, quotients.
      2. Groups acting on topological spaces
      3. Gluing constructions, simplicial complexes
      4. Homotopies between continuous maps, degree of a map, fundamental group.
      5. Seifert-van Kampen Theorem.
      6. Covering spaces.
      7. Simplicial homology
      8. Combinatorial applications

      Suggested reading

      Literature:

      1. M. A. Armstron: Basic Topology, Springer UTM
      2. Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website
      3. Jirí Matoušek: Using the Borsuk-Ulam Theorem, Springer UTX
      4. Mark de Longueville: A Course in Topological Combinatorics, Springer UTX
      5. Tammo tom Dieck: Topologie, De Gruyter Lehrbuch
      6. Klaus Jänich: Topologie, Springer-Verlag
      7. Gerd Laures, Markus Szymik: Grundkurs Topologie, Spektrum Akademischer Verlag
      8. James R. Munkres: Topology, Prentice Hall
    • 19214501 Lecture
      Basic Module: Algebra II (Holger Reich)
      Schedule: Mo 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-04)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisits: Comutitive algebra

      Comments

      The course deals with the fundamentals of homological algebra, sheaf theory, and the theory of ringed spaces and schemes.

      Possible topics include: 
      - categories and functors
      - additive and abelian categories
      - cohomology
      - sheaf theory
      - ringed spaces
      - schemes
      - separated and proper morphisms
      - blowing up
      - embeddings into projective spaces, divisors, invertible sheaves 
      - Riemann-Roch -Gröbner bases.

      Suggested reading

      For example: Introduction to Schemes, Geir Ellingsrud and John Christian Otten
    • 19214701 Lecture
      Discrete Mathematics I (Ralf Borndörfer)
      Schedule: Di 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group:

      BMS students, Master and Bachelor students

      Whiteboard:

      You need access to the whiteboard in order to receive information and participate in the exercises.

      Large tutorial:

      Participation is recommended, but non-mandatory.

      Exams:

      1st exam: Thurday July 17, 14:00-16:00, room tba, i.e., in the last lecture
      2nd exam: Thursday October 09, 10:00-12:00, room tba, i.e., in the last week before the lectures of the winter semester start

      Comments

      Content:

      Selection from the following topics:

      • Enumeration (twelvefold way, inclusion-exclusion, double counting, recursions, generating functions, inversion, Ramsey's Theorem, asymptotic counting)
      • Discrete Structures (graphs, set systems, designs, posets, matroids)
      • Graph Theory (trees, matchings, connectivity, planarity, colorings)

      Suggested reading

      • J. Matousek, J. Nesetril (2002/2007): An Invitation to Discrete Mathematics, Oxford University Press, Oxford/Diskrete Mathematik, Springer Verlag, Berlin, Heidelberg.
      • L. Lovasz, J. Pelikan, K. Vesztergombi (2003): Discrete Mathemtics - Elementary and Beyond/Diskrete Mathematik, Springer Verlag, New York.
      • N. Biggs (2004): Discrete Mathematics. Oxford University Press, Oxford.
      • M. Aigner (2004/2007): Diskrete Mathematik, Vieweg Verlag, Wiesbaden/Discrete Mathemattics, American Mathematical Society, USA.
      • D. West (2011): Introduction to Graph Theory. Pearson Education, New York.
    • 19214901 Lecture
      Basic Module: Discrete Geometrie II (Georg Loho)
      Schedule: Di 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-04-15)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Solid background in linear algebra and some analysis. Basic knowledge and experience with polytopes and/or convexity (as from the course "Discrete Geometry I") will be helpful. .

      Comments

      Inhalt:

      This is the second in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures with an emphasis on metric and convex geometric properties. In the course we will develop central themes in metric and convex geometry including proof techniques and applications to other areas in mathematics.

      The material will be a selection of the following topics:
      Linear programming and some applications

       

      • Linear programming and duality
      • Pivot rules and the diameter of polytopes

      Subdivisions and triangulations

      • Delaunay and Voronoi
      • Delaunay triangulations and inscribable polytopes
      • Weighted Voronoi diagrams and optimal transport

      Basic structures in convex geometry

       

      • convexity and separation theorems
      • convex bodies and polytopes/polyhedra
      • polarity
      • Mahler’s conjecture
      • approximation by polytopes

      Volumes and roundness

      • Hilbert’s third problem
      • volumes and mixed volumes
      • volume computations and estimates
      • Löwner-John ellipsoids and roundness
      • valuations

      Geometric inequalities

      • Brunn-Minkowski and Alexandrov-Fenchel inequality
      • isoperimetric inequalities
      • measure concentration and phenomena in high-dimensions

      Geometry of numbers

      • lattices
      • Minkowski's (first) theorem
      • successive minima
      • lattice points in convex bodies and Ehrhart's theorem
      • Ehrhart-Macdonald reciprocity

      Sphere packings

      • lattice packings and coverings
      • the Theorem of Minkowski-Hlawka
      • analytic methods

      Applications in optimization, number theory, algebra, algebraic geometry, and functional analysis

      Suggested reading

      The course will use material from P. M. Gruber, " Convex and Discrete Geometry" (Springer 2007) and various other sources. There will be brief lecture notes available for course participants with detailed pointers to the literature.
    • 19215201 Lecture
      Basic Module: Numerics III (Volker John)
      Schedule: Mo 10:00-12:00, Mo 14:00-16:00 (Class starts on: 2025-04-28)
      Location: A6/SR 031 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisites

      Prerequisites for this course are basic knowledge in calculus (Analysis I-III) and Numerical Analysis (Numerik I). Some knowledge in Functional Analysis will help a lot.

      Comments

      The mathematical modeling of many processes in nature and industry leads to partial differential equations. Generally, such equations cannot be solved analytically. It is only possible to compute numerical approximations to the solution on the basis of discretized equations. This course studies discretizations of elliptic partial differential equations. Major topics are finite difference methods and finite element methods.

       

      Suggested reading

      • D. Braess: Finite Elemente. Springer, 3. Auflage (2002)
      • A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements (2004)
    • 19215601 Lecture Cancelled
      Basic Module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

      <p>Analysis I to III and Lineare Algebra I and II.</p>¶¶

      Comments

      Dynamical Systems are concerned with anything that moves. They are typically described by ordinary, functional, or partial differential equations, or, in the case of discrete time, by iterations. In this course, we will study flows and evolutions, first integrals, the existence and uniqueness of solutions, as well as ω-limit sets and Lyapunov functions. Dynamical systems have a vast range of applications, from physics and biology to economics and engineering.

      Requirements: Analysis 1 & 2, Linear Algebra 1 & 2. An interest in applications is advantageous.

      Suggested reading

      L.C. Evans, Partial Differential Equations. Gelegentlich: W. Strauss, Partial Differential Equation. Alle Exemplare beider Texte stehen im Handapparat Ecker.

      Vorausgesetztes Material zu Analysis II und III siehe z.B. Appendices in diesem Buch (vor allem Appendix C und E (Maß- und Integrationstheorie).
    • 19241301 Lecture
      Partial Differential Equations I (André Erhardt)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Comments

      • Basic differential equations (Laplace,- heat and wave equations)
      • Representation formulas
      • Solution methods
      • Introduction to Hilbert space methods

      This can serve as the basis for a BSc and/or MSc project.  

      Suggested reading

      L.C. Evans, Partial Differential Equations
       
    • 19248101 Lecture
      Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
      Schedule: Mo 14:00-16:00, Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

      Terminhinweis: Die Veranstaltung findet regelmäßig Mo 12‒16 und Di 14‒16 Uhr statt, allerdings mit folgender Ausnahme: Aufgrund des Dies Academicus, den das Institut für Mathematik am ersten Tag des Semesters veranstaltet, gibt es in der ersten Woche abweichende Termine. Für die Einteilung in Kleingruppen, in denen man das Semester über arbeitet, ist es notwendig, beim ersten Treffen am Dienstag, 15. April von 14‒18 Uhr anwesend zu sein.
       

      Leitidee der Veranstaltung
      Ziel der Veranstaltung ist es, einen Überblick über die Bedeutung und Anwendbarkeit diverser mathematischer Gebiete im Kontext von Nachhaltigkeit zu bekommen. Ferner soll dies anhand kleinerer Probleme selbst angewendet werden können. Mathematik ist bekanntermaßen überall und besitzt eine hohe gesellschaftliche Relevanz. Insbesondere im Kontext Nachhaltigkeit sollten wir als mathematische Community Verantwortung übernehmen, einen lebenswerten Planeten zu erhalten und unsere Erkenntnisse, Methoden, Verfahren etc. gemeinwohlorientiert einzusetzen. Dies involviert auch die Aufbereitung und Kommunikation der behandelten mathematischen Themenbereiche.

      Inhaltliche Schwerpunkte
      Wir werden eine Einführung in die vier mathematischen Bereiche Optimierung, Spieltheorie, Statistik, Dynamische Systeme geben. Mittels mathematischer Modellierung werden wir identifizieren, wie diese Bereiche zum Verständnis und mit Lösungsansätzen zu Klimakrise, Verlust von Biodiversität, Ressourcenverknappung und sozialer Ungleichheit beitragen. 

      Methodische Konzeption
      Diese Veranstaltung wird durch ein zeitgemäßes didaktisches Konzept begleitet. Dazu gehören Elemente aus dem Design Thinking, New Work-Methoden wie agiles Arbeiten, aber auch der Ansatz der student agency. Dies bedeutet, dass Lernende Verantwortung für ihren Lernerfolg und Kompetenzzuwachs übernehmen, dabei aber natürlich nicht auf sich alleine gestellt sind, sondern auf diverse inhaltliche bzw. methodische Ressourcen zurückgreifen können. 

      Die inhaltliche Arbeit erfolgt in festen Kleingruppen, die zu jedem mathematischen Themenfeld ein Anwendungsszenario erarbeitet. Dazu werden kleinere reale Probleme bzw. entsprechende mathematische Forschungspaper als Aufhänger und Ausgangspunkt für die Gruppenarbeit ausgewählt. 
      Jeder dieser thematischen „eduSCRUM-Sprints“ besteht aus Planung, Durchführung, Präsentation und endet mit der Reflexion der Arbeitsweisen innerhalb des Teams.

      Zu jedem der vier mathematischen Bereiche gibt es einen Sprint von ca. drei Wochen. Zwischen den Sprints wird zu jedem Themengebiet eine kleine Challenge (zwei bis drei kurze Aufgaben) veröffentlicht, die in Gruppen bearbeitet abzugeben ist. Der Workload dieser Veranstaltung verteilt sich anteilig ungefähr wie folgt: 30% Präsenztermine (Montag & Dienstag) + 10% Challenges + 60% eduScrum-Projektarbeit
       

      Überblick über die wöchentliche Struktur der Veranstaltung 

      • Dienstag 14–16 Uhr: Die Vorlesungstermine dienen der kompakten Aufbereitung der benötigten mathematischen Gebiete und bilden damit die fundamentale  inhaltliche Grundlage für die Projektarbeit. Wir geben dabei einen Einblick in diverse mathematische Gebiete und ihren Anwendungsbezug. 
      • Projektarbeitsphase (zwischen Dienstag 16 Uhr und Montag 12 Uhr): Die Projektarbeitsphase dient dem agilen Arbeiten in Kleingruppen, welche über das Semester verteilt mehrere Anwendungen von Mathematik in SDG-Kontext erarbeiten und aufbereiten. Dabei wird sich an der Methode eduSCRUM orientiert, um über das Semester verteilt in mehreren agilen Sprints über jeweils 2-3 Wochen fokussiert zu arbeiten. Erfahrungen im agilen Arbeiten werden nicht vorausgesetzt. Die erarbeiteten Anwendungsszenarien sollen dabei jeweils passend zu den vier inhaltlichen Themenblöcken der Veranstaltung gestaltet werden, wobei die Kleingruppen durch den Einbau partizipativer Elemente an diversen Stellen Gestaltungsspielraum haben.
      • Montag 12–16 Uhr: Die „Übungstermine“ dienen dem Austausch zwischen den Gruppen, hier werden die in den Sprints erarbeiteten Themen untereinander vorgestellt und ausführlich diskutiert. Nach jedem Sprint werden innerhalb der Gruppen die Arbeitsweise reflektiert und Absprachen für den folgenden Sprint getroffen. Weiterhin können auch inhaltliche Fragen besprochen oder methodische Unterstützung bei eduScrum angeboten werden.

       

      Lernziele
      Die übergeordneten Lernziele dieser Veranstaltung verteilen sich auf fünf Bereiche: Mathematische Grundlagen verstehen und anwenden, Mathematische Modelle anwenden, Modelle beurteilen, Kommunikation von Mathematik im SDG-Kontext & Reflexion des eigenen Lernprozesses.

      Nach erfolgreicher Teilnahme an der Veranstaltung haben Teilnehmer*innen die folgenden Kompetenzen erlangt:

      • Sie verstehen die Bedeutung grundlegender mathematischer Konzepte und Verfahren (aus Optimierung, Spieltheorie, Statistik, Dynamische Systeme). Insbesondere können sie die Terminologie und mathematischen Aussagen präzise erklären und Anwendungsgebiete anhand ausgewählter inner- und außermathematischer Problemstellungen erläutern. 
      • Sie können mathematische Modelle nutzen, um reale Fragestellungen zu beschreiben und zu analysieren.  Dabei können sie verschiedene mathematische Werkzeuge und Techniken verwenden, um qualitative und quantitative Aussagen über die Auswirkungen von Entscheidungen und Maßnahmen zu treffen. 
      • Sie können die Gültigkeit, Angemessenheit und Grenzen mathematischer Modelle beurteilen, indem sie etwa Modellannahmen, verwendete Daten oder Sensitivität der Ergebnisse analysieren, um fundierte Entscheidungen über die Nutzung dieser Modelle im Bereich nachhaltiger Entwicklung zu treffen.
      • Die Ergebnisse mathematischer Analysen und Modelle können klar und prägnant an verschiedene Zielgruppen unter Nutzung verschiedener Medien und Formate kommuniziert werden. Dies geschieht mit dem Ziel, das gesellschaftliche Bewusstsein für die Bedeutung von Mathematik für BNE sowie transformative Prozesse zu fördern.
      • Sie können die eigenen Lernerfahrungen reflektieren, indem sie individuelle Stärken, Lernstrategien, Einstellungen zur Mathematik und ihr mathematisches Selbstkonzept analysieren, um ihre mathematischen Kompetenzen weiterzuentwickeln und so später ihre Rolle als mündige und verantwortungsvolle Bürger*innen in der Gesellschaft auszufüllen.

       

      Formalia & Organisatorisches
      a) Für die regelmäßige Teilnahme ist regelmäßig und in Person an den Terminen montags teilzunehmen. 
      b) Die aktive Teilnahme an der Projektarbeit besteht aus mehreren Aspekten, die über das Semester verteilt in Kleingruppen bearbeitet werden: 

      • Die im Rahmen der eduSCRUM-Sprints erarbeiteten Anwendungsszenarien werden zum Ende des Sprints präsentiert und zugleich durch ein passendes digitales Produkt gesichert. 
      • Die Challenges werden nicht differenziert bewertet, sollen aber bestanden werden.
      • Um das formale Aufschreiben von Mathematik zu lernen, ist eine kurze, nicht differenziert bewertete schriftliche Einzelleistung zu einem mathematischen Inhalt vorgesehen.

      c) Modulabschlussprüfung: Die Veranstaltung kann entweder im Modul „Spezialthemen der Mathematik“ (B.Sc. Mathematik Mono/Lehramt) oder im Modul „Ergänzungsmodul: Ausgewählte Themen A/B/C“ (M.Sc. Mathematik) belegt werden. Bitte beachten Sie, dass je nach Studiengang differenzierte inhaltliche Anforderungen gestellt werden. Beide Module entsprechen vom Workload-Umfang 10 LP. Als Modulabschlussprüfung werden vsl. mündliche Einzelprüfungen angeboten. Die Details werden in der ersten Sitzung bekanntgegeben. 
       
    • 20110401 Lecture
      Quantum information theory (Jens Eisert)
      Schedule: Di 08:00-10:00, Do 08:00-10:00 (Class starts on: 2025-04-15)
      Location: Di 0.1.01 Hörsaal B (Arnimallee 14), Do 0.1.01 Hörsaal B (Arnimallee 14)

      Comments

      Information theory usually abstracts from the underlying physical carriers of information: There is no "hard-drive information" any different from "newspaper information". This is because one type of information can be transformed into another one in a lossless fashion, and hence the actual physical carrier does not matter when it comes to thinking about what ways of processing of information are possible. Things change dramatically, however, if single quantum systems - such as trapped ions, cold atoms, or light quanta - are taken as elementary carriers of information. This course will give an introduction into what is possible pursuing this idea. We will discuss applications of quantum key distribution (allowing for the secure transmission of information), quantum computing (giving rise to computers that can solve some problems faster than conventional supercomputers), quantum simulation (allowing to simulate other complex quantum systems) and sensing devices. For this, we will develop the underlying quantum information theory, with notions of entanglement taking center stage. These applications are subsumed into what is now often called quantum technologies. Specific emphasis will finally be put onto elaborating on the intersection of quantum information theory on the one hand and condensed-matter physics on the other, where new perspectives arise.
    • 19205402 Practice seminar
      Exercise for Basic Module: Topology I (Sofia Garzón Mora)
      Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-28)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    • 19214502 Practice seminar
      Practice seminar for Basic Module: Algebra II (Georg Lehner)
      Schedule: Mi 08:00-10:00, Do 14:00-16:00 (Class starts on: 2025-04-23)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19214702 Practice seminar
      Practice seminar for Discrete Mathematics I (Silas Rathke)
      Schedule: Di 16:00-18:00, Do 14:00-16:00 (Class starts on: 2025-04-22)
      Location: A3/SR 119 (Arnimallee 3-5)

      Comments

      Content:

      Selection from the following topics:

      • Counting (basics, double counting, Pigeonhole Principle, recursions, generating functions, Inclusion-Exclusion, inversion, Polya theory)
      • Discrete Structures (graphs, set systems, designs, posets, matroids)
      • Graph Theory (trees, matchings, connectivity, planarity, colorings)
      • Algorithms (asymptotic running time, BFS, DFS, Dijkstra, Greedy, Kruskal, Hungarian, Ford-Fulkerson)
    • 19214902 Practice seminar
      Practice seminar for BasicM: Discrete Geometry II (Georg Loho)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19215202 Practice seminar
      Practice seminar for Basic Module: Numerics III (André-Alexander Zepernick)
      Schedule: Fr 08:00-10:00 (Class starts on: 2025-04-25)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Comments

      Homepage:Wiki der Numerik II
    • 19215602 Practice seminar Cancelled
      Practice seminar for Basis module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
      Location: 0.1.01 Hörsaal B (Arnimallee 14)

      Comments

      Am 23. April findet keine Übung statt.
    • 19241302 Practice seminar
      Exercises to Partial Differential Equations I (Piotr Pawel Wozniak)
      Schedule: Di 16:00-18:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
      Location: 0.1.01 Hörsaal B (Arnimallee 14)
    • 19248102 Practice seminar
      Practice seminar for Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
      Schedule: Mo 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: A3/019 Seminarraum (Arnimallee 3-5)
    • 20110402 Practice seminar
      Quantum information theory (Jens Eisert)
      Schedule: Mo 14:00-16:00, Mo 16:00-18:00, Di 16:00-18:00 (Class starts on: 2025-04-22)
      Location: Mo 1.1.53 Seminarraum E2 (Arnimallee 14), Mo 1.3.48 Seminarraum T3 (Arnimallee 14), Mo 1.4.31 Seminarraum E3 (Arnimallee 14), Di 1.1.16 FB-Raum (Arnimallee 14)

  • Complementary Module: Selected Topics C

    0280cA4.3
    • 19205401 Lecture
      Basic module: Topology I (Christian Haase)
      Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: 1.3.14 Hörsaal A (Arnimallee 14)

      Comments


      Course Overview This is a beginning course from the series of three courses Topology I—III:

      1. Basic notions: topological spaces, continuous maps, connectedness, compactness, products, coproducts, quotients.
      2. Groups acting on topological spaces
      3. Gluing constructions, simplicial complexes
      4. Homotopies between continuous maps, degree of a map, fundamental group.
      5. Seifert-van Kampen Theorem.
      6. Covering spaces.
      7. Simplicial homology
      8. Combinatorial applications

      Suggested reading

      Literature:

      1. M. A. Armstron: Basic Topology, Springer UTM
      2. Allen Hatcher: Algebraic Topology, Chapter I. Also available online from the author's website
      3. Jirí Matoušek: Using the Borsuk-Ulam Theorem, Springer UTX
      4. Mark de Longueville: A Course in Topological Combinatorics, Springer UTX
      5. Tammo tom Dieck: Topologie, De Gruyter Lehrbuch
      6. Klaus Jänich: Topologie, Springer-Verlag
      7. Gerd Laures, Markus Szymik: Grundkurs Topologie, Spektrum Akademischer Verlag
      8. James R. Munkres: Topology, Prentice Hall
    • 19214501 Lecture
      Basic Module: Algebra II (Holger Reich)
      Schedule: Mo 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-04)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisits: Comutitive algebra

      Comments

      The course deals with the fundamentals of homological algebra, sheaf theory, and the theory of ringed spaces and schemes.

      Possible topics include: 
      - categories and functors
      - additive and abelian categories
      - cohomology
      - sheaf theory
      - ringed spaces
      - schemes
      - separated and proper morphisms
      - blowing up
      - embeddings into projective spaces, divisors, invertible sheaves 
      - Riemann-Roch -Gröbner bases.

      Suggested reading

      For example: Introduction to Schemes, Geir Ellingsrud and John Christian Otten
    • 19214701 Lecture
      Discrete Mathematics I (Ralf Borndörfer)
      Schedule: Di 14:00-16:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

      Target group:

      BMS students, Master and Bachelor students

      Whiteboard:

      You need access to the whiteboard in order to receive information and participate in the exercises.

      Large tutorial:

      Participation is recommended, but non-mandatory.

      Exams:

      1st exam: Thurday July 17, 14:00-16:00, room tba, i.e., in the last lecture
      2nd exam: Thursday October 09, 10:00-12:00, room tba, i.e., in the last week before the lectures of the winter semester start

      Comments

      Content:

      Selection from the following topics:

      • Enumeration (twelvefold way, inclusion-exclusion, double counting, recursions, generating functions, inversion, Ramsey's Theorem, asymptotic counting)
      • Discrete Structures (graphs, set systems, designs, posets, matroids)
      • Graph Theory (trees, matchings, connectivity, planarity, colorings)

      Suggested reading

      • J. Matousek, J. Nesetril (2002/2007): An Invitation to Discrete Mathematics, Oxford University Press, Oxford/Diskrete Mathematik, Springer Verlag, Berlin, Heidelberg.
      • L. Lovasz, J. Pelikan, K. Vesztergombi (2003): Discrete Mathemtics - Elementary and Beyond/Diskrete Mathematik, Springer Verlag, New York.
      • N. Biggs (2004): Discrete Mathematics. Oxford University Press, Oxford.
      • M. Aigner (2004/2007): Diskrete Mathematik, Vieweg Verlag, Wiesbaden/Discrete Mathemattics, American Mathematical Society, USA.
      • D. West (2011): Introduction to Graph Theory. Pearson Education, New York.
    • 19214901 Lecture
      Basic Module: Discrete Geometrie II (Georg Loho)
      Schedule: Di 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-04-15)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Solid background in linear algebra and some analysis. Basic knowledge and experience with polytopes and/or convexity (as from the course "Discrete Geometry I") will be helpful. .

      Comments

      Inhalt:

      This is the second in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures with an emphasis on metric and convex geometric properties. In the course we will develop central themes in metric and convex geometry including proof techniques and applications to other areas in mathematics.

      The material will be a selection of the following topics:
      Linear programming and some applications

       

      • Linear programming and duality
      • Pivot rules and the diameter of polytopes

      Subdivisions and triangulations

      • Delaunay and Voronoi
      • Delaunay triangulations and inscribable polytopes
      • Weighted Voronoi diagrams and optimal transport

      Basic structures in convex geometry

       

      • convexity and separation theorems
      • convex bodies and polytopes/polyhedra
      • polarity
      • Mahler’s conjecture
      • approximation by polytopes

      Volumes and roundness

      • Hilbert’s third problem
      • volumes and mixed volumes
      • volume computations and estimates
      • Löwner-John ellipsoids and roundness
      • valuations

      Geometric inequalities

      • Brunn-Minkowski and Alexandrov-Fenchel inequality
      • isoperimetric inequalities
      • measure concentration and phenomena in high-dimensions

      Geometry of numbers

      • lattices
      • Minkowski's (first) theorem
      • successive minima
      • lattice points in convex bodies and Ehrhart's theorem
      • Ehrhart-Macdonald reciprocity

      Sphere packings

      • lattice packings and coverings
      • the Theorem of Minkowski-Hlawka
      • analytic methods

      Applications in optimization, number theory, algebra, algebraic geometry, and functional analysis

      Suggested reading

      The course will use material from P. M. Gruber, " Convex and Discrete Geometry" (Springer 2007) and various other sources. There will be brief lecture notes available for course participants with detailed pointers to the literature.
    • 19215201 Lecture
      Basic Module: Numerics III (Volker John)
      Schedule: Mo 10:00-12:00, Mo 14:00-16:00 (Class starts on: 2025-04-28)
      Location: A6/SR 031 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisites

      Prerequisites for this course are basic knowledge in calculus (Analysis I-III) and Numerical Analysis (Numerik I). Some knowledge in Functional Analysis will help a lot.

      Comments

      The mathematical modeling of many processes in nature and industry leads to partial differential equations. Generally, such equations cannot be solved analytically. It is only possible to compute numerical approximations to the solution on the basis of discretized equations. This course studies discretizations of elliptic partial differential equations. Major topics are finite difference methods and finite element methods.

       

      Suggested reading

      • D. Braess: Finite Elemente. Springer, 3. Auflage (2002)
      • A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements (2004)
    • 19215601 Lecture Cancelled
      Basic Module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

      <p>Analysis I to III and Lineare Algebra I and II.</p>¶¶

      Comments

      Dynamical Systems are concerned with anything that moves. They are typically described by ordinary, functional, or partial differential equations, or, in the case of discrete time, by iterations. In this course, we will study flows and evolutions, first integrals, the existence and uniqueness of solutions, as well as ω-limit sets and Lyapunov functions. Dynamical systems have a vast range of applications, from physics and biology to economics and engineering.

      Requirements: Analysis 1 & 2, Linear Algebra 1 & 2. An interest in applications is advantageous.

      Suggested reading

      L.C. Evans, Partial Differential Equations. Gelegentlich: W. Strauss, Partial Differential Equation. Alle Exemplare beider Texte stehen im Handapparat Ecker.

      Vorausgesetztes Material zu Analysis II und III siehe z.B. Appendices in diesem Buch (vor allem Appendix C und E (Maß- und Integrationstheorie).
    • 19241301 Lecture
      Partial Differential Equations I (André Erhardt)
      Schedule: Di 12:00-14:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Comments

      • Basic differential equations (Laplace,- heat and wave equations)
      • Representation formulas
      • Solution methods
      • Introduction to Hilbert space methods

      This can serve as the basis for a BSc and/or MSc project.  

      Suggested reading

      L.C. Evans, Partial Differential Equations
       
    • 19248101 Lecture
      Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
      Schedule: Mo 14:00-16:00, Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

      Terminhinweis: Die Veranstaltung findet regelmäßig Mo 12‒16 und Di 14‒16 Uhr statt, allerdings mit folgender Ausnahme: Aufgrund des Dies Academicus, den das Institut für Mathematik am ersten Tag des Semesters veranstaltet, gibt es in der ersten Woche abweichende Termine. Für die Einteilung in Kleingruppen, in denen man das Semester über arbeitet, ist es notwendig, beim ersten Treffen am Dienstag, 15. April von 14‒18 Uhr anwesend zu sein.
       

      Leitidee der Veranstaltung
      Ziel der Veranstaltung ist es, einen Überblick über die Bedeutung und Anwendbarkeit diverser mathematischer Gebiete im Kontext von Nachhaltigkeit zu bekommen. Ferner soll dies anhand kleinerer Probleme selbst angewendet werden können. Mathematik ist bekanntermaßen überall und besitzt eine hohe gesellschaftliche Relevanz. Insbesondere im Kontext Nachhaltigkeit sollten wir als mathematische Community Verantwortung übernehmen, einen lebenswerten Planeten zu erhalten und unsere Erkenntnisse, Methoden, Verfahren etc. gemeinwohlorientiert einzusetzen. Dies involviert auch die Aufbereitung und Kommunikation der behandelten mathematischen Themenbereiche.

      Inhaltliche Schwerpunkte
      Wir werden eine Einführung in die vier mathematischen Bereiche Optimierung, Spieltheorie, Statistik, Dynamische Systeme geben. Mittels mathematischer Modellierung werden wir identifizieren, wie diese Bereiche zum Verständnis und mit Lösungsansätzen zu Klimakrise, Verlust von Biodiversität, Ressourcenverknappung und sozialer Ungleichheit beitragen. 

      Methodische Konzeption
      Diese Veranstaltung wird durch ein zeitgemäßes didaktisches Konzept begleitet. Dazu gehören Elemente aus dem Design Thinking, New Work-Methoden wie agiles Arbeiten, aber auch der Ansatz der student agency. Dies bedeutet, dass Lernende Verantwortung für ihren Lernerfolg und Kompetenzzuwachs übernehmen, dabei aber natürlich nicht auf sich alleine gestellt sind, sondern auf diverse inhaltliche bzw. methodische Ressourcen zurückgreifen können. 

      Die inhaltliche Arbeit erfolgt in festen Kleingruppen, die zu jedem mathematischen Themenfeld ein Anwendungsszenario erarbeitet. Dazu werden kleinere reale Probleme bzw. entsprechende mathematische Forschungspaper als Aufhänger und Ausgangspunkt für die Gruppenarbeit ausgewählt. 
      Jeder dieser thematischen „eduSCRUM-Sprints“ besteht aus Planung, Durchführung, Präsentation und endet mit der Reflexion der Arbeitsweisen innerhalb des Teams.

      Zu jedem der vier mathematischen Bereiche gibt es einen Sprint von ca. drei Wochen. Zwischen den Sprints wird zu jedem Themengebiet eine kleine Challenge (zwei bis drei kurze Aufgaben) veröffentlicht, die in Gruppen bearbeitet abzugeben ist. Der Workload dieser Veranstaltung verteilt sich anteilig ungefähr wie folgt: 30% Präsenztermine (Montag & Dienstag) + 10% Challenges + 60% eduScrum-Projektarbeit
       

      Überblick über die wöchentliche Struktur der Veranstaltung 

      • Dienstag 14–16 Uhr: Die Vorlesungstermine dienen der kompakten Aufbereitung der benötigten mathematischen Gebiete und bilden damit die fundamentale  inhaltliche Grundlage für die Projektarbeit. Wir geben dabei einen Einblick in diverse mathematische Gebiete und ihren Anwendungsbezug. 
      • Projektarbeitsphase (zwischen Dienstag 16 Uhr und Montag 12 Uhr): Die Projektarbeitsphase dient dem agilen Arbeiten in Kleingruppen, welche über das Semester verteilt mehrere Anwendungen von Mathematik in SDG-Kontext erarbeiten und aufbereiten. Dabei wird sich an der Methode eduSCRUM orientiert, um über das Semester verteilt in mehreren agilen Sprints über jeweils 2-3 Wochen fokussiert zu arbeiten. Erfahrungen im agilen Arbeiten werden nicht vorausgesetzt. Die erarbeiteten Anwendungsszenarien sollen dabei jeweils passend zu den vier inhaltlichen Themenblöcken der Veranstaltung gestaltet werden, wobei die Kleingruppen durch den Einbau partizipativer Elemente an diversen Stellen Gestaltungsspielraum haben.
      • Montag 12–16 Uhr: Die „Übungstermine“ dienen dem Austausch zwischen den Gruppen, hier werden die in den Sprints erarbeiteten Themen untereinander vorgestellt und ausführlich diskutiert. Nach jedem Sprint werden innerhalb der Gruppen die Arbeitsweise reflektiert und Absprachen für den folgenden Sprint getroffen. Weiterhin können auch inhaltliche Fragen besprochen oder methodische Unterstützung bei eduScrum angeboten werden.

       

      Lernziele
      Die übergeordneten Lernziele dieser Veranstaltung verteilen sich auf fünf Bereiche: Mathematische Grundlagen verstehen und anwenden, Mathematische Modelle anwenden, Modelle beurteilen, Kommunikation von Mathematik im SDG-Kontext & Reflexion des eigenen Lernprozesses.

      Nach erfolgreicher Teilnahme an der Veranstaltung haben Teilnehmer*innen die folgenden Kompetenzen erlangt:

      • Sie verstehen die Bedeutung grundlegender mathematischer Konzepte und Verfahren (aus Optimierung, Spieltheorie, Statistik, Dynamische Systeme). Insbesondere können sie die Terminologie und mathematischen Aussagen präzise erklären und Anwendungsgebiete anhand ausgewählter inner- und außermathematischer Problemstellungen erläutern. 
      • Sie können mathematische Modelle nutzen, um reale Fragestellungen zu beschreiben und zu analysieren.  Dabei können sie verschiedene mathematische Werkzeuge und Techniken verwenden, um qualitative und quantitative Aussagen über die Auswirkungen von Entscheidungen und Maßnahmen zu treffen. 
      • Sie können die Gültigkeit, Angemessenheit und Grenzen mathematischer Modelle beurteilen, indem sie etwa Modellannahmen, verwendete Daten oder Sensitivität der Ergebnisse analysieren, um fundierte Entscheidungen über die Nutzung dieser Modelle im Bereich nachhaltiger Entwicklung zu treffen.
      • Die Ergebnisse mathematischer Analysen und Modelle können klar und prägnant an verschiedene Zielgruppen unter Nutzung verschiedener Medien und Formate kommuniziert werden. Dies geschieht mit dem Ziel, das gesellschaftliche Bewusstsein für die Bedeutung von Mathematik für BNE sowie transformative Prozesse zu fördern.
      • Sie können die eigenen Lernerfahrungen reflektieren, indem sie individuelle Stärken, Lernstrategien, Einstellungen zur Mathematik und ihr mathematisches Selbstkonzept analysieren, um ihre mathematischen Kompetenzen weiterzuentwickeln und so später ihre Rolle als mündige und verantwortungsvolle Bürger*innen in der Gesellschaft auszufüllen.

       

      Formalia & Organisatorisches
      a) Für die regelmäßige Teilnahme ist regelmäßig und in Person an den Terminen montags teilzunehmen. 
      b) Die aktive Teilnahme an der Projektarbeit besteht aus mehreren Aspekten, die über das Semester verteilt in Kleingruppen bearbeitet werden: 

      • Die im Rahmen der eduSCRUM-Sprints erarbeiteten Anwendungsszenarien werden zum Ende des Sprints präsentiert und zugleich durch ein passendes digitales Produkt gesichert. 
      • Die Challenges werden nicht differenziert bewertet, sollen aber bestanden werden.
      • Um das formale Aufschreiben von Mathematik zu lernen, ist eine kurze, nicht differenziert bewertete schriftliche Einzelleistung zu einem mathematischen Inhalt vorgesehen.

      c) Modulabschlussprüfung: Die Veranstaltung kann entweder im Modul „Spezialthemen der Mathematik“ (B.Sc. Mathematik Mono/Lehramt) oder im Modul „Ergänzungsmodul: Ausgewählte Themen A/B/C“ (M.Sc. Mathematik) belegt werden. Bitte beachten Sie, dass je nach Studiengang differenzierte inhaltliche Anforderungen gestellt werden. Beide Module entsprechen vom Workload-Umfang 10 LP. Als Modulabschlussprüfung werden vsl. mündliche Einzelprüfungen angeboten. Die Details werden in der ersten Sitzung bekanntgegeben. 
       
    • 20110401 Lecture
      Quantum information theory (Jens Eisert)
      Schedule: Di 08:00-10:00, Do 08:00-10:00 (Class starts on: 2025-04-15)
      Location: Di 0.1.01 Hörsaal B (Arnimallee 14), Do 0.1.01 Hörsaal B (Arnimallee 14)

      Comments

      Information theory usually abstracts from the underlying physical carriers of information: There is no "hard-drive information" any different from "newspaper information". This is because one type of information can be transformed into another one in a lossless fashion, and hence the actual physical carrier does not matter when it comes to thinking about what ways of processing of information are possible. Things change dramatically, however, if single quantum systems - such as trapped ions, cold atoms, or light quanta - are taken as elementary carriers of information. This course will give an introduction into what is possible pursuing this idea. We will discuss applications of quantum key distribution (allowing for the secure transmission of information), quantum computing (giving rise to computers that can solve some problems faster than conventional supercomputers), quantum simulation (allowing to simulate other complex quantum systems) and sensing devices. For this, we will develop the underlying quantum information theory, with notions of entanglement taking center stage. These applications are subsumed into what is now often called quantum technologies. Specific emphasis will finally be put onto elaborating on the intersection of quantum information theory on the one hand and condensed-matter physics on the other, where new perspectives arise.
    • 19205402 Practice seminar
      Exercise for Basic Module: Topology I (Sofia Garzón Mora)
      Schedule: Mo 16:00-18:00 (Class starts on: 2025-04-28)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    • 19214502 Practice seminar
      Practice seminar for Basic Module: Algebra II (Georg Lehner)
      Schedule: Mi 08:00-10:00, Do 14:00-16:00 (Class starts on: 2025-04-23)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19214702 Practice seminar
      Practice seminar for Discrete Mathematics I (Silas Rathke)
      Schedule: Di 16:00-18:00, Do 14:00-16:00 (Class starts on: 2025-04-22)
      Location: A3/SR 119 (Arnimallee 3-5)

      Comments

      Content:

      Selection from the following topics:

      • Counting (basics, double counting, Pigeonhole Principle, recursions, generating functions, Inclusion-Exclusion, inversion, Polya theory)
      • Discrete Structures (graphs, set systems, designs, posets, matroids)
      • Graph Theory (trees, matchings, connectivity, planarity, colorings)
      • Algorithms (asymptotic running time, BFS, DFS, Dijkstra, Greedy, Kruskal, Hungarian, Ford-Fulkerson)
    • 19214902 Practice seminar
      Practice seminar for BasicM: Discrete Geometry II (Georg Loho)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19215202 Practice seminar
      Practice seminar for Basic Module: Numerics III (André-Alexander Zepernick)
      Schedule: Fr 08:00-10:00 (Class starts on: 2025-04-25)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Comments

      Homepage:Wiki der Numerik II
    • 19215602 Practice seminar Cancelled
      Practice seminar for Basis module: Differential Equations I - Dynamical Systems I (Isabelle Schneider)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-22)
      Location: 0.1.01 Hörsaal B (Arnimallee 14)

      Comments

      Am 23. April findet keine Übung statt.
    • 19241302 Practice seminar
      Exercises to Partial Differential Equations I (Piotr Pawel Wozniak)
      Schedule: Di 16:00-18:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
      Location: 0.1.01 Hörsaal B (Arnimallee 14)
    • 19248102 Practice seminar
      Practice seminar for Mathematics and sustainability (Georg Loho, Jan-Hendrik de Wiljes, Benedikt Weygandt)
      Schedule: Mo 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: A3/019 Seminarraum (Arnimallee 3-5)
    • 20110402 Practice seminar
      Quantum information theory (Jens Eisert)
      Schedule: Mo 14:00-16:00, Mo 16:00-18:00, Di 16:00-18:00 (Class starts on: 2025-04-22)
      Location: Mo 1.1.53 Seminarraum E2 (Arnimallee 14), Mo 1.3.48 Seminarraum T3 (Arnimallee 14), Mo 1.4.31 Seminarraum E3 (Arnimallee 14), Di 1.1.16 FB-Raum (Arnimallee 14)

  • Complementary Module: Specific Aspects A

    0280cA4.4
    • 19207101 Lecture
      Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: 1.3.14 Hörsaal A (Arnimallee 14)

      Comments

      Many problems in the sciences are determined by processes on several scales. Such problems are denoted as multi-scale problems. One example for a multi-scale problem is the partial differential equations (PDEs), which govern geophysical fluid flows. Averaging methods can be used for the analytical description of the slow scales. These descriptions are beneficial for numerical time-stepping schemes, as they allow for taking bigger time-steps than the unaveraged problem. The focus of this course will be on averaging methods for PDEs describing fluid flows and the design of parallelisable numerical time stepping methods, which are versions of the Parareal method and incorporate averaging techniques.

      Requirements: basic courses in analysis, basic course numerical mathematics

      Literature:

      Wingate, B.A.; Rosemeier, J.; Haut, T., Mean Flow from Phase Averages in the 2D Boussinesq Equations. Atmosphere 2023, 14, 1523.
      https://doi.org/10.3390/atmos14101523

      T. Haut, B. Wingate,  An asymptotic parallel-in-time method for highly oscillatory pde's, SIAM Journal on Scientific Computing, 36 (2014), pp. A693-A713

      J.-L. Lions, G. Turinici, A "parareal" in time discretization of PDE's, Comptes Rendus de l'Academie des Sciences - Series I - Mathematics, 332 (2001), pp. 661-668

      Sanders, F. Verhulst, J. Murdock,  Averaging Methods in Nonlinear Dynamical Systems, Springer New York, NY, 2ed., 2000
    • 19215001 Lecture
      Constructive Combinatorics (Tibor Szabo)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A3/SR 119 (Arnimallee 3-5)

      Additional information / Pre-requisites

      Basic Bachelor Algebra, Probability, and Disrete Mathematics.

      Comments

      Abstract:
      Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
      The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
      Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
      For further details please check Prof. Szabó's homepage.

      Suggested reading

      A script will be provided.
    • 19215301 Lecture
      Mathematical Modelling in Climate Research (Rupert Klein)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)

      Comments

      Content:

      Mathematics plays a central role in the development and analysis of models for weather prediction. Controlled physical experiments are out of question, and the only way we can study Earth’s weather and climate system is through mathematical models, computational experiments, and data analysis.

      Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and consequently no general solutions to problems in turbulent flows are available. Instead, scientists rely on conceptual models and statistical descriptions to understand the essence of daily weather and how that feeds back on climate behavior.

       

      This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.

      The course will cover a selection from the following topics

      1. Conservation laws and governing equations,

      2. Numerical methods for geophysical flow simulations,

      3. Dynamical systems and bifurcation theory,

      4. Data-based characterization of atmospheric flows

       

      This course can be attended as the second part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered by the course 19235701 + 19235702 "Introduction to Mathematical Modeling with Partial Differential Equations" abgedeckt, which is offered at FU Berlin in winter terms. 

      Suggested reading

      Literaturhinweise werden anfangs des Semesters in Abhängigkeit von der Themenauswahl gegeben. Interessante Startpunkte, die einen ersten Einstieg in obige drei Hauptpunkte erlauben, sind Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., vol. 42, 249-274 (2010) D. Durran, Numerical Methods for Fluid Dynamics with Applications to Geophysics, Springer, Computational Science and Engineering Series, (2010) Metzner Ph., Putzig L., Horenko I., Analysis of persistent nonstationary time series and applications Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)

      Tennekes and Lumley, A first course in Turbulence, MIT Press (1974)

       
    • 19222601 Lecture
      Numerical methods for stochastic differential equations (Ana Djurdjevac)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Zielgruppe: Students who are interested in stochastics and numerics
      Voraussetzungen: Stochastik I + II, Numerik I + II

      Comments

      Inhalt der Veranstaltung:
      The lecture will cover the following topics (not exhaustive)

      • Brownian motion 
      • Numerical discretization of stochastic differential equations
      • Monte Carlo methods
      • Representations of random fields
      • Modelling with stochastic differential equations
      • Applications

      Suggested reading

      Literatur:

      1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
      2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
      3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
      4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
      5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014
    • 19223901 Lecture
      Uncertainty Quantification and Quasi-Monte Carlo (Claudia Schillings)
      Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Comments

      High-dimensional numerical integration plays a central role in contemporary study of uncertainty quantification. The analysis of how uncertainties associated with material parameters or the measurement configuration propagate within mathematical models leads to challenging high-dimensional integration problems, fueling the need to develop efficient numerical methods for this task. Modern quasi-Monte Carlo (QMC) methods are based on tailoring specially designed cubature rules for high-dimensional integration problems. By leveraging the smoothness and anisotropy of an integrand, it is possible to achieve faster-than-Monte Carlo convergence rates. QMC methods have become a popular tool for solving partial differential equations (PDEs) involving random coefficients, a central topic within the field of uncertainty quantification. This course provides an introduction to uncertainty quantification and how QMC methods can be applied to solve problems arising within this field.

      Suggested reading

      The following books will be relevant:

      • O. P. Le Maître and O. M. Knio. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. Scientific Computation. Springer, New York, 2010.
      • R. C. Smith. Uncertainty Quantification: Theory, Implementation, and Applications, volume 12 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2014.
      • T. J. Sullivan. Introduction to Uncertainty Quantification. Springer, New York, in press.
      • D. Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton, NJ, 2010.
    • 19229601 Lecture Cancelled
      Stochastic dynamics in fluids (Felix Höfling)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Additional information / Pre-requisites

      Target audience: M.Sc. Computational Sciences/Mathematik/Physik

      Requirements: some advanced course on either statistical physics or stochastic processes

      Comments

      The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond standard Brownian motion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

      The course is at the interface of probability theory and statistical mechanics. Noting that fluids constitute high-dimensional stochastic processes, I will give an introduction to the principles of liquid state theory, and we will derive the mathematical structure of the relevant correlation functions. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

      Keywords:

      • Brownian motion, diffusion, and stochastic processes in fluids
      • harmonic analysis of correlation functions
      • Zwanzig-Mori projection operator formalism
      • mode-coupling approximations, long-time tails
      • critical dynamics and transport anomalies

      Suggested reading

      • Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
      • Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

      Further literature will be given during the course.
    • 19234501 Lecture
      Mathematical strategies for complex stochastic dynamics (Wei Zhang)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
      Location: T9/053 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Prerequisites: Basic knowledge of stochastics, and numerical methods

      Comments

      Content:

      Stochastic dynamics are widely studied in scientific fields such as physics, biology, and climate. Understanding these dynamics is often challenging due to their high dimensionality and multiscale characteristics. This lecture provides an introduction to theoretical and numerical techniques, including machine learning techniques, for studying such complex stochastic dynamics. The following topics will be covered:

      - Basic of stochastic processes:

      Langevin dynamics, overdamped Langevin dynamics, Markov chains, generators and Fokker-Planck equation, convergence to equilibrium, Ito’s formula

      - Model reduction techniques for stochastic dynamics:

      averaging technique, effective dynamics, Markov state modeling

      - Machine learning techniques using/for stochastic dynamics: 

      dynamics of stochastic gradient descent, autoencoders, solving eigenvalue problems by deep learning, generative modeling using diffusion models, continuous normalizing flow, or flow-matching

      Suggested reading

      1) Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. 5th. Springer, 2000

      2) Kevin P. Murphy. Probabilistic Machine Learning: An introduction. MIT Press, 2022. url: probml.ai

      3) J.-H. Prinz et al. “Markov models of molecular kinetics: Generation and validation”. In: J. Chem. Phys. 134.17, 174105 (2011), p. 174105

      4) W. Zhang, C. Hartmann, and C. Schütte. “Effective dynamics along given reaction coordinates and reaction rate theory”. In: Faraday Discuss. 195 (2016), pp. 365–394

      5) Mardt, A., Pasquali, L., Wu, H. et al. VAMPnets for deep learning of molecular kinetics. Nat Commun 9, 5 (2018).

      6)  Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole, ICLR 2021.
    • 19240701 Lecture
      Functional Analysis Applied to Modeling of Molecular Systems (Luigi Delle Site)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      Die Vorlesung findet Dienstags von 14-16 Uhr in der Arnimallee 9 statt.

      Die Übung findet Montags von von 14-16 Uhr in der Arnimallee 9 statt.

      Comments

      Prpgram:

      -Existence of ordinary matter as a mathematical problem -the existence of the thermodynamic limit -One concrete way to model molecules: Density Functional theory and its mathematical structure -Existence/non-existence of relativistic matter, Dirac Operator on scalar fields -Spinors, Second Quantization and Fock space

    • 19242101 Lecture
      Stochastics IV: (Guilherme de Lima Feltes, Nicolas Perkowski)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisite: Stochastics I, II, III. 
      Recommended: Functional Analysis.

      Comments

      Content: We will learn two different methods for solving stochastic partial differential equations. The classical method is based on Ito calculus, and we will use it to solve semilinear SPDEs with space-time white noise in one space dimension. But we will see that in higher dimensions this theory only works for linear equations, and motivated by that we will introduce "paracontrolled distributions“, which we developed in the last years based on ideas from harmonic analysis and rough paths, and which allow us to solve some interesting semilinear equations in higher dimensions. Along the way we will learn about regularity theory for semilinear PDEs, Gaussian Hilbert spaces, and much more.

      • Ito calculus for Gaussian random measures;
      • semilinear stochastic PDEs in one dimension;
      • Schauder estimates;
      • Gaussian hypercontractivity;
      • paraproducts and paracontrolled distributions;
      • local existence and uniqueness for semilinear SPDEs in higher dimensions;
      • properties of solutions

      Detailed Information can be found on the Homepage of 19246301 SPDEs: Classical and New.

      Suggested reading

      Literature
      There will be lecture notes.
    • 19243001 Lecture
      Partial Differential Equations III (Erica Ipocoana)
      Schedule: Di 08:00-10:00 (Class starts on: 2025-04-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Voraussetzungen: Partielle Differentialgleichungen I und II

      Comments

      The course builds upon the the PDE II course offered in the previous winter term. Methods for boundary value problems of elliptic PDEs are deepend. A central aspect of the course are variational methods, in particular multi-dimensional calculus of variations. 

       

      Suggested reading

      Wird in der Vorlesung bekannt gegeben / to be announced.
    • 19207102 Practice seminar
      Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)
    • 19215002 Practice seminar
      Constructive Combinatorics exercises (Tibor Szabo)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Comments

      Abstract:
      Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
      The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
      Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
      For further details please check Prof. Szabó's homepage.
    • 19215302 Practice seminar
      Practice seminar for Mathematical Modelling in Climate Research (Rupert Klein)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    • 19222602 Practice seminar
      Practice seminar for Numerical methods for stochastic differential equations (Ana Djurdjevac)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19223902 Practice seminar
      Übung zu UQ and QMC (Claudia Schillings)
      Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
      Location: A3/SR 120 (Arnimallee 3-5)
    • 19229602 Practice seminar Cancelled
      Exercises to Stochastic processes in fluids (Felix Höfling)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-29)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19234502 Practice seminar
      Practice seminar for Mathematical strategies for complex stochastic dynamics (Wei Zhang)
      Schedule: Fr 10:00-12:00 (Class starts on: 2025-04-25)
      Location: T9/046 Seminarraum (Takustr. 9)

      Comments

      Concrete and simple stochastic dynamics will be studied to illustrate analytical and numerical techniques. Numerical methods will be demonstrated using Jupyter Notebook.
    • 19240702 Practice seminar
      Practice seminar for Functional Analysis applied to modeling of molecular systems (Luigi Delle Site)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    • 19242102 Practice seminar
      Exercise: Stochastics IV (Guilherme de Lima Feltes)
      Schedule: Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)
    • 19243002 Practice seminar
      Tutorial Partial Differential Equations III (Erica Ipocoana)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-24)
      Location: A3/SR 119 (Arnimallee 3-5)

  • Complementary Module: Specific Aspects B

    0280cA4.5
    • 19207101 Lecture
      Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: 1.3.14 Hörsaal A (Arnimallee 14)

      Comments

      Many problems in the sciences are determined by processes on several scales. Such problems are denoted as multi-scale problems. One example for a multi-scale problem is the partial differential equations (PDEs), which govern geophysical fluid flows. Averaging methods can be used for the analytical description of the slow scales. These descriptions are beneficial for numerical time-stepping schemes, as they allow for taking bigger time-steps than the unaveraged problem. The focus of this course will be on averaging methods for PDEs describing fluid flows and the design of parallelisable numerical time stepping methods, which are versions of the Parareal method and incorporate averaging techniques.

      Requirements: basic courses in analysis, basic course numerical mathematics

      Literature:

      Wingate, B.A.; Rosemeier, J.; Haut, T., Mean Flow from Phase Averages in the 2D Boussinesq Equations. Atmosphere 2023, 14, 1523.
      https://doi.org/10.3390/atmos14101523

      T. Haut, B. Wingate,  An asymptotic parallel-in-time method for highly oscillatory pde's, SIAM Journal on Scientific Computing, 36 (2014), pp. A693-A713

      J.-L. Lions, G. Turinici, A "parareal" in time discretization of PDE's, Comptes Rendus de l'Academie des Sciences - Series I - Mathematics, 332 (2001), pp. 661-668

      Sanders, F. Verhulst, J. Murdock,  Averaging Methods in Nonlinear Dynamical Systems, Springer New York, NY, 2ed., 2000
    • 19215001 Lecture
      Constructive Combinatorics (Tibor Szabo)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A3/SR 119 (Arnimallee 3-5)

      Additional information / Pre-requisites

      Basic Bachelor Algebra, Probability, and Disrete Mathematics.

      Comments

      Abstract:
      Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
      The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
      Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
      For further details please check Prof. Szabó's homepage.

      Suggested reading

      A script will be provided.
    • 19215301 Lecture
      Mathematical Modelling in Climate Research (Rupert Klein)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)

      Comments

      Content:

      Mathematics plays a central role in the development and analysis of models for weather prediction. Controlled physical experiments are out of question, and the only way we can study Earth’s weather and climate system is through mathematical models, computational experiments, and data analysis.

      Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and consequently no general solutions to problems in turbulent flows are available. Instead, scientists rely on conceptual models and statistical descriptions to understand the essence of daily weather and how that feeds back on climate behavior.

       

      This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.

      The course will cover a selection from the following topics

      1. Conservation laws and governing equations,

      2. Numerical methods for geophysical flow simulations,

      3. Dynamical systems and bifurcation theory,

      4. Data-based characterization of atmospheric flows

       

      This course can be attended as the second part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered by the course 19235701 + 19235702 "Introduction to Mathematical Modeling with Partial Differential Equations" abgedeckt, which is offered at FU Berlin in winter terms. 

      Suggested reading

      Literaturhinweise werden anfangs des Semesters in Abhängigkeit von der Themenauswahl gegeben. Interessante Startpunkte, die einen ersten Einstieg in obige drei Hauptpunkte erlauben, sind Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., vol. 42, 249-274 (2010) D. Durran, Numerical Methods for Fluid Dynamics with Applications to Geophysics, Springer, Computational Science and Engineering Series, (2010) Metzner Ph., Putzig L., Horenko I., Analysis of persistent nonstationary time series and applications Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)

      Tennekes and Lumley, A first course in Turbulence, MIT Press (1974)

       
    • 19222601 Lecture
      Numerical methods for stochastic differential equations (Ana Djurdjevac)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Zielgruppe: Students who are interested in stochastics and numerics
      Voraussetzungen: Stochastik I + II, Numerik I + II

      Comments

      Inhalt der Veranstaltung:
      The lecture will cover the following topics (not exhaustive)

      • Brownian motion 
      • Numerical discretization of stochastic differential equations
      • Monte Carlo methods
      • Representations of random fields
      • Modelling with stochastic differential equations
      • Applications

      Suggested reading

      Literatur:

      1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
      2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
      3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
      4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
      5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014
    • 19223901 Lecture
      Uncertainty Quantification and Quasi-Monte Carlo (Claudia Schillings)
      Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Comments

      High-dimensional numerical integration plays a central role in contemporary study of uncertainty quantification. The analysis of how uncertainties associated with material parameters or the measurement configuration propagate within mathematical models leads to challenging high-dimensional integration problems, fueling the need to develop efficient numerical methods for this task. Modern quasi-Monte Carlo (QMC) methods are based on tailoring specially designed cubature rules for high-dimensional integration problems. By leveraging the smoothness and anisotropy of an integrand, it is possible to achieve faster-than-Monte Carlo convergence rates. QMC methods have become a popular tool for solving partial differential equations (PDEs) involving random coefficients, a central topic within the field of uncertainty quantification. This course provides an introduction to uncertainty quantification and how QMC methods can be applied to solve problems arising within this field.

      Suggested reading

      The following books will be relevant:

      • O. P. Le Maître and O. M. Knio. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. Scientific Computation. Springer, New York, 2010.
      • R. C. Smith. Uncertainty Quantification: Theory, Implementation, and Applications, volume 12 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2014.
      • T. J. Sullivan. Introduction to Uncertainty Quantification. Springer, New York, in press.
      • D. Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton, NJ, 2010.
    • 19229601 Lecture Cancelled
      Stochastic dynamics in fluids (Felix Höfling)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Additional information / Pre-requisites

      Target audience: M.Sc. Computational Sciences/Mathematik/Physik

      Requirements: some advanced course on either statistical physics or stochastic processes

      Comments

      The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond standard Brownian motion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

      The course is at the interface of probability theory and statistical mechanics. Noting that fluids constitute high-dimensional stochastic processes, I will give an introduction to the principles of liquid state theory, and we will derive the mathematical structure of the relevant correlation functions. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

      Keywords:

      • Brownian motion, diffusion, and stochastic processes in fluids
      • harmonic analysis of correlation functions
      • Zwanzig-Mori projection operator formalism
      • mode-coupling approximations, long-time tails
      • critical dynamics and transport anomalies

      Suggested reading

      • Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
      • Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

      Further literature will be given during the course.
    • 19234501 Lecture
      Mathematical strategies for complex stochastic dynamics (Wei Zhang)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
      Location: T9/053 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Prerequisites: Basic knowledge of stochastics, and numerical methods

      Comments

      Content:

      Stochastic dynamics are widely studied in scientific fields such as physics, biology, and climate. Understanding these dynamics is often challenging due to their high dimensionality and multiscale characteristics. This lecture provides an introduction to theoretical and numerical techniques, including machine learning techniques, for studying such complex stochastic dynamics. The following topics will be covered:

      - Basic of stochastic processes:

      Langevin dynamics, overdamped Langevin dynamics, Markov chains, generators and Fokker-Planck equation, convergence to equilibrium, Ito’s formula

      - Model reduction techniques for stochastic dynamics:

      averaging technique, effective dynamics, Markov state modeling

      - Machine learning techniques using/for stochastic dynamics: 

      dynamics of stochastic gradient descent, autoencoders, solving eigenvalue problems by deep learning, generative modeling using diffusion models, continuous normalizing flow, or flow-matching

      Suggested reading

      1) Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. 5th. Springer, 2000

      2) Kevin P. Murphy. Probabilistic Machine Learning: An introduction. MIT Press, 2022. url: probml.ai

      3) J.-H. Prinz et al. “Markov models of molecular kinetics: Generation and validation”. In: J. Chem. Phys. 134.17, 174105 (2011), p. 174105

      4) W. Zhang, C. Hartmann, and C. Schütte. “Effective dynamics along given reaction coordinates and reaction rate theory”. In: Faraday Discuss. 195 (2016), pp. 365–394

      5) Mardt, A., Pasquali, L., Wu, H. et al. VAMPnets for deep learning of molecular kinetics. Nat Commun 9, 5 (2018).

      6)  Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole, ICLR 2021.
    • 19240701 Lecture
      Functional Analysis Applied to Modeling of Molecular Systems (Luigi Delle Site)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      Die Vorlesung findet Dienstags von 14-16 Uhr in der Arnimallee 9 statt.

      Die Übung findet Montags von von 14-16 Uhr in der Arnimallee 9 statt.

      Comments

      Prpgram:

      -Existence of ordinary matter as a mathematical problem -the existence of the thermodynamic limit -One concrete way to model molecules: Density Functional theory and its mathematical structure -Existence/non-existence of relativistic matter, Dirac Operator on scalar fields -Spinors, Second Quantization and Fock space

    • 19242101 Lecture
      Stochastics IV: (Guilherme de Lima Feltes, Nicolas Perkowski)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisite: Stochastics I, II, III. 
      Recommended: Functional Analysis.

      Comments

      Content: We will learn two different methods for solving stochastic partial differential equations. The classical method is based on Ito calculus, and we will use it to solve semilinear SPDEs with space-time white noise in one space dimension. But we will see that in higher dimensions this theory only works for linear equations, and motivated by that we will introduce "paracontrolled distributions“, which we developed in the last years based on ideas from harmonic analysis and rough paths, and which allow us to solve some interesting semilinear equations in higher dimensions. Along the way we will learn about regularity theory for semilinear PDEs, Gaussian Hilbert spaces, and much more.

      • Ito calculus for Gaussian random measures;
      • semilinear stochastic PDEs in one dimension;
      • Schauder estimates;
      • Gaussian hypercontractivity;
      • paraproducts and paracontrolled distributions;
      • local existence and uniqueness for semilinear SPDEs in higher dimensions;
      • properties of solutions

      Detailed Information can be found on the Homepage of 19246301 SPDEs: Classical and New.

      Suggested reading

      Literature
      There will be lecture notes.
    • 19243001 Lecture
      Partial Differential Equations III (Erica Ipocoana)
      Schedule: Di 08:00-10:00 (Class starts on: 2025-04-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Voraussetzungen: Partielle Differentialgleichungen I und II

      Comments

      The course builds upon the the PDE II course offered in the previous winter term. Methods for boundary value problems of elliptic PDEs are deepend. A central aspect of the course are variational methods, in particular multi-dimensional calculus of variations. 

       

      Suggested reading

      Wird in der Vorlesung bekannt gegeben / to be announced.
    • 19207102 Practice seminar
      Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)
    • 19215002 Practice seminar
      Constructive Combinatorics exercises (Tibor Szabo)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Comments

      Abstract:
      Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
      The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
      Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
      For further details please check Prof. Szabó's homepage.
    • 19215302 Practice seminar
      Practice seminar for Mathematical Modelling in Climate Research (Rupert Klein)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    • 19222602 Practice seminar
      Practice seminar for Numerical methods for stochastic differential equations (Ana Djurdjevac)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19223902 Practice seminar
      Übung zu UQ and QMC (Claudia Schillings)
      Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
      Location: A3/SR 120 (Arnimallee 3-5)
    • 19229602 Practice seminar Cancelled
      Exercises to Stochastic processes in fluids (Felix Höfling)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-29)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19234502 Practice seminar
      Practice seminar for Mathematical strategies for complex stochastic dynamics (Wei Zhang)
      Schedule: Fr 10:00-12:00 (Class starts on: 2025-04-25)
      Location: T9/046 Seminarraum (Takustr. 9)

      Comments

      Concrete and simple stochastic dynamics will be studied to illustrate analytical and numerical techniques. Numerical methods will be demonstrated using Jupyter Notebook.
    • 19240702 Practice seminar
      Practice seminar for Functional Analysis applied to modeling of molecular systems (Luigi Delle Site)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    • 19242102 Practice seminar
      Exercise: Stochastics IV (Guilherme de Lima Feltes)
      Schedule: Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)
    • 19243002 Practice seminar
      Tutorial Partial Differential Equations III (Erica Ipocoana)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-24)
      Location: A3/SR 119 (Arnimallee 3-5)

  • Complementary Module: Specific Aspects C

    0280cA4.6
    • 19207101 Lecture
      Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: 1.3.14 Hörsaal A (Arnimallee 14)

      Comments

      Many problems in the sciences are determined by processes on several scales. Such problems are denoted as multi-scale problems. One example for a multi-scale problem is the partial differential equations (PDEs), which govern geophysical fluid flows. Averaging methods can be used for the analytical description of the slow scales. These descriptions are beneficial for numerical time-stepping schemes, as they allow for taking bigger time-steps than the unaveraged problem. The focus of this course will be on averaging methods for PDEs describing fluid flows and the design of parallelisable numerical time stepping methods, which are versions of the Parareal method and incorporate averaging techniques.

      Requirements: basic courses in analysis, basic course numerical mathematics

      Literature:

      Wingate, B.A.; Rosemeier, J.; Haut, T., Mean Flow from Phase Averages in the 2D Boussinesq Equations. Atmosphere 2023, 14, 1523.
      https://doi.org/10.3390/atmos14101523

      T. Haut, B. Wingate,  An asymptotic parallel-in-time method for highly oscillatory pde's, SIAM Journal on Scientific Computing, 36 (2014), pp. A693-A713

      J.-L. Lions, G. Turinici, A "parareal" in time discretization of PDE's, Comptes Rendus de l'Academie des Sciences - Series I - Mathematics, 332 (2001), pp. 661-668

      Sanders, F. Verhulst, J. Murdock,  Averaging Methods in Nonlinear Dynamical Systems, Springer New York, NY, 2ed., 2000
    • 19215001 Lecture
      Constructive Combinatorics (Tibor Szabo)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: A3/SR 119 (Arnimallee 3-5)

      Additional information / Pre-requisites

      Basic Bachelor Algebra, Probability, and Disrete Mathematics.

      Comments

      Abstract:
      Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
      The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
      Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
      For further details please check Prof. Szabó's homepage.

      Suggested reading

      A script will be provided.
    • 19215301 Lecture
      Mathematical Modelling in Climate Research (Rupert Klein)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)

      Comments

      Content:

      Mathematics plays a central role in the development and analysis of models for weather prediction. Controlled physical experiments are out of question, and the only way we can study Earth’s weather and climate system is through mathematical models, computational experiments, and data analysis.

      Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and consequently no general solutions to problems in turbulent flows are available. Instead, scientists rely on conceptual models and statistical descriptions to understand the essence of daily weather and how that feeds back on climate behavior.

       

      This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.

      The course will cover a selection from the following topics

      1. Conservation laws and governing equations,

      2. Numerical methods for geophysical flow simulations,

      3. Dynamical systems and bifurcation theory,

      4. Data-based characterization of atmospheric flows

       

      This course can be attended as the second part of the BMS Basic Course "Mathematical Modeling with PDEs", which stretches over two semesters at FU Berlin. The second part will be covered by the course 19235701 + 19235702 "Introduction to Mathematical Modeling with Partial Differential Equations" abgedeckt, which is offered at FU Berlin in winter terms. 

      Suggested reading

      Literaturhinweise werden anfangs des Semesters in Abhängigkeit von der Themenauswahl gegeben. Interessante Startpunkte, die einen ersten Einstieg in obige drei Hauptpunkte erlauben, sind Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., vol. 42, 249-274 (2010) D. Durran, Numerical Methods for Fluid Dynamics with Applications to Geophysics, Springer, Computational Science and Engineering Series, (2010) Metzner Ph., Putzig L., Horenko I., Analysis of persistent nonstationary time series and applications Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)

      Tennekes and Lumley, A first course in Turbulence, MIT Press (1974)

       
    • 19222601 Lecture
      Numerical methods for stochastic differential equations (Ana Djurdjevac)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Zielgruppe: Students who are interested in stochastics and numerics
      Voraussetzungen: Stochastik I + II, Numerik I + II

      Comments

      Inhalt der Veranstaltung:
      The lecture will cover the following topics (not exhaustive)

      • Brownian motion 
      • Numerical discretization of stochastic differential equations
      • Monte Carlo methods
      • Representations of random fields
      • Modelling with stochastic differential equations
      • Applications

      Suggested reading

      Literatur:

      1. D. Higham, D. and  Kloeden, P.  An introduction to the numerical simulation of stochastic differential equations. SIAM, 2021
      2. E. Kloeden, E. Platen and H. Schurz. Numerical Solution of SDEs through computer experiments. Springer, Berlin, 2002
      3. B. Lapeyre, E. Pardoux, and R. Sentis, Introduction to Monte-Carlo Methods for Transport and Diffusion Equations, Oxford University Press, 2003.
      4. B. Oksendal. Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin, 2003
      5. Lord, G. J., Powell, C. E., and Shardlow, T. An introduction to computational stochastic PDEs (Vol. 50). Cambridge University Press, 2014
    • 19223901 Lecture
      Uncertainty Quantification and Quasi-Monte Carlo (Claudia Schillings)
      Schedule: Mo 10:00-12:00 (Class starts on: 2025-04-14)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Comments

      High-dimensional numerical integration plays a central role in contemporary study of uncertainty quantification. The analysis of how uncertainties associated with material parameters or the measurement configuration propagate within mathematical models leads to challenging high-dimensional integration problems, fueling the need to develop efficient numerical methods for this task. Modern quasi-Monte Carlo (QMC) methods are based on tailoring specially designed cubature rules for high-dimensional integration problems. By leveraging the smoothness and anisotropy of an integrand, it is possible to achieve faster-than-Monte Carlo convergence rates. QMC methods have become a popular tool for solving partial differential equations (PDEs) involving random coefficients, a central topic within the field of uncertainty quantification. This course provides an introduction to uncertainty quantification and how QMC methods can be applied to solve problems arising within this field.

      Suggested reading

      The following books will be relevant:

      • O. P. Le Maître and O. M. Knio. Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics. Scientific Computation. Springer, New York, 2010.
      • R. C. Smith. Uncertainty Quantification: Theory, Implementation, and Applications, volume 12 of Computational Science & Engineering. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2014.
      • T. J. Sullivan. Introduction to Uncertainty Quantification. Springer, New York, in press.
      • D. Xiu. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton University Press, Princeton, NJ, 2010.
    • 19229601 Lecture Cancelled
      Stochastic dynamics in fluids (Felix Höfling)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Additional information / Pre-requisites

      Target audience: M.Sc. Computational Sciences/Mathematik/Physik

      Requirements: some advanced course on either statistical physics or stochastic processes

      Comments

      The liquid state comprises a large class of materials ranging from simple fluids (argon, methane) and molecular fluids (water) to soft matter systems such as polymer solutions (ketchup), colloidal suspensions (wall paint), and heterogeneous media (cell cytoplasm). The basic transport mode in liquids is that of diffusion due to thermal fluctuations, but already the simplest liquids exhibit a non-trivial dynamic response well beyond standard Brownian motion. From the early days of the field, computer simulations have played a central role in identifying complex dynamics and testing the approximations of their theoretical descriptions. On the other hand, theory imposes constraints on the analysis of experimental or simulation data.

      The course is at the interface of probability theory and statistical mechanics. Noting that fluids constitute high-dimensional stochastic processes, I will give an introduction to the principles of liquid state theory, and we will derive the mathematical structure of the relevant correlation functions. The second part makes contact to recent research and gives an overview on selected topics. The exercises are split into a theoretical part, discussed in biweekly lessons, and a practical part in form of a small simulation project conducted during a block session (2 days) after the lecture phase.

      Keywords:

      • Brownian motion, diffusion, and stochastic processes in fluids
      • harmonic analysis of correlation functions
      • Zwanzig-Mori projection operator formalism
      • mode-coupling approximations, long-time tails
      • critical dynamics and transport anomalies

      Suggested reading

      • Hansen and McDonald: Theory of simple liquids (Academic Press, 2006).
      • Höfling and Franosch, Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602 (2013).

      Further literature will be given during the course.
    • 19234501 Lecture
      Mathematical strategies for complex stochastic dynamics (Wei Zhang)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-23)
      Location: T9/053 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Prerequisites: Basic knowledge of stochastics, and numerical methods

      Comments

      Content:

      Stochastic dynamics are widely studied in scientific fields such as physics, biology, and climate. Understanding these dynamics is often challenging due to their high dimensionality and multiscale characteristics. This lecture provides an introduction to theoretical and numerical techniques, including machine learning techniques, for studying such complex stochastic dynamics. The following topics will be covered:

      - Basic of stochastic processes:

      Langevin dynamics, overdamped Langevin dynamics, Markov chains, generators and Fokker-Planck equation, convergence to equilibrium, Ito’s formula

      - Model reduction techniques for stochastic dynamics:

      averaging technique, effective dynamics, Markov state modeling

      - Machine learning techniques using/for stochastic dynamics: 

      dynamics of stochastic gradient descent, autoencoders, solving eigenvalue problems by deep learning, generative modeling using diffusion models, continuous normalizing flow, or flow-matching

      Suggested reading

      1) Bernt Øksendal. Stochastic Differential Equations: An Introduction with Applications. 5th. Springer, 2000

      2) Kevin P. Murphy. Probabilistic Machine Learning: An introduction. MIT Press, 2022. url: probml.ai

      3) J.-H. Prinz et al. “Markov models of molecular kinetics: Generation and validation”. In: J. Chem. Phys. 134.17, 174105 (2011), p. 174105

      4) W. Zhang, C. Hartmann, and C. Schütte. “Effective dynamics along given reaction coordinates and reaction rate theory”. In: Faraday Discuss. 195 (2016), pp. 365–394

      5) Mardt, A., Pasquali, L., Wu, H. et al. VAMPnets for deep learning of molecular kinetics. Nat Commun 9, 5 (2018).

      6)  Score-Based Generative Modeling through Stochastic Differential Equations, Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole, ICLR 2021.
    • 19240701 Lecture
      Functional Analysis Applied to Modeling of Molecular Systems (Luigi Delle Site)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-15)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      Die Vorlesung findet Dienstags von 14-16 Uhr in der Arnimallee 9 statt.

      Die Übung findet Montags von von 14-16 Uhr in der Arnimallee 9 statt.

      Comments

      Prpgram:

      -Existence of ordinary matter as a mathematical problem -the existence of the thermodynamic limit -One concrete way to model molecules: Density Functional theory and its mathematical structure -Existence/non-existence of relativistic matter, Dirac Operator on scalar fields -Spinors, Second Quantization and Fock space

    • 19242101 Lecture
      Stochastics IV: (Guilherme de Lima Feltes, Nicolas Perkowski)
      Schedule: Mi 10:00-12:00 (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Prerequisite: Stochastics I, II, III. 
      Recommended: Functional Analysis.

      Comments

      Content: We will learn two different methods for solving stochastic partial differential equations. The classical method is based on Ito calculus, and we will use it to solve semilinear SPDEs with space-time white noise in one space dimension. But we will see that in higher dimensions this theory only works for linear equations, and motivated by that we will introduce "paracontrolled distributions“, which we developed in the last years based on ideas from harmonic analysis and rough paths, and which allow us to solve some interesting semilinear equations in higher dimensions. Along the way we will learn about regularity theory for semilinear PDEs, Gaussian Hilbert spaces, and much more.

      • Ito calculus for Gaussian random measures;
      • semilinear stochastic PDEs in one dimension;
      • Schauder estimates;
      • Gaussian hypercontractivity;
      • paraproducts and paracontrolled distributions;
      • local existence and uniqueness for semilinear SPDEs in higher dimensions;
      • properties of solutions

      Detailed Information can be found on the Homepage of 19246301 SPDEs: Classical and New.

      Suggested reading

      Literature
      There will be lecture notes.
    • 19243001 Lecture
      Partial Differential Equations III (Erica Ipocoana)
      Schedule: Di 08:00-10:00 (Class starts on: 2025-04-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Voraussetzungen: Partielle Differentialgleichungen I und II

      Comments

      The course builds upon the the PDE II course offered in the previous winter term. Methods for boundary value problems of elliptic PDEs are deepend. A central aspect of the course are variational methods, in particular multi-dimensional calculus of variations. 

       

      Suggested reading

      Wird in der Vorlesung bekannt gegeben / to be announced.
    • 19207102 Practice seminar
      Partial differential equations with multiple scales: Theory and computation (Rupert Klein)
      Schedule: Mi 14:00-16:00 (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)
    • 19215002 Practice seminar
      Constructive Combinatorics exercises (Tibor Szabo)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Comments

      Abstract:
      Despite the effectiveness of the probabilistic method in extremal combinatorics, explicit constructive approaches remain of paramount importance. On the one hand, they are often superior to purely existential arguments, and, even when they are not, the search for the most efficient deterministic combinatorial structure is naturally motivated by questions of complexity.
      The course discusses classic Turan- and Ramsay-type problems of extremal combinatorics from this constructive perspective.
      Besides combinatorics, the methods often involve algebraic and probabilistic techniques (affine and projective geometries over finite fields, eigenvalues and quasirandom graphs, the discrete Fourier transform).
      For further details please check Prof. Szabó's homepage.
    • 19215302 Practice seminar
      Practice seminar for Mathematical Modelling in Climate Research (Rupert Klein)
      Schedule: Di 16:00-18:00 (Class starts on: 2025-04-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)
    • 19222602 Practice seminar
      Practice seminar for Numerical methods for stochastic differential equations (Ana Djurdjevac)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-17)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19223902 Practice seminar
      Übung zu UQ and QMC (Claudia Schillings)
      Schedule: Di 10:00-12:00 (Class starts on: 2025-04-15)
      Location: A3/SR 120 (Arnimallee 3-5)
    • 19229602 Practice seminar Cancelled
      Exercises to Stochastic processes in fluids (Felix Höfling)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-04-29)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)
    • 19234502 Practice seminar
      Practice seminar for Mathematical strategies for complex stochastic dynamics (Wei Zhang)
      Schedule: Fr 10:00-12:00 (Class starts on: 2025-04-25)
      Location: T9/046 Seminarraum (Takustr. 9)

      Comments

      Concrete and simple stochastic dynamics will be studied to illustrate analytical and numerical techniques. Numerical methods will be demonstrated using Jupyter Notebook.
    • 19240702 Practice seminar
      Practice seminar for Functional Analysis applied to modeling of molecular systems (Luigi Delle Site)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-04-14)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).
    • 19242102 Practice seminar
      Exercise: Stochastics IV (Guilherme de Lima Feltes)
      Schedule: Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)
    • 19243002 Practice seminar
      Tutorial Partial Differential Equations III (Erica Ipocoana)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-04-24)
      Location: A3/SR 119 (Arnimallee 3-5)

  • Complementary Module: Current Research Topics A

    0280cA4.7
    • 19206011 Seminar
      Discrete Mathematics Masterseminar (Tibor Szabo)
      Schedule: Fr 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-11)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

       

       

      Comments

      Content:
      The seminar covers advanced topics in Extremal and Probabilistic Combinatorics.
      Target audience:
      BMS students, Master students, or advanced Bachelor students.
      Prerequisites:
      Prerequisite is the successful completion of the modul Discrete Mathematics II or III (or equivalent background: please contact the instructor).

       
    • 19226511 Seminar
      Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      Audience: At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

      Comments

      Content: The seminar will concern the discussion of state-of-art techniques in molecular simulation which allow for a simulation of several space (especially) and time scale within one computational approach.

      The discussion will concerns both, specific computational coding and conceptual developments.

      Suggested reading

      Related Basic Literature:

      (1) M.Praprotnik, L.Delle Site and K.Kremer, Ann.Rev.Phys.Chem.59, 545-571 (2008)

      (2) C.Peter, L.Delle Site and K.Kremer, Soft Matter 4, 859-869 (2008).

      (3) M.Praprotnik and L.Delle Site, in "Biomolecular Simulations: Methods and Protocols" L.Monticelli and E.Salonen Eds. Vol.924, 567-583 (2012) Methods Mol. Biol. Springer-Science
    • 19226611 Seminar
      Seminar Quantum Computational Methods (Luigi Delle Site)
      Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

      Die Veranstaltung findet Mittwochs von 12-14 Uhr in der Arnimallee 9 statt.

      Comments

      The seminar will focus on the literature related to the most popular molecular simulation methods for quantum mechanical systems.
      In particular we will read and discuss the paper at the foundation of Path Integral Molecular Dynamics, Quantum Monte Carlo techniques and Density Functional Theory. A new development became relevant in the last yeras, i.e. quantum calculations on quantum computers, part of the seminar will treat also such novel aspects.
      Moreover the reading and the discussion will be complemented by paper about the latest developments and applications of the methods.

      Suggested reading

      Related Basic Literature:
      (1) David M.Ceperley, Reviews of Modern Physics 67 279 (1995)
      (2) Miguel A. Morales, Raymond Clay, Carlo Pierleoni, and David M. Ceperley, Entropy 2014, 16(1), 287-321
      (3) P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864-B871
    • 19227611 Seminar
      Seminar Uncertainty Quantification & Inverse Problems (Claudia Schillings)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-24)
      Location: A3/SR 115 (Arnimallee 3-5)

      Comments

      The seminar covers advanced topics of uncertainty quantification and inverse problems.
    • 19239711 Seminar
      Advanced Dynamical Systems (Bernold Fiedler)
      Schedule: Do 16:00-18:00 (Class starts on: 2025-04-17)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Students present recent papers on topics in delay equations. Dates only by arrangement.
    • 19239911 Seminar
      Advanced Differential Equations (Bernold Fiedler)
      Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Students present recent papers on topics in dynamical systems. Dates only by arrangement.
    • 19247111 Seminar
      Variational methods & Gamma-convergence (Marita Thomas)
      Schedule: Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Comments

      This seminar addresses bachelor and master students interested in the analysis of partial differential equations (PDEs). It focuses on elliptic PDEs, where the direct method of the calculus of variations provides a powerful tool to handle linear as well as nonlinear problems by investigating the minimality properties of the functional associated with the PDE. Closely related to this is the method of Gamma-convergence, which allows it to study sequences of functionals and minimization problems. A background with courses in analysis, functional analysis, and introduction to PDEs is useful to attend the seminar, but the topics for the presentations will be adapted to the background of the participants.   The main part of the seminar will be held en block in the teaching-free period.

  • Complementary Module: Current Research Topics B

    0280cA4.8
    • 19206011 Seminar
      Discrete Mathematics Masterseminar (Tibor Szabo)
      Schedule: Fr 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-11)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

       

       

      Comments

      Content:
      The seminar covers advanced topics in Extremal and Probabilistic Combinatorics.
      Target audience:
      BMS students, Master students, or advanced Bachelor students.
      Prerequisites:
      Prerequisite is the successful completion of the modul Discrete Mathematics II or III (or equivalent background: please contact the instructor).

       
    • 19226511 Seminar
      Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      Audience: At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

      Comments

      Content: The seminar will concern the discussion of state-of-art techniques in molecular simulation which allow for a simulation of several space (especially) and time scale within one computational approach.

      The discussion will concerns both, specific computational coding and conceptual developments.

      Suggested reading

      Related Basic Literature:

      (1) M.Praprotnik, L.Delle Site and K.Kremer, Ann.Rev.Phys.Chem.59, 545-571 (2008)

      (2) C.Peter, L.Delle Site and K.Kremer, Soft Matter 4, 859-869 (2008).

      (3) M.Praprotnik and L.Delle Site, in "Biomolecular Simulations: Methods and Protocols" L.Monticelli and E.Salonen Eds. Vol.924, 567-583 (2012) Methods Mol. Biol. Springer-Science
    • 19226611 Seminar
      Seminar Quantum Computational Methods (Luigi Delle Site)
      Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

      Die Veranstaltung findet Mittwochs von 12-14 Uhr in der Arnimallee 9 statt.

      Comments

      The seminar will focus on the literature related to the most popular molecular simulation methods for quantum mechanical systems.
      In particular we will read and discuss the paper at the foundation of Path Integral Molecular Dynamics, Quantum Monte Carlo techniques and Density Functional Theory. A new development became relevant in the last yeras, i.e. quantum calculations on quantum computers, part of the seminar will treat also such novel aspects.
      Moreover the reading and the discussion will be complemented by paper about the latest developments and applications of the methods.

      Suggested reading

      Related Basic Literature:
      (1) David M.Ceperley, Reviews of Modern Physics 67 279 (1995)
      (2) Miguel A. Morales, Raymond Clay, Carlo Pierleoni, and David M. Ceperley, Entropy 2014, 16(1), 287-321
      (3) P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864-B871
    • 19227611 Seminar
      Seminar Uncertainty Quantification & Inverse Problems (Claudia Schillings)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-24)
      Location: A3/SR 115 (Arnimallee 3-5)

      Comments

      The seminar covers advanced topics of uncertainty quantification and inverse problems.
    • 19239711 Seminar
      Advanced Dynamical Systems (Bernold Fiedler)
      Schedule: Do 16:00-18:00 (Class starts on: 2025-04-17)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Students present recent papers on topics in delay equations. Dates only by arrangement.
    • 19239911 Seminar
      Advanced Differential Equations (Bernold Fiedler)
      Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Students present recent papers on topics in dynamical systems. Dates only by arrangement.
    • 19247111 Seminar
      Variational methods & Gamma-convergence (Marita Thomas)
      Schedule: Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Comments

      This seminar addresses bachelor and master students interested in the analysis of partial differential equations (PDEs). It focuses on elliptic PDEs, where the direct method of the calculus of variations provides a powerful tool to handle linear as well as nonlinear problems by investigating the minimality properties of the functional associated with the PDE. Closely related to this is the method of Gamma-convergence, which allows it to study sequences of functionals and minimization problems. A background with courses in analysis, functional analysis, and introduction to PDEs is useful to attend the seminar, but the topics for the presentations will be adapted to the background of the participants.   The main part of the seminar will be held en block in the teaching-free period.

  • Complementary Module: Current Research Topics C

    0280cA4.9
    • 19206011 Seminar
      Discrete Mathematics Masterseminar (Tibor Szabo)
      Schedule: Fr 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-11)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Additional information / Pre-requisites

       

       

      Comments

      Content:
      The seminar covers advanced topics in Extremal and Probabilistic Combinatorics.
      Target audience:
      BMS students, Master students, or advanced Bachelor students.
      Prerequisites:
      Prerequisite is the successful completion of the modul Discrete Mathematics II or III (or equivalent background: please contact the instructor).

       
    • 19226511 Seminar
      Seminar Multiscale Methods in Molecular Simulations (Luigi Delle Site)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      Audience: At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

      Comments

      Content: The seminar will concern the discussion of state-of-art techniques in molecular simulation which allow for a simulation of several space (especially) and time scale within one computational approach.

      The discussion will concerns both, specific computational coding and conceptual developments.

      Suggested reading

      Related Basic Literature:

      (1) M.Praprotnik, L.Delle Site and K.Kremer, Ann.Rev.Phys.Chem.59, 545-571 (2008)

      (2) C.Peter, L.Delle Site and K.Kremer, Soft Matter 4, 859-869 (2008).

      (3) M.Praprotnik and L.Delle Site, in "Biomolecular Simulations: Methods and Protocols" L.Monticelli and E.Salonen Eds. Vol.924, 567-583 (2012) Methods Mol. Biol. Springer-Science
    • 19226611 Seminar
      Seminar Quantum Computational Methods (Luigi Delle Site)
      Schedule: Mi 12:00-14:00 (Class starts on: 2025-04-16)
      Location: Die Veranstaltung findet in der Arnimallee 9 statt (Seminarraum).

      Additional information / Pre-requisites

      At least 6th semester with a background in statistical and quantum mechanics, Master students and PhD students (even postdocs) are welcome.

      Die Veranstaltung findet Mittwochs von 12-14 Uhr in der Arnimallee 9 statt.

      Comments

      The seminar will focus on the literature related to the most popular molecular simulation methods for quantum mechanical systems.
      In particular we will read and discuss the paper at the foundation of Path Integral Molecular Dynamics, Quantum Monte Carlo techniques and Density Functional Theory. A new development became relevant in the last yeras, i.e. quantum calculations on quantum computers, part of the seminar will treat also such novel aspects.
      Moreover the reading and the discussion will be complemented by paper about the latest developments and applications of the methods.

      Suggested reading

      Related Basic Literature:
      (1) David M.Ceperley, Reviews of Modern Physics 67 279 (1995)
      (2) Miguel A. Morales, Raymond Clay, Carlo Pierleoni, and David M. Ceperley, Entropy 2014, 16(1), 287-321
      (3) P. Hohenberg and W. Kohn, Phys. Rev. 136 (1964) B864-B871
    • 19227611 Seminar
      Seminar Uncertainty Quantification & Inverse Problems (Claudia Schillings)
      Schedule: Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-24)
      Location: A3/SR 115 (Arnimallee 3-5)

      Comments

      The seminar covers advanced topics of uncertainty quantification and inverse problems.
    • 19239711 Seminar
      Advanced Dynamical Systems (Bernold Fiedler)
      Schedule: Do 16:00-18:00 (Class starts on: 2025-04-17)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Students present recent papers on topics in delay equations. Dates only by arrangement.
    • 19239911 Seminar
      Advanced Differential Equations (Bernold Fiedler)
      Schedule: Do 14:00-16:00 (Class starts on: 2025-04-17)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Students present recent papers on topics in dynamical systems. Dates only by arrangement.
    • 19247111 Seminar
      Variational methods & Gamma-convergence (Marita Thomas)
      Schedule: Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Comments

      This seminar addresses bachelor and master students interested in the analysis of partial differential equations (PDEs). It focuses on elliptic PDEs, where the direct method of the calculus of variations provides a powerful tool to handle linear as well as nonlinear problems by investigating the minimality properties of the functional associated with the PDE. Closely related to this is the method of Gamma-convergence, which allows it to study sequences of functionals and minimization problems. A background with courses in analysis, functional analysis, and introduction to PDEs is useful to attend the seminar, but the topics for the presentations will be adapted to the background of the participants.   The main part of the seminar will be held en block in the teaching-free period.

  • Statistics I for Students of Life Sciences

    0260cA2.5
    • 60100001 Lecture
      Statistics I for bioinformatics (Konrad Neumann)
      Schedule: Do 16:00-18:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-17)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Additional information / Pre-requisites

       

       

                     

      Comments

      Content:

      see German desciption

                     

    • 60100002 Practice seminar
      Practice seminar for Statistics I for bioinformatics (Konrad Neumann)
      Schedule: Mi 16:00-18:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: A7/SR 031 (Arnimallee 7)

  • Molecular Biology and Biochemistry I

    0260cA3.3
    • 21601a Lecture
      Biochemistry I - Fundamentals of Biochemistry (Helge Ewers, Florian Heyd, Markus Wahl)
      Schedule: Mi 12:00 - 14:00 Uhr; Vorbesprechung Di, 15.04.25, 12:00 - 14:00 Uhr (HS Anorganik Fabeckstraße 34/36)) (Class starts on: 2025-04-15)
      Location: Hs Anorganik (Fabeckstr. 34 / 36)

      Information for students

      Entspricht Molekularbiologie und Biochemie I für Bioinformatiker.

      Comments

      Qualifikationsziele:
      Die Studentinnen und Studenten kennen die Entstehung und molekulare Struktur der wichtigsten zellulären Makromoleküle und Stoffklassen sowie ihren biologischen Kontext. Der Schwerpunkt liegt auf einem chemischen Grundverständnis des molekularen Aufbaus von Biomolekülen.

      Inhalte:
      Chemische und zellbiologische Grundlagen, Struktur von DNA und RNA, Replikation und Transkription, Proteinbiosynthese, Regulation der Genexpression, gentechnologische Methoden, Aminosäuren und Peptide, Proteinstruktur und Proteinfaltung, Proteom, posttranslationale Modifikationen, Methoden der Proteinforschung, Enzyme, Kohlenhydrate, Lipide und Biomembranen, Einführung in den Stoffwechsel und die Stoffwechselregulation.

      Prof. Dr. H. Ewers: helge.ewers@fu-berlin.de
      Prof. Dr. F. Heyd: florian.heyd@fu-berlin.de
      Prof. Dr. M. Wahl: mwahl@zedat.fu-berlin.de

    • 21601b Practice seminar
      Tutorial for Biochemistry I - Fundamentals of Biochemistry (Helge Ewers, Florian Heyd, Markus Wahl)
      Schedule: Di/Mi 22.4.25-17.7.25 (s. Lektionen, LV-Details) (Class starts on: 2025-04-22)
      Location: Ort nach Ansage je nach Übungsgruppe

      Additional information / Pre-requisites

      Die Übungen finden n.V. in kleineren Gruppen i.d.R. dienstags von 12:00 - 14:00 Uhr bzw. mittwochs von 10:00 - 12:00 Uhr Uhr statt. Die Verteilung findet im Rahmen der Vorbesprechung (s. 21601a) statt.

      Comments

      Qualifikationsziele: Die Studentinnen und Studenten kennen die Entstehung und molekulare Struktur der wichtigsten zellulären Makromoleküle und Stoffklassen sowie ihren biologischen Kontext. Der Schwerpunkt liegt auf einem chemischen Grundverständnis des molekularen Aufbaus von Biomolekülen. Inhalte: Chemische und zellbiologische Grundlagen, Struktur von DNA und RNA, Replikation und Transkription, Proteinbiosynthese, Regulation der Genexpression, gentechnologische Methoden, Aminosäuren und Peptide, Proteinstruktur und Proteinfaltung, Proteom, posttranslationale Modifikationen, Methoden der Proteinforschung, Enzyme, Kohlenhydrate, Lipide und Biomembranen, Einführung in den Stoffwechsel und die Stoffwechselregulation. Prof. Dr. H. Ewers: helge.ewers@fu-berlin.de Prof. Dr. F. Heyd: florian.heyd@fu-berlin.de Prof. Dr. M. Wahl: mwahl@zedat.fu-berlin.de

  • Molecular Biology and Biochemistry III

    0260cA3.5
    • 21699a Lecture
      Molecular Biology and Biochemistry III (Sutapa Chakrabarti, Sigmar Stricker, Holger Sieg)
      Schedule: erster Termin: Fr. 25.04.2025, 10:15 - 11:45 (Class starts on: 2025-04-25)
      Location: Hörsaal Thielallee 67

      Information for students

      Vorlesung für Studierende der Bioinformatik

      UN Sustainable Development Goals (SDGs): 3, <a

      Additional information / Pre-requisites

      Qualification goals: The basic understanding acquired in Molecular Biology and Biochemistry II is placed in the context of complex biological systems. These are: Understanding of receptor-mediated signal transduction and the regulation of cell cycle and cell death. Understanding the molecular biological and cell biological properties of metastatic tumor cells Understanding the interactions of pathogens, host cells and the immune system Understanding of the principles of DNA medicine Contents: Growth factors, receptors and signal transduction for the regulation of cell cycle and cell death Fundamentals of immunology: innate, acquired immune defense Antigen-presenting cells, effector cells PAMP and DAMP concepts of antigen processing in infection and tumor control DNA medicine and gene therapy

    • 21699b Practice seminar
      Tutorial - Molecular Biology and Biochemistry III (Sutapa Chakrabarti, Sigmar Stricker, Holger Sieg)
      Schedule: erster Termin: Mi. 30.04.2025, 12:15-13:45 h (Class starts on: 2025-04-30)
      Location: Hörsaal Thielallee 67

      Information for students

      Übungen zu 21699a für Studierende der Bioinformatik

      UN Sustainable Development Goals (SDGs): 3, 14, 15

      Additional information / Pre-requisites

      Qualifikationsziele:
      Das in Molekularbiologie und Biochemie II erlangte Grundlagenverständnis wird in den Zusammenhang komplexer biologischer Systeme gestellt. Diese sind:
      Verständnis der Rezeptorvermittelten Signaltransduktion und der Regulation von Zellzyklus und Zelltod.
      Verständnis der molekularbiologischen und zellbiologischen Eigenschaften von metastasierenden Tumorzellen
      Verständnis der Wechselwirkungen von Pathogenen, Wirtszellen und Immunsystem
      Verständnis der Prinzipien der DNA-Medizin

      Inhalte:
      Wachstumsfaktoren, Rezeptoren und Signaltransduktion zur Regulation von Zellzyklus und Zelltod
      Grundlagen der Immunologie: angeborene, erworbene Immunabwehr
      Antigen-präsentierende Zellen, Effektorzellen
      PAMP- und DAMP-Konzepte der Antigen-Prozessierung bei Infektion und Tumor-Bekämpfung
      DNA-Medizin und Gentherapie

      Comments

      Qualification goals: 
      The basic understanding acquired in Molecular Biology and Biochemistry II is placed in the context of complex biological systems. These are:
      Understanding of receptor-mediated signal transduction and the regulation of cell cycle and cell death. 
      Understanding the molecular biological and cell biological properties of metastatic tumor cells 
      Understanding the interactions of pathogens, host cells and the immune system 
      Understanding of the principles of DNA medicine 

      Contents:
      Growth factors, receptors and signal transduction for the regulation of cell cycle and cell death 
      Fundamentals of immunology: innate, acquired immune defense 
      Antigen-presenting cells, effector cells 
      PAMP and DAMP concepts of antigen processing in infection and tumor control 
      DNA medicine and gene therapy 

  • Medical Physiology

    0260cA3.7

  • Data Structures and Data Abstraction with Applications

    0084dB2.8
    • 19300101 Lecture
      Algorithms and Data Structures (Wolfgang Mulzer)
      Schedule: Di 16:00-18:00, Fr 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: Gr. Hörsaal (Raum B.001) (Arnimallee 22)

      Comments

      Qualification goals

      The students can analyze algorithms and data structures and their implementations with respect to running time, space requirements, and correctness. The students can describe different algorithms and data structures for typical applications and know how to use them in concrete settings. They can choose appropriate algorithms and data structures for a given task and are able to adapt them accordingly. Students can explain, identify and use different paradigms for designing new algorithms.

      Contents

      • abstract machine models
      • running time, correctness and space requirements
      • worst-case analysis
      • algorithms and randomness
      • algorithmic paradigms: divide and conquer, greedy, dynamic programming, exhaustive search
      • priority queues
      • ordered and unordered dictionaries (e.g., search trees, hash tables, skiplists)
      • algorithms for strings (string searching and radix trees)
      • graph algorithms 

      Suggested reading

      • P. Morin: Open Data Structures, an open content textboox.
      • T. H. Cormen, C. Leiserson, R. Rivest, C. Stein: Introduction to Algorithms, MIT Press, 2022.
      • R. Sedgewick, K. Wayne: Algorithms, Addison-Wesley, 2011.
      • M. Dietzfelbinger, K. Mehlhorn, P. Sanders. Algorithmen und Datenstrukturen: Die Grundwerkzeuge, Springer, 2014.
      • J. Erickson. Algorithms, 2019
      • T. Roughgarden. Algorithms Illuminated. Cambridge University Press, 2022.
    • 19300102 Practice seminar
      Practice seminar for Algorithms and Data Structures (Wolfgang Mulzer)
      Schedule: Mo 14:00-16:00, Mo 16:00-18:00, Di 12:00-14:00, Mi 12:00-14:00, Mi 14:00-16:00, Mi 16:00-18:00, Do 16:00-18:00, Fr 14:00-16:00, Fr 16:00-18:00 (Class starts on: 2025-04-14)
      Location: T9/051 Seminarraum (Takustr. 9)

  • Modules w/o courses in this semester

    118 Modules
    • Image Processing 0089cA1.1
    • Medical Image Processing 0089cA1.10
    • Model-driven Software Development 0089cA1.11
    • Pattern Recognition 0089cA1.12
    • Network-Based Information Systems 0089cA1.13
    • Project Management 0089cA1.14
    • Project Management (Specialization) 0089cA1.15
    • Computer Security 0089cA1.16
    • Semantic Business Process Management 0089cA1.17
    • Software Processes 0089cA1.18
    • Compiler Construction 0089cA1.19
    • Computer Graphics 0089cA1.2
    • Distributed Systems 0089cA1.20
    • XML Technology 0089cA1.21
    • Practices in Professional Software Development 0089cA1.22
    • Advanced Topics in Data Management 0089cA1.29
    • Computer Vision 0089cA1.3
    • Database Technology 0089cA1.4
    • Fundamentals of Software Testing 0089cA1.7
    • Artificial Intelligence 0089cA1.9
    • Starting a Business in IT 0159cA2.2
    • Advanced Algorithms 0089cA2.1
    • Model Checking 0089cA2.2
    • Cryptography and Security in Distributed Systems 0089cA2.8
    • Semantics of Programming Languages 0089cA2.9
    • Operating Systems 0089cA3.1
    • Selected Topics in Technical Computer Science 0089cA3.12
    • Telematics 0089cA3.5
    • Analysis III 0084dA1.3
    • Computer-Oriented Mathematics I 0084dA1.6
    • Probability and Statistics I 0084dA1.8
    • Higher Analysis 0084dB2.1
    • Current Topics in Mathematics 0084dB2.10
    • Special topics in Pure Mathematics 0084dB2.12
    • Special topics in Applied Mathematics 0084dB2.13
    • Functional Analysis 0084dB2.2
    • Probability and Statistics II 0084dB2.4
    • Algebra and Number Theroy 0084dB2.5
    • Elementary Geometry 0084dB2.6
    • Algebra I 0084dB3.3
    • Numerical Mathematics II 0084dB3.4
    • Differential Geometry I 0084dB3.5
    • Advanced and Applied Algorithms 0084dB3.7
    • Visualization 0084dB3.8.
    • Computer Algebra 0162bA1.2
    • Statistics Software (CoSta) 0162bA1.3
    • Introduction to Visualization 0162bA1.4
    • Panorama of Mathematics 0162bA1.5
    • Introductory Module: Differential Geometry I 0280bA1.1
    • Introductory Module: Differential Geometry II 0280bA1.2
    • Advanced Module: Differential Geometry III 0280bA1.3
    • Research Module: Differential Geometry 0280bA1.4
    • Introductory Module: Algebra I 0280bA2.1
    • Advanced Module: Algebra III 0280bA2.3
    • Research Module: Algebra 0280bA2.4
    • Introductory Module: Discrete Mathematics II 0280bA3.2
    • Introductory Module: Discrete Geometry I 0280bA3.3
    • Advanced Module: Discrete Geometry III 0280bA3.6
    • Research Module: Discrete Geometry 0280bA3.8
    • Introductory Module: Topology II 0280bA4.2
    • Introductory Module: Visualization 0280bA4.3
    • Advanced Module: Topology III 0280bA4.4
    • Introductory Module: Numerical Analysis II 0280bA5.1
    • Research Module: Numerical Mathematics 0280bA5.4
    • Introductory Module: Differential Equations II 0280bA6.2
    • Research Module: Applied Analysis and Differential Equations 0280bA6.4
    • Complementary Module: Research Project 0280bA7.6
    • Complementary Module: Probability and Statistics II 0280bA7.7
    • Introductory Module: Algebra I 0280cA1.1
    • Introductory Module: Dynamical Systems II 0280cA1.10
    • Introductory Module: Numerical Mathematics II 0280cA1.11
    • Introductory Module: Partial Differential Equations II 0280cA1.14
    • Introductory Module: Probability and Statistics II 0280cA1.15
    • Introductory Module: Probability and Statistics III 0280cA1.16
    • Introductory Module: Topology II 0280cA1.18
    • Introductory Module: Number Theory II 0280cA1.19
    • Introductory Module: Differential Geometry I 0280cA1.3
    • Introductory Module: Differential Geometry II 0280cA1.4
    • Introductory Module: Discrete Geometry I 0280cA1.5
    • Introductory Module: Discrete Mathematics II 0280cA1.8
    • Advanced Module: Algebra III 0280cA2.1
    • Advanced Module: Number Theory III 0280cA2.10
    • Advanced Module: Differential Geometry III 0280cA2.2
    • Advanced Module: Discrete Geometry III 0280cA2.3
    • Advanced Module: Dynamical Systems III 0280cA2.5
    • Advanced Module: Topology III 0280cA2.9
    • Specialization Module: Master's Seminar on Algebra 0280cA3.1
    • Specialization Module: Master's Seminar on Number Theory 0280cA3.10
    • Specialization Module: Master's Seminar on Differential Geometry 0280cA3.2
    • Specialization Module: Master's Seminar on Discrete Geometry 0280cA3.3
    • Specialization Module: Master’s Seminar on Dynamical Systems 0280cA3.5
    • Specialization Module: Master’s Seminar on Probability and Statistics 0280cA3.8
    • Complementary Module: Research Project 0280cA4.11
    • Algorithmic Bioinformatics 0260cA1.5
    • Statistics II for Students of Life Sciences 0260cA2.6
    • General Chemistry 0260cA3.1
    • Molecular Biology and Biochemistry II 0260cA3.4
    • Genetics and Genome Research 0260cA3.6
    • Neurobiology 0260cA3.8
    • Biodiversity and Evolution 0262bB1.1
    • Medical Bioinformatics 0262bB1.2
    • Network Analysis 0262bB1.3
    • Physiology 0262bB1.4
    • Sequence Analysis 0262bB1.5
    • Structural Bioinformatics 0262bB1.6
    • Current Topics in Cell Physiology 0262bB2.1
    • Applied Sequence Analysis 0262bB2.2
    • Measurement and Analysis of Physiological Processes 0262bB2.3
    • Computational Systems Biology 0262bB2.4
    • Environmental Metagenomics 0262bB2.5
    • Current Topics in Medical Genomics 0262bB2.6
    • Current Topics in Structural Bioinformatics 0262bB2.7
    • Research Modules: Module A 0262bB3.1
    • Research Modules: Module B 0262bB3.2
    • Applied Modules: All Other Subjects 0089cD9.1
    • Elective Area (all other subjects) 0089cD9.2
    • Elective Area (all other subjects) 0089cD9.3
    • Elective Area (all other subjects) 0089cD9.4