Computer Science

• Analysis I

  0084dA1.1
  • 19202801 Lecture
    Analysis I (Elena Mäder-Baumdicker)
    Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
    Location: T9/Gr. Hörsaal (Takustr. 9)
    

    Comments

    Content:
    This is the first part of a three semester introduction into the basic mathematical field of Analysis. Differential and integral calculus in a real variable will be covered. Topics:

    1. fundamentals, elementary logic, ordered pairs, relations, functions, domain and range of a function, inverse functions (injectivity, surjectivity)
    2. numbers, induction, calculations in R, C
    3. arrangement of R, maximum and minimum, supremum and infimum of real sets, supremum / infimum completeness of R, absolute value of a real number, Q is dense in R
    4. sequences and series, limits, cauchy sequences, convergence criteria, series and basic principles of convergence
    5. topological aspects of R, open, closed, and compact real sets
    6. sequences of functions, series of functions, power series
    7. properties of functions, boundedness, monotony, convexity
    8. continuity, limits and continuity of functions, uniform continuity, intermediate value theorems, continuity and compactness
    9. differentiability, concept of the derivative, differentiation rules, mean value theorem, local and global extrema, curvature, monotony, convexity
    10. elementary functions, rational functions, root functions, exponential functions, angular functions, hyperbolic functions, real logarithm, inverse trigonometric functions, curve sketching
    11. beginnings of integral calculus

     

    Suggested reading

    Literature:

    • Bröcker, Theodor: Analysis 1, Spektrum der Wissenschaft-Verlag.
    • Forster, Otto: Analysis 1, Vieweg-Verlag.
    • Spivak, Michael: Calculus, 4th Edition.

    Viele Analysis Bücher sind auch über die Fachbibliothek der FU Berlin elektronisch verfügbar.

    Bei Schwierigkeiten mit den Grundbegriffen Menge, Abbildung etc. ist die folgende Ausarbeitung empfehlenswert:

    • Scheerer, Hans: Brückenkurs, Skript FU Berlin 2006.

  • 19202802 Practice seminar
    Tutorial: Analysis I (Elena Mäder-Baumdicker)
    Schedule: Mi 12:00-14:00, Mi 14:00-16:00, Fr 08:00-10:00, Fr 10:00-12:00 (Class starts on: 2025-10-15)
    Location: Mi A3/SR 119 (Arnimallee 3-5), Fr A3/SR 119 (Arnimallee 3-5), Fr A6/SR 025/026 Seminarraum (Arnimallee 6)
    

• Linear Algebra I

  0084dA1.4
  • 19201401 Lecture
    Linear Algebra I (Georg Loho)
    Schedule: Mo 08:00-10:00, Mi 08:00-10:00 (Class starts on: 2025-10-15)
    Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)
    

    Comments

    Content:

    • Basic terms/concepts: sets, maps, equivalence relations, groups, rings,
    • fields
    • Linear equation systems: solvability criteria, Gauss algorithm
    • Vector spaces: linear independence, generating systems and bases, dimension,
    • subspaces, quotient spaces, cross products in R3
    • Linear maps: image and rank, relationship to matrices, behaviour under
    • change of basis
    • Dual vector spaces: multilinear forms, alternating and symmetric bilinear
    • forms, relationship to matices, change of basis
    • Determinants: Cramer's rule, Eigenvalues and Eigenvectors

    
    Prerequisites:

    Participation in the preparatory course (Brückenkurs) is highly recommended.

     

    Suggested reading

    • Siegfried Bosch, Lineare Algebra, 4. Auflage, Springer-Verlag, 2008;
    • Gerd Fischer, Lernbuch Lineare Algebra und Analytische Geometrie, Springer-Verlag, 2017;
    • Bartel Leendert van der Waerden, Algebra Volume I, 9th Edition, Springer 1993;

    Zu den Grundlagen

    • Kevin Houston, Wie man mathematisch denkt: Eine Einführung in die mathematische Arbeitstechnik für Studienanfänger, Spektrum Akademischer Verlag, 2012

  • 19201402 Practice seminar
    Practice seminar for Linear Algebra I (Georg Loho, Jan-Hendrik de Wiljes)
    Schedule: Mo 10:00-12:00, Mo 16:00-18:00, Mi 10:00-12:00, Do 08:00-10:00, Do 12:00-14:00, Fr 10:00-12:00 (Class starts on: 2025-10-15)
    Location: Mo A3/SR 115 (Arnimallee 3-5), Mo A6/SR 009 Seminarraum (Arnimallee 6), Mi A6/SR 009 Seminarraum (Arnimallee 6), Do A6/SR 007/008 Seminarraum (Arnimallee 6), Do A6/SR 032 Seminarraum (Arnimallee 6), Fr A6/SR 031 Seminarraum (Arnimallee 6)
    

• Discrete Mathematics I

  0084cB3.2
  • 19202001 Lecture
    Discrete Geometrie I (Christian Haase)
    Schedule: Di 10:00-12:00, Mi 12:00-14:00 (Class starts on: 2025-10-14)
    Location: A3/SR 120 (Arnimallee 3-5)
    

    Additional information / Pre-requisites

    Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.

    Comments

    This is the first in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures including analysis and proof techniques. The material will be a selection of the following topics:
    Basic structures in discrete geometry

    • polyhedra and polyhedral complexes
    • configurations of points, hyperplanes, subspaces
    • Subdivisions and triangulations (including Delaunay and Voronoi)
    • Polytope theory
    • Representations and the theorem of Minkowski-Weyl
    • polarity, simple/simplicial polytopes, shellability
    • shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
    • graphs, diameters, Hirsch (ex-)conjecture
    • Geometry of linear programming
    • linear programs, simplex algorithm, LP-duality
    • Combinatorial geometry / Geometric combinatorics
    • Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres
    • Arrangements, zonotopes, zonotopal tilings, oriented matroids
    • Examples, examples, examples
    • regular polytopes, centrally symmetric polytopes
    • extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
    • combinatorial optimization and 0/1-polytopes

     

    For students with an interest in discrete mathematics and geometry, this is the starting point to specialize in discrete geometry. The topics addressed in the course supplement and deepen the understanding for discrete-geometric structures appearing in differential geometry, topology, combinatorics, and algebraic geometry.

     

     

     

     

     

     

     

     

     

    Suggested reading

    • G.M. Ziegler "Lectures in Polytopes"
    • J. Matousek "Lectures on Discrete Geometry"
    • Further literature will be announced in class.

  • 19202002 Practice seminar
    Practice seminar for Discrete Geometrie I (Sofia Garzón Mora, Christian Haase)
    Schedule: Mi 14:00-16:00 (Class starts on: 2025-10-15)
    Location: A6/SR 031 Seminarraum (Arnimallee 6)
    

• Modules w/o courses in this semester

  150 Modules
  • Functional Programming 0086bA1.1
  • Object-Oriented Programming 0086bA1.2
  • Data Structures and Data Abstraction 0086bA1.3
  • Non-Sequential Programming 0086bA1.4
  • Network Programming 0086bA1.5
  • Fundamentals of Computer Systems 0086bA2.1
  • Computer Architecture 0086bA2.2
  • Operating and Communication Systems 0086bA2.3
  • Computer Engineering Lab 0086bA2.4
  • Operating Systems 0089cA3.1
  • Current Research Topics in Computer Systems 0089cA3.10
  • Special Aspects of Computer Systems 0089cA3.11
  • Selected Topics in Technical Computer Science 0089cA3.12
  • Microprocessor Lab 0089cA3.2
  • Mobile Communications 0089cA3.3
  • Telematics 0089cA3.5
  • Fundamentals of Theoretical Computer Science 0086bA3.1
  • Proseminar: Computer Science 0086bA3.2
  • Database Systems 0086bA3.3
  • Software Project 0086bA3.4
  • Model-driven Software Development 0089cA1.11
  • Computer Security 0089cA1.16
  • Compiler Construction 0089cA1.19
  • Computer Graphics 0089cA1.2
  • Practices in Professional Software Development 0089cA1.22
  • Current research topics in Applied Computer Science 0089cA1.27
  • Special Aspects of Applied Computer Science 0089cA1.28
  • Special Aspects of Software Development 0089cA1.30
  • Selected Topics in Applied Computer Science 0089cA1.31
  • Fundamentals of Software Testing 0089cA1.7
  • Advanced Algorithms 0089cA2.1
  • Model Checking 0089cA2.2
  • Current Research Topics in Theoretical Computer Science 0089cA2.3
  • Computational Geometry 0089cA2.4
  • Selected Topics in Theoretical Computer Science 0089cA2.5
  • Advanced topics in Theoretical Computer Science 0089cA2.6
  • Special aspects of Theoretical Computer Science 0089cA2.7
  • Cryptography and Security in Distributed Systems 0089cA2.8
  • Analysis I 0084aA1.1
  • Linear Algebra I 0084aA2.1
  • Logic and Discrete Mathematics 0086bA4.1
  • Analysis 0086bA4.2
  • Linear Algebra 0086bA4.4
  • Specialization Module (Lecture 4+2 hrs/wk) 0086bA5.1
  • Specialization Module II (Lecture 2+2 hrs/wk) 0086bA5.10
  • Specialization Module I (Lecture 2 hrs/wk) 0086bA5.11
  • Specialization Module I (Seminar) 0086bA5.12
  • Specialization Module (Project 4 hrs/wk) 0086bA5.13
  • Specialization Module II (Lecture 4+2 hrs/wk) 0086bA5.14
  • Specialization Module III (Lecture 4+2 hrs/wk) 0086bA5.15
  • Specialization Module IV (Lecture 2+2 hrs/wk) 0086bA5.16
  • Specialization Module (Lecture 2+2 hrs/wk, MiniProject) 0086bA5.17
  • Specialization Module I (Lecture 2+2 hrs/wk, MiniProject) 0086bA5.18
  • Specialization Module (incl. Project 2 hrs/wk, 3 CP) 0086bA5.19
  • Specialization Module (Lecture 2+2 hrs/wk) 0086bA5.2
  • Specialization Module I (incl. Project 2 hrs/wk, 3 CP) 0086bA5.20
  • Specialization Module (incl. Project, 3 CP) 0086bA5.21
  • Specialization Module I (incl. Project, 3 CP) 0086bA5.22
  • Specialization Module I (Project 4 hrs/wk) 0086bA5.23
  • Specialization Module II (Lecture 2 hrs/wk, 3 CP) 0086bA5.24
  • Specialization Module (Lecture 2+1 hrs/wk, 4 CP) 0086bA5.25
  • Specialization Module (Lecture 2+2 hrs/wk, 6 CP) 0086bA5.26
  • Specialization Module (Lecture 3+1 hrs/wk, 7 CP) 0086bA5.27
  • Specialization Module (Lecture 3+2 hrs/wk, 9 CP) 0086bA5.28
  • Specialization Module I (Lecture 2+1 hrs/wk, 4 CP) 0086bA5.29
  • Specialization Module (Lecture 2 hrs/wk) 0086bA5.3
  • Specialization Module I (Lecture 2+2 hrs/wk, 6 CP) 0086bA5.30
  • Specialization Module I (Lecture 3+1 hrs/wk, 7 CP) 0086bA5.31
  • Specialization Module I (Lecture 3+2 hrs/wk, 9 CP) 0086bA5.32
  • Specialization Module (Seminar) 0086bA5.4
  • Specialization Module (Lab/Project 2 hrs/wk) 0086bA5.5
  • Specialization Module (Lab/Project 3 hrs/wk) 0086bA5.6
  • Specialization Module (Lab/Project 4 hrs/wk) 0086bA5.7
  • Specialization Module (Lecture 4+2 hrs/wk) 0086bA5.8
  • Specialization Module IV (Lecture 2+2 hrs/wk) 0086bA5.85
  • Specialization Module (4+2 hrs/wk, 10 CP) 0086bA5.86
  • Specialization Module I (4+2 hrs/wk, 10 CP) 0086bA5.87
  • Specialization Module (Seminar, 5 CP) 0086bA5.88
  • Specialization Module I (Seminar, 5 CP) 0086bA5.89
  • Specialization Module (Lecture 4+2 hrs/wk) 0086bA5.9
  • Specialization Module (2 hrs/wk Lab, 4 CP) 0086bA5.90
  • Specialization Module I (2 hrs/wk Lab, 4 CP) 0086bA5.91
  • Specialization Module (Lecture 2 + lab 2 hrs/wk, 5 CP) 0086bA5.92
  • Specialization Module I (Lecture 2 + lab 2 hrs/wk, 5 CP) 0086bA5.93
  • Operating Systems 0089bA1.1
  • Mobile Communications 0089bA1.10
  • Pattern Recognition 0089bA1.11
  • Network-Based Information Systems 0089bA1.12
  • Project Seminar: Data Management Systems 0089bA1.13
  • Robotics 0089bA1.14
  • Semantic Business Process Management 0089bA1.15
  • Semantics of Programming Languages 0089bA1.16
  • Seminar: Contributions to Software Engineering 0089bA1.17
  • Seminar: Data Management 0089bA1.18
  • Seminar: Artificial Intelligence 0089bA1.19
  • Image Processing 0089bA1.2
  • Seminar: Programming Languages 0089bA1.20
  • Software Project: Data Management 0089bA1.21
  • Software Project: Mobile Communications 0089bA1.22
  • Software Project: Compiler Construction 0089bA1.23
  • Software Project: Web Technologies 0089bA1.24
  • Software Processes 0089bA1.25
  • Advanced Topics in Data Management 0089bA1.26
  • Telematics 0089bA1.27
  • Transactional Systems 0089bA1.28
  • Compiler Construction 0089bA1.29
  • Computer Graphics 0089bA1.3
  • Distributed Systems 0089bA1.30
  • XML Technology 0089bA1.31
  • Telematics Project 0089bA1.32
  • Seminar: Database Systems 0089bA1.33
  • Seminar: Modern Web Technology 0089bA1.34
  • Software Technology Project 0089bA1.35
  • Software Project: Artificial Intelligence 0089bA1.36
  • Computer Vision 0089bA1.4
  • Seminar: IT Security 0089bA1.49
  • Database Technology 0089bA1.5
  • Empirical Evaluation in Computer Science 0089bA1.6
  • Advanced Aspects of Functional Programming 0089bA1.7
  • Computer Security 0089bA1.8
  • Artificial Intelligence 0089bA1.9
  • Current Research Topics in Algorithmics 0089bA2.1
  • Software Project: Application of Algorithms 0089bA2.11
  • Computational Geometry 0089bA2.2
  • Selected Topics in Algorithims 0089bA2.3
  • Advanced Algorithms 0089bA2.4
  • Cryptography and Security in Distributed Systems 0089bA2.6
  • Model Checking 0089bA2.7
  • Seminar: Algorithms 0089bA2.8
  • Microprocessor Lab 0089bA3.2
  • Seminar: Computer Systems 0089bA3.6
  • Project Management 0089bA4.25
  • Starting a Business in IT 0089bA4.27
  • Digital Video 0089bA4.5
  • E-Learning Platforms 0089bA4.6
  • Medical Image Processing 0089bA4.9
  • Elementary Geometry 0082aB1.3
  • Analysis II 0084aA1.2
  • Linear Algebra II 0084aA2.2
  • Computer-Oriented Mathematics I 0084aA3.1
  • Computer-Oriented Mathematics II 0084aA3.2
  • Introduction to Numerical Mathematics (Numerical Mathematics I) 0084aA4.1
  • Introduction to Probability and Statistics (Probability and Statistics I) 0084aA4.2
  • Introduction to Elementary Probability and Statistics 0084bA4.2
  • Seminar: Mathematics 0084cB1.1
  • Algorithmische Bioinformatik 0260aA1.4
  • Statistics I for Students of Life Sciences 0260aA2.5
  • Physics for Biology, Geosciences, Computer Science and Mathematics 0086bK3.1
  • Physics Internship for Geo-Sciences, Computer Science and Mathematics 0086bK3.2
  • Additional Courses in Computer Science 0086bL1.1