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Lehramt für Mathematik

Bachelor's programme in Mathematics (Teacher Education, 2017 study regulations)

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  • Discovering Mathematics I (10 CP)

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    • 19233701 Lecture
      Discovering Mathematics I (N.N.)
      Schedule: Mi 10:00-12:00, Fr 10:00-12:00 (Class starts on: 2025-10-15)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Additional information / Pre-requisites

      This course is aimed at students of teacher training courses.

      Comments

      subject matter

      The focus is on practicing mathematical ways of thinking and working. These are trained on the basis of problems from combinatorics, elementary number theory and elementary geometry.

      compulsory attendance

      Attendance is mandatory for the central exercise on Monday.
    • 19233702 Practice seminar
      Practice seminar for Discovering Mathematics I (N.N.)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-24)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

  • Mathematical Panorama (5 CP)

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    • 19236101 Lecture
      Mathematisches Panorama (Anina Mischau, Sarah Wolf)
      Schedule: Mi 12:00-14:00 (Class starts on: 2025-10-15)
      Location: T9/SR 005 Übungsraum (Takustr. 9)

      Comments

      This is for a course in German - Short explanation in English:

      Mathematical Panorama is a two-hour overview course for First-Semester students of Mathematics (in particular, but not only, for teacher students) that presents the wide field of modern Mathematics - its history, its topics, its problems, its methods, some basic concepts, applications, etc.

       

      Suggested reading

      • Günter M. Ziegler und Andreas Loos: Panorama der Mathematik, Springer-Spektrum 2018, in Vorbereitung (wird in Auszügen zur Verfügung gestellt)
      • Hans Wußing, 6000 Jahre Mathematik: Eine kulturgeschichtliche Zeitreise, Springer 2009
        • Band 1: Von den Anfängen bis Leibniz und Newton
        • Band 2: Von Euler bis zur Gegenwart
      • Heinz-Wilhelm Alten et al., 4000 Jahre Algebra, Springer 2008
      • Christoph J. Scriba, 5000 Jahre Geometrie, Springer 2009
      • Heinz Niels Jahnke, Geschichte der Analysis: Texte zur Didaktik der Mathematik, Spektrum 1999
      • Richard Courant und Herbert Robbins, What is Mathematics?, Oxford UP 1941 (deutsch: Springer 2010)
      • Phillip J. Davis, Reuben Hersh, The Mathematical Experience, Mariner Books 1999
    • 19236102 Practice seminar
      Übung zu: Mathematisches Panorama (Anina Mischau)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-24)
      Location: A6/SR 007/008 Seminarraum (Arnimallee 6)

  • Analysis I (10 CP)

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    • 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:
    • 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 (10 CP)

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    • 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)

  • Analysis II (10 CP)

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    • 19211601 Lecture
      Analysis II (Pavle Blagojevic)
      Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Comments

      Content

      1. Additions to Analysis I. Non-authentic integrals
      2. Uniform convergence of function sequences. Power series. Sentence of Taylor.
      3. Elements of topology. Standardized and metric spaces. Open quantities. Convergence. Completed quantities. Consistency. Compactness
      4. Differential calculus of several variables. Partial, total and continuous differentiability. Block via the inverse function. Block of implicit functions.
      5. Iterated integrals.
      6. Ordinary differential equations. Basic terms, elementary solvable differential equations, existential and unambiguous results for systems.

      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.

  • Linear Algebra II (10 CP)

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    • 19211702 Practice seminar
      Practice seminar for Linear Algebra II (Marcus Weber)
      Schedule: Di 08:00-10:00, Di 14:00-16:00, Mi 12:00-14:00, Do 16:00-18:00, Fr 08:00-10:00 (Class starts on: 2025-10-14)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

  • Numbers, Equations, Algebraic Structures (10 CP)

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    • 19200701 Lecture
      Algebra and Theory of Numbers (Alexander Schmitt)
      Schedule: Mo 08:00-10:00, Mi 08:00-10:00 (Class starts on: 2025-10-15)
      Location: T9/Gr. Hörsaal (Takustr. 9)

      Comments

      Subject matter:
      Selected topics from:

          Divisibility into rings (especially Z- and polynomial rings); residual classes and congruencies; modules and ideals
          Euclidean, principal ideal and factorial rings
          The quadratic law of reciprocity
          Primality tests and cryptography
          The structure of abel groups (or modules about main ideal rings)
          Symmetric function set
          Body extensions, Galois correspondence; constructions with compasses and rulers
          Non-Label groups (set of Lagrange, normal dividers, dissolvability, sylow groups)
    • 19200702 Practice seminar
      Practice seminar for Algebra and Theory of Numbers (Alexander Schmitt)
      Schedule: Mi 14:00-16:00, Do 14:00-16:00 (Class starts on: 2025-10-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

  • Probability and Statistics (10 CP)

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    • 19220901 Lecture
      Probability and Statistics (N.N.)
      Schedule: Di 12:00-14:00, Do 08:00-10:00 (Class starts on: 2025-10-14)
      Location: A6/SR 031 Seminarraum (Arnimallee 6)

      Comments

      Es werden insbesondere folgende Inhalte vermittelt.
      –  Diskrete Wahrscheinlichkeitsräume und -maße
      –  Diskrete und stetige Zufallsvariablen und ihre Verteilungen, wichtige Beispiele
      –  Erwartungswert, (Ko-)Varianz, Korrelation
      –  Bedingte Wahrscheinlichkeit, Unabhängigkeit
      –  Schwaches Gesetz der großen Zahl
      –  Zentraler Grenzwertsatz
      –  Datenanalyse und deskriptive Statistik: Histogramme; empirische Verteilung; Kenngrößen von Stichprobenver-teilungen; Beispiele irreführender deskriptiver Statistiken; lineare Regression
      –  Elementare Begriffe und Techniken des Testens und Schätzens: Maximum-Likelihood-Prinzip; Konfidenzinter-valle; Hypothesentests; Fehler erster und zweiter Art 

       

      Suggested reading

      E. Behrends: Elementary Stochastics, Springer, 2013
          H.-O. Georgii: Stochastics: Introduction to Probability Theory and Statistics, De Gruyter, 2007
          U. Krengel: Introduction to probability theory and statistics, Vieweg, 2005
          D. Meintrup, S. Schäffler, Stochastics: Theory and Applications, Springer, 2005.
          Most of the books listed below are available online at the UB. For this purpose, there is an extensive hand apparatus for stochastics in the mathematic library.
    • 19220941 Zentralübung
      Practice seminar for Probability and Statistics (N.N.)
      Schedule: Di 10:00-12:00, Di 14:00-16:00, Mi 10:00-12:00, Fr 08:00-10:00 (Class starts on: 2025-10-14)
      Location: A6/SR 007/008 Seminarraum (Arnimallee 6)

  • Proseminar Mathematics - Teacher Training

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    • 19201510 Proseminar
      Undergraduate Seminar: Linar Algebra (Alexander Schmitt)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-10-13)
      Location: A3/SR 119 (Arnimallee 3-5)

      Comments


       
    • 19214010 Proseminar
      Undergraduate Seminar "Magic Tricks with Mathematical Background" (Ehrhard Behrends)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-10-20)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

      Magic tricks with a mathematical background will be analyzed.

      Suggested reading

      Literatur: Mein 2017 bei Springer Spektrum erschienenes Buch "Zaubern und Mathematik" sowie einige Originalarbeiten zum Thema.
    • 19214210 Proseminar
      Proseminar "Mathematik für die Öffentlichkeit“ (Anna Maria Hartkopf)
      Schedule: Termine siehe LV-Details (Class starts on: 2026-03-25)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)
    • 19240317 Seminar / Undergraduate Course
      Advancing mathematics with AI (Georg Loho)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-10-14)
      Location: A3/SR 120 (Arnimallee 3-5)

      Comments

      The course will probably be held in German. 
    • 19241710 Proseminar
      Proseminar Mathematics Panorama (Anna Maria Hartkopf)
      Schedule: Mo 14:00-16:00 (Class starts on: 2025-10-20)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      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
    • 19245910 Proseminar
      Undergraduate Seminar: Good mathematical teaching at university level (Jan-Hendrik de Wiljes, Benedikt Weygandt)
      Schedule: Di 10:00-12:00 (Class starts on: 2025-10-14)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      Comments

      Undergraduate seminar “Good Mathematical Teaching at University”

      What actually happens when students reflect on university teaching and redesign it to promote learning?

      It is always easy to criticize existing concepts—but that alone does not change anything! That's why we want to take the frequently demanded student participation literally and give you the opportunity to contribute your experiences, expertise, and perspective as learners to the further development of good university teaching.

      Let's engage in a thought experiment—perhaps a crazy one?

      • What would happen if students designed a math lecture that was meaningful and useful to them? Or even an entire module?
      • What kind of tutorials do you think are useful? What activities (thinking, calculating, discussing...) should take place in the respective courses (lectures, exercises, central exercises...) and in what format (frontal, individual, group...)?
      • And what about the teaching materials: What should exercises look like? Lecture notes? Exams?

      Procedure

      After a short general introduction, we will devote three weeks to each topic (designing lectures, (central) exercises, lecture notes, exercise sheets, exams), gather inspiration, and then work out our “good” approaches in pairs.

      At the end of the semester, we want to discuss and try out the ideas, approaches, and concepts you have developed with university lecturers!

       

      Requirements

      It is essential that you already have some experience with university teaching! You should have attended at least 2‒3 introductory lectures in mathematics. The focus will not so much be on the content taught there, but rather on becoming familiar with mathematical work at the university. More important than the individual subject content is a basic understanding of mathematical thinking and working methods—and, in particular, an interest in contemporary teaching.    

      Note: It is not planned to write a bachelor's thesis based on this proseminar. If you would like to write a thesis on a topic related to your proseminar, we recommend one of the other courses offered.

  • Computer-Oriented Mathematics I (5 CP)

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    • 19200501 Lecture
      Computerorientated Mathematics I (5 LP) (Claudia Schillings)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-10-17)
      Location: T9/Gr. Hörsaal (Takustr. 9)

      Comments

      Contents:
      Computers play an important role in (almost) all situations in life today. Computer-oriented mathematics provides basic knowledge in dealing with computers for solving mathematical problems and an introduction to algorithmic thinking. At the same time, typical mathematical software such as Matlab and Mathematica will be introduced. The motivation for the questions under consideration is provided by simple application examples from the aforementioned areas. The content of the first part includes fundamental terms of numerical calculation: number representation and rounding errors, condition, efficiency and stability.

      Homepage: All current information on lectures and lectures

      Suggested reading

      Literatur: R. Kornhuber, C. Schuette, A. Fest: Mit Zahlen Rechnen (Skript zur Vorlesung)
    • 19200502 Practice seminar
      Practice seminar for Computerorientated Mathematics I (5 LP) (N.N.)
      Schedule: Mo 12:00-14:00, Mo 14:00-16:00, Di 08:00-10:00, Di 16:00-18:00, Mi 10:00-12:00, Do 14:00-16:00, Fr 08:00-10:00 (Class starts on: 2025-10-13)
      Location: A6/SR 031 Seminarraum (Arnimallee 6)