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 Subject 2: Math...  
 Course

Master's programme in Teacher Education (120 cp)

Subject 2: Mathematics

0564a_m42

  • Analysis II (10 CP)

    0082fA2.1
    • 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)

    0082fA2.2
    • 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)

    0082fA2.3
    • 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)

  • Computer-Oriented Mathematics I

    0084dA1.6
    • 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)

  • Special topics in Mathematics

    0084dB2.11
    • 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)

  • Functional Analysis

    0084dB2.2
    • 19201901 Lecture
      Functional Analysis (Dirk Werner)
      Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-10-14)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      Comments

      Content:
      Functional analysis is the branch of mathematics dealing with the study of normed (or general topological) vector spaces and continuous mappings between them. Thus, analysis, topology and algebra are linked.
      The course deals with Banach and Hilbert spaces, linear operators and functionals as well as spectral theory of compact operators.

      Target group: Students from the 3rd/4th semester on.

      Requirements: Good command of the material of the courses Analysis I/II and Linear Algebra I/II.

      Suggested reading

      Literatur:

      • Dirk Werner: Funktionalanalysis, 8. Auflage, Springer-Verlag 2018
    • 19201902 Practice seminar
      Tutorial: Functional Analysis (Dirk Werner)
      Schedule: Do 12:00-14:00 (Class starts on: 2025-10-16)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)

      Comments

      Inhalt:
      Die Funktionalanalysis ist der Zweig der Mathematik, der sich mit der Untersuchung von normierten (oder allgemeiner topologischen) Vektorräumen und stetigen Abbildungen zwischen ihnen befasst. Hierbei werden Analysis, Topologie und Algebra verknüpft.
      Die Vorlesung behandelt Banach- und Hilberträume, lineare Operatoren und Funktionale sowie Spektraltheorie kompakter Operatoren.

      Zielgruppe: Studierende vom 4. Semester an.

      Voraussetzungen: Sicheres Beherrschen des Stoffs der Vorlesungen Analysis I/II und Lineare Algebra I/II.

      Literatur:

       

      • Dirk Werner: Funktionalanalysis, 6. Auflage, Springer-Verlag 2007, ISBN 978-3-540-72533-6
      • Hans Wilhelm Alt: Lineare Funktionalanalysis : eine anwendungsorientierte Einführung. 5. Auflage. Springer-Verlag, 2006, ISBN 3-540-34186-2
      • Harro Heuser: Funktionalanalysis: Theorie und Anwendung. 3. Auflage. Teubner-Verlag, 1992, ISBN 3-519-22206-X

       

  • Probability and Statistics II

    0084dB2.4
    • 19212901 Lecture
      Stochastics II (Felix Höfling)
      Schedule: Di 12:00-14:00, Do 08:00-10:00 (Class starts on: 2025-10-14)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Additional information / Pre-requisites

      Prerequisite: Stochastics I  and  Analysis I — III.

      Comments

      Contents:

      • Basics: conditional expectation, characteristic function, convergence types, uniform integrability;
      • Construction of stochastic processes and examples: Gaussian processes, Lévy processes, Brownian motion;
      • martingales in discrete time: convergence, stopping theorems, inequalities;
      • Markov chains in discrete and continuous time: recurrence and transience, invariant measures.

      Suggested reading

      • Klenke: Wahrscheinlichkeitstheorie
      • Durrett: Probability. Theory and Examples.

      Weitere Literatur wird im Lauf der Vorlesung bekannt gegeben.
      Further literature will be given during the lecture.
    • 19212902 Practice seminar
      Practice seminar for Stochastics II (Felix Höfling)
      Schedule: Di 14:00-16:00 (Class starts on: 2025-10-14)
      Location: A6/SR 031 Seminarraum (Arnimallee 6)

      Comments

      Inhalt

       

       

      • This course is the sequel of the course of Stochastics I. The main objective is to go beyond the first principles in probability theory by introducing the general language of measure theory, and the application of this framework in a wide variety of probabilistic scenarios.
        More precisely, the course will cover the following aspects of probability theory:
      • Measure theory and the Lebesgue integral
      • Convergence of random variables and 0-1 laws
      • Generating functions: branching processes and characteristic functions
      • Markov chains
      • Introduction to martingales

       

       

  • Numerical Mathematics II

    0084dB3.4
    • 19202101 Lecture
      Basic Module: Numeric II (Robert Gruhlke)
      Schedule: Mo 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-10-15)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Comments

      Description: Extending basic knowledge on odes from Numerik I, we first concentrate on one-step methods for stiff and differential-algebraic systems and then discuss Hamiltonian systems. In the second part of the lecture we consider the iterative solution of large linear systems.

      Target Audience: Students of Bachelor and Master courses in Mathematics and of BMS

      Prerequisites: Basics of calculus (Analysis I, II) linear algebra (Lineare Algebra I, II) and numerical analysis (Numerik I)
    • 19202102 Practice seminar
      Practice seminar for Basic Module: Numeric II (André-Alexander Zepernick)
      Schedule: Mi 10:00-12:00, Fr 08:00-10:00 (Class starts on: 2025-10-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

  • Differential Geometry I

    0084dB3.5
    • 19202601 Lecture
      Differential Geometry I (Konrad Polthier)
      Schedule: Mo 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2025-10-15)
      Location: KöLu24-26/SR 006 Neuro/Mathe (Königin-Luise-Str. 24 / 26)

      Additional information / Pre-requisites

      For further information, see Lecture Homepage.

      Comments

      Topics of the lecture will be:

      • curves and surfaces in Euclidean space,
      • metrics and (Riemannian) manifolds,
      • surface tension, notions of curvature,
      • vector fields, tensors, covariant derivative
      • geodesic curves, exponential map,
      • Gauß-Bonnet theorem, topology,
      • connection to discrete differential geometry.

      This course is a BMS course and will be held in English on request.

      Prerequisits:

      Analysis I, II, III and Linear Algebra I, II

       

       

      Suggested reading

      Literature

      • W. Kühnel: Differentialgeometrie:Kurven - Flächen - Mannigfaltigkeiten, Springer, 2012
      • M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall
      • J.-H. Eschenburg, J. Jost: Differentialgeometrie und Minimalflächen, Springer, 2014
      • C. Bär: Elementare Differentialgeometrie, de Gruyter, 2001
    • 19202602 Practice seminar
      Practice seminar for Differential Geometry I (Tillmann Kleiner, Konrad Polthier)
      Schedule: Mi 08:00-10:00 (Class starts on: 2025-10-15)
      Location: A6/SR 031 Seminarraum (Arnimallee 6)

  • Didactics of Mathematics: Development, Evaluation, and Research

    0563aA1.2
    • 19230515 Advanced seminar
      Mathematics Education - Development, Evaluation and Research (Brigitte Lutz-Westphal)
      Schedule: Di 09:00-12:00 (Class starts on: 2025-10-14)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

      In this seminar we will deal with a current field of research in mathematics education. Innovative teaching concepts (e.g. research-based/self-organized/dialogical learning) form the main focus of the seminar and are developed in a theoretical and practical context.

      On the basis, methods and results of mathematics education research, own questions for learning and teaching mathematics are formulated, discussed and concretely developed. The students gain an insight into the methods of mathematics education research.

      Individual meetings may be held in blocks.

      Suggested reading

      Ruf, Urs & Gallin, Peter (1998 bzw. spätere Auflagen): Dialogisches Lernen in Sprache und Mathematik, Band 1 und 2

      Ruf, Urs; Keller, Stefan & Winter, Felix (2008): Besser lernen im Dialog

      lerndialoge.ch

  • Elective Module: Specialization in Didactics of Mathematics

    0563aA1.24
    • 19230515 Advanced seminar
      Mathematics Education - Development, Evaluation and Research (Brigitte Lutz-Westphal)
      Schedule: Di 09:00-12:00 (Class starts on: 2025-10-14)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

      In this seminar we will deal with a current field of research in mathematics education. Innovative teaching concepts (e.g. research-based/self-organized/dialogical learning) form the main focus of the seminar and are developed in a theoretical and practical context.

      On the basis, methods and results of mathematics education research, own questions for learning and teaching mathematics are formulated, discussed and concretely developed. The students gain an insight into the methods of mathematics education research.

      Individual meetings may be held in blocks.

      Suggested reading

      Ruf, Urs & Gallin, Peter (1998 bzw. spätere Auflagen): Dialogisches Lernen in Sprache und Mathematik, Band 1 und 2

      Ruf, Urs; Keller, Stefan & Winter, Felix (2008): Besser lernen im Dialog

      lerndialoge.ch

  • Elective module: proseminar Mathematics - specialisation for teaching

    0563aA1.25
    • 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.
    • 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: Mathematical Games (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)

      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

      In diesem Proseminar werden Spiele behandelt, die in irgendeiner Form einen Bezug zu Mathematik haben. Beispiele sind Sudoku, Solitär, Lights Out, Dobble und Nim-Spiele.

      Das Hauptziel des Proseminars ist das Kennenlernen verschiedener Spiele und die Erarbeitung mathematischer Methoden, die zur Lösung zugehöriger Fragestellungen benutzt werden. Diese Methoden stammen aus verschiedensten Bereichen der Mathematik, etwa aus der Linearen Algebra oder der Kombinatorik.

      Die Aufgabe der Teilnehmenden ist die (angeleitete) Erarbeitung von Fachartikeln zu Spielen; diese Literatur ist in der Regel nur in englischer Sprache vorhanden. Dabei sollen Beweisideen verstanden und den anderen Teilnehmenden in einem Vortrag präsentiert werden. Die Einbindung der Zuhörenden ist sehr erwünscht.

      Es gibt eine verpflichtende Vorbesprechung am 25.02.2022 von 10-12 Uhr. Diese wird online stattfinden und ist über folgenden Link erreichbar: https://fu-berlin.webex.com/fu-berlin/j.php?MTID=mdf50fc829d3a738c52fdb93987207441

      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?

  • Student Teaching Lab: Mathematics (Subject 2)

    0564aA1.3

  • Modules w/o courses in this semester

    17 Modules
    • Computer-Oriented Mathematics II 0084dA1.7
    • Higher Analysis 0084dB2.1
    • Complex Analysis 0084dB2.3
    • Geometry 0084dB2.7
    • Data Structures and Data Abstraction with Applications 0084dB2.8
    • Mathematical Project 0084dB2.9
    • Differential Equations I 0084dB3.1
    • Discrete Mathematics I 0084dB3.2
    • Algebra I 0084dB3.3
    • Topology I 0084dB3.6
    • Advanced and Applied Algorithms 0084dB3.7
    • Visualization 0084dB3.8.
    • Computer Algebra 0162bA1.2
    • Didactics of Mathematics: Selected Topics 0563aA1.1
    • Elective Module: Mathematical Panorama 2A 0563aA1.26
    • Elective Module: Mathematical Panorama 2B 0563aA1.27
    • Elective Module: Gender and Diversity in Mathematics Teaching 0563aA1.28