WiSe 24/25  
 Centre for Teac...  
 Fach 2 Mathemat...  
 Course

Master's programme in Teacher Education (120 cp)

Fach 2 Mathematik

0564b_m42

  • Analysis II (10 CP)

    0082fA2.1
    • 19211601 Lecture
      Analysis II (Isabelle Schneider)
      Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2024-10-15)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      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 (Isabelle Schneider)
      Schedule: Mo 10:00-12:00, Mi 10:00-12:00, Fr 10:00-12:00 (Class starts on: 2024-10-14)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

  • Linear Algebra II (10 CP)

    0082fA2.2
    • 19211701 Lecture
      Linear Algebra II (N.N.)
      Schedule: Mi 12:00-14:00, Fr 08:00-10:00 (Class starts on: 2024-10-16)
      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 (N.N.)
      Schedule: Mo 10:00-16:00 (Class starts on: 2024-10-14)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

  • Numbers, Equations, Algebraic Structures (10 CP)

    0082fA2.3
    • 19200701 Lecture
      Algebra and Theory of Numbers (Kivanc Ersoy)
      Schedule: Mo 08:00-10:00, Mi 08:00-10:00 (Class starts on: 2024-10-14)
      Location: A3/SR 120 (Arnimallee 3-5)

      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 (N.N.)
      Schedule: Mi 12:00-18:00 (Class starts on: 2024-10-16)
      Location: A3/SR 119 (Arnimallee 3-5)

  • Computer-Oriented Mathematics I

    0084dA1.6
    • 19200501 Lecture
      Computerorientated Mathematics I (5 LP) (Ralf Kornhuber, Claudia Schillings)
      Schedule: Fr 12:00-14:00 (Class starts on: 2024-10-18)
      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) (André-Alexander Zepernick)
      Schedule: Mo 08:00-16:00 (Class starts on: 2024-10-14)
      Location: A3/SR 119 (Arnimallee 3-5)

  • Special topics in Mathematics

    0084dB2.11
    • 19202001 Lecture
      Discrete Geometrie I (Georg Loho)
      Schedule: Di 10:00-12:00, Mi 10:00-12:00 (Class starts on: 2024-10-15)
      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 (Sophie Rehberg)
      Schedule: Mo 16:00-18:00, Fr 10:00-12:00 (Class starts on: 2024-10-14)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

  • Functional Analysis

    0084dB2.2
    • 19201901 Lecture
      Functional Analysis (Pavle Blagojevic)
      Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2024-10-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Comments

      Content:
      Functional analysis is the branch of mathematics dealing with the study of normalized (or general topological) vector spaces and continuous images between them. Analysis, topology and algebra are linked.
      The lecture deals with Banach and Hilbert spaces, linear operators and functional 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 lectures Analysis I/II and Linear Algebra I/II.

      Suggested reading

      Literatur:

      • Dirk Werner: Funktionalanalysis, 7. Auflage, Springer-Verlag 2011, ISBN 978-3-642-21016-7
    • 19201902 Practice seminar
      Tutorial: Functional Analysis (Pavle Blagojevic, N.N.)
      Schedule: Do 16:00-18:00 (Class starts on: 2024-10-17)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      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

       

  • 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, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-16)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Ggf können Veranstaltungen mit Schüler*innen 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 bzw. Aspekten der Wissenschaftskommunikation. So werden z.B. Grundlagen des Kommunikationsformats erarbeitet (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 hergestellt. Praktisch arbeiten die Studierenden in Gruppen an eigenen Modellen und entwerfen Elemente, die in Zusammenhang mit einem Decision Theatre im schulischen Kontext oder mit anderen gesellschaftlichen Zielgruppen verwendet werden können. Das Anwendungsthema ist nachhaltige Mobilität.

      In dem Projektseminar ist ein intensiver Austausch zwischen Studierenden aus dem Monostudiengang und aus dem Lehramtsstudiengang der Mathematik intendiert. Durch das Kennenlernen von und die Mitwirkung in einem aktuellen mathematischen wie didaktischen Forschungsprojekt und durch den Einblick in dessen Abläufe und 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 und Beobachtung von Schüler*innengruppen

      Schwerpunkte im Bereich mathematische Forschung:

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

      Suggested reading

      Wird in den Sitzungen bekannt gegeben.

  • Algebra I

    0084dB3.3
    • 19202501 Lecture
      Basic Module: Algebra I (Alexandru Constantinescu)
      Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-14)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Comments

      Content


      This is the first part of a three semester course on algebraic geometry. Commutative algebra is the theory of commutative rings and their modules. It formally includes affine algebraic and local analytic geometry. Topics include:

      ? Affine algebraic varieties

      ? Rings, ideals, and modules

      ? Noetherian rings

      ? Local rings and localization

      ? Primary decompositione

      ? Finite and integral extensions

      ? Dimension theory

      ? Regular rings

      Target Group
      Students with the prerequisites mentioned below.

      Prerequisites
      ? Linear Algebra I+II ? Algebra and Number Theory

      Literature
      ? Atiyah, M.F.; Macdonald, I.G.: Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969 ix+128 pp. (This book is probably the best entry to the subject. It is short, concise, and clearly written.)
      ? Further literature will be announced in class.


      Homepage: Professor Alexander Schmitt
    • 19202502 Practice seminar
      Practice seminar for Basic Module: Algebra I (Alexandru Constantinescu)
      Schedule: Mo 08:00-10:00 (Class starts on: 2024-10-21)
      Location: A6/SR 031 Seminarraum (Arnimallee 6)

  • Numerical Mathematics II

    0084dB3.4
    • 19202101 Lecture
      Basic Module: Numeric II (Volker John)
      Schedule: Mo 10:00-12:00, Mo 14:00-20:00 (Class starts on: 2024-10-14)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

      Comments

      Description: Extending basic knowledge on initial value problems with ordinary differential equations from Numerik I, the course presents methods for stiff problems and multistep methods. In the second part of the course iterative methods for solving linear systems of equations are studied.

      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: Do 12:00-14:00 (Class starts on: 2024-10-17)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

  • Computer Algebra

    0162bA1.2
    • 19203419 Seminar with practice
      Computer Algebra (Sofia Garzón Mora)
      Schedule: Termine siehe LV-Details (Class starts on: 2025-02-24)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

      1) Prime number tests, factorization in Z

      2) LLL-algorithums

      3) Polynomial factorization over finite fields over Z, Q or in K [x1,...,xn]

      4) Gröbner bases, resultatants, eliminations

      5) Primary decompostion, radical ideals, Syzygies and free resolutions

      6) Practical applications, such as the examination of processors, states of balance in economic models, the description of configuration spaces in molecules, robotics or Sudoku

      For all topics the emphasis is on practical work using a concrete computer-algebra system (such as Singular).

       

      • Prerequisite Lineare Algebra I

         
    • 19207219 Seminar with practice
      Formal Proof Vetification (Tibor Szabo)
      Schedule: -
      Location: keine Angabe

      Comments

      Selected topics from:

      • Installation of LEAN, using the proof assistant and setting up your own project
      • Fundamentals of Dependent Type Theory and Propositions as Types 
      • Functional proofs and tactics 
      • Basics of logic in LEAN 
      • Inductive types and proofs by induction 
      • Selection of well-known mathematical concepts in LEAN (set theory, integers, vector spaces, convergence, ...)
      • Selection of simple proofs and proof strategies (infinitely many prime numbers, stable sets in hypercube, ...)
      • The mathlib library 

      For all topics, the focus is on practical work with a concrete proof assistant (e.g., LEAN).

      Prerquisites: Linaer Algebra I and Analysis I

      Suggested reading

      Literatur:

      • The Hitchhiker’s Guide to Logical Verification von Anne Baanen, Alexander Bentkamp, Jasmin Blanchette, Johannes Hölzl und Jannis Limperg
      • The Mechanics of Proof by Heather Macbeth 
      • Functional Programming in Lean von David Thrane Christiansen 
      • Theorem Proving in Lean 4 von Jeremy Avigad, Leonardo de Moura, Soonho Kong und Sebastian Ullrich
      • Mathematics in Lean

  • Modules w/o courses in this semester

    16 Modules
    • Computer-Oriented Mathematics II 0084dA1.7
    • Higher Analysis 0084dB2.1
    • Complex Analysis 0084dB2.3
    • Probability and Statistics II 0084dB2.4
    • Geometry 0084dB2.7
    • Discrete Mathematics I 0084dB3.2
    • Differential Geometry I 0084dB3.5
    • Topology I 0084dB3.6
    • Didactics of Mathematics: Selected Topics 0563bA1.1
    • Didactics of Mathematics: Development, Evaluation, and Research 0563bA1.2
    • Wahlmodul: Vertiefung Fachdidaktik Mathematik 0563bA1.20
    • Wahlmodul: Proseminar Mathematik - Vertiefung Lehramt 0563bA1.21
    • Wahlmodul: Mathematisches Panorama 2A 0563bA1.22
    • Wahlmodul: Mathematisches Panorama 2B 0563bA1.23
    • Wahlmodul: Gender und Diversity im Mathematikunterricht 0563bA1.24
    • Schulpraktische Studien im Unterrichtsfach Mathematik - Fach 2 0564bA1.3