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Master's programme in Teacher Education (120 cp)

Subject 2 Mathematics

0564a_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)

  • Advanced and Applied Algorithms

    0084dB3.7
    • 19303501 Lecture
      Advanced Algorithms (László Kozma)
      Schedule: Di 10:00-12:00, Fr 10:00-12:00 (Class starts on: 2024-10-15)
      Location: T9/SR 006 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Target audience

      All Master and Bachelor students who are interested in algorithms.

      Prerequisites

      Basic familiarity with the design and analysis of algorithms.

      Comments

      This course will focus on the design and analysis of algorithms, with topics including:

      • general principles of algorithm design,
      • randomized algorithms,
      • dynamic programming,
      • flow problems on graphs,
      • amortized analysis and advanced data structures,
      • theory of NP-completeness,
      • approximation methods for hard problems,
      • other topics.

      Prerequisites are basic knowledge of algorithms and relevant mathematics. All Bachelor and Master students interested in advanced algorithmic techniques are welcome. Lectures are in English.

      Suggested reading

      • Cormen, Leiserson, Rivest, Stein: Introduction to Algorithms, 4th Ed. MIT Press 2022
      • Kleinberg, Tardos: Algorithm Design, Addison-Wesley 2005.
      • Sedgewick, Wayne: Algorithms, 4th Ed., Addison-Wesley 2016
    • 19303502 Practice seminar
      Practice seminar for Advanced Algorithms (László Kozma)
      Schedule: Fr 08:00-10:00, Fr 14:00-16:00 (Class starts on: 2024-10-18)
      Location: T9/046 Seminarraum (Takustr. 9)

  • 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

  • Teaching methodology Mathematics - selected topics

    0563aA1.1
    • 19230015 Advanced seminar
      Mathematics Education - Selected Topics (N.N.)
      Schedule: Do 12:00-15:00 (Class starts on: 2024-10-17)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

       

    • 19230215 Advanced seminar
      Mathematics Education - Selected Topics (Thorsten Scheiner)
      Schedule: Termine siehe LV-Details (Class starts on: 2025-01-17)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      Comments

       

  • Teaching methodology 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: 2024-10-15)
      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
    • 19230615 Advanced seminar
      Mathematics Education - Development, Evaluation and Research (N.N.)
      Schedule: Mi 11:00-14:00 (Class starts on: 2024-10-16)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

       

    • 19230815 Advanced seminar
      Mathematics Education - Development, Evaluation and Research (Thorsten Scheiner)
      Schedule: Termine siehe LV-Details (Class starts on: 2024-10-04)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      Comments

      Titel des Seminars: Stärkenbasierter Mathematikunterricht

      Seminarbeschreibung: Ziel dieses Seminars ist es, Lehramtsstudierenden die Fähigkeit zu vermitteln, die mathematischen Fähigkeiten ihrer Schüler:innen zu identifizieren und diese gezielt zu fördern. Durch den Einsatz praktischer Analysewerkzeuge und die Reflexion von Schülerbeispielen erlernen die Teilnehmer:innen, wie sie ein Lernumfeld schaffen können, das alle Schüler:innen in ihren individuellen Stärken unterstützt und motiviert. Besonderes Augenmerk liegt zudem auf der Schaffung eines positiven Lernumfelds, das für die Entwicklung einer starken mathematischen Identität und Selbstwirksamkeit der Schüler:innen essentiell ist.

      Das Seminar findet als Blockveranstaltung an zwei Wochenenden statt (siehe Termine).

      Aktive Teilnahmeformen umfassen die Lektüre von Texten, das Verfassen schriftlicher Ausarbeitungen zu Seminaraufgaben, die Analyse von Schülerarbeiten und eigenen Wahrnehmungsaktivitäten sowie die aktive Teilnahme an den Seminarsitzungen. Des Weiteren wird ein Reflektionsportfolio erstellt.

      Modulprüfung: Hausarbeit

  • Elective module: specialisation in teaching methodology for Mathematics

    0563aA1.24
    • 19230015 Advanced seminar
      Mathematics Education - Selected Topics (N.N.)
      Schedule: Do 12:00-15:00 (Class starts on: 2024-10-17)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

       

    • 19230215 Advanced seminar
      Mathematics Education - Selected Topics (Thorsten Scheiner)
      Schedule: Termine siehe LV-Details (Class starts on: 2025-01-17)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      Comments

       
    • 19230515 Advanced seminar
      Mathematics Education - Development, Evaluation and Research (Brigitte Lutz-Westphal)
      Schedule: Di 09:00-12:00 (Class starts on: 2024-10-15)
      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
    • 19230615 Advanced seminar
      Mathematics Education - Development, Evaluation and Research (N.N.)
      Schedule: Mi 11:00-14:00 (Class starts on: 2024-10-16)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

       

    • 19230815 Advanced seminar
      Mathematics Education - Development, Evaluation and Research (Thorsten Scheiner)
      Schedule: Termine siehe LV-Details (Class starts on: 2024-10-04)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      Comments

      Titel des Seminars: Stärkenbasierter Mathematikunterricht

      Seminarbeschreibung: Ziel dieses Seminars ist es, Lehramtsstudierenden die Fähigkeit zu vermitteln, die mathematischen Fähigkeiten ihrer Schüler:innen zu identifizieren und diese gezielt zu fördern. Durch den Einsatz praktischer Analysewerkzeuge und die Reflexion von Schülerbeispielen erlernen die Teilnehmer:innen, wie sie ein Lernumfeld schaffen können, das alle Schüler:innen in ihren individuellen Stärken unterstützt und motiviert. Besonderes Augenmerk liegt zudem auf der Schaffung eines positiven Lernumfelds, das für die Entwicklung einer starken mathematischen Identität und Selbstwirksamkeit der Schüler:innen essentiell ist.

      Das Seminar findet als Blockveranstaltung an zwei Wochenenden statt (siehe Termine).

      Aktive Teilnahmeformen umfassen die Lektüre von Texten, das Verfassen schriftlicher Ausarbeitungen zu Seminaraufgaben, die Analyse von Schülerarbeiten und eigenen Wahrnehmungsaktivitäten sowie die aktive Teilnahme an den Seminarsitzungen. Des Weiteren wird ein Reflektionsportfolio erstellt.

      Modulprüfung: Hausarbeit

  • Elective module: proseminar Mathematics - specialisation for teaching

    0563aA1.25
    • 19213417 Seminar / Undergraduate Course
      Undergraduate Seminar: Analysis (Ehrhard Behrends)
      Schedule: Mo 14:00-16:00 (Class starts on: 2024-10-14)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

      Comments

      Basics of non-standard analysis (according to Nelson)

      In the analysis, calculating with in?nitesimalen sizes is formalized by the Grenzwertbegri?. Robinson has extended the body of real numbers so that it contains in?nitesimale elements, i.e. positive numbers that are smaller than all positive real numbers. Nelson later observed that the axioms of set theory can be expanded so that the "usual body" of the real numbers "standard" and "non-standard elements". Among the non-standard elements ?nden are again those that are positive and smaller than all positive standard elements.

       

      The proseminar will discuss how the basic statements of the analysis can be reformulated and proven with the help of the in?nitesimalen elements. The proseminar is divided into the following sections:

      I. Logical basis of NSA

      II. Analysis I in the language of the NSA

      III. advanced applications of NSA

      IV. A look at Robinson's NSA

      Homepage Prof. Schmitt

       

      Suggested reading

      Behrends: Analysis I und II
    • 19234810 Proseminar
      Women in the History of Mathematics and Computer Science (N.N.)
      Schedule: -
      Location: keine Angabe

      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: -
      Location: keine Angabe

      Comments

      Science Communication on Mathematics

      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

  • Elective Module: Gender and Diversity in Mathematics Teaching

    0563aA1.28
    • 19233011 Seminar
      Elective Module - Gender & Diversity (N.N.)
      Schedule: -
      Location: keine Angabe

      Comments

      Refer to German description. Courses of Mathematics Education are part of the German teacher-training and held in German only.
    • 19234810 Proseminar
      Women in the History of Mathematics and Computer Science (N.N.)
      Schedule: -
      Location: keine Angabe

      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.

  • F2 Mathematics - teaching Mathematics in schools - subject 2

    0564aA1.3

  • Modules w/o courses in this semester

    13 Modules
    • Computer-Oriented Mathematics II 0084dA1.7
    • Higher Analysis 0084dB2.1
    • Complex Analysis 0084dB2.3
    • Probability and Statistics II 0084dB2.4
    • Geometry 0084dB2.7
    • Data Structures and Data Abstraction with Applications 0084dB2.8
    • Differential Equations I 0084dB3.1
    • Discrete Mathematics I 0084dB3.2
    • Differential Geometry I 0084dB3.5
    • Topology I 0084dB3.6
    • Visualization 0084dB3.8
    • Elective Module: Mathematical Panorama 2A 0563aA1.26
    • Elective Module: Mathematical Panorama 2B 0563aA1.27