SoSe 24  
 Mathematics and...  
 60 cp Module of...  
 Course

SoSe 24: Lehramt für Mathematik

60 cp Module offering in Mathematics (2017 study regulations)

0083e_m60

  • Analysis I (10 CP)

    0082fA1.4
    • 19202801 Lecture
      Analysis I (Isabelle Schneider)
      Schedule: Di 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-04-16)
      Location: T9/Gr. Hörsaal (Takustr. 9)

      Comments

      Welcome to the university and in the exciting field of mathematics! You chose a challenging degree course, which offers you unlimited possibilities. Mathematics is the language of the universe, and studying it means to decipher the secrets behind everything, from the movement of the stars to the software in your smartphones.

      In Analysis I you will get acquainted with the basics of mathematics, from natural numbers to more complex topics like differentiation and integration. From optimizing flows of traffic, to understanding financial markets, to developing new technologies -- the abilities that you gain here have real, tangible applications that go far beyond the lecture hall.

      The importance of the tutorials and of Zentralübung can’t be stressed enough. In the tutorials you will not only discuss the exercises, but also learn how to explain mathematical concepts to others -- an essential ability in mathematics and beyond. In the Zentralübung we will discuss your questions informally and in an interactive way, which is necessary for a comprehensive understanding.

      Good luck on your journey to success!

      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 (Isabelle Schneider)
      Schedule: Di 14:00-16:00, Mi 10:00-12:00, Mi 14:00-16:00, Do 08:00-10:00 (Class starts on: 2024-04-16)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

  • Linear Algebra I (10 CP)

    0082fA1.5
    • 19201401 Lecture
      Linear Algebra I (Klaus Altmann)
      Schedule: Di 12:00-14:00, Fr 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-04-16)
      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 (Klaus Altmann)
      Schedule: Di 14:00-16:00, Mi 12:00-14:00, Do 12:00-14:00 (Class starts on: 2024-04-16)
      Location: A3/SR 119 (Arnimallee 3-5)

  • Analysis II (10 CP)

    0082fA2.1
    • 19211601 Lecture
      Analysis II Sommer (Holger Reich)
      Schedule: Di 10:00-12:00, Do 10:00-12:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-04-16)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Comments

      Content

      0. Additions to Analysis I.
      1. Basic topological notions.
      2. Normed and metric spaces. Convergence
      3. Continuity, compactness.
      4. Differential calculus in several variables. Partial, total and continuous diferentiability.
      5. Curves and integrals over curves.
      6. Theorem on the inverse function. The implicit function theorem.

      On the Homepage you will find detailed Information of our research seminar.

      Suggested reading

      • Bröcker, Theodor, Analysis I, Analysis II und Analysis III, Spektrum der Wissenschaft-Verlag.
      • Forster, Otto, Analysis 2, Vieweg-Verlag.
      • Alle genannten Bücher sind auch über die Fachbibliothek der FU Berlin elektronisch verfügbar.
    • 19211602 Practice seminar
      Practice seminar for Analysis II (Holger Reich)
      Schedule: Mo 10:00-12:00, Mi 10:00-12:00, Do 12:00-14:00, Do 16:00-18:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-04-15)
      Location: A3/SR 115 (Arnimallee 3-5)

  • Linear Algebra II (10 CP)

    0082fA2.2
    • 19211701 Lecture
      Linear Algebra II (Alexandru Constantinescu)
      Schedule: Mo 12:00-14:00, Mi 12:00-14:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-04-15)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Additional information / Pre-requisites

      See http://page.mi.fu-berlin.de/werner99/.

      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 (Alexandru Constantinescu)
      Schedule: Do 08:00-10:00, Do 10:00-12:00, Do 16:00-18:00, Fr 08:00-10:00, Fr 10:00-12:00 (Class starts on: 2024-04-18)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

  • Proseminar Mathematics - Teacher Training

    0082fA3.2
    • 19200810 Proseminar
      Undergraduate Seminar: History + Contextualization of Mathematics (Anina Mischau)
      Schedule: Do 12:00-14:00 (Class starts on: 2024-04-18)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Comments

      This proseminar, specially designed for teacher training students, focuses on the discovery and development of mathematics as part of culture and society. From the point of view of "becoming mathematics", the main focus will be on the intra-mathematical development of selected mathematical topics and findings, their historical and cultural contextualisation and the actors involved in this development. In addition, some of these topics and findings will be examined as examples of where and to what extent they have found their way into other areas and contexts, e.g. in art, music, architecture or other scientific disciplines.

      Suggested reading

      ... wird im Seminar bekannt gegeben.
    • 19203311 Seminar Cancelled
      Proseminar/Seminar Gruppentheorie (Kivanc Ersoy)
      Schedule: Di 14:00-16:00 (Class starts on: 2024-04-16)
      Location: A6/SR 009 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Participants should feel comfortable with the contents of 'Linear algebra 1', and perhaps 'Linear algebra 2'. If there are interested students who have already done the 'Algebra und Zahlentheorie' module, we will also be able to find interesting topics for them.

      Comments

      Fundamental concepts of infinite group theory, series of subgroups, radicals and residuals, finiteness conditions: finitely generated and finitely presented groups, groups with finite rank, periodic and locally finite groups, maximal and minimal conditions. Solvable and nilpotent groups, properties of upper and lower central series, residually finite groups, generalized nilpotent groups, Engel groups, local theorems and generalized solvable groups.

      Textbook: Finiteness conditions and Generalized Solvable groups, Derek Robinson

      The course will be held in English
    • 19221917 Seminar / Undergraduate Course
      Introduction to Representation Theory (Georg Lehner)
      Schedule: Mi 10:00-12:00 (Class starts on: 2024-04-17)
      Location: A6/SR 007/008 Seminarraum (Arnimallee 6)

      Additional information / Pre-requisites

      Lineare Algebra I

      Comments

      If one has an object with symmetries, for example a polytope, or also a polynomial, one has a group - namely the group of symmetries of said object. The study of groups thus forms one of the most central topics in mathematics. A group can be studied by its action on such objects. We are going to study, in some sense, the easiest possible actions of finite groups: the linear actions on vector spaces. Such actions are called representations of finite groups. The study of such actions combines the methods of linear algebra with group theory, and has numerous applications in different areas of mathematics.

      Preliminary program:

      Generalities on linear representations, irreducible representations and operation on representations. Character theory, Schur’s lemma, decompositions of representations. Subgroups and induced representations. Explicit examples. Representations of the symmetric group.

      Suggested reading


      W. Fulton, J. Harris, Representation Theory - A First Course, GTM 129
    • 19229917 Seminar / Undergraduate Course
      Proofs from The Book (Pavle Blagojevic)
      Schedule: -
      Location: keine Angabe

      Comments

      The goal of the seminar is for students to get introduced to beautiful and important proofs from all areas of mathematics for which deep mathematical knowledge is not necessary. In the seminar we will read and present different chapters of the celebrated book "Proofs from THE BOOK" by Martin Aigner and Günter Ziegler. It is to our advantage that the book is available in multiple languages and is written in a very accessible way.
      The plan is to meet once a week. Each weak there will be a talk from one of the students.
      Further details will be discussed on the first meeting.

      -- Literature --


      Deutsche Version:
      https://link.springer.com/book/10.1007/978-3-642-02259-3

      English Version:
      https://link.springer.com/book/10.1007/978-3-662-57265-8

      Suggested reading

      Aigner & Ziegler: Das Buch der Beweise.

      Deutsche Version:
      https://link.springer.com/book/10.1007/978-3-642-02259-3

      English Version:
      https://link.springer.com/book/10.1007/978-3-662-57265-8
    • 19234810 Proseminar
      Women in the History of Mathematics and Computer Science (Anina Mischau)
      Schedule: Di 14:00-16:00 (Class starts on: 2024-04-16)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      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.

  • Modules w/o courses in this semester

    6 Modules
    • Discovering Mathematics I (10 CP) 0082fA1.1
    • Computer-Oriented Mathematics I (5 CP) 0082fA4.1
    • Computer-Oriented Mathematics II (5 CP) 0082fA4.2
    • Computer Algebra 0082fA4.3
    • Numbers, Equations, Algebraic Structures (10 CP) 0082fA2.3
    • Probability and Statistics (10 CP) 0082fA3.1