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AUSGELAUFEN: Lehramt Gymnasium – Quereinstieg (ab 2016 bis Ende SoSe 2021)

Subject Didactics

0513a_m72

  • Analysis I

    0084dA1.1
    • 19202801 Lecture
      Analysis I (Pavle Blagojevic)
      Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      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

      Detailed Information can be found on the Homepage of 19202801 Analysis I.

      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 (Pavle Blagojevic)
      Schedule: Di 14:00-16:00, Mi 10:00-12:00, Mi 14:00-16:00, Do 08:00-10:00 (Class starts on: 2025-04-15)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

  • Analysis II

    0084dA1.2
    • 19211601 Lecture
      Analysis II (Marita Thomas)
      Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2025-04-15)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Comments

      Content

      This is the continuation of the Analysis I course taught in the previous winter term. Central topics of the course are integration in one space dimension and differential calculus of several variables. 

      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 (Marita Thomas)
      Schedule: Mi 14:00-16:00, Do 16:00-18:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-16)
      Location: 1.1.53 Seminarraum E2 (Arnimallee 14)

  • Linear Algebra I

    0084dA1.4
    • 19201401 Lecture
      Linear Algebra I (Niels Lindner)
      Schedule: Di 12:00-14:00, Fr 10:00-12:00 (Class starts on: 2025-04-15)
      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 (Niels Lindner)
      Schedule: Di 14:00-16:00, Mi 12:00-14:00, Do 12:00-14:00 (Class starts on: 2025-04-15)
      Location: 1.1.26 Seminarraum E1 (Arnimallee 14)

  • Linear Algebra II

    0084dA1.5
    • 19211701 Lecture
      Linear Algebra II (Alexander Schmitt)
      Schedule: Mo 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-04-14)
      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 (Alexander Schmitt)
      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: 2025-04-17)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

  • Geometry

    0084dB2.7
    • 19213101 Lecture
      Geometry (Giulia Codenotti)
      Schedule: Di 12:00-14:00, Mi 12:00-14:00 (Class starts on: 2025-04-15)
      Location: A6/SR 032 Seminarraum (Arnimallee 6)

      Comments

      Inhalt

      Diese Vorlesung für das Bachelorstudium soll als natürliche Fortsetzung von Lineare Algebra I und II Fundamente legen für Vorlesungen/Zyklen wie Diskrete Geometrie, Algebraische Geometrie und Differenzialgeometrie.

      Sie behandelt grundlegende Modelle der Geometrie, insbesondere

      euklidische, affine, sphärische, projektive und hyperbolische Geometrie,Möbiusgeometrie, Polarität und Dualität Strukturgruppen, Messen (Längen, Winkel, Volumina), explizite Berechnungen und Anwendungen, Beispiele sowie Illustrationsthemen;

      Dabei werden weitere Bezüge hergestellt, zum Beispiel zur Funktionentheorie und zur Numerik.

      Suggested reading

      Literatur

      1. Marcel Berger. Geometry I
      2. David A. Brannan, Matthew F. Esplen, and Jeremy J. Gray. Geometry
      3. Gerd Fischer. Analytische Geometrie
      4. V.V. Prasolov und V.M. Tikhomirov. Geometry
    • 19213102 Practice seminar
      Practice seminar for Geometry (Giulia Codenotti)
      Schedule: Mo 10:00-12:00, Mo 16:00-18:00 (Class starts on: 2025-04-14)
      Location: A3/SR 119 (Arnimallee 3-5)

  • Computer-Oriented Mathematics II

    0084dA1.7
    • 19211901 Lecture
      Computer-oriented Mathematics II (Robert Gruhlke)
      Schedule: Fr 12:00-14:00 (Class starts on: 2025-04-25)
      Location: T9/Gr. Hörsaal (Takustr. 9)

      Additional information / Pre-requisites

      Studierende der Mathematik (Monobachelor und Lehramt) und Bioinformatik, sowie Numerikinteressierte aus Physik, Informatik und anderen Natur- und Geisteswissenschaften.

      Comments

      Inhalt:

      Die Auswahl der behandelten numerischen Verfahren enthält Polynominterpolation, Newton-Cotes-Formeln zur numerische Integration und Euler-Verfahren für lineare Differentialgleichungen.
    • 19211902 Practice seminar
      Practice seminar for Computer-oriented Mathematics II (Robert Gruhlke)
      Schedule: Di 08:00-10:00, Di 16:00-18:00, Mi 16:00-18:00, Do 08:00-10:00, zusätzliche Termine siehe LV-Details (Class starts on: 2025-04-15)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

  • Modules w/o courses in this semester

    9 Modules
    • Teaching methodology Mathematics - selected topics 0213bA1.1
    • Teaching methodology Mathematics - development, evaluation and research 0213bA1.2
    • Student Teaching Lab: Mathematics (Subject 2) 0214bA1.3
    • Mathematics area of specialisation 0213bA1.4
    • Probability and Statistics I 0084dA1.8
    • Algebra and Number Theroy 0084dB2.5
    • Elementary Geometry 0084dB2.6
    • Proseminar Mathematics - Teacher Training 0082eB1.3
    • Computer-Oriented Mathematics I 0084dA1.6