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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 (Marita Thomas)
      Schedule: Di 10:00-12:00, Do 10:00-12:00 (Class starts on: 2024-10-15)
      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

      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 (Marita Thomas)
      Schedule: Mi 12:00-14:00, Mi 14:00-16:00, Mi 16:00-18:00, Fr 08:00-10:00 (Class starts on: 2024-10-16)
      Location: A7/SR 140 Seminarraum (Hinterhaus) (Arnimallee 7)

  • Analysis II

    0084dA1.2
    • 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

       

    • 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 I

    0084dA1.4
    • 19201401 Lecture
      Linear Algebra I (Alexander Schmitt)
      Schedule: Mo 08:00-10:00, Mi 08:00-10:00 (Class starts on: 2024-10-16)
      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 (Alexander Schmitt)
      Schedule: Mo 10:00-12:00, Mo 16:00-18:00, Mi 10:00-12:00, Fr 14:00-16:00 (Class starts on: 2024-10-14)
      Location: A3/SR 119 (Arnimallee 3-5)

  • Linear Algebra II

    0084dA1.5
    • 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)

  • Probability and Statistics I

    0084dA1.8
    • 19200601 Lecture
      Stochastics I (Ana Djurdjevac)
      Schedule: Mo 14:00-16:00, Mi 12:00-14:00 (Class starts on: 2024-10-14)
      Location: T9/SR 006 Seminarraum (Takustr. 9)

      Additional information / Pre-requisites

      Zielgruppe: Studierende ab dem 3. Semester
      Voraussetzungen: Grundkenntnisse aus Analysis und Linearer Algebra

      Comments

      Inhalt:

      • Prinzipien des Zählens; Elemente der Kombinatorik
      • Modelle vom Zufall abhängiger Vorgänge: Wahrscheinlichkeitsräume, Wahrscheinlichkeitsmaße
      • Bedingte Wahrscheinlichkeiten; Unabhängigkeit; Bayes'sche Regel
      • Zufallsvariablen und ihre Verteilungen; Kenngrössen der Verteilungen: Erwartungswert und Varianz
      • Diskrete Verteilungen: Laplace-Verteilung; Binomialverteilung; geometrische Verteilung
      • Approximation der Binomialverteilung durch die Normalverteilung;
      • Approximation der Binomialverteilung durch die Poissonverteilung
      • Verteilungen mit Dichten: Gleichverteilung; Normalverteilung; Exponentialverteilung
      • Gemeinsame Verteilungen von mehreren Zufallsvariablen: diskret und mit Dichten; Unabhängigkeit von Zufallsvariablen; bedingte Verteilungen; Summen unabhängiger Zufallsvariablen und ihre Verteilungen
      • Kenngrößen gemeinsamer Verteilungen: Erwartungswert, Kovarianz und Korrelation; bedingte Erwartung
      • Grenzwertsätze: schwaches Gesetz der großen Zahl und relative Häufigkeiten; der zentrale Grenzwertsatz
      • Datenanalyse und deskriptive Statistik: Histogramme; empirische Verteilung; Kenngrößen von Stichprobenverteilungen; Beispiele irreführender deskriptiver Statistiken; lineare Regression
      • Elementare Begriffe und Techniken des Testens und Schätzens: Maximum-Likelihood-Prinzip; Konfidenzintervalle; Hypothesentests; Fehler erster und zweiter Art

      Suggested reading

      Literatur:

      • E. Behrends: Elementare Stochastik, Springer, 2013
      • H.-O. Georgii: Stochastik: Einführung in die Wahrscheinlichkeitstheorie und Statistik, De Gruyter, 2007
      • U. Krengel: Einführung in die Wahrscheinlichkeitstheorie und Statistik, Vieweg, 2005
      • D. Meintrup, S. Schäffler, Stochastik: Theorie und Anwendungen, Springer, 2005.
      • Die meisten der oben aufgeführten Bücher gibt es online über die UB.
    • 19200602 Practice seminar
      Tutorial: Stochastics I (N.N.)
      Schedule: Mo 12:00-14:00, Di 08:00-10:00 (Class starts on: 2024-10-14)
      Location: A6/SR 025/026 Seminarraum (Arnimallee 6)

  • Algebra and Number Theroy

    0084dB2.5
    • 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)

  • Modules w/o courses in this semester

    8 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
    • Elementary Geometry 0084dB2.6
    • Geometry 0084dB2.7
    • Proseminar Mathematics - Teacher Training 0082eB1.3
    • Computer-Oriented Mathematics II 0084dA1.7