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Course

Lehramt an Integrierten Sekundarschulen und Gymnasien – Quereinstieg (ab WiSe 2019)

Fachwissenschaft und Fachdidaktik Mathematik 2

0513b_m72
  • Grundlagen und Vertiefung Fachdidaktik Mathematik im Profil Quereinstieg

    0504bA1.1
    • 19224301 Lecture
      Basics of Mathematics Education (Brigitte Lutz-Westphal, Benedikt Weygandt)
      Schedule: Mo 12:00-14:00 (Class starts on: 2024-10-14)
      Location: T9/Gr. Hörsaal (Takustr. 9)

      Comments

      The lecture deals with fundamental topics of mathematics education, which are taken up again and deepened in the seminars. It takes place on 8 dates as a double lesson.

    • 19224411 Seminar
      Basics of Mathematics Education 1 (N.N.)
      Schedule: Mo 14:00-16:00, zusätzliche Termine siehe LV-Details (Class starts on: 2024-10-14)
      Location: A3/ 024 Seminarraum (Arnimallee 3-5)

      Comments

      In this seminar material didactic questions, i.e. for the respective topic characteristic possibilities, difficulties and hurdles for learning are treated. This seminar is offered on several parallel dates, some of which focus on different topics. Please select one of the seminars offered.

    • 19224511 Seminar
      Basics of Mathematics Education 1 (N.N.)
      Schedule: Di 10:00-12:00 (Class starts on: 2024-10-15)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      Comments

      In this seminar material didactic questions, i.e. for the respective topic characteristic possibilities, difficulties and hurdles for learning are treated. This seminar is offered on several parallel dates, some of which focus on different topics. Please select one of the seminars offered.

    • 19224611 Seminar
      Basics of Mathematics Education 1 (Martina Lenze)
      Schedule: Di 14:00-16:00 (Class starts on: 2024-10-15)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      Comments

      In this seminar material didactic questions, i.e. for the respective topic characteristic possibilities, difficulties and hurdles for learning are treated. This seminar is offered on several parallel dates, some of which focus on different topics. Please select one of the seminars offered.

    • 19224711 Seminar
      Basics of Mathematics Education 1 (Benedikt Weygandt)
      Schedule: Do 10:00-12:00 (Class starts on: 2024-10-17)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      Comments

      In this seminar material didactic questions, i.e. for the respective topic characteristic possibilities, difficulties and hurdles for learning are treated. This seminar is offered on several parallel dates, some of which focus on different topics. Please select one of the seminars offered.

    • 19224811 Seminar
      Basics of Mathematics Education 1 (Benedikt Weygandt)
      Schedule: Do 12:00-14:00 (Class starts on: 2024-10-17)
      Location: A3/019 Seminarraum (Arnimallee 3-5)

      Comments

      In this seminar material didactic questions, i.e. for the respective topic characteristic possibilities, difficulties and hurdles for learning are treated. This seminar is offered on several parallel dates, some of which focus on different topics. Please select one of the seminars offered.

  • Vertiefung Fachdidaktik Mathematik im Profil Quereinstieg

    0504bA1.2
    • 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

  • F2 Mathematics - teaching Mathematics in schools - subject 2

    0564aA1.3
  • Mathematics area of specialisation

    0513bA2.1
    • 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)

    • 19201401 Lecture
      Linear Algebra I (Alexander Schmitt)
      Schedule: Mo 08:00-10:00, Mi 08:00-10:00 (Class starts on: 2024-10-14)
      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

    • 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:

    • 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.

    • 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.

    • 19220901 Lecture
      Probability and Statistics (Olaf Parczyk)
      Schedule: Di 08:00-10:00, Do 08:00-10:00 (Class starts on: 2024-10-15)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Comments

      Es werden insbesondere folgende Inhalte vermittelt.
      –  Diskrete Wahrscheinlichkeitsräume und -maße
      –  Diskrete und stetige Zufallsvariablen und ihre Verteilungen, wichtige Beispiele
      –  Erwartungswert, (Ko-)Varianz, Korrelation
      –  Bedingte Wahrscheinlichkeit, Unabhängigkeit
      –  Schwaches Gesetz der großen Zahl
      –  Zentraler Grenzwertsatz
      –  Datenanalyse und deskriptive Statistik: Histogramme; empirische Verteilung; Kenngrößen von Stichprobenver-teilungen; Beispiele irreführender deskriptiver Statistiken; lineare Regression
      –  Elementare Begriffe und Techniken des Testens und Schätzens: Maximum-Likelihood-Prinzip; Konfidenzinter-valle; Hypothesentests; Fehler erster und zweiter Art 

       

      Suggested reading

      E. Behrends: Elementary Stochastics, Springer, 2013
          H.-O. Georgii: Stochastics: Introduction to Probability Theory and Statistics, De Gruyter, 2007
          U. Krengel: Introduction to probability theory and statistics, Vieweg, 2005
          D. Meintrup, S. Schäffler, Stochastics: Theory and Applications, Springer, 2005.
          Most of the books listed below are available online at the UB. For this purpose, there is an extensive hand apparatus for stochastics in the mathematic library.

    • 19233701 Lecture
      Discovering Mathematics I (Alexandru Constantinescu)
      Schedule: Mi 10:00-12:00, Fr 10:00-12:00 (Class starts on: 2024-10-16)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Additional information / Pre-requisites

      This course is aimed at students of teacher training courses.

      Comments

      subject matter

      The focus is on practicing mathematical ways of thinking and working. These are trained on the basis of problems from elementary number theory and elementary geometry.

      compulsory attendance

      Attendance is mandatory for the central exercise on Monday.

    • 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)
    • 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)
    • 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)
    • 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)
    • 19220902 Practice seminar
      Practice seminar for Probability and Statistics (Olaf Parczyk)
      Schedule: Mo 10:00-12:00, Mo 12:00-14:00, Do 10:00-12:00 (Class starts on: 2024-10-14)
      Location: 1.3.48 Seminarraum T3 (Arnimallee 14)
    • 19233702 Practice seminar
      Practice seminar for Discovering Mathematics I (Alexandru Constantinescu)
      Schedule: Mo 14:00-16:00, Mo 16:00-18:00, Di 08:00-10:00, Mi 14:00-16:00, Do 12:00-14:00, Do 14:00-16:00 (Class starts on: 2024-10-14)
      Location: A7/SR 031 (Arnimallee 7)
    • 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.

  • Discovering Mathematics I (10 CP)

    0082fA1.1
    • 19233701 Lecture
      Discovering Mathematics I (Alexandru Constantinescu)
      Schedule: Mi 10:00-12:00, Fr 10:00-12:00 (Class starts on: 2024-10-16)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Additional information / Pre-requisites

      This course is aimed at students of teacher training courses.

      Comments

      subject matter

      The focus is on practicing mathematical ways of thinking and working. These are trained on the basis of problems from elementary number theory and elementary geometry.

      compulsory attendance

      Attendance is mandatory for the central exercise on Monday.

    • 19233702 Practice seminar
      Practice seminar for Discovering Mathematics I (Alexandru Constantinescu)
      Schedule: Mo 14:00-16:00, Mo 16:00-18:00, Di 08:00-10:00, Mi 14:00-16:00, Do 12:00-14:00, Do 14:00-16:00 (Class starts on: 2024-10-14)
      Location: A7/SR 031 (Arnimallee 7)
  • Probability and Statistics (10 CP)

    0082fA3.1
    • 19220901 Lecture
      Probability and Statistics (Olaf Parczyk)
      Schedule: Di 08:00-10:00, Do 08:00-10:00 (Class starts on: 2024-10-15)
      Location: A3/Hs 001 Hörsaal (Arnimallee 3-5)

      Comments

      Es werden insbesondere folgende Inhalte vermittelt.
      –  Diskrete Wahrscheinlichkeitsräume und -maße
      –  Diskrete und stetige Zufallsvariablen und ihre Verteilungen, wichtige Beispiele
      –  Erwartungswert, (Ko-)Varianz, Korrelation
      –  Bedingte Wahrscheinlichkeit, Unabhängigkeit
      –  Schwaches Gesetz der großen Zahl
      –  Zentraler Grenzwertsatz
      –  Datenanalyse und deskriptive Statistik: Histogramme; empirische Verteilung; Kenngrößen von Stichprobenver-teilungen; Beispiele irreführender deskriptiver Statistiken; lineare Regression
      –  Elementare Begriffe und Techniken des Testens und Schätzens: Maximum-Likelihood-Prinzip; Konfidenzinter-valle; Hypothesentests; Fehler erster und zweiter Art 

       

      Suggested reading

      E. Behrends: Elementary Stochastics, Springer, 2013
          H.-O. Georgii: Stochastics: Introduction to Probability Theory and Statistics, De Gruyter, 2007
          U. Krengel: Introduction to probability theory and statistics, Vieweg, 2005
          D. Meintrup, S. Schäffler, Stochastics: Theory and Applications, Springer, 2005.
          Most of the books listed below are available online at the UB. For this purpose, there is an extensive hand apparatus for stochastics in the mathematic library.

    • 19220902 Practice seminar
      Practice seminar for Probability and Statistics (Olaf Parczyk)
      Schedule: Mo 10:00-12:00, Mo 12:00-14:00, Do 10:00-12:00 (Class starts on: 2024-10-14)
      Location: 1.3.48 Seminarraum T3 (Arnimallee 14)
  • 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

      • 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 I

    0084dA1.4
    • 19201401 Lecture
      Linear Algebra I (Alexander Schmitt)
      Schedule: Mo 08:00-10:00, Mi 08:00-10:00 (Class starts on: 2024-10-14)
      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)
  • 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)
  • Proseminar Mathematics - Teacher Training

    0082fA3.2
    • 19203311 Seminar
      Proseminar/Seminar Gruppentheorie (N.N.)
      Schedule: -
      Location: keine Angabe

      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

      In this (pro)seminar we will recapitulate the basics of group theory and study a few deeper properties and theorems. Possible topics are: solvable groups, nilpotent groups, representations of finite groups, the theorem of Schur-Zassenhaus, the theorems of P. Hall.

    • 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

    • 19214210 Proseminar
      Science Communication on Mathematics (Anna Maria Hartkopf)
      Schedule: -
      Location: keine Angabe

      Comments

      The goal of this seminar is the development of a science communication format on a mathematical topic. 

    • 19229917 Seminar / Undergraduate Course
      Proseminar/Seminar Geometrie / Optimierung / KI / Spieltheorie (Georg Loho)
      Schedule: Di 16:00-18:00 (Class starts on: 2024-10-15)
      Location: A7/SR 031 (Arnimallee 7)

      Comments

      Je nach Bedarf: 

      "KI als Werkzeug in der Mathematik" oder "Geometrie & Optimierung" oder etwas wie "Spieltheorie & Gesellschaft"

      Suggested reading

      G. D. James "The representation theory of the symmetric group" Springer, Lecture Notes in Mathemtaics vol 682, 1978

      B. E. Sagan "The Symmetric Group - Representations, Combinatorial Algorithms, and Symmetric Functions" 2nd Edition, 2000

    • 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

  • 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)