Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-12-20L_ERW-M-3

Topic Module A: Mathematics in the Interplay between Abstraction and Concretisation (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-12-20L_ERW-M-3 Topic Module A: Mathematics in the Interplay between Abstraction and Concretisation 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in WiSe/SuSe
Level [3] Bachelor (Core)
Language [DE] German
Module Manager
Lecturers
Area of study [MAT-EDU] Mathematics (B.Ed./M.Ed.)
Reference course of study [MAT-B4.105-SG] ZEP LaG Mathematics
Livecycle-State [NORM] Active

Notice

This module can only be chosen by students who are studying mathematics in the certificate course of study [MAT-B4.105-SG].

Courses

Choice of courses amounting to 4V+2U from the following list:
Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+1U MAT-12-22-K-3
Introduction to Algebra
WP 42 h 93 h - - PL1 4.5 WiSe
2V+1U MAT-12-23-K-3
Introduction to Functional Analysis
WP 42 h 93 h - - PL1 4.5 WiSe
2V+1U MAT-12-24-K-3
Introduction to Complex Analysis
WP 42 h 93 h - - PL1 4.5 WiSe
2V+1U MAT-12-26-K-3
Introduction to Topology
WP 42 h 93 h - - PL1 4.5 SuSe
2V+1U MAT-12-21-K-3
Elementary Number Theory
WP 42 h 93 h - - PL1 4.5 SuSe
2V+1U MAT-12-28-K-3
Measure and Integration Theory
WP 42 h 93 h - - PL1 4.5 SuSe
  • About [MAT-12-22-K-3]: Title: "Introduction to Algebra"; Presence-Time: 42 h; Self-Study: 93 h
  • About [MAT-12-23-K-3]: Title: "Introduction to Functional Analysis"; Presence-Time: 42 h; Self-Study: 93 h
  • About [MAT-12-24-K-3]: Title: "Introduction to Complex Analysis"; Presence-Time: 42 h; Self-Study: 93 h
  • About [MAT-12-26-K-3]: Title: "Introduction to Topology"; Presence-Time: 42 h; Self-Study: 93 h
  • About [MAT-12-21-K-3]: Title: "Elementary Number Theory"; Presence-Time: 42 h; Self-Study: 93 h
  • About [MAT-12-28-K-3]: Title: "Measure and Integration Theory"; Presence-Time: 42 h; Self-Study: 93 h
Besides the courses in the above list, other lectures with exercises offered by the Department of Mathematics on a subject which is selectable for this module according to the curricular standards maybe selected, too.

The course [MAT-12-22-K-3] "Introduction to Algebra" can only be selected if it has not already been used for the module [MAT-12-10L-M-2] "Fundamentals of Mathematics C: Geometry, Elementary Algebra and Number Theory".

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
    It is generally possible to give the module examination PL1 totally or in parts to different courses than the required study achievements (proofs of successful participation in the exercise classes). This requires that none of the courses involved has already been included in another module.

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

Choice of one or more topics from the following areas:
  • General Algebraic Systems,
  • Functional Analysis,
  • Complex Analysis,
  • Geometry / Differential Geometry,
  • Group Theory,
  • Field Theory,
  • Manifolds and Cell Complexes,
  • Topology.

Competencies / intended learning achievements

The students
  • know current fields of application and are able to work independently using scientific methods;
  • have experience in presenting and teaching mathematical topics.

Literature

see the respective course descriptions.

Materials

Exercise material will be provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance of the module (informal)

Depending on the choice, additional (special) content requirements, see the respective course descriptions.

Modules:

Requirements for attendance of the module (formal)

Only students who have already passed one of the modules [MAT-10-11-M-2] Grundlagen der Mathematik A: Lineare Algebra I und Analysis I or [MAT-10-12L_ERW-M-2] Grundlagen der Mathematik B: Lineare Algebra II und Analysis II may take the module examination for this advanced module.

References to Module / Module Number [MAT-12-20L_ERW-M-3]

Course of Study Section Choice/Obligation
[MAT-B4.105-SG] ZEP LaG Mathematics [Compulsory Modules] Compulsory Modules [P] Compulsory