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 |
Lecturers of the department Mathematics
|
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 |
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 (informal)
Depending on the choice, additional (special) content requirements, see the respective course descriptions.
Modules:
- [MAT-10-11-M-2] Fundamentals of Mathematics A: Linear Algebra I and Analysis I (M, 15.0 LP)
- [MAT-10-12L-M-2] Fundamentals of Mathematics B: Linear Algebra II and Analysis II (M, 9.0 LP)
Requirements for attendance (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 | [P] Compulsory |
Notice