Course MAT-12-26-K-3
Introduction to Topology (2V+1U, 4.5 LP)
Course Type
| SWS | Type | Course Form | CP (Effort) | Presence-Time / Self-Study | |
|---|---|---|---|---|---|
| - | K | Lecture with exercise classes (V/U) | 4.5 CP | 93 h | |
| 2 | V | Lecture | 28 h | ||
| 1 | U | Exercise class (in small groups) | 14 h | ||
| (2V+1U) | 4.5 CP | 42 h | 93 h | ||
Basedata
| SWS | 2V+1U |
|---|---|
| CP, Effort | 4.5 CP = 135 h |
| Position of the semester | 1 Sem. in SuSe |
| Level | [3] Bachelor (Core) |
| Language | [DE] German |
| Lecturers |
+ further Lecturers of the department Mathematics
|
| Area of study | [MAT-GRU] Mathematics (B.Sc. year 1 and 2) |
| Livecycle-State | [NORM] Active |
Possible Study achievement
- Verification of study performance: proof of successful participation in the exercise classes (ungraded)
- Examination number (Study achievement): 83150 ("Exercise Class Introduction to Topology")
- Details of the examination (type, duration, criteria) will be announced at the beginning of the course.
Contents
- set-theoretical topology: topological spaces and continuous mappings, connection, separation axioms, compactness, constructions (in particular: products, quotients),
- homotopy of mappings,
- fundamental group.
Competencies / intended learning achievements
The students know the basic concepts, statements and methods of set-theoretical topology. They have learned how to generalize the concept of continuity on metric spaces to abstract topological spaces, thus enlarging their capacity for abstraction. The Students are able to apply topological concepts in various areas of mathematics. In particular, they were taught how to translate descriptive arguments into mathematical proofs. By treating the fundamental group as a topological invariant, the students have learnt how to use algebraic methods to answer purely topological questions. In particular, they developed a deeper understanding of the interplay of mathematical disciplines.
Literature
- M.A. Armstrong: Basic Topology,
- A.T. Fomenko: Visual Geometry and Topology,
- D.B. Fuks, V.A. Rokhlin: Beginner`s Course in Topology,
- K. Jänich: Topologie,
- H. Seifert, W. Threlfall: Lehrbuch der Topologie.
Materials
Further literature will be announced in the lecture(s); exercise material is provided.
Registration
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
Modules:
Requirements for attendance (formal)
None
References to Course [MAT-12-26-K-3]
| Module | Name | Context | |
|---|---|---|---|
| [MAT-12-20L_ERW-M-3] | Topic Module A: Mathematics in the Interplay between Abstraction and Concretisation | WP: Obligation to choose | 2V+1U, 4.5 LP |
| [MAT-12-20L-M-3] | Topic Module A: Mathematics in the Interplay between Abstraction and Concretisation | WP: Obligation to choose | 2V+1U, 4.5 LP |
| Course-Pool | Name | ||
| [MAT-10-KPOOL-3] | Pure Mathematics (B.Sc. Mathematics) |