## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-12-26-K-3

## 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 4.5 CP = 135 h 1 Sem. in SuSe [3] Bachelor (Core) [DE] German Gathmann, Andreas, Prof. Dr. (PROF | DEPT: MAT) Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Thiel, Ulrich, Prof. Dr. (PROF | DEPT: MAT) [MAT-GRU] Mathematics (B.Sc. year 1 and 2) [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).

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)