|Level, degree of commitment in original study programme||Intermediate module, compulsory elective module|
|Forms of teaching and learning,
|Lecture (4 SWS), recitation class (2 SWS), |
270 hours (90 h attendance, 180 h private study)
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
|German,The grading is done with 0 to 15 points according to the examination regulations for study course B.Sc. Mathematics.|
|Original study programme||B.Sc. Mathematik / Mathematik Wahlpflichtmodule|
|One semester, |
Regelmäßig im Wechsel mit anderen intermediate moduleen der Geometrie
|Person in charge of the module's outline||Prof. Dr. Ilka Agricola, Prof. Dr. Pablo Ramacher, Prof. Dr. Volkmar Welker|
- Fundamentals of set-theoretic topology: Open sets, continuous mappings.
- Bases, construction of topological spaces, connectivity, separation properties
- Compactness and metrizability: Central theorems on compactness,
- metrizability conditions
- Homotopy,: homotopy classes and equivalence, mappings of and in spheres
- Coverings: lifting properties, fundamental group
- understand basic principles of topological structures and recognize that such structures can be found in many parts of mathematics,
- practice the axiomatic approach and train their abstraction skills,
- develop a deeper understanding of the implications of elementary conditions on a topological space,
- practice mathematical methods (development of mathematical intuition and its formal justification in proofs),
- improve their oral communication skills in the recitation class by practicing free speech in front of an audience and during discussions.
None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis.
- tom Dieck, Tammo: Topologie. Walter de Gruyter, 2000.
- Jänich, K.: Topologie, Springer 2001.
- Schubert, H.: Topologie, Teubner 1975.
This page describes a module according to the latest valid module guide in Wintersemester 2021/22. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:
- WiSe 2016/17 (no corresponding element)
- SoSe 2018 (no corresponding element)
- WiSe 2018/19
- WiSe 2019/20
- WiSe 2020/21
- SoSe 2021
- WiSe 2021/22
- WiSe 2022/23
The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.
The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.