(dt. Elementare Topologie)
|Level, degree of commitment in original study programme||Intermediate module, compulsory elective module|
|Forms of teaching and learning,
|Lecture (3 SWS), recitation class (1 SWS), |
180 hours (60 h attendance, 120 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, |
|Person in charge of the module's outline||Prof. Dr. Ilka Agricola|
- Topological spaces and manifolds
- Elementary properties of topological spaces: compactness, orientability, boundary. Many examples: Möbius band, Klein's bottle, projective space etc.
- Classification of surfaces, genus of a surface, triangulations, Boy's surface
- Euler Characteristic and Euler's polyhedron theorem
- Fundamental group, mapping degree and coverings
The students shall
- understand basic principles of topological structures and recognize that such structures can be found in many parts of mathematics,
- practice axiomatic procedures and train their abstraction skills,
- practice mathematical working methods (development of mathematical intuition and its formal justification, proof techniques),
- improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.
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.
- - Boltjanskij, V.G. und Efremovic, V.A.: Anschauliche kombinatorische Topologie. VEB Deutscher Verlag der Wissenschaften (1986).
- - Hatcher, A.: Algebraic topology. Cambridge University Press (2002).
- - Hu, S.-T.: Homotopy Theory. Academic Press (1959).
- - Ossa, E.: Topologie. Vieweg-Verlag (1992).
- - Pontrjagin, L.S.: Grundzüge der kombinatorischen Topologie. VEB Deutscher Verlag der Wissenschaften (1956).
- - Stöcker, R. und Zieschang, H.: Algebraische Topologie. Eine Einführung. Teubner-Verlag (1988).
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.