(dt. Algebraische Topologie)
|Level, degree of commitment in original study programme||Advanced 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 M.Sc. Mathematics.|
|Original study programme||M.Sc. Mathematik / Vertiefungsbereich Mathematik|
|One semester, |
|Person in charge of the module's outline||Prof. Dr. Sönke Rollenske, Prof. Dr. Volkmar Welker|
Algebraic invariants of topological spaces are constructed (homology, cohomology or homotopy). As application elegant solutions for classical problems of topology are derived (invariance of dimension, fixed point theorems).
- know basic topological constructions,
- can use algebraic invariants to solve topological problems,
- can recognize and use functorial relationships.
- the practice of mathematical methods (development of mathematical intuition and its formal justification, training of the ability of abstraction, formulations of proofs),
- in the recitation classes, their oral communication skills through discussion and free speech in front of an audience.
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, Algebra. In addition, we recommend the knowledge of topology that will be taught in an introductory course.
- - Hatcher, Allen Algebraic topology. Cambridge University Press, Cambridge, 2002.
- - May, J. P. A concise course in algebraic topology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1999
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
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.