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This entry is from Winter semester 2019/20 and might be obsolete. No current equivalent could be found.
Algebraic Topology
(dt. Algebraische Topologie)
Level, degree of commitment | Specialization module, compulsory elective module |
Forms of teaching and learning, workload |
Lecture (4 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 180 h private study) |
Credit points, formal requirements |
9 CP Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written or oral examination |
Language, Grading |
German,The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Mathematics. |
Duration, frequency |
One semester, irregular |
Person in charge of the module's outline | Prof. Dr. Sönke Rollenske, Prof. Dr. Volkmar Welker |
Contents
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).
Qualification Goals
The students
- know basic topological constructions,
- can use algebraic invariants to solve topological problems,
- can recognize and use functorial relationships.
They deepen
- 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.
Prerequisites
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.
Applicability
The module can be attended at FB12 in study program(s)
- B.Sc. Mathematics
- M.Sc. Computer Science
- M.Sc. Mathematics
- LAaG Mathematics
When studying M.Sc. Mathematics, this module can be attended in the study area Specialization Modules in Mathematics.
The module can also be used in other study programs (export module).
Die Wahlmöglichkeit des Moduls ist dadurch beschränkt, dass es der Reinen Mathematics zugeordnet ist.
Recommended Reading
- 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
Please note:
This page describes a module according to the latest valid module guide in Winter semester 2019/20. 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:
- Winter 2016/17
- Summer 2018
- Winter 2018/19
- Winter 2019/20
- Winter 2020/21
- Summer 2021
- Winter 2021/22
- Winter 2022/23
- Winter 2023/24 (no corresponding element)
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.