This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Module version of SS 2022 (current)
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
|available module versions|
|SS 2022||WS 2020/1||SS 2020||SS 2015||WS 2011/2|
MA3241 is a semester module in English language at Master’s level which is offered irregular.
This Module is included in the following catalogues within the study programs in physics.
- Catalogue of non-physics elective courses
|Total workload||Contact hours||Credits (ECTS)|
|270 h||90 h||9 CP|
Content, Learning Outcome and Preconditions
Part 2: fundamental group: paths, multiplication of paths, homotopy of paths, fundamental group, fundamental group of a circle, if time permits also: Brouwer Fixed Point Theorem, free groups, Theorem of Seifert and Van Kampen, Introduction to homology
MA1001/MA0001 (Analysis 1) , MA1002/MA0002 (Analysis 2), MA1101/MA0004 (Linear Algebra and Discrete Structures 1), MA1102/MA0005 (Linear Algebra and Discrete Structures 2)
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
|UE||2||Topology (Exercise Session)|
Learning and Teaching Methods
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress. At the beginning of the module, the practice sessions will be offered under guidance, but during the term the sessions will become more independent, and intensify learning individually as well as in small groups.
Laures, Szymik: Grundkurs Topologie
Bradley, Bryson, Terilla: Topology: A Categorical Approach
Hatcher: Algebraic Topology
Description of exams and course work
It tests if the students are able to reproduce and verify definitions and main assertions introduced in the lecture and to apply them to specific examples. In part of the questions, students will be asked for the final result of a calculation or to merely state a particular example, in others they have to present a shorter proof, a complete calculation, or a more involved example.
The exam may be repeated at the end of the semester.