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German original

Elementary Topology
(dt. Elementare Topologie)

Level, degree of commitment in original study programme Intermediate module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements
6 CP
Translation missing. German original:
Studienleistung: Erreichen von mindestens 50 Prozent der Punkte aus den wöchentlich zu bearbeitenden Übungsaufgaben.
Prüfungsleistung: Klausur oder mündliche Prüfung
Language,
Grading
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
Duration,
frequency
One semester,
irregular
Person in charge of the module's outline Prof. Dr. Ilka Agricola

Contents

  • 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

Qualification Goals

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.

Prerequisites

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die in den Basismodulen vermittelt werden.


Recommended Reading

  • - 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).



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2018/19. 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:

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.