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Module MA5203

This Module is offered by TUM Department of Mathematics.

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.

Basic Information

MA5203 is a semester module in English language at Master’s level which is offered irregular.

This module description is valid from WS 2010/1 to WS 2012/3.

Total workloadContact hoursCredits (ECTS)
90 h 30 h 3 CP

Content, Learning Outcome and Preconditions


manifolds, (semi-) riemannian geometry, curvature theory, vector bundles, Lie groups.

Learning Outcome

At the end of the module students are able to apply the differential geometric concepts of differentiable manifolds. They are able to handle curved spaces using analytic methods.


MA1001 Analysis 1, MA1002 Analysis 2, MA1101 Linear Algebra 1, MA1102 Linear Algebra 2 or equivalent knowledge in linear algebra and analysis. MA2204 Elementary Differential Geometry is useful, but not necessary.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

VO 2 Manifolds Hoffmann, T. documents

Learning and Teaching Methods

Vorlesung, Übung, Übungsaufgaben zum Selbststudium




Barret O'Neil: semi-riemanian geometry with applications to relativity, Academic Press Inc. 1983, ISBN 0-12-526740-1.
S. W. Hawking and G. F. Ellis: The large scale structure of space-time, Cambridge University Press, 1973, ISBN 0-521-09906-4.

Module Exam

Description of exams and course work

Klausur oder mündliche Prüfung

Exam Repetition

The exam may be repeated at the end of the semester.

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