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

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

There is a possibility to take the exam at the end of the semester.

Condensed Matter

When atoms interact things can get interesting. Fundamental research on the underlying properties of materials and nanostructures and exploration of the potential they provide for applications.

Nuclei, Particles, Astrophysics

A journey of discovery to understanding our world at the subatomic scale, from the nuclei inside atoms down to the most elementary building blocks of matter. Are you ready for the adventure?


Biological systems, from proteins to living cells and organisms, obey physical principles. Our research groups in biophysics shape one of Germany's largest scientific clusters in this area.