## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-40-21-K-6

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U)
4 V Lecture 6.0 CP 56 h 124 h
2 U Exercise class (in small groups) 3.0 CP 28 h 62 h
(4V+2U) 9.0 CP 84 h 186 h

## Basedata

SWS 4V+2U 9.0 CP = 270 h 1 Sem. irreg. [6] Master (General) [EN] English [MAT-AGCA] Algebra, Geometry and Computer Algebra [NORM] Active

## Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

## Contents

• Concept of manifold, in particular differentiable manifold,
• tangential and other vector bundles to manifolds,
• partition of unity,
• orientation
• differential equations on manifolds, Ehresmann's fibration theorem,
• differential forms and integration, general theorem of Stokes,
• special structures on manifolds (e.g. basic concepts of complex, Riemannian and symplectic manifolds).

## Literature

• T. Bröcker, K. Jänich: Introduction to Differential Topology,
• K. Jänich: Vector Analysis,
• S. Lang: Introduction to Differentiable Manifolds,
• J.M. Lee: Introduction to Smooth Manifolds,
• M. Spivak: Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus.

## Materials

Further literature will be announced in the lecture; Exercise material is provided.

## Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)

## Requirements for attendance (informal)

Additional knowledge from the courses [MAT-12-25-K-3] and [MAT-12-27-K-3] is useful but not necessarily required.

None

## References to Course [MAT-40-21-K-6]

Module Name Context
[MAT-40-21-M-6] Manifolds P: Obligatory 4V+2U, 9.0 LP
Course-Pool Name
[MAT-40-4V-KPOOL-4] Elective Courses Algebra, Geometry and Computeralgebra (4V, B.Sc.)
[MAT-70-4V-KPOOL-4] Elective Courses Analysis and Stochastics (4V, B.Sc.)