Course MAT-40-21-K-6

Manifolds (4V+2U, 9.0 LP)

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

SWS	4V+2U
CP, Effort	9.0 CP = 270 h
Position of the semester	1 Sem. irreg.
Level	[6] Master (General)
Language	[EN] English
Lecturers	The Lecturers of the department Mathematics
Area of study	[MAT-AGCA] Algebra, Geometry and Computer Algebra
Additional informations
Livecycle-State	[NORM] Active

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.

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).

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.

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

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

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

None

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.)