- Concept of manifold, in particular differentiable manifold,
- tangential and other vector bundles to manifolds,
- partition of unity,
- 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).
Manifolds (M, 9.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-40-21-M-6||Manifolds||9.0 CP (270 h)|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (General)|
|Area of study||[MAT-AGCA] Algebra, Geometry and Computer Algebra|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
|P||84 h||186 h||
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: irregular (by arrangement)
- Examination number: 84155 ("Manifolds")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
By completing the given exercises, the students will have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. In addition, they have learnt how to apply these techniques to new problems, analyze them and develop solution strategies independently or by team work.
- 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.
Requirements for attendance of the module (informal)
Requirements for attendance of the module (formal)None
References to Module / Module Number [MAT-40-21-M-6]
|Course of Study||Section||Choice/Obligation|
|[MAT-88.105-SG] M.Sc. Mathematics||[Core Modules (non specialised)] Pure Mathematics||[WP] Compulsory Elective|
|[MAT-88.706-SG] M.Sc. Mathematics International||[Core Modules (non specialised)] Pure Mathematics||[WP] Compulsory Elective|
|[MAT-GM-MPOOL-5]||General Mathematics (Introductory Modules M.Sc.)|