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## Differential Geometry

2018-2019
Dit vak wordt in het Engels aangeboden. Omschrijvingen kunnen daardoor mogelijk alleen in het Engels worden weergegeven.

### Doel vak

The student understands how to read and write in the language of
coordinate free analysis and geometry.
She can reproduce the most important arguments and constructions in
differential geometry.
She can apply these to compute on concrete geometric objects
(manifolds).
The student can translate between geometric intuition and mathematical
statements.

### Inhoud vak

This course is an introduction to the theory of manifolds. Apart from
giving the most relevant definitions from differential geometry
(manifolds, vector bundles and differential forms), we make short
excursions to Riemannian geometry (Riemannian metrics), dynamical
systems (flows of vector fields), as well as to algebraic topology
(fundamental group and de Rham cohomology). More precisely, the subject
list includes:

- Submanifolds, manifolds, tangent vectors
- Smooth maps (between manifolds),
differential,immersions/submersions/embeddings
- Vector fields and their flows, Lie bracket, Lie groups
- Vector bundles, tangent bundles, tensor products, sections
- Riemannian metrics, distances on Riemannian manifolds
- Differential forms, pullbacks, exterior derivative
- Stokes’ Theorem and De Rham cohomology
- Fundamental group and outlook towards algebraic topology

### Onderwijsvorm

Lectures (2 hours per week) and exercise classes (2 hours per week)

### Toetsvorm

Homework (makes up for 30% of the final grade), written final exam
(70%). A grade of 5/10 is required for the final exam to pass the
course.

### Vereiste voorkennis

Single Variable and Multi Variable Calculus, Mathematical Analysis,
Linear Algebra.

### Literatuur

Lee, Introduction to smooth manifolds, Springer

3W, 3W-B

Topology

### Algemene informatie

Vakcode X_400631 6 EC P1+2 400 Engels Faculteit der Bètawetenschappen dr. O. Fabert dr. O. Fabert dr. O. Fabert

### Praktische informatie

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