### Instruction

### Target group

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

### Prerequisites

Linear algebra I & II, Algebra I, Vector analysis, Topology I & II

### Learning outcomes

Basic homotopy theory and theory of vector bundles

### Timing

Recommended time/stage of studies for completion: 1. or 2. year

Term/teaching period when the course will be offered: varying

### Contents

Homotopy theory and the fundamental group; basic theory of differentiable manifolds, tangent bundles and more generally vector bundles; homotopy classification of vector bundles

### Activities and teaching methods in support of learning

Lectures and exercise classes

### Study materials

Lecture notes; J. Milnor, J. Stasheff: Characteristic classes; D. Husemoller: Fibre bundles

### Assessment practices and criteria

Exam and excercises, Course will be graded with grades 1-5

### Completion methods

Exam, other methods will be described later