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.

Edeltävät opinnot tai edeltävä osaaminen

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


Basic homotopy theory and theory of vector bundles


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

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


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

Oppimista tukevat aktiviteetit ja opetusmenetelmät

Lectures and exercise classes


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

Arviointimenetelmät ja -kriteerit

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


Exam, other methods will be described later