Modulets indhold, forløb og pædagogik

Læringsmål

Viden

• know central notions and results about smooth manifolds, their tangent spaces, smooth maps, both in theory and for essential examples
• have acquired knowledge about differential geometric issues among several of the following topics: vector bundles and vector fields, differential  forms, Riemannian manifolds, curvature notions, Lie groups, geodesics, integration and/or dynamical systems on manifolds
• have acquired knowledge about differential topological issues among several of the following topics: regular and critical points, embedding, immersion, transversality

Færdigheder

• are able to present proofs of central results within differential geometry and topology
• can apply notions and methods from these subjects to important examples
• can through analysis and calculations explain properties of geometric objects

Kompetencer

• are able to understand and to apply results from analysis and (linear) algebra for questions originating in geometry
• can independently formulate relevant questions and acquire new insights with point of departure in interactions of analysis, linear algebra and geometry

Undervisningsform

Forelæsninger med tilhørende opgaveregning.

Omfang og forventet arbejdsindsats

Kursusmodulets omfang er 5 ECTS svarende til 150 timers studieindsats.

Eksamen

Prøver