Entry requirements

B.SC. with 90 credit points Mathematics

Learning outcomes

In order to pass the course (grade 3) the student should

master the various manifold concepts that are introduced in the course, be able to give an account of their definitions and know how to use them in specific situations;

be familiar with the central theorems of the theory, know how to use these theorems and how to prove them;

be able to describe some important applications of the theory.

Content

Manifolds with and without boundary, tangent spaces, vector fields, differential forms, Stokes' theorem, Poincaré's lemma, de Rham cohomology, the Laplace operator, harmonic forms, Hodge theory, flows of vectorfields, Frobenius' theorem, symplectic forms, contact forms, mechanics.

Instruction

Lectures and problem solving sessions.

Assessment

Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.