Entry requirements

BSc and the courses Real Analysis and Topology I.

Learning outcomes

In order to pass the course the student should

• be able to define the various manifold concepts that are introduced during the course and know how to apply and interpret them in specific examples;
• be familiar with the central theorems of the theory, know how to use these theorems and how to prove them;
• be able to use the theory, methods and techniques of the course to solve problems.

Content

Manifolds, partition of the unit, tangent space, differentials, submanifolds, the tangent bundle and associated tensor bundles, vector fields. Differential forms, integration, Stokes’ theorem, Poincaré’s lemma, deRham cohomology, degree of a map. Transversality, the Sard lemma.

Instruction

Lectures and problem solving sessions.

Assessment

Written andoral examination at the end of the course.