Course content

The course deals with fundamental concepts from differential topology, providing a connection between topology and analysis and an understanding of modern geometric reasoning. The topics to be studied are: Manifolds, tangent spaces, differential forms local and global, de Rham cohomology, Stokes's theorem in n dimensions. Topological and geometric applications.

Learning outcome

1. Knowledge. The student has knowledge of fundamental concepts and methods concerning differential forms, de Rham cohomology and integration on manifolds.

2. Skills. The student is able to apply his or her knowledge of differential topology to formulate and solve problem of an analytic-geometrical nature in mathematics, theoretical physics and cybernetics, through the use of integration on manifolds and other tools.

Learning methods and activities

Lectures, exercises and projects. The final grade is based 100% on the final exam.

The lectures will be given in English if they are attended by students
from the Master's Programme in Mathematics for International students.

Recommended previous knowledge

TMA4190 Manifolds may be an advantage,but not necessary. Some knowledge of analysis beyond basic calculus is an advantage.

Course materials

Will be announced at the start of the course.

Credit reductions