Course content

The aim of the course is to show how basic geometric structures may be studied by transforming them into algebraic questions that then are subject to computations, thus measuring geometric and topological complexity. These methods are often used in other parts of mathematics, and also in physics and other areas of application. The course is meant to give a basis for studies in topology, geometry, algebra, and theoretical physics. An introdution to cell complexes, homotopy theory, category theory, homology and cohomology theory, and duality is given, along with pecific examples of homological and cohomological computations.

Learning outcome

To give an introduction to algebraic topology by introducing homology and cohomology theory along with some of their applications. This is of interest not only to students in topology/geometry, but also
to students in algebra, analysis and theoretical physics.

Learning methods and activities

Lectures and projects-/term paper. Oral exam which counts 100 %. 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

The course is based on TMA4100 Calculus I, TMA4105 Calculus 2, TMA4110/4115 Calculus 3 and TMA4120/4125/4130/4135 Calculus 4. Some knowledge of general topology, for example MA3002 General Topology and MA2201 Algebra, is an advantage.

Course materials

Will be announced at the start of the course.

Credit reductions