Course content

The aim of the course is to show how basic geometric structures may be studied by transforming them into algebraic questions that are then 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

1. Knowledge. The student has knowledge of fundamental concepts and methods in algebraic topology, in particular singular homology and cohomology theory.

2. Skills. The student is able to apply his or her knowledge of algebraic topology to formulate and solve problems of a geometric-topological nature in mathematics and theoretical physics.

Learning methods and activities

Lectures and project/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 and algebra, for example MA3002 General Topology and MA2201 Algebra, is an advantage.

Course materials

Will be announced at the start of the course.

Credit reductions