TMA4190 - Introduction to Topology


Examination arrangement

Examination arrangement: Written examination
Grade: Letters

Evaluation form Weighting Duration Examination aids Grade deviation
Written examination 100/100 4 hours D

Course content

The aim of the course is to introduce fundamental concepts and examples in differential topology and the idea of using algebraic invariants to study geometric objects. The course discusses the inverse function theorem, differentiable structures and smooth manifolds, tangent bundles, embeddings, submersions and regular/critical points. Important examples of spaces are surfaces, spheres, and projective spaces. Other key concepts are homotopy, the fundamental group and covering spaces. Applications presented in the course may range from Brouwer's fixed point theorem to vector fields on spheres. These methods and ideas have been influential to and are used in many other parts of mathematics, but also in physics and other areas of application.

Learning outcome

1. Knowledge. The student has knowledge of fundamental concepts and methods in differential and algebraic topology, and examples of manifolds.

2. Skills. The student is able to apply his or her knowledge of differential and algebraic topology to formulate and solve problems of a geometrical nature in mathematics, theoretical physics and cybernetics, by the use of dynamical systems on manifolds and other tools.

Learning methods and activities

Lectures and exercises. The lectures will be given in English if they are attended by students from the Master's Programme in Mathematics for International students. If the course is taught in English, the exam will be given only in English. Students are free to choose Norwegian or English for written assessments. Written examination. Retake of examination may be given as an oral examination.

Course materials

Will be announced at the start of the course.

Credit reductions

Course code Reduction From To
SIF5034 7.5


Detailed timetable


Examination arrangement: Written examination

Term Statuskode Evaluation form Weighting Examination aids Date Time Room *
Spring ORD Written examination 100/100 D 2017-06-09 09:00 Datasal 10345 , D1 , K3

Examination arrangement: Oral examination

Term Statuskode Evaluation form Weighting Examination aids Date Time Room *
Summer KONT Oral examination 100/100 2017-08-07
  • * The location (room) for a written examination is published 3 days before examination date.
If more than one room is listed, you will find your room at Studentweb.