NMAA05038U  Algebraic Topology (AlgTop)

Volume 2018/2019

MSc Programme in Mathematics


This course is a first introduction to algebraic topology, the area of mathematics in which algebra is used to study topological spaces.  We will define the fundamental group and singular homology and study their basic properties and applications.


Learning Outcome

The course introduces foundational competences in algebraic topology. Important concepts are homotopy, homotopy equivalence, fundamental group, covering space, chain complex, homology.

At the end of the course, the students are expected to be able to:

- Know the definition of the concepts listed under knowledge.
- Compute the fundamental group and homology groups of simple topological spaces.

The course will strengthen the student's competencies in
- abstract and precise thinking.
- elegance of exposition.

Examples of course literature:

The first two chapters of the book Algebraic Topology by Allen Hatcher.

Knowledge about general topology and abelian groups, as obtained e.g., through Topology (Top) and Algebra 2 (Alg2).
4 hours lectures and 3 hours exercises each week for 7 weeks.
7,5 ECTS
Type of assessment
Oral examination, 20 minutes
Oral exam with 20 minutes preparation time.
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship

Same as ordinary exam.

Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.

  • Category
  • Hours
  • Lectures
  • 28
  • Theory exercises
  • 21
  • Preparation
  • 127
  • Exam
  • 30
  • Total
  • 206