NMAA05038U Algebraic Topology (AlgTop)

Volume 2023/2024

MSc Programme in Mathematics

MSc Programme in Mathematics with a minor subject


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 competencies in algebraic topology. Important concepts include 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 definitions of the concepts introduced in this class.
- Understand the main results, their proofs, and their significance.
- Compute the fundamental group and singular homology of simple topological spaces.

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

Examples of course literature: lecture notes, possibly supplemented with other resources such as the textbooks by Hatcher or May.

Knowledge about general topology and abelian groups, as obtained e.g., through Topology (Top) and Algebra 2 (Alg2).

Academic qualifications equivalent to a BSc degree is recommended.
4 hours lectures and 3 hours exercises each week for 7 weeks.
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 156
  • Theory exercises
  • 21
  • Exam
  • 1
  • Total
  • 206

Written feedback on non-mandatory assignments will be given by TA.  By participating actively in the weekly exercises, the students will receive feedback from the TA and from fellow students.

7,5 ECTS
Type of assessment
Oral examination, 20 minutes
Type of assessment details
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 should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.