Algebraic Topology (AlgTop)

Course content

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.

 

Education

MSc Programme in Mathematics

Learning outcome

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

Skills:
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.


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

4 hours lectures and 3 hours exercises each week for 7 weeks.

Examples of course litterature:

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).

ECTS
7,5 ECTS
Type of assessment
Oral examination, 20 minutes
Oral exam with 20 minutes preparation time.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
Criteria for exam assessment

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

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 30
  • Theory exercises
  • 21
  • Preparation
  • 125
  • Exam
  • 30
  • English
  • 206