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 competencies in algebraic topology. Important concepts include 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 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.


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 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.

Written
Oral

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.

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
  • 28
  • Preparation
  • 127
  • Theory exercises
  • 21
  • Exam
  • 30
  • English
  • 206