NMAA05038U Algebraic Topology (AlgTop)
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.
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 litterature:
The first two chapters of the book Algebraic Topology by Allen Hatcher.
- 7,5 ECTS
- Type of assessment
- Oral examination, 20 minutesOral 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.
- Theory exercises