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 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.
Academic qualifications equivalent to a BSc degree is recommended.
- Theory exercises
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 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.