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.
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
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 4 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).
Advanced Vector Spaces (AdVec).
Academic qualifications equivalent to a BSc degree is
recommended.
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 (20-minute preparation time)
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
- Re-exam
-
Same as ordinary exam
Criteria for exam assessment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Single subject courses (day)
- Category
- Hours
- Lectures
- 28
- Preparation
- 149
- Theory exercises
- 28
- Exam
- 1
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAA05038U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Placement
- Block 1
- Schedulegroup
-
C
- Capacity
- No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Nathalie Wahl (4-7a646b6f437064776b316e7831676e)
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Kursusinformation for indskrevne studerende