MM864: Introduction to algebraic topology
Study Board of Science
Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310074102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Master's level course approved as PhD course
STADS ID (UVA): N310074101
ECTS value: 5
Date of Approval: 11-10-2021
Duration: 1 semester
Version: Approved - active
Comment
Entry requirements
Academic preconditions
Students taking the course are expected to:
- Have a basic knowledge of algebra and topology, corresponding to the courses MM551 (Algebra 1), MM539 (Algebra 2) and MM549 (Topology and complex analysis).
- Be able to use basic algebraic and topological arguments.
- Be able to work independently with basic concepts in algebra and topology.
Course introduction
The aim of the course is to introduce the student to one or more topics in algebraic topology and present them with the relevant tools and techniques.
The course primarily builds on the knowledge acquired in the courses MM551 (Algebra 1), MM539 (Algebra 2) and MM549 (Topology and complex analysis) and gives the student insight into the many aspects of algebra and topology and how these two disciplines interact with one another.
In relation to the competence profile of the degree it is the explicit focus of the course to:
- Give the competence to take responsibility for the academic development and specialisation.
- Give the competence to develop an overview of the interplay between different mathematical disciplines.
- Give skills to work concretely with new mathematical tools and objects.
- Give skills to learn and understand advanced mathematical theories at a more independent level.
- Give knowledge and understanding of one or more concrete disciplines within algebraic topology.
- Bring perspective into the students mathematical knowledge.
Expected learning outcome
The learning objectives of the course are that the student demonstrates the ability to:
- Reproduce definitions and results covered in the course.
- Be able to use these results to analyse concrete examples.
- Formulate and present definitions, proofs and calculations in a mathematically rigorous way.
Content
The following main topics are contained in the course: Introduction to one or more topics in algebraic topology. This could, for example, be:
- The fundamental group of a topological space.
- Van Kampen's theorem.
- Homology theory.
- Simplicial homology and singular homology.
- Cell complexes.
- Cohomology theory.
- Cup products.
- Poincaré duality.
Literature
Examination regulations
Exam element a)
Timing
Spring
Tests
Mandatory assignment
EKA
N310074102
Assessment
Second examiner: Internal
Grading
7-point grading scale
Identification
Full name and SDU username
Language
Normally, the same as teaching language
Examination aids
Allowed, a closer description of the exam rules will be posted in itslearning.
ECTS value
5
Indicative number of lessons
Teaching Method
The teaching method is based on three phase model.
- Intro phase: 28 hours
- Skills training phase: 14 hours, hereof: Tutorials: 14 hours
Activities during the study phase:
- The students are expected to familiarise themselves with the material covered in the lectures.
- To acquire knowledge of selected topics independently.
Teacher responsible
Additional teachers
Timetable
Administrative Unit
Team at Educational Law & Registration
Offered in
Recommended course of study
Transition rules
Transitional arrangements describe how a course replaces another course when changes are made to the course of study.
If a transitional arrangement has been made for a course, it will be stated in the list.
See transitional arrangements for all courses at the Faculty of Science.