| Unit name | Algebraic Topology |
|---|---|
| Unit code | MATHM1200 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Professor. Rickard |
| Open unit status | Not open |
| Pre-requisites |
Level 2 Analysis. Level 3 Group Theory. |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Many problems about continuous mappings between geometrical sets can be very difficult, because there are so many possible maps - consider how many maps there are from the reals to the reals. One such problem is answered by Brouwers fixed point theorem: every continuous transformation from a disc (including the boundary) to itself has some point of the disc as a fixed point. The aim of algebraic topology is to tackle such problems by turning them into more manageable problems in algebra. For example, we shall prove Brouwers theorem by transforming it into a very trivial question about group theory. The methods of the course will be mainly algebraic, involving some of the elementary theory of groups, (mostly abelian), but we shall apply this algebra to several specific problems in geometry.
