| Unit name | Algebraic Topology |
|---|---|
| Unit code | MATHM1200 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Dr. Mark Hagen |
| Open unit status | Not open |
| Pre-requisites | |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Unit Aims
The aim of the unit is to give an introduction to algebraic topology with an emphasis on cell complexes, fundamental groups and homology.
Unit Description
Algebraic Topology concerns constructing and understanding topological spaces through algebraic, combinatorial and geometric techniques. In particular, groups are associated to spaces to reveal their essential structural features and to distinguish them. In cruder terms, it is about adjectives that capture and distinguish essential features of spaces.
The theory is powerful. We will give applications including proofs of The Fundamental Theory of Algebra and Brouwer's Fixed Point Theorem (which is important in economics).
Relation to Other Units
This is one of three Level M units which develop group theory in various directions. The others are Representation Theory and Galois Theory.
Learning Objectives
Students should absorb the idea of algebraic invariants to distinguish between complex objects, their geometric intuition should be sharpened, they should have a better appreciation of the interconnectivity of different fields of mathematics, and they should have a keener sense of the power and applicability of abstract theories.
Transferable Skills
Lectures, problem sets and discussion of problems, student presentations.
50% Exam, 50% Coursework - assessed problem sheets
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