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 | Professor. Rickard |
Open unit status | Not open |
Pre-requisites |
MATH 20200 Metric Spaces 2 and MATH33300 Group Theory |
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.
General Description of the Unit
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.
Additional unit information can be found at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html
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.
There will be no final examination. The final assessment mark for Algebraic Topology is calculated from:
The coursework and presentation will be marked against the criteria on the 0-100 scale.
Reading and references are available at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html