| Unit name | Galois Theory |
|---|---|
| Unit code | MATHM2700 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Dr. Walling |
| Open unit status | Not open |
| Pre-requisites | |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Unit Aims
To present an introduction to Galois theory in the context of arbitrary field extensions and apply it to a number of historically important mathematical problems.
Unit Description
Consider a field, such as the rational numbers, and consider a larger field containing it, which can also be thought of as a vector space over the original field. One question that can be asked is: what symmetries (or automorphisms) of the bigger field exist that act as the identity on the smaller field? The Galois Correspondence connects the answer to this question with the properties of a group of permutations of the roots of a polynomial. This relationship can be used in different directions to translate a problem from one part of algebra to another part where it may be easier to solve.
Relation to Other Units
This is one of three Level 7 units which develop group theory in various directions. The others are Representation Theory and Algebraic Topology.
Learning Objectives
To gain an understanding and appreciation of Galois theory and its most important applications. To be able to use the theory in specific examples.
Transferable Skills
Using an abstract framework to better understand how to attack a concrete problem.
Lectures and exercises.
90% Examination
10% Coursework
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
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