| Unit name | Galois Theory |
|---|---|
| Unit code | MATHM2700 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Dr. Walling |
| Open unit status | Not open |
| Pre-requisites | |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
After reviewing some basic properties of polynomials rings, we will introduce the basic objects of study: field extensions and the automorphism groups associated to them. We will discuss certain desirable properties for field extensions and then demonstrate the fundamental Galois correspondence. This will be used to analyse some specific polynomials and in particular to exhibit a quintic which is not soluble by radicals. We will end with applications to finite fields and to the fundamental theorem of algebra.
