Lectures
There are two lectures per week:
- Monday 2pm, Lecture Theatre A
- Friday 10am, Lecture Theatre 6
Office hours
Tuesdays 3-4pm in room J13
Lecture notes
I’ll be posting the lecture notes here throughout the course.
- Chapters 1-4 – Introduction, solving polynomials, splitting fields, cyclotomic extensions (last updated: 1/3/2019)
- Chapters 5-6 – Galois extensions, the main theorem, including proof (last updated 14/3/2019)
- Chapters 7-9 – Solvable groups, solubility by radicals, insolubility of the quintic (last updated 28/3/2019)
- Chapter 10 – Consists of many examples computing the Galois groups of various polynomials of small degree. I probably won’t have time to get through all of these in the lectures! (last updated 2/6/2019)
- Chapter 11 – The discriminant of a polynomial (last updated 28/3/2019)
- Examples of groups (last updated 1/3/2019)
- Complete notes (last updated 28/3/2019) (warning: individual chapters may be more up to date!)
Problem sheets
- Problem sheet 1: solving polynomial equations.
- Problem sheet 2: splitting fields and cyclotomic extensions.
- Problem sheet 3: Galois extensions and computing Galois groups.
- Problem sheet 4: The Galois correspondence.
- Problem sheet 5: Discriminants and *lots* of examples computing Galois groups of polynomials.
More information is available on the course page.
Homework
- Homework 1: questions 1, 3, 5 of problem sheet 2. Due date: Friday 8th March
- Homework 2: questions 2, 3, 5 of problem sheet 3. Due date: Friday 22nd March
- Homework 3: questions 1, 2, 3 of problem sheet 4 and question 6 of problem sheet 5. Due date: Monday 29th April