Galois Theory

This is the page of the course MP11 (Galois Theory) 2020.

You will be able to access all course materials from this page. The key logistics are summarised HERE.


You can find the latest version of my notes HERE.

You can find unofficial notes for the 2019  course, written and made available by David Angdinata HERE.


Tue 14:00–15:00 in 144, Wed 9:00–10:00 in 341, & Thu 15:00–16:00 in 145

Revision Class: Monday 27 Apr as a MS Teams Live Event

Office Hours: Tuesday at 12:00 in Huxley 673

Assessment and Feedback

Progress Tests

There will be two 1-hour long in-class progress tests on the following dates. Each progress test is worth 5% of your total mark for the course. We will give you individual feedback notes upon returning the progress tests to you.

Test 1, Wed, 12th February

Test 2, Wed, 18th March.

Final Exam

Wed 27 March 9:00–11:00 (3rd year students) and 9:00–11:30 (4th year and MSc)


Worksheet 1Worksheet2Worksheet 3Worksheet 4

Solutions to worksheets

Worksheet 1Worksheet 2Worksheet 3Worksheet 4

Progress tests: solutions and feedback

Test1 (with answers)Feedback 1

Test2 (with answers)Feedback2

Mastery topic 2020

The mastery topic is Galois groups of cubics and quartics (not in characteristic 2). The reading assignment is Keith Conrad’s expository paper, which you can find here.

Make sure that you know:

(a) the possible transitive subgroups of \(\mathfrak{S}_4\) and how they sit in \( \mathfrak{S}_4\) (you don’t need to know the proof of this fact);

(b) the basic definitions properties of the discriminant and the cubic resolvent (you don’t need, of course, to memorise their formulas);

(c) the statement and use of Theorem 3.6, and the Theorem of Kappe and Warren from Keith Conrad’s paper.

Also, make sure that you understand all the worked examples in the paper of Keith Conrad.

Mastery topic 2019 (for re-sit students)

In 2019, the mastery topic was cyclotomic extensions of \(\mathbb{Q}\). The reading assignment was:

(1) the expository paper Cyclotomic Extensions by Keith Conrad, which you can find HERE

(2) Serge Lang, Algebra, VIII Section 3 “Roots of unity” (pg. 203–208 in my edition) and Section 9 “The equation \(X^n-a\)” (pg. 221–224)

(3) Do the relevant questions (that is, questions 10, 11, 12, 13, 14, 15, 16) on pg. 80 in Miles Reid’s notes on Galois Theory which you find HERE.


Please let me know if you find misprints, errors, etc. in handouts, worksheets, solutions, tests and other course materials.