Galois Theory 2017-18

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

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

Notes

You can find unofficial notes for the course, written and made available by Wanlong Zheng HERE.

I wrote some notes of my own and you can find them HERE. These are very sketchy but they cover the theory as I explained in class. I do NOT recommend that you use these as your main source for Galois Theory or to prepare for the exam, but you MIGHT find them useful when all else has failed.

Timetable

Mon 17:00–18:00 in 140 & Tue 12:00–14:00 in 342

Revision Class: Fri 4 May, 15:00–17:00, Huxley 139

Office Hours: Tue 18:00–19:00 in 673

Assessment and Feedback

There will be two 1-hour long in-class progress tests on: Mon, 12th February and Mon, 12th March. 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.

Final Exam

Wed 23 May, 10:00–12:00, Huxley 341–2 (M3) and

Fri 26 May, 10:00–12:30, Huxley 340 (M4/M5)

Worksheets

Worksheet 1Worksheet 2Worksheet 3

Solutions to worksheets

Worksheet 1Worksheet 2Worksheet 3

Progress test

Test 1Feedback 1

Test 2Solutions 2Feedback 2

Mastery material

In the final examination, students in the 4th year (MSci and MSc) answer an additional “mastery question” on a mastery topic.

The topic is lifts of Frobenius, with application to determination of Galois groups over \({\mathbb Q}\). You can find this material on N. Jacobson, Basic Algebra I, section 4.16 “Mod \(p\) reduction.” (I own the second edition of the book and for me this section is on pages 301–05.)

N.B.

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