THIS IS AN OLD COURSE HOME PAGE -- THIS IS NOT THE 2015 GALOIS THEORY COURSE. THE 2015 COURSE PAGE IS HERE.
Galois Theory (M3,4,5P11)
The course ran October to December 2014.
Galois Theory example sheets.
Note: these are the 2014 sheets. I will change and edit them for 2015.
Sheet one
and solutions.
Sheet two
and solutions.
Sheet three
and solutions.
Sheet four
and solutions.
Sheet five
and solutions.
Sheet six
and solutions.
[there are six sheets]
Group theory hand-out.
I needed some "pure" group theory for the stuff on the quintic
equation, and instead of lecturing it I decided I'd put it on a
handout. Here it is. I would not
expect you to know these proofs for the exam, but I would expect
you to know the statements -- you can treat them as a "black box".
Galois theory tests.
Note: these are the 2014 tests. The 2015 tests will be different.
There were two tests:
First one (6/11/14) questions and solutions.
Second one (4/12/14) questions and solutions.
Failure to produce multiple choice questions.
I had a dream that I would write some clever little program which would
produce multiple-choice Galois theory questions on the fly. It never happened.
As a very poor substitute, here are some of the ideas
I was thinking about.
Revision classes.
Note: for the most up-to-date information check out Chris Sisson's timetable pages. The classes are now timetabled. Tuesday 28th April 4-5 in 130 (note: on a provisional timetable this was 11-12, it has *moved*) and Friday 1st May 12-1 (in 139).
Office hours, summer term (Apr-Jun 2015).
Thursday 30th April, 4-5pm.
Tuesday 5th May, 3-4pm.
Thursday 7th May, 4-5pm.
Mastery/Comprehension (M4,M5).
This is not for 3rd year undergraduates; this is for that funny exam that MSc and MSci students take, with one question from each course.
Here is the mastery handout (final version).
It's on how
the fundamental theorem of Galois theory works for infinite extensions.
Here is also
an extremely long example sheet
(final version) and solutions (final
version).
Please read the bit at the top which says that you
don't have to do all these questions, before you have a nervous breakdown.
Recommended texts.
My illustrious predecessor Martin Liebeck used to recommend these:
C. Hadlock, Field theory and its classical problems
I. Stewart, Galois Theory
J. Rotman, Galois Theory
J. Fraleigh, A first course in abstract algebra
I. Herstein, Topics in algebra
I personally bought this book when I was an undergraduate:
D. J. H. Garling, A course in Galois Theory
but actually I learnt Galois theory from my lecture
notes, so perhaps I'm not the best person to ask about books.