This page is a copy of http://www2.warwick.ac.uk/fac/sci/maths/undergrad/ughandbook/resources/ma3d5/ for convenience. If anything doesn't work, follow that link instead.
lecturer: Marco Streng, office C2.29, M.Streng@Warwick.ac.uk
problem class: David Holmes, office B2.01, D.S.T.Holmes@Warwick.ac.uk
Short version: You could use Daan Krammer's lecture notes [Kr],
see the detailed timetable below to match the sections of the notes
with the lectures. It does not fit completely, so it is good to take
notes.
Long version: There are many books on Galois theory. See for example this detailed list of alternative books by Daan Krammer, including a correspondence between chapters in the books and chapters in [Kr]. Another list of books can be found on page 19 of [Re].
We will more or less follow last year's notes by Martin Bright. They
have not been typed up, and it is generally advisable to take notes
during lectures. It is also advisable to prepare lectures by skimming
over the appropriate theory. For that, and for having notes that are not
literally the same as what I write on the board, I recommend [Kr],
because that is reasonably close to the notes we are using. I will
provide references for the lectures in the detailed timetable below, as
well as exercises.
[Br] Martin Bright's note on fraction fields and rational function fields
[cy] note on cyclotomic fields
[Kr] Daan Krammer's lecture notes
[Re] Miles Reid's lecture notes
[St] Ian Stewart  Galois Theory, Chapman & Hall, Third Edition 2004.
The grade will be based for 15% on 4 homework assignments and for 85% on a final exam. The deadlines for the assignments are:
Besides the assignments, there are also homework excercises that
don't count for your grade. Those will be made available via the
detailed timetable below.
Assignments will be made available 13 days before the deadline. Part
of the problems can be solved with the theory taught up to that moment,
and I recommend that you do so. The rest of the problems can be solved
with the theory taught at least 6 days before the deadline. For details
on which problems can be solved after which lecture, see the detailed
timetable below.
(references are approximate)
date  keywords  references  exercises 

Tues 4 Oct 
I. Fields and Polynomials rings, fields, the characterstic of a field, prime fields, polynomials, rational functions, division with remainder for polynomials 
[Kr] 1.1, 2.1, 2.3 (or: [Re] 1.1, 1.2, 2.1, 2.3, [Br]) 
page 1 of exercises; all of bonus 1; 1(a,b), 3(d) of assignment 1 
Fri 7 Oct 
euclid's algorithm for polynomials, (unique) factorization of polynomials 
[Kr] 2.2 (or: [Re] 2.1  2.3) 
half of page 2 of exercises 
Tues 11 Oct 
modular arithmetic for polynomials, fields that are quotient rings of polynomial rings, i.e., polynomial rings modulo ideals algebraic versus transcendental numbers, the minimal polynomial, checking irreducibility of polynomials 
[Kr] 2.2, 3.1, 3.3 (or: [Re] 2.1, 2.3, 2.4) 
page 2 of exercises; 1,4 of assignment 1 (also 3 if you assume 2) 
Fri 14 Oct 
checking irreducibility of polynomials: Gauss' lemma, reduction modulo prime numbers and Eisenstein polynomials, how to find the minimal polynomial 
[Kr] 3.1 (or: [Re] 2.4) 
assignment 1; 
Tues 18 Oct 
II. Field extensions field extension, degree, finite and infinite extensions, algebraic and transcendental extensions, the tower law, morphisms, primitive extensions, bijection between roots and morphisms 
[Kr] 3.2  3.6, 5.1, 5.2 (or: [Re] 3.1) 
page 3 of exercises; 1, 2(a),(b), 3(a), 4(a) of assignment 2

Fri 21 Oct 
Interlude. Ruler and compass constructions 
[Re] 3.2 and use your notes for the definition of constructible field extensions and constructible points, and what these have to do with each other 
3(b) of assignment 2; or spend more time on page 3 of exercises; 
Tues 25 Oct 
III. The Galois correspondence 
[Kr] 1.6, 4.1  Proposition 77 and Definition 80 
assignment 2; 
Fri 28 Oct 
how many automorphisms is "enough"? 
[Kr] Proposition 78 without its proof (mistake in proof) 
assignment 2; 
Tues 1 Nov 
Artin's lemma 
[Re] Proposition 4.8 together with 4 of assignment 3 and [Kr] 4.4  4.6, 5.3 and 
22, 23 of exercises; 4 of assignment 3 
Fri 4 Nov  continuation of example, and another example: Q(4th root of 2, i) 
[St] 13 (or: [Re] 4.22) 
24 of exercises; 1, 4 of assignment 3 
Tues 8 Nov 
continuation of example 
[Kr] 6.1: page 47 
25 of exercises 
Fri 11 Nov  normal extensions versus splitting fields, Galois groups of splitting fields as permutation groups of roots, normal closure  [Kr] 6.2, 8.1 
26 and 27 of exercises 
Tues 15 Nov 
continuation of normal closure, remark on algebraically closed fields 
[Kr] 8.1, remainder of Chapter 6 
1 of assignment 4; 28 and 29 of exercises 
Fri 18 Nov 
Galois if and only if normal and separable (proof), statement without proof of the primitive element theorem 
[Kr] Chapter 6 (again) and Chapter 7 (for finite fields) 
1 and 2 of assignment 4; 30 of exercises; (7.3) of [Kr] 
Tues 22 Nov 
the splitting field of x^{q}x, existence and uniqueness, Galois groups of finite fields 
[Kr] Chapter 7 (finite fields) [cy] (cyclotomic fields) 
1, 2, 3 of assignment 4; [Kr] (7.2), (7.4)(7.7) 
Fri 25 Nov  abelian extensions, statement of the KroneckerWeber theorem,(in)constructibility of a regular ngon IX. Solvability in radicals definition of a solvable extension, and what this has to do with roots 
[cy] and [Kr] 1.3, 8.3 
assignment 4 ; 31 and 34 of exercises 
Tues 29 Nov  normal closure of a solvable
extension, definition of a solvable polynomial, lemma on cyclic
extensions, solvable groups, examples of solvable groups, solvable
polynomials imply solvable groups 
[Kr] 1.3, 8.2, 8.3  32, 33, 34 of exercises 
Fri 2 Dec 
statement without proof of the converse, S_{5} is not solvable, a sufficient criterion for the Galois group to be S_{5}. 
[Kr] 8.3 
35 and 36 of exercises 
Tues 6 Dec  example of a nonsolvable polynomial, insolvability of the general quintic! X. Calculating Galois groups elementary symmetric polynomials, discriminants, odd and even permutations of the roots, transitive groups, cubic polynomials, explicitly solving cubics in radicals 
[Kr] 1.4 (symmetric polynomials), 1.7 (solving the cubic) and take notes (discriminant, odd and even permutations versus discriminant, Galois group of a cubic)  37  39 of exercises 
Fri 9 Dec 
XI. Quadratic reciprocity 
take notes 
40  42 of exercises 
Exam 
Everything mentioned above, except the last lecture 
everything mentioned above, plus old exams and their solutions 