The list below is a plan for Spring 2000.
Books: Contemporary Abstract Algebra, 4th edition by J. Gallian [G], Galois theory, 2nd edition by I. Stewart [S].
1. Review and New Examples - [G] p. 242
2. Homomorphism Theorems - [G] Chapter 15; [S] Chapter 1
3. Quotients and Ideals - [G] Chapter 14; [S] Chapter 1
4. Integral Domains - PID, VFD, Euclidean Rings, Fields - [G] Chapter 3 and Chapter 18.
5. Field of Quotients - [G] Chapter 15; [S] Chapter 1
6. R[x] - [G] Chapter 16; [S] Chapter 1
7. Irreducible, Primes in R[x] - [G] Chapter 17; [S] Chapter 2
8. Divisibility and Associates in Integral Domains - [G] Chapter 18
9. Vector Spaces - [G] Chapter 19
10. Extension Fields - [G] Chapter 20; [S] Chapter 3
11. Splitting Fields and Normal Extensions - [S] Chapter 8
12. Algebraic Extensions - [G] Chapter 21; [S] Chapter 3
13. Galois Theory - Overview - [S] Chapter 7
14. Fundamental Theorem - [G] Chapter 32, [S] Chapter 11