Galois Theory

Galois Theory
Ian Stewart

1. Background
2. Factorization of polynomials
3. Field extensions
4. The degree of an extension
5. Ruler and compasses
6. Trancendental numbers
7. The idea behind Galois theory
8. Normality and separability
9. Field degrees and group orders
10. Monomorphisms, automorphisms, and normal closures
11. The Galois correspondence
12. A specific example
13. Some group theorie
14. Solution of equations by radicals
15. The general polynomial equation
16. Finite fields
17. Regular polygons
18. The 'fundamental theorem of algebra'
19. Later developments