Chapter 13. The Galois Group Of A Polynomial

Chapters in this book

1. Frontmatter i
2. Contents ix
3. Foreword xv
4. Preface To The Paperback Edition xxi
5. Preface xxv
6. Acknowledgments xxxi
7. Greek Alphabet xxxiii
8. Part One. Algebraic Preliminaries
9. Chapter 1. Representations 3
10. Chapter 2. Groups 13
11. Chapter 3. Permutations 21
12. Chapter 4. Modular Arithmetic 31
13. Chapter 5. Complex Numbers 42
14. Chapter 6. Equations and Varieties 49
15. Chapter 7. Quadratic Reciprocity 67
16. Part Two. Galois Theory and Representations
17. Chapter 8. Galois Theory 87
18. Chapter 9. Elliptic Curves 103
19. Chapter 10. Matrices 114
20. Chapter 11. Groups of Matrices 124
21. Chapter 12. Group Representations 135
22. Chapter 13. The Galois Group Of A Polynomial 149
23. Chapter 14. The Restriction Morphism 157
24. Chapter 15. The Greeks Had a Name for it 162
25. Chapter 16. Frobenius 177
26. Part Three. Reciprocity Laws
27. Chapter 17. Reciprocity Laws 193
28. Chapter 18. One- And Two-Dimensional Representations 200
29. Chapter 19. Quadratic Reciprocity Revisited 216
30. Chapter 20. A Machine for Making Galois Representations 225
31. Chapter 21. A Last Look at Reciprocity 233
32. Chapter 22. Fermat’s Last Theorem and Generalized Fermat Equations 242
33. Chapter 23. Retrospect 257
34. Bibliography 265
35. Index 269