7. Field extensions and splitting fields

Chapters in this book

1. Frontmatter I
2. Preface V
3. Contents VII
4. 1. The natural, integral and rational numbers 1
5. 2. Division and factorization in the integers 19
6. 3. Modular arithmetic 39
7. 4. Exceptional numbers 61
8. 5. Pythagorean triples and sums of squares 83
9. 6. Polynomials and unique factorization 95
10. 7. Field extensions and splitting fields 125
11. 8. Permutations and symmetric polynomials 141
12. 9. Real numbers 157
13. 10. The complex numbers, the Fundamental Theorem of Algebra and polynomial equations 189
14. 11. Quadratic number fields and Pell’s equation 227
15. 12. Transcendental numbers and the numbers e and π 249
16. 13. Compass and straightedge constructions and the classical problems 289
17. 14. Euclidean vector spaces 303
18. Bibliography 327
19. Index 329