| Date | Topic | Book | Homework | |
|---|---|---|---|---|
| Jan. | 4 | Introduction to the course | ||
| 6 | Fields and field extensions | |||
| 7 | Degree of a field extension | |||
| 11 | Minimal polynomials | |||
| 13 | Degree of a simple extension | |||
| 14 | Irreducibility criteria over Q | H1 | ||
| 18 | Field Automorphisms | A1 | ||
| 20 | Automorphisms fixing a subfield | |||
| 21 | Bound on size of the automorphisms group | H2 | ||
| 25 | Characteristic of a field; prime field | A2 | ||
| 27 | Separable extensions I | |||
| 28 | Normal extensions I | H3 | ||
| Feb. | 1 | The key lifting lemma | A3 | |
| 3 | Separable and normal extensions II | |||
| 4 | Galois extensions | H4 | ||
| 8 | The Galois correspondence I | A4 | ||
| 10 | Artin's lemma | |||
| 11 | The Galois correspondence II | H5 | ||
| 15 | ||||
| 17 | Reading Week | |||
| 18 | ||||
| 22 | An example | A5 | ||
| 24 | An example, continued | |||
| 25 | A more complicated example | H6 | ||
| 29 | Finite fields I | A6 | ||
| Mar. | 2 | Finite fields II | ||
| 3 | Finite fields III | H7 | ||
| 7 | Elementary Symmetric Polynomials | A7 | ||
| 9 | The Discriminant | |||
| 10 | Computation of Galois groups in small degree | H8 | ||
| 14 | Computation of Galois groups in slightly larger degree | A8 | ||
| 16 | The theorem of the primitive element | |||
| 17 | Radical extensions | H9 | ||
| 21 | Solvable groups | A9 | ||
| 23 | Galois's theorem | |||
| 24 | Galois groups of radical extensions | H10 | ||
| 28 | Cyclic extensions | A10 | ||
| 30 | Theorem on natural irrationalities | |||
| 31 | Examples of unsolvable extensions | H11 | ||
| Apr. | 4 | A11 | ||
| 6 | ||||
| 7 | H12 | |||
| 11 | A12 | |||
| 13 | Take Home Final | |||
| 14 |