| Day | Topics | Reading |
|---|---|---|
| Th. 1/18 | The integers and polynomial ring over a field. Similarities and differences. |
[OS] 1.1, 1.3 |
| Tu. 1/23 | Derivatives. | [OS] 6.3 |
| Th. 1/25 | Big Problems: Z and k[x].
Mason-Stothers theorem |
[OS] 6.1 |
| Tu. 1/30 | Unique factorization for a polynomial ring over a UFD. |
[OS] 6.5 |
| Th. 2/1 | Work on unique factorization problems. | [OS] 6.5 |
| Tu. 2/6 | Sage: Finite fields and number fields. | [OS] 5.1-3 |
| Th. 2/8 | Sage: Multivariate polynomial rings and quotient rings. | [OS] |
| Tu. 2/13 | Tests for irreducibility. | [OS] 6.6 |
| Th. 2/15 | Worksheet on irreducible polynomials, function fields. | [OS] 6.6 |
| Tu. 2/20 | Algebraic field extensions. | [OS] 5.1-3 |
| Th. 2/22 | Algebraic extensions, splitting fields, algebraic closure. | [OS] 7.1 |
| Tu. 2/27 | More on algebraic extensions, normality. | [OS] 7.2 |
| Th. 2/29 | Separability, normal field extensions. | [OS] 7.3,4 |
| Tu. 3/5 | Galois' theorem. | [OS] 7.5,6 |
| Th. 3/7 | Work on Galois extensions (x^2-2)(x^2-3), x^3-3x+1, x^5-1. | [OS] 7.6 |
| Tu. 3/12 | Discussion: Galois extensions x^5-1, x^7-1, x^2-2.
Finite fields. |
[OS] 7.6 |
| Th. 3/14 | Group actions, examples. Orbit-stabilizer theorem. |
[Ash] 5.1,2 |
| Tu. 3/19 | The class equation. Sylow theorems. | [Ash] 5.2,4 (skip 5.3) |
| Th. 3/21 | Sylow theorem problems. | [Ash] 5.4,5 |
| Tu. 3/26 | Composition series and solvability. | [Ash] 5.6,7 |
| Th. 3/28 | Problems: Sylow applications, composition series, solvability. | [Ash] 5.6,7 |