| Date | Chapter | Description | |
|---|---|---|---|
| Jan 12 | 2.1-2.2 | Introduction, Group defintion and examples | |
| Jan 14 | 2.3-2.4 | Basic facts, subgroups | |
| Jan 16 | 2.4 | Subgroups and cosets | |
| Jan 19 | Martin Luther King day! (no class) | ||
| Jan 21 | Counting, normal subgroups | ||
| HW 1 due | |||
| Jan 23 | Homomorphisms, isomorphisms, and automorphisms | ||
| Jan 26 | Kernels and the Isomorphism Theorem | ||
| Jan 28 | The Isomorphism Theorem and Sylow sgs | ||
| HW 2 due | |||
| Jan 30 | The Correspondence Theorem | ||
| Feb 2 | The Diamond Theorem; automorphisms | ||
| Feb 4 | Group actions and Cayley's Theorem | ||
| HW 3 due | |||
| Feb 6 | Group actions, normal subgroups, and orbits | ||
| Feb 9 | Group actions and counting | ||
| Feb 11 | Sn: cycle decomposition and conjugacy | ||
| HW 4 due | |||
| Feb 13 | Sn: transpositions and sign | ||
| Feb 16 | An; The Sylow E Theorem | ||
| Feb 18 | In class midterm #1 | ||
| Feb 20 | The Sylow C and D Theorems | ||
| HW 5 due | |||
| Feb 23 | Sylow subgroups -> normal subgroups; Direct products | ||
| Feb 25 | Introducing rings | ||
| Feb 27 | Ideals and quotients | ||
| Mar 2 | Isomorphism Theorems and maximal ideals | ||
| Mar 4 | Maximal ideals, Zorn's Lemma, and fraction fields | ||
| Mar 6 | Euclidean domains | ||
| Mar 9 | Spring Break! (no class) | ||
| Mar 11 | Spring Break! (no class) | ||
| Mar 13 | Spring Break! (no class) | ||
| Mar 16 | More Euclidean domains | ||
| Mar 18 | Polynomial rings | ||
| Mar 20 | UFDs and polynomial rings | ||
| Mar 23 | More UFDs and polynomial rings | ||
| Mar 25 | Face rings; the Eisenstein criterion | ||
| Mar 27 | Fields extensions: degree and dimension | ||
| Mar 30 | Degree of algebraic field extensions | ||
| Apr 1 | In class midterm #2 | ||
| Apr 3 | Algebraic over algebraic extensions | ||
| Apr 6 | More algebraic over algebraic extensions | ||
| Apr 8 | Algebraic extensions and roots | ||
| Apr 10 | Splitting extensions and splitting fields | ||
| Apr 13 | Splitting fields are unique up to isomorphism | ||
| Apr 15 | Ruler and compass constructions | ||
| Apr 17 | Matrix groups (with Raj Mehta) | ||
| Apr 20 | Galois groups and the Galois correspondence | ||
| Apr 22 | When is the Galois correspondence a bijection? | ||
| Apr 24 | Galois answers; Conclusion | ||
| May 6 | Final exam (10:30 am - 12:30 pm) | ||