| 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) |