| Date | Class Topic | Reading (Hungerford) |
|---|---|---|
| 1/16 | Structure of finite abelian groups | 8.2 |
| 1/18 | More on structure of finite abelian groups | 8.2 |
| 1/21 | No class -- Martin Luther King day | 8.2 |
| 1/23 | Elementary divisors and invariant factors | 8.2 |
| 1/25 | What the Sylow theorems say; Problem Set 1 due | 8.3 |
| 1/28 | Conjugacy and the class equation | 8.4 |
| 1/30 | Proofs of the Sylow theorems | 8.4 |
| 2/1 | Structure of finite groups; Problem Set 2 due | 8.5 |
| 2/4 | More on structure of finite groups | 8.5 |
| 2/6 | Review of vector spaces | 10.1 |
| 2/8 | Extension fields; Problem Set 3 due | 10.2 |
| 2/11 | More on extension fields | 10.2 |
| 2/13 | Algebraic and transcendental extensions | 10.3 |
| 2/15 | More on algebraic extensions; Problem Set 4 due | 10.3 |
| 2/18 | Splitting fields | 10.4 |
| 2/20 | More on splitting fields | 10.4 |
| 2/22 | Separable extensions; Problem Set 5 due | 10.5 |
| 2/25 | More on separable extensions | 10.5 |
| 2/27 | Spare day; Exam I given in evening | |
| 2/29 | Spare day | 10.6 |
| 3/3,5,7 | No class -- Spring break | |
| 3/10 | Finite fields | 10.6 |
| 3/12 | More on structure of finite fields | 10.6 |
| 3/14 | Geometric constructions; Problem Set 6 due | Chapter 15 |
| 3/17 | Impossibility proofs for geometric constructions | Chapter 15 |
| 3/19 | The Galois group of an extension field | 11.1 |
| 3/21,24 | No class -- Easter break | 11.1 |
| 3/26 | More on the Galois group | 11.1 |
| 3/28 | The Galois correspondence; Problem Set 7 due | 11.2 |
| 3/31 | More on fundamental theorem of Galois theory | 11.2 |
| 4/2 | Proof of fundamental theorem | 11.2 |
| 4/4 | Solvability by radicals; Problem Set 8 due | 11.3 |
| 4/7 | Solvable extensions and solvable groups | 11.3 |
| 4/9 | The alternating groups, revisited | 11.3 |
| 4/11 | Nonsolvability of the general quintic equation; Problem Set 9 due | 11.3 |
| 4/14 | Application: error-control coding theory | 16.1 |
| 4/16 | Linear codes; Exam II given in evening | 16.1 |
| 4/18 | The decoding problem | 16.2 |
| 4/21 | Syndrome decoding for linear codes | 16.2 |
| 4/23 | Finite field structure and BCH codes | 16.3 |
| 4/25 | More on BCH codes; Problem set 10 due | 16.3 |
| 4/28 | Course wrap-up |
Last modified: January 1, 2008