| Class Number |
Date |
Sections in Text |
Brief Description |
| 1 |
Monday, 1/24 |
1.1 |
Overview, Field Extensions, Group Review, Automorphisms of Groups |
| 2 |
Wednesday, 1/26 |
1.1, 1.2 |
Group Review, Quotients, The Isomorphism and Correspondence Theorems |
| 3 |
Friday, 1/28 |
1.2, 1.4 |
Correspondence Theorem, Ring Review |
| 4 |
Monday, 1/31 |
1.5 |
Polynomial Rings over Fields |
| - |
Wednesday, 2/2 |
- |
No Class (Snow Day) |
| 5 |
Friday, 2/4 |
1.5, C.1, C.2 |
Irreducible Polynomials, Vector Spaces, Bases |
| 6 |
Monday, 2/7 |
C.2, 2.1 |
Dimension, Simple Extensions |
| 7 |
Wednesday, 2/9 |
2.1 |
Simple Extensions, Minimal Polynomials |
| 8 |
Friday, 2/11 |
2.1 |
Simple Extensions, Automorphisms |
| 9 |
Monday, 2/14 |
2.1 |
Automorphisms, Extending Isomorphisms |
| 10 |
Wednesday, 2/16 |
2.2 |
Towers of Extensions |
| 11 |
Friday, 2/18 |
2.2, 2.3 |
Algebraic Extensions, Splitting Fields |
| 12 |
Monday, 2/21 |
2.2, 2.3 |
Splitting Fields, Algebraically Closed Fields |
| 13 |
Wednesday, 2/23 |
2.3 |
Normal Extensions |
| 14 |
Friday, 2/25 |
2.3 |
Existence and Uniqueness of Finite Fields |
| 15 |
Monday, 2/28 |
2.3 |
Structure of Finite Fields |
| 16 |
Wednesday, 3/2 |
2.3 |
Subfields of Finite Fields, Separable Polynomials |
| 17 |
Friday, 3/4 |
3.1 |
Separable Extensions, The Galois Group of a Field Extension |
| 18 |
Monday, 3/7 |
3.1 |
Examples of Galois Groups, Fixed Fields |
| 19 |
Wednesday, 3/9 |
3.1 |
Normal Extensions and Normal Subgroups |
| 20 |
Friday, 3/11 |
3.1 |
Dimensions and Indices |
| 21 |
Monday, 3/14 |
3.1 |
Galois Extensions |
| 22 |
Wednesday, 3/16 |
3.1 |
The Fundamental Theorem of Galois Theory |
| 23 |
Friday, 3/18 |
3.1 |
Examples of the Fundamental Theorem |
| - |
Monday, 3/21 |
- |
Spring Break |
| - |
Wednesday, 3/23 |
- |
Spring Break |
| - |
Friday, 3/25 |
- |
Spring Break |
| - |
Monday, 3/28 |
- |
Spring Break |
| - |
Wednesday, 3/30 |
- |
Spring Break |
| - |
Friday, 4/1 |
- |
Spring Break |
| 24 |
Monday, 4/4 |
3.1 |
Normal Closure, Primitive Element Theorem |
| 25 |
Wednesday, 4/6 |
1.2 |
Conjugation, The Class Equation, Cauchy's Theorem |
| 26 |
Friday, 4/8 |
1.2, 3.1 |
Sylow Subgroups, The Fundamental Theorem of Algebra |
| 27 |
Monday, 4/11 |
1.3 |
Solvable Groups |
| 28 |
Wednesday, 4/13 |
1.3 |
Solvable Groups, Simplicity of A_5 |
| 29 |
Friday, 4/15 |
3.2 |
Radical Extensions |
| 30 |
Monday, 4/18 |
3.2 |
Radical Extensions and Solvable Galois Groups |
| 31 |
Wednesday, 4/20 |
3.2 |
Polynomials Not Solvable by Radicals |
| 32 |
Friday, 4/22 |
3.2 |
Radical Extensions and Solvable Galois Groups |
| 33 |
Monday, 4/25 |
4.2 |
Cyclotomic Polynomials |
| 34 |
Wednesday, 4/27 |
4.2, 4.4 |
Cyclotomic Polynomials, Cyclotomic Extensions |
| 35 |
Friday, 4/29 |
4.4 |
Dirichlet's Theorem (Special Case), Realizing Abelian Groups as
Galois Groups |
| 36 |
Monday, 5/2 |
4.1 |
Straightedge and Compass Constructions |
| 37 |
Wednesday, 5/4 |
4.1 |
Constructibility, Doubling a Cube, Squaring a Circle |
| 38 |
Friday, 5/6 |
4.1 |
Constructibility, Trisecting Angles, Regular Polygons |
| 39 |
Monday, 5/9 |
- |
Transcendental Extensions, Polynomials in Many Variables |
| 40 |
Wednesday, 5/11 |
- |
Algebraically Independent Sets, Transcendence Bases |
| 41 |
Friday, 5/13 |
4.3 |
Transcendence Degree, Wedderburn's Theorem |