| Date |
Material |
Keune |
Homework |
| September 2 |
Recap of field theory: field extensions, algebraic and transcendental elements, homomorphisms of field extensions |
|
The non-asterisked parts of these exercises |
| September 9 |
Adjoining roots of polynomials, splitting fields of polynomials, properties of Hom-sets of such extensions |
end of chapter 1, first half of chapter 4 |
These exercises |
| September 16 |
normal extensions, Galois extensions |
second half of chapter 4, most of chapter 3 |
These exercises |
| September 23 |
normal extensions, separable extensions, Galois extensions and groups |
|
These exercises |
| September 30 |
separable extensions, primitive element theorem |
|
These exercises |
| October 7 |
properties of separability, fundamental theorem of Galois theory, cyclotomic extensions |
|
The non-asterisked parts of these exercises |
| October 14 | Galois group of cyclotomic fields | |
The non-asterisked parts of these exercises |
| October 21 |
proof and historical motivation of the fundamental theorem |
|
These exercises |
| November 11 |
No lecture! | | No Exercise class! |
| November 18 |
Symmetric polynomials and their use in constructing Galois extensions |
|
The non-asterisked parts of these exercises |
| November 25 |
Radical extensions and solvable groups |
|
These exercises |
| December 2 |
non-solvability of the general quintic equation, Galois groups of extensions of Q, reductions mod p |
|
These exercises |
| December 9 |
small degree extensions of Q, Kummer theory, normal basis theorem |
|
The non-asterisked parts of these exercises |
| December 16 |
Last part of exam material, first part of infinite Galois theory |
|
The non-asterisked parts of these exercises |
| January 6 |
| January 13 |