Field & Galois Theory
A 21-module path through field & galois theory, in study order from foundations to the frontier.
Modules
- Field Extensions and Subfields
- Algebraic and Transcendental Elements
- The Minimal Polynomial
- Simple Extensions and F(alpha)
- The Tower Law
- Finitely Generated Algebraic Extensions
- Splitting Fields
- Uniqueness of Splitting Fields
- Algebraic Closure
- Separable Extensions
- Perfect Fields and Inseparability
- The Primitive Element Theorem
- Finite Fields
- Normal Extensions
- The Galois Group of an Extension
- Galois Extensions
- The Fundamental Theorem of Galois Theory
- Cyclotomic Extensions
- Solvability by Radicals
- Insolvability of the Quintic
- Constructible Numbers and Classical Problems