MATH338: Galois Theory
This follows the usual path through to Galois groups, but just for subfields of the complex numbers.
It takes as its goal the insolubility of polynomials by radicals.
This is as far as we normally reach, though there is an additional chapter that gives an algebraic proof of the Fundamental Theorem of Algebra, using Sylow theory.
[Please note that all links are to Adobe .pdf documents. They will open in a separate browser window.]
- Chapter 1: Polynomials
- Chapter 2: Field Extensions (The Impossibility of Angle Trisection)
- Chapter 3: Solubility by Radicals (Why Quintics are not Soluble by Radicals)
- Chapter 4: Examples of Galois Groups
- Chapter 5: The Fundamental Theorem of Algebra
(Why Every Polynomial Over C Has a Zero) - Appendices
- Answers to the Exercises
