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
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- Chapter
0: Contents and Preliminaries
- 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
