This Week's Finds in Mathematical Physics, Week 201
by John Baez · University of California, Riverside
John Baez's 2004 expository column introducing Galois theory through symmetry: Galois groups of field extensions, quadratic and cyclotomic number fields, the fundamental theorem, why the quintic has no radical solution, and classical construction problems, with pointers toward class field theory.
More resources on Galois Theory
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
nLab Galois Theory
Entry in nLab, the research-level wiki for category theory and higher mathematics, presenting Galois theory as an equivalence between field extensions and Galois-set categories, plus Grothendieck's generalisation to fundamental groups and covering spaces. Readers see how the classical correspondence fits unifying categorical frameworks.
Galois Theory
Learn Galois Theory from Kevin Buzzard's engaging course. Explore field extensions, polynomial roots, and group theory applications!
Abstract Algebra
Learn Galois Theory with Benedict Gross's Abstract Algebra course. Explore field extensions, polynomial roots, and group theory concepts.
Galois Theory
A widely used undergraduate textbook that develops Galois theory from its historical motivation, the solution of polynomial equations by radicals. It covers field extensions, ruler-and-compass constructions, the Galois correspondence and insolubility of the quintic, preparing readers to prove these classical results themselves.