Mathematics · Avançado · Nível 4

Abstract algebra II

Group actions, orbits and stabilisers, counting with Burnside's lemma, the class equation and the Sylow theorems with the counting arguments that settle the structure of small groups; normal and composition series, Jordan-Hölder, solvable groups, the derived series and the simplicity of the alternating group; divisibility in an integral domain, Euclidean domains, principal ideal domains, unique factorisation and Noetherian rings; field extensions and degree, minimal polynomials, splitting fields, the classification of the finite fields and the classical impossible constructions; and Galois theory — Galois groups, normality and separability, the fundamental correspondence, cyclotomic extensions, and why the quintic has no formula in radicals.

Ages 18+ 26 lessons about 13 hours in all

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