An intermediate course in the theory of groups and fields. Group theory: group actions, Sylow theorems, solvable, nilpotent and p-groups, simplicity of alternating groups and PSL(n,q). Field theory: algebraic and transcendental extensions, separability and normality, Galois theory, insolvability of the general quintic equation, and computation of Galois groups over the rationals.
This course may not be repeated for credit.Syllabus

Sections

This course will be offered next in Fall 2020.