MATH 580 - Modern Algebra I

Prerequisite, MATH 380, or 460. A first semester graduate course in algebra. Group Theory (solvable groups, Sylow Theorems, free groups, finitely presented groups, permutation groups, orbits, stabilizers, G-sets, applications to combinatorics, representation theory, character tables), (noncommutative) rings, polynomial rings, Groebner bases, modules, Hilbert’s Nullstellensatz, fields, Galois Theory, fundamental theorem of algebra, commutative algebras, Lie groups and Lie algebras, classification of finite simple groups, and applications. (Offered as needed.) 3 credits