Abstract Algebra

Introduction to abstract algebra, groups, rings, and fields. Topics include binary operations, groups, subgroups, cyclic groups, groups of permutations, cosets, finitely generated groups, homeomorphisms, isomorphisms, factor groups, rings, fields, and integral domains. Additional topics may include fields of quotients, rings of polynomials, factor rings, ideals, unique factorization domains, and the Sylow Theorems.