Ma 5/105 abc - Introduction to Abstract Algebra

Introduction to groups, rings, fields, and modules. The first term is devoted to groups and includes treatments of semidirect products and Sylow's theorem. The second term discusses rings and modules and includes a proof that principal ideal domains have unique factorization and the classification of finitely generated modules over principal ideal domains. The third term covers field theory, Galois theory, and an introduction to character theory for finite groups.