MATH432

An introduction to the algebraic structures known as groups, rings and fields. These structures are a basic part of the theory and language of modern mathematics. About two-thirds of the course will study topics from group theory: groups, subgroups, cyclic groups, permutation groups, Lagrange's Theorem, finitely generated abelian groups, homomorphisms and isomorphisms, normal subgroups, and factor groups. The remainder of the course will be an introduction to rings and fields and associated topics including: rings, fields, integral domains, polynomial rings, the quaternions, prime and maximal ideals and their factor rings. The course will emphasize understanding abstract structures, and reading and writing mathematical proofs.