Topics in Abstract Algebra

MAT 3[4-9]NN

An advanced course with an emphasis on learning to understand, construct, and present proofs. The following topics are included: groups and group action, Sylow theorems, the free group, generators and relations, the Todd-Coxeter algorithm, ring theory, Hilbert’s Nullstellensatz, unique factorization domains, Noetherian rings, modules, free modules, generators and relations, Hilbert basis theorem, the structure theorem for abelian groups, fields, algebraic and transcendental elements, algebraically closed fields, and the fundamental theorem of algebra. As an application, this course suggests either an introduction to Galois theory or introduction to commutative and noncommutative Groebner basis. This course also requires an accompanying weekly seminar.