Prerequisite: An undergraduate course in abstract algebra, including:

• Groups (subgroups, Lagrange's theorem, normal subgroups, quotient groups, normalizers, homomorphisms);
• Rings (subrings, ideals, quotient rings, homomorphisms, Euclidean rings, unique factorization, polynomial rings);
• Fields (roots of polynomials and factorization of polynomials, extension fields, degrees of extensions, adjoining of roots).

Math 504 (Autumn): Group theory.

Math 505 (Winter): Rings and modules.

Math 506 (Spring): Fields and Galois theory.