For some topics we will use Algebra: An Approach via Module Theory by William A. Adkins and Steven H. Weintraub, which is on reserve at Kelvin Smith Library. I may also draw on J.S. Milne's Fields and Galois Theory course notes available on his web site.
Basic properties of groups, rings, modules and fields. Isomorphism theorems for groups; Sylow theorem; nilpotency and solvability of groups; Jordan-Holder theorem; Gauss lemma and Eisenstein's criterion; finitely generated modules over principal ideal domains with applications to abelian groups and canonical forms for matrices; categories and functors; tensor product of modules, bilinear and quadratic forms; field extensions; fundamental theorem of Galois theory, solving equations by radicals.
In Math 402 we will cover chapters V, IV, and VII of the book by Hungerford (in that order); and parts of the book by Adkins and Weintraub, especially from chapters 6 and 8.