Math 741: Abstract Algebra I

This is the first semester of our basic one year course in
abstract algebra. Here we stress the noncommutative
aspects of the subject, namely group theory and
noncommutative ring theory. The group theory material
includes permutation groups, the Sylow theorems, solvable
and nilpotent groups, and some simple groups. The ring
theory material includes the radical and Density theorem,
Artinian rings, the Wedderburn theorems, and completely
reducible modules. Numerous examples will be offered to
illustrate the theory.