MATH 4580: Abstract Algebra I

4580-4581 includes group theory, ring theory, vector spaces over arbitrary fields, and field theory. Math 4580-4581 constitutes a two-semester sequence on abstract algebra, intended to introduce students the main concepts of this subject area. Focused on groups, rings and fields, this course gives the students a deep understanding of these three basic algebraic structures, and provides a good foundation for more specialized work. A significant goal of the course is to improve mathematical reasoning and proof writing. Math 4580 presents special classes of groups, group actions on sets, vector spaces, and field theory that concludes with elements of Galois theory. The course places these topics in their historical context where possible.

Required Textbook: Abstract Algebra: Theory and Applications by Tom Judson, 2019

Supplementary Textbook: Math 4580 course notes by Ronald Solomon, 2018