MATH 4581: Abstract Algebra II
This page is part of my personal academic record, not an official course website.
Course description
MATH 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 to 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 4581 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.
Textbooks and resources
Required textbook
- Math 4581 course notes by Ronald Solomon, 2013
Supplementary textbooks
- Abstract Algebra: Theory and Applications by Tom Judson, 2020
- Basic Algebra I by Nathan Jacobson, 2nd edition, 2009, Dover Publications