The first quarter will be concentrate on module theory, starting with a general introduction from Chapter 10 of Dummit and Foote, moving to the classification of finitely generated modules over a PID and its applications to linear algebra (Chapter 12), then returning to Chapter 10 to do some homological algebra, and finally winding up with representations of finite groups (Chapters 18 and 19), regarded as modules over the group ring. The course will broadly follow the text, but some topics will be omitted topics, cover others will be covered in greater depth, and additional topics not included in the text may be covered as well.

Math 505 will cover additional topics in homological algebra and Galois theory. Math 506 will cover commutative algebra and basic algebraic geometry.

Text: Abstract Algebra by Dummit and Foote, (3rd ed., Wiley, 2004).

Prerequisites: Math 404 or equivalent.