Step 30 of 37
Undergraduate algebra again, deeper and faster, plus modules and representations.
Topics, in order
- Modules over a principal ideal domain
- Tensor products
- Galois theory in depth
- Commutative algebra: Noetherian rings and localization
- Representations of finite groups
- Categories and functors
- Homological algebra basics
Learn from
- Dummit and Foote, Abstract Algebra (later chapters)
- Aluffi, Algebra: Chapter 0
- Atiyah and Macdonald, Introduction to Commutative Algebra
- Lang, Algebra
Move on when
You can classify finitely generated modules over a principal ideal domain and derive Jordan form from it.