Commutative Algebra · Mathematics
Matsumura's text, a bit of category theory and cohomology, lots about modules
This course is very hard, but Prof. Urban is a very knowledgeable professor and his teaching skills are excellent, so I like the course but if anyone wants to take it please reconsider because it is indeed very hard.
Basically everything it says in the course description. I really got a lt from this course. It was very rigorous and the homework problems were fun and at times challenging (in a good way).
Knowledge: Various topics across commutative algebra: associated primes, dimension theory, Noether normalization, Artinian rings, etc. Perspective: Prof. de Jong did everything rather geometrically (a lot of the homework emphasized this). It would help to go into the class with some prior background or intuition from algebraic geometry.
You will not understand everything as an undergrad, but you will learn loads if you can keep up.
I think the course might be tough without some geometric intuition. 1 Columbia University: Arts & Sciences Fall 2021 Course: MATHGR6261_001_2021_3-COMMUTATIVEALGEBRA : MATHGR6261_001_2021_3 - COMMUTATIVE ALGEBRA Instructor: Johan De Jong