Preparation for a graduate commutative algebra course based on Eisenbud

Question

I am an undergraduate with two semesters of algebra(groups,rings, Galois theory, etc) under my belt and I am planning on going through Atiyah and MacDonald's book over the summer. Is this sufficient preparation for a graduate course based on Eisenbud? The course will move very quickly and cover virtually the whole text. If not, what else should I learn?

Answer 1

Truthfully, this does not seem like a very useful course unless you are somehow already passionately devoted to commutative algebra. Spending your time in a course where you will have time to master what you are learning and solve a variety of problems is much better than taking a very difficult course that does not really sound appropriate for someone with an undergraduate background.

But if you are committed to taking the course on Eisenbud's book, I think a basic introduction to algebraic geometry will be very helpful to understand the motivation for many of the constructions in commutative algebra. Brendan Hassett's Introduction to Algebraic Geometry and Karen Smith et al's An Invitation to Algebraic Geometry are two suggested first books in algebraic geometry. Reading Atiyah and Macdonald is also a good idea.