Math 689: Special Topics in Algebra
Introduction to Commutative and Homological Algebra
Fall 2015

Instructor: Sarah Witherspoon
Email: sjw AT
Office: Blocker 513B

Course description
This course will cover the basics of commutative and homological algebra, in preparation for more advanced work in algebra and related fields. We will plan to work through material from approximately the first 18 sections of the text Commutative Ring Theory, Matsumura, Cambridge, 1986. Specifically, this includes Noetherian rings, primary decomposition, integral dependence, Nullstellensatz, dimension theory, chain complexes, resolutions, the Hilbert Syzygy Theorem, Ext, Tor, and further topics as time permits, such as projective dimension, depth, and Cohen-Macaulay and Gorenstein rings.

Course requirements and grades
Course prerequisite: Math 654 or equivalent. The course is designed particularly for graduate students in their second year or beyond, with an interest in algebra, geometry, or topology. Students who plan to take Math 620 (Algebraic Geometry) in Spring 2016 may benefit by taking this course.
Course grades will be based on homework and class participation.