Math 689: Introduction to Commutative and Homological Algebra Prerequisite: Math 654 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 work through material from approximately the first 18 sections of the text by Matsumura, Commutative Ring Theory. 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. My syllabus from Fall 2015 is at http://www.math.tamu.edu/~sjw/math689_syllabus.html and I do not expect to make any major changes to this.