Math 662: Seminar in Algebra
Introduction to Commutative and Homological Algebra
Fall 2017

Instructor: Sarah Witherspoon
Email: sjw AT math.tamu.edu
Office and hours: Blocker 513B, MF 9-10 am, T 1-2 pm, or by appointment

Course web address: /~sjw/math662.html

Class meetings: MWF 1:50-2:40 pm, in Blocker 624

Optional Texts: Commutative Ring Theory, Hideyuki Matsumura, Cambridge University Press, 1986.
An Introduction to Homological Algebra, C. A. Weibel, Cambridge University Press, 1994.

Other optional sources for some of the course material are:
Introduction to Commutative Algebra, M. F. Atiyah and I. G. MacDonald, Addison-Wesley, 1969.
Commutative Algebra with a View Toward Algebraic Geometry, David Eisenbud, Springer, 2004.
A Course in Homological Algebra, P. J. Hilton and U. Stammbach, Springer-Verlag, 1971.
Basic Homological Algebra, M. S. Osborne, Springer, 2000.
An Introduction to Homological Algebra, J. J. Rotman, Springer, 2009.


Course requirements and grades
Course prerequisite: Math 654 or equivalent.
Course grades will be based on homework, which will be assigned approximately every two weeks. Grades are assigned as follows based on homework average: A (80-100%), B(60-79%), C(40-59%), D(20-39%), F(0-19%).

Course description
3.0 credits. Selected topics in algebra. May be repeated for credit.

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 most of the first 18 sections of the text by Matsumura, with additional homological algebra material taken from the text by Weibel and other sources. Specifically, this includes chain complexes, resolutions, Ext, Tor, the Hilbert Syzygy Theorem, derived functors, Noetherian rings, primary decomposition, integral dependence, Nullstellensatz, dimension theory, and further topics as time permits, such as projective dimension, depth, and Cohen-Macaulay and Gorenstein rings.


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