Math 689 – Fall 2011
Commutative and Homological Algebra
Course Information
Catalog Title and Description: Math 689. Special Topics in Algebra: Introduction to Commutative and Homological Algebra, especially over the polynomial ring. Prerequisites: Math 653 or
approval of the instructor.
Learning Outcomes:
This course will cover basics of Commutative and Homological Algebra, in preparation for more
advanced work in Algebra, Algebraic Geometry and Number Theory. Students interested in any
subfield of Algebra will benefit from learning this material, but it is also recommended for those
interested in Geometry and Topology. Students taking Algebraic Geometry in Spring 2012 are
especially encouraged to take this class.
Required Text:
Commutative Algebra, with a view toward Algebraic Geometry, by David Eisenbud.
Other recommended texts:
Introduction to Commutative Algebra, by M. F. Atiyah and I. G. MacDonald.
Commutative Ring Theory, by Hideyuki Matusumura.
Cohen–Macaulay rings, by Winfried Bruns and Jürgen Herzog.
An introduction to Homological Algebra by Charles Weibel.
Instructor Information
Instructor: Laura Felicia Matusevich
Office: Milner 221
Email: laura@math.tamu.edu
Website: http://www.math.tamu.edu/˜laura
Office Hours: MWF 2:00 – 3:00
Classes
Lecture MW 5:45 – 7:00 pm BLOC 113.
Exams and Grading
Course Grade: The course grade will be based entirely on weekly homework, as follows: Homework grades will count for 80% of the class grade. The remaining 20% will come from solution-
writing assignments. The usual cutoffs apply, namely more than 90% guarantees an A, more than
80% guarantees a B, more than 70% guarantees a C, and more than 60% guarantees a D.
Attendance of all lectures is required. Make-up work or deadline extensions will be given only in
case of absences authorized under Student Rules: Attendance.
Course Topics
Quick review of rings and ideals.
Noetherian rings, Primary Decomposition.
Integral dependence and the Nullstellensatz.
Introduction to Dimension Theory.
Chain Complexes.
Review of projective, injective, flat modules.
Resolutions, the Hilbert Syzygy Theorem.
Ext and Tor and their long exact sequences.
Further topics in homological commutative algebra as time permits: projective dimension, depth,
the Auslander–Buchsbaum formula, Cohen–Macaulay and Gorenstein rings.
Other
ADA Policy Statement: The Americans with Disabilities Act (ADA) is a federal anti-discrimination
statute that provides comprehensive civil rights protection for persons with disabilities. Among
other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accomodation of their disabilities. If you believe you have a disability requiring an accomodation, please contact the Department of
Student Life, Services for Students with Disabilities, in Room B118 of the Cain Hall or call
845-1637.
Copyright: All printed handouts and web-materials for this course are protected by US Copyright
Laws. No multiple copies can be made without written permission by the instructor.
Scholastic Honesty: Always abide by the Aggie Code of Honor: An Aggie does not lie, cheat,
or steal or tolerate those who do. Please refer to Honor Council Rules and Procedures
at http://www.tamu.edu/aggiehonor for more information on academic integrity
and scholastic dishonesty.