Math 662: Seminar in Algebra
Homological Algebra
Spring 2025

Instructor: Sarah Witherspoon
Email: sjw AT tamu.edu
Office and hours: Blocker 513B, TR 5:10 - 6 pm, or by appointment

Course web address: https://people.tamu.edu/~sjw/math662_2025.html

Class meetings: MWF 1:50-2:40, in Blocker 148

Optional Texts: An Introduction to Homological Algebra, C. A. Weibel, Cambridge University Press, 1994.
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.
Appendix to Hochschild Cohomology for Algebras, S. J. Witherspoon, GSM 204, American Mathematical Society, 2019, available at https://www.math.tamu.edu/~sjw/pub/gsm204.pdf.


Course requirements and grades
Course prerequisite: Math 654 or equivalent.
Course grades will be based on homework, to be assigned approximately every 3 weeks, and class participation. Grades are assigned as follows based on homework: 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 homological algebra, in preparation for more advanced study and research in fields in which homological techniques are used. Topics will be taken from the optional textbooks listed above and from other sources. This will include chain complexes, resolutions, Ext, Tor, long exact sequences, homological dimension, Hilbert Syzygy Theorem, derived functors, derived categories, Künneth Theorem, spectral sequences, and further topics as time permits.


Academic Integrity Statement "An Aggie does not lie, cheat, or steal or tolerate those who do." The Aggie Code of Honor is an effort to unify the aims of all Texas A&M men and women toward a high code of ethics and personal dignity. For most, living under this code will be no problem, as it asks nothing of a person that is beyond reason. It only calls for honesty and integrity, characteristics that Aggies have always exemplified. The Aggie Code of Honor functions as a symbol to all Aggies, promoting understanding and loyalty to truth and confidence in each other. Violations of the Aggie Honor Code and the handling of such violations are discussed at the web site http://aggiehonor.tamu.edu.

ADA Statement The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with diabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accomodations 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 118 of Cain Hall or call 845-1637.

Title IX and Statement on Limits to Confidentiality Texas A&M University and the College of Science are committed to fostering a learning environment that is safe and productive for all. University policies and federal and state laws provide guidance for achieving such an environment. Although class materials are generally considered confidential pursuant to student record policies and laws, University employees — including instructors — cannot maintain confidentiality when it conflicts with their responsibility to report certain issues that jeopardize the health and safety of our community. As the instructor, I must report (per Texas A&M System Regulation 08.01.01) the following information to other University offices if you share it with me, even if you do not want the disclosed information to be shared: Allegations of sexual assault, sexual discrimination, or sexual harassment when they involve TAMU students, faculty, or staff, or third parties visiting campus. These reports may trigger contact from a campus official who will want to talk with you about the incident that you have shared. In many cases, it will be your decision whether or not you wish to speak with that individual. If you would like to talk about these events in a more confidential setting, you are encouraged to make an appointment with the Student Counseling Service (https://scs.tamu.edu/). Students and faculty can report non-emergency behavior that causes them to be concerned at http://tellsomebody.tamu.edu.