HOME PAGE OF MATH 321:

An Introduction to Homological Algebra

Spring 2008

Sarah Glaz

glaz@math.uconn.edux

(click on link and remove end x)

Office: MSB 202

CLASS:

T, Th 11:00 - 12:15, MSB 311

BOOKS:

Main Textbook: An Introduction
to Homological Algebra, by Joseph Rotman, Academic Press, Inc.

(May be ordered new from amazon.com. I recommend
ordering a used copy in good condition from amazon.com, alibris.com,
abebooks.com, or strandbooks.com)

Other Texts: An Introduction to Homological Algebra,
by Charles Weibel

Commutative
Coherent Rings, by Sarah Glaz

Commutative
Algebra, by Bourbaki

Commutative
Rings, by Irving Kaplansky

COURSE OUTLINE:

Homological
Algebra is a powerful tool used in a number of areas of mathematics to
deepen
the understanding of the structure of its objects of investigation. In
this
course we will develop

the fundamental notions of Homological Algebra and their
uses in Commutative Algebra, with short

relation
to Projectivity, Flatness, and Injectivity of modules; the introduction
of the
Ext and Tor functors, and ways of computing them in some settings; the
development of the ring invariants:

global dimension, weak global dimension,
and several other homological dimensions, and their uses in describing
properties
of rings. Other topics may be introduced as time allows. We

anticipate covering
portions from Chapters 2, 3, 4, 6, 7, 8, and 9 from the main textbook,
supplemented
from the other texts mentioned above.

GRADING:

Grading
would be
based on a homework grade (50%), and a semester project grade (50%).
There will
be 5 - 7 homework assignments, each comprising of 2 - 4 exercises.
Students are

encouraged to discuss the homework assignments with each other, but
need
to
formulate, write, and hand in their own individual solutions. The
semester
project will be on a topic chosen by

the Instructor in collaboration with each
student. Each students will hand in a typed report (5 - 10 pages) and
give a
class presentation on his/her project. Topics will be assigned a few
weeks

into
the semester. Reports and presentations will begin after Spring Break.

SPECIAL DAYS:

Spring Break: Sunday, March 9 - Sunday, March 16

Last Day of Classes: Friday, May 2