|
Home
Syllabus
Lecture Topics
Homework
Policies
|
|
Math 8174: Topics in Algebra,
Spring 2010
|
|
Syllabus
|
|
|
Course description:
This course will be an introduction to homological algebra.
We will study categories and functors, abelian categories,
chain complexes, derived functors, Tor and Ext,
homological dimension, group homology and cohomology,
and spectral sequences.
|
Prerequisites:
MATH 6130, 6140.
|
Text:
An Introduction to
Homological Algebra, by Charles Weibel (1995).
|
Other Fine Books on the Subject:
♦
Homological Algebra, by Cartan and Eilenberg (1956).
♦
Homology, by MacLane (1963).
♦
A Course in Homological Algebra, by Hilton and Stammbach, (1971).
(2nd ed. (1997).)
♦
An
Introduction to Homological Algebra, by Rotman (1979).
(2nd ed. (2009).)
|
Books on Related Topics:
♦
Abstract Algebra (Chapters 10 and 17), by Dummit and Foote.
♦
Categories for the Working Mathematician, by MacLane (1971).
(2nd ed. (1998).)
♦
Abelian Categories, by Freyd, (1964).
|
Homework:
If you are enrolled for a grade I will ask you to solve
some problems. You will be asked to work on the problems
in small groups of 2-3. Different groups will be assigned different problems.
You will typically have a week for your group to solve its assigned
problem(s) and submit the solution(s).
(This deadline is not strict. but
I'll check in with you if I don't get
solutions within a couple days of the due date.)
If you are solving Problem M of HW N, please submit
the solution as a PDF file called homNpM.pdf.
After receiving your solution I will correspond
with you about improvements
and corrections,
if I can think of any. (This step
in the process should take at most one week.)
You are not obligated to take any of my advice,
but if one of my comments involves a correction,
then you should correct that part in some way.
(For example, if I say "Here is a shorter way to do it",
you don't have to change anything unless you want to.
If I say "The first displayed equation is wrong. Here is
how to fix it …", then you should fix the
error, not necessarily along the lines of my suggestion.)
New assignments will be posted every other week
starting the second week. Solutions to old assignments will
be posted when they are in final form.
You should read your classmates' solutions.
|
|
|