Markus Schmidmeier
Mathematical Sciences
Florida Atlantic University

Homological Algebra

Welcome to my course on Homological Algebra (MAS 6396/ MAT 4930)! We meet Tuesdays and Thursdays 9:30 - 10:50 a.m. in BU 102.

Modules are ubiquitous in modern mathematics, and by now you have met them on several occasions, for example disguised as abelian groups (Z-modules), as vector spaces (k-modules), in Intro Abstract Algebra (as modules over Euclidean domains), in group theory (as representations) etc.

Working with modules is like lego playing. There are the simple modules, the bricks, they come in several different shapes and colors. Many modules are semisimple (that is, direct sums of simples), we can think of them just as a bunch of lego bricks. This is boring.


The fun begins when you put the bricks together. This is what homological algebra is all about. We can stick many bricks together, and we can stick them together in many ways. What we get is called an extension and such things can get really fancy.

Topics

An introduction to homological algebra, in particular for students with interests in algebra, geometry or topology. We will be covering:

Objectives

Textbook

C. M. Ringel and J. Schröer, Representation Theory of Algebras, 2nd preliminary version. I plan to cover selected sections in Part 1 (Categories and modules, examples), Part 3 (Modules over rings), Part 4 (Projective modules) and Part 5 (Homological Algebra I).

The textbook by Rotman, Homological Algebra, is recommended for this course. It is now available in the 2nd edition. I also list (in alphabetical order) several common textbooks that show the extent to which methods from homological algebra are used in algebra, geometry, topology...

Credit

Homework:  There will be biweekly homework assignments, the 6 best will count for 60% of the grade.

Presentation:   Two presentations will count for each 20% of the grade.

Final Exam Day:   The last class meeting will be on Thursday, April 27, during 7:45 - 10:15.

Here you can find some general information about my courses.

Contact Me

Office hours:   TR 4-5:30 p.m. in SE 272

Course Web Page:   http://math.fau.edu/markus/homalg17.html

E-mail:   markus@math.fau.edu.


Last modified:  by Markus Schmidmeier