This paragraph is about homework. TLDR: if you really don't want to do homework, please still register for the course and come learn! However, if you want to learn efficiently, you should do homeworks! They will be fun, and I insist that you cap the amount of time spent on them each week, so they should not be an undue burden or stressful.
Homological algebra is numbered as a 607 course, and like all post-quals classes, this means students are inclined not to do any homework. However, this is not a topics course but a tools course. I am a firm believer that without doing exercises you will not acquire tools (and will eventually fall behind in the class too). So, I will try to assign one short exercise per day, expecting it to be done before the next class. BUT! I don't want this to stress anyone out: please limit the amount of time you spend on homework to 1 hour per assignment and 1.5 hours total per week! Partial assignments will be given full credit if you ran out of time.
As a post-quals course, your grade is mostly irrelevant... but carrots help. With the exception of students with attendance issues, which flavor of A you receive for your grade will depend on the amount of homework done. See the syllabus for grading information.
We will mostly be working from Weibel's book An Introduction to Homological Algebra. You can find a pdf online if you look, but this is an excellent reference so it is worth buying. Some topics will be taken from MacLane's Categories for the Working Mathematician which is also a recommended purchase. If you seek monetary assistance in buying books, let me know.
We will use quiver representations as toy examples in exercises throughout the quarter. Crawley-Boevey's lecture notes on quivers can be found here.
An excerpt from a textbook by Kiehl and Weissauer is on Canvas.
Khovanov's paper on Hopfological algebra is here.
I will keep one file with the exercises, and will update it periodically. It is here. It also contains recommended reading.
I will be posting notes here as they appear. I'm making improvements to the lecture notes from the previous times I taught this course.
Introductory Lecture
Baby rep theory and quivers
On projective objects
The scoop on cones
Derived functors
Additive and abelian categories
Reflection Functors
Gaussian Elimination
Yoneda Ext
Homological Dimension
Koszul Complexes
Spectral sequences
Triangulated Categories