I'm going to try a new approach to homework. This is a topics course and often this means people don't do the homework (often for lack of time and too much inertia). However, 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 (less than half an hour of work, especially if worked in groups), expecting it to be done before the next class.
It's also a topics course, so your grade is almost entirely irrelevant. But some people like carrots, so your grade for the course will be dependent entirely on the homework done. See the syllabus for details.
I have a pdf with my notes from last time I taught the course, but I think I will make a new pdf with course notes, in an attempt to fix various errors and improve the curriculum. So expect this to be posted online soon as well.
More accurately, I've started making complete notes somewhere in the middle of the class, so here they are, sorted by topic.
Homological dimension
More on Koszul complexes
Ext and extensions, the Yoneda product
Stuff on Cones
Triangulated categories and the definition of derived categories
My teaching aid for the octahedral axiom. The vertices represent objects (up to shift), and the edges maps (there is some orientation). The solid triangles are commutative, while the hollow triangles are distinguished. The solid square is commutative. The outer square (with attempted green highlighting) is anticommutative! (The third square is oriented cyclically.)
