Handouts, homework assignments, and other information will be available via links from this page.
- Syllabus and course information
- Course materials from fall semester (MTG 6256)
- Miscellaneous notes and handouts
- Bump-functions and the locality of Leibnizian linear operators
- Some notes on tensor products. These notes are still under construction, but are mostly complete; enough has been written for the current version to be a useful resource. Since I may occasionally update these notes, a version-date is posted near the top of the first page.
- \({\mathcal F}\)-linearity, tensoriality, and related notions
- Pullbacks of vector bundles and connections
Homework Assignments
Last updated Wed Dec 3 04:30 EST 2025Each assignment will have a few required problems—the only ones you have to hand in—and a (usually larger) number of optional problems.
Generally, I recommend that you try to at least read the optional problems; I may sometimes refer to these in a later class. You're not required to do the optional problems, but the more of them you do, the more you'll get out of the course. (And since you can do these without handing them in, you're saved the time and effort needed to write up a solution neatly.)
Students planning to do research in differential geometry are advised to do all the optional problems by the end of the semester. (Don't hand them in; just do them.) Every problem on my homework assignments is designed to teach something that someone doing a PhD in differential geometry ought to know. Squandering this opportunity to gain that knowledge before you start in earnest on your thesis project is something you may regret later.