Handouts, homework assignments, and other information will be available via links from this page.
- MTG 6256–6257 sequence summary
- Syllabus and course information
- Some references on differential geometry and differential topology
- Miscellaneous notes and handouts
- Point-Set Topology: Glossary and Review
- Some facts about normed vector spaces. Please bear with the elementary tone of these notes; they were written for MAA 4212 (Advanced Calculus 2). You may still find them a useful reference.
- Review of Advanced Calculus
- Notes on Riemann Integration. These notes were written for MAA 4212 (Advanced Calculus 2) prior to the 2020 restructuring of the MAA 4211–4212 sequence. I'm posting these notes here because Section 7 of the above "Review of Advanced Calculus" involves integration of vector-valued functions on an interval, and refers to the "triangle inequality for integrals"—valid for continuously differentiable functions from an interval to any Banach space (in particular, any finite-dimensional normed vector space)—for which the best proof I know is contained in Section 1.9 (Proposition 1.92) of these integration notes. There is some notation and terminology used in Section 1.9 that's defined earlier in the notes, but there's an index (Section 1.10) to make definitions of these objects easier to find.
- Bump-functions and the locality of Leibnizian linear operators
- Sufficient conditions for paracompactness
Homework Assignments
Last updated Sun Nov 23 00:18 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.Problem Set 1. Due date: Monday, 9/22/25. Problem Set 2. Due date: Wednesday 10/1/25. Problem Set 3. Due date: Friday, 11/21/25. Problem Set 4. Due date: Wednesday, 12/3/25.