Class Home Page for Differential Geometry II
MTG 6257—Section 1958 (30152)
MAT 4930—Section 9401 (31980)
Spring 2022

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
  • Sufficient conditions for paracompactness

  • Review of Advanced Calculus (updated 1/29/22). I've inserted a new Section 7, with an important lemma (Lemma 7.2) that I did not have time to cover in our review last semester.

  • 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 updated "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—for which the best proof I know is contained in Section 1.9 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.

  • Some notes on tensor products. These notes are under construction and may have typos. At any time, in any location, material may be inserted, corrected, deleted, re-ordered, etc. But enough has been written that you may find the current version a useful resource. A version-date is posted near the top of the first page.
    I will continue update these notes, sporadically, after the course is over. The most up-to-date version will be found here.

  • \({\mathcal F}\)-linearity, tensoriality, and related notions

  • Pullbacks of vector bundles and connections

Problem Set 1. Due date: Wednesday, 2/2/22.

Problem Set 2. Due date: Monday, 2/28/22.

Problem Set 3. Due date: Monday, 4/4/22.

Problem Set 4. Due date: Wednesday, 4/27/22 (extended from the original 4/20/22 date).