Some MAP Chat members have decided to group-read several math texts and discuss as a way to learn together. We aim for these readings to be reasonable and flexible – it should be fun! To that end, we do not schedule out excerpts far into the future. Rather, we discuss together each week about the week or two ahead, and set goals as a group.
Motivating Mathematical Physics Allusions
The choice of reading topics has largely been motivated by concepts mentioned in passing but not examined in detail during theoretical physics research. Some of our favorite “sentences we want to rigorously understand” are below.
- “The connection on the principal bundle is the gauge boson field“
- “Tetrads in GR are solder forms that glue charts to local frames“
- “In general, which punctures on a manifold are removable?“
Current Readings
The current readings are spread across two texts:
- Dummit and Foote, Abstract Algebra (Amazon, PDF)
- Lee, Introduction to Smooth Manifolds (Amazon, PDF)
The below table summarizes currently planned readings, as well as previous week’s readings. A more detailed table of contents for each text can be found in a Google Sheet, with information about number of pages per section.
| Week | Meeting Date (Due) | Lee | Dummit & Foote |
|---|---|---|---|
| 9 | 2024-04-09 | 3.* | 4.* |
| 8 | 2024-04-02 | 2.1 - 2.3 | 3.2 - 3.5 |
| 7 | 2024-03-26 | 1.6 (problems) | 3.1 - 3.2 |
| 6 | 2024-03-19 | 1.3 - 1.5 | 2.4 - 2.5 |
| 5 | 2024-03-12 | 1.1 - 1.2 | 2.1 - 2.3 |
| 4 | 2024-02-27 | Skim App B - D | 1.3 - 1.7 |
| 3 | 2024-02-20 | App A "Subspaces" - "Homotopy" | 1.1 - 1.2 |
| 2 | 2024-02-13 | App A "Topological Spaces" | 0.* Preliminaries |
| 1 | 2024-02-06 | None | None |