Math / Physics

I did undergraduate and graduate work in physics and mathematics at MIT and UC Berkeley, but I guess academia wasn’t for me. I still love the subject though, and continue to try to do some work independently. I recently took some time off to work on some ideas, resulting in a book that is about 90% done…hopefully I’ll find the month or so to finish it sometime soon.

Here’s a few of my favorite books:

Differential Geometry, Gauge Theories, and Gravity

Differential Geometry, Gauge Theories, and Gravity (Cambridge Monographs on Mathematical Physics) by M. Göckeler and T. Schücker

This is an excellent self-contained overview of differential geometry and fiber bundles as applied to (pre-quantized) gauge theories and gravity, all in the compact “Cartan formalism.” From a mathematical viewpoint, it’s helpful to see a unified treatment of most of the structures used in gauge theories, and from a physical viewpoint, this is a good introduction to seeing general relativity as a gauge theory.

Mathematical Physics

Mathematical Physics (Chicago Lectures in Physics) by Robert Geroch

This is a great complement to the above, in that it also covers many mathematical structures as they relate to theoretical physics, but it focuses more on algebraic objects and “hybrid” objects such as Lie groups and Hilbert spaces. Basic category theory helps unify the treatment, and Geroch’s amazing intuitive explanations help to make formal proofs “click” in a way that usually takes a long time to happen.

Algebraic Topology

Algebraic Topology by Allen Hatcher

Unlike the previous two books, this is a straightforward textbook in a specific subject. But it’s so well-written, well-formatted, and inspired in its explanations and pictures that I ended up learning way more about the subject than I really needed to for my purposes. Plus, the book is available as a free PDF download at the author’s site, so you can search the PDF and then read the results on paper! This is so useful, it seems like all books ought to be sold this way…


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