If I'm going to spend lots of time explaining a concept in math and physics to someone (even myself!), I may as well make the explanation public so that others can benefit as well. There isn't a lot here yet, but I hope to keep adding to this section over time.

I call these "tutorials", but the name doesn't always fit perfectly. The tutorials are at very different levels: each assumes that you have learned enough background to be "ready" for the topic. (Thus, I don't attempt to explain what a gradient is in the Lagrange multipliers tutorial, and I don't attempt to explain basic differential geometry in the "GR with Torsion" document.)

## Tutorials

- Lagrange multipliers: a method for finding extrema of functions of several variables when the solution must satisfy a set of constraints, and for the analogous problem in the calculus of variations (often used in physics when studying Lagrangian mechanics).
- An Introduction to String Theory: Not precisely a tutorial, this is a talk that I gave in Feb. 2004 to the Chicago chapter of the MIT alumni club. It's aimed at an audience who've had a year or two of college physics, possibly a long time ago, and who want to see at least a few of the equations of string theory (presumably without being overwhelmed). I don't know if that's possible, but I tried.
*General Relativity*with Torsion (200 KB PDF; 18 pages): Most applications of differential geometry, including general relativity, assume that the connection is "torsion free": that vectors do not rotate during parallel transport. Because some extensions of GR (such as string theory) do include torsion, it is useful to see how torsion appears in standard geometrical definitions and formulas in modern language. In this review article, I step through chapter 3, "Curvature", of Robert Wald's textbook*General Relativity*and show what changes when the torsion-free condition is relaxed.

Up to my teaching page.

Up to my professional page.

My personal site is also available.

Any questions or comments? Write to me: jensens@alma.edu

Copyright © 2006 by Steuard Jensen.