The inverse function theorem

I'd like to see a proof of the inverse function theorem in the setting of synthetic differential geometry. It seems awkward that such a basic geometrical fact needs analysis to prove.

Using Dimensional Analysis at Home!

My older son came to me with a question about speed limits on train tracks, and how they might change with curvature. He had one example, and wanted to know what would happen if he doubled the curvature. Assuming that acceleration was the key idea, we just wrote down the units, keeping a fixed acceleration, and a formula relating curvature and train speed popped out. Unfortunately Microsoft Train Simulator doesn't actually let your trains derail, so we were not able to test it out, uh, "empirically".

Dover books

OK, this isn't really micro, except maybe the prices, but Dover is suddenly reprinting lots of my favorite books from the 1980's: Introduction to Global Analysis, Melzak's Concrete Mathematics series, Goldblatt's book on Topoi. Run out and buy them before they go out of print again!