The course description is as follows:
The art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Application to mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.)Personally, I always thought the epsilons and deltas were harming me. The text (a draft version of which can be found on the course web page) stresses the idea that approximate answers, heuristics, etc. are more valuable than they are often claimed to be, which is a question that Mahajan also took on in his PhD thesis, which is a combination of a version of such a textbook and some extended examples on what one might call "research-level" problems, one of which is a probabilistic model of the primes which it is too late at night to seriously read.
From a quick poke around the web page, it looks like Mahajan also offered a similar, but more physics-oriented course in IAP 2006, as well as TAing a couple more substantial courses in the same vein at Caltech called "Order-of-Magnitude Physics". (The MIT IAP course meets three hours a week for four weeks and carries one-quarter the credit that a "normal" course at MIT would carry; the Caltech courses appear to have met three hours a week for ten weeks. As such, they have more problem sets. But they're also more physics-y, which may be good or bad depending on how you feel about physics.