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Well... MIT has you covered. It's called Street-Fighting Mathematics. From the course description:
OK, I admit it, I'm a geek, but I'm excited that this is actually a free offering via MIT's Open CourseWare system.
This course teaches 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. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.)
OK, I admit it, I'm a geek, but I'm excited that this is actually a free offering via MIT's Open CourseWare system.