Street-Fighting Math: down and dirty guide to approximation and problem-solving

Street-Fighting Mathematics looks like a fun read: it's a Creative Commons-licensed math textbook that teaches approximation and "down-and-dirty, opportunistic problem solving." It's based on a MIT course taught by the author, Sanjoy Mahajan.

In problem solving, as in street fighting, rules are for fools: do whatever works–don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation.

In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge–from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool–the general principle–from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest.