Sanjoy Mahajan’s book, Street-fighting Mathematics, is about the art of educated guessing and opportunistic problem solving.
In problem solving, as in street fighting, rules are for fools: do whatever works—don’t just stand there! 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.
The book is available in traditional dead-tree format and also for download under a Creative Commons license.