An excellent book that that shows how mathematics is really done in the real world.
Rather than following the pure mathematical approach where-by students are forced to prove every step with an epsilon-delta type argument this book teaches another philosophy.
Street-fighting mathematics solves problems the way most science is really done: you take wild guesses, you use approximations, plays with analogies, and uses every possible method at your disposal to make progress on your problem. Who cares about mathematical rigor if you can't get even the coarsest solution to your problem. In this book Mahajan presents a number of problem solving strategies and then provides examples at using them. This book is a true treasure to read. Readers unfamiliar with this book can see what others have said here.
To learn this material as well as possible I worked through all of the book's end of chapter problems, wrote the solutions up in the LaTeX mathematical typesetting language, and produced a PDF of the solutions. For about a year now I had been giving this material away for free to anyone who requested a copy. Recently I've decide to try to sell this material. I converted the PDF format to a format I thought more people would find easier to read. You can preview and buy a kindle version of the book here. If you are interested in purchasing the PDF version please contact me below.
As always, I am interested in hearing about any errors that might exist in this material.