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.
Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems.
Street-Fighting Mathematics is available in print and online under a Creative Commons Noncommercial Share Alike license.
About the Author
Sanjoy Mahajan studied mathematics at the University of Oxford and received a PhD in theoretical physics at the California Institute of Technology. He is now Associate Director of the Teaching and Learning Laboratory and a Lecturer in the Department of Electrical Engineering and Computer Science at MIT. Before coming to MIT, he was a Fellow of Corpus Christi College, Cambridge, and a Lecturer in Physics in the University of Cambridge.
"'Too much mathematical rigor teaches rigor mortis.' This is Sanjoy Mahajan's way of saying 'failure to make timely approximations leads to algebraic paralysis.' Approximations are essential in the design process, and his book legitimizes, accelerates, and extends the methods that students eventually have to learn on their own anyway."
R. David Middlebrook, Professor Emeritus of Electrical Engineering, California Institute of Technology
"All students and teachers of mathematics and science, whatever their level, will find a wealth of fun and practical tools in this fantastic book."
David MacKay, Fellow of the Royal Society, Professor of Natural Philosophy, Cavendish Laboratory, University of Cambridge, Chief Scientific Advisor, UK Department of Energy and Climate Change
"Many everyday problems require quick, approximate answers. Street-Fighting Mathematics teaches a crucial skill that the traditional science curriculum fails to develop: how to obtain order-of-magnitude estimates for a broad variety of problems. This book will be invaluable to anyone wishing to become a better informed professional."
Eric Mazur, Balkanski Professor of Physics and of Applied Physics, Harvard University
"Street-Fighting Mathematics taught me things I wish I'd learned years ago. It's fun, fast, and smart. Master it and you'll be dangerous."
Steven Strogatz, Cornell University, author of The Calculus of Friendship