Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving

by Sanjoy Mahajan, Carver A. Mead

Overview

An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation.

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 will appear in print and online under a Creative Commons Noncommercial Share Alike license.

Product Details

ISBN-13:	9780262514293
Publisher:	MIT Press
Publication date:	03/05/2010
Series:	The MIT Press
Pages:	134
Product dimensions:	6.80(w) x 8.90(h) x 0.60(d)
Age Range:	18 Years

About the Author

Sanjoy Mahajan is Associate Professor of Applied Science and Engineering at Olin College of Engineering and Visiting Associate Professor of Electrical Engineering and Computer Science at MIT. He was a Marshall Scholar at Oxford University and a Fellow of Corpus Christi College in the University of Cambridge, where he was a member of the physics faculty. He is the author of Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving (MIT Press).

Carver A. Mead is the Gordon and Betty Moore Professor of Engineering and Applied Science, Emeritus, at the California Institute of Technology. He won the 1999 Lemelson-MIT Prize for Invention and Innovation.

What People are Saying About This

Steven Strogatz

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.

David MacKay

All students and teachers of mathematics and science, whatever their level, will find a wealth of fun and practical tools in this fantastic book.

Endorsement

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

From the Publisher

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

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

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

David Mackay

"Every student or teacher of mathematics and science, whatever their level, will find a wealth of fun and practical tools in this fantastic book."--David MacKay, Professor of Natural Philosophy, Cavendish Laboratory,
University of Cambridge, Chief Scientific Advisor, UK Department of Energy and Climate Change

Eric Mazur

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.