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

21 customer reviews
ISBN-13: 978-0262514293
ISBN-10: 026251429X
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Editorial Reviews


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.

"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

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.

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Product Details

  • Paperback: 152 pages
  • Publisher: The MIT Press; New edition (March 5, 2010)
  • Language: English
  • ISBN-10: 026251429X
  • ISBN-13: 978-0262514293
  • Product Dimensions: 7 x 0.2 x 9 inches
  • Shipping Weight: 8.8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (21 customer reviews)
  • Amazon Best Sellers Rank: #140,913 in Books (See Top 100 in Books)

More About the Author

Sanjoy Mahajan obtained his PhD in theoretical physics from the California Institute of Technology, and has undergraduate degrees in mathematics from Oxford University and in physics from Stanford University. Due to his many inspiring teachers, he became interested in science teaching, an interest he followed as faculty member in the Physics Department at the University of Cambridge and as a Fellow of Corpus Christi College, Cambridge.

While at Cambridge, he helped start the African Institute for Mathematical Sciences (AIMS) in Cape Town, South Africa, where he was the first Curriculum Director and taught the first courses in physics and computer science. There he wrote the free software to automate barcoding and cataloging the 5,000 donated books that started the Institute's library.

At MIT he has taught courses across the Institute in the mathematics, electrical engineering, and mechanical engineering departments. He is currently Visiting Associate Professor of Applied Science and Engineering at Olin College of Engineering.

Customer Reviews

Most Helpful Customer Reviews

98 of 100 people found the following review helpful By N on March 24, 2010
Format: Paperback
Dr. Mahajan's has been teaching this sort of course for a while now and has been generous enough to make almost all his material available through his course web pages at MIT for The Art of Approximation and Street-Fighting Mathematics. If you want to preview this book I suggest you check those websites out.

The book is reminiscent of Consider a Spherical Cow by Harte, The Art and Craft of Problem-Solving by Zeitz, and How to Solve It by Polya. Although much of the book focuses on how to avoid doing integrals and taking derivatives, it presumes the reader is familiar with calculus. In this respect it's different from the books I just mentioned and other ones out there on approximation, e.g. Guesstimation. The example problems are diverse, most are borrowed from physics, geometry, and math, with a few are that are Fermi-type "real-world" scenarios.

My main complaint is that the book is so short. I wish the author had combined this book with material from his Order of Magnitude Physics and Art of Approximation courses, which are marvelous not only for the problem-solving on display but also for the physics content.

This type of book addresses a serious gap in American math-science education. Learning techniques for approximation allows one to tackle the sort of ill-posed problems one is most likely to encounter in the real-world. It is also intimately tied to recognizing the salient features of a problem, such as the physical principles involved in a physics problem or the most questionable assumption in an economic model. Street-Fighting Math deserves a wide readership and will hopefully influence other math-science teachers and authors.
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65 of 67 people found the following review helpful By John Regehr on June 9, 2010
Format: Paperback
The Trinity test occurred on a calm morning. Enrico Fermi, one of the observers, began dropping bits of paper about 40 seconds after the explosion; pieces in the air when the blast wave arrived were deflected by about 2.5 meters. From this crude measurement, Fermi estimated the bomb's yield to be ten kilotons; he was accurate within a factor of two. Although Street-Fighting Mathematics does not address the problem of estimating bomb yields, it gives us a reasonably generic toolbox for generating quantitative estimates from a few facts, a lot of intuition, and impressively little calculus. As one of the reviews on Amazon says, this book makes us smarter.

Street-Fighting Mathematics -- the title refers to the fact that in a street fight, it's better to have a quick and dirty answer than to stand there thinking about the right thing to do -- is based on the premise that we can and should use rapid estimation techniques to get rough answers to difficult problems. There are good reasons for preferring estimation over rigorous methods: the answer is arrived at quickly, the full set of input data may not be needed, and messy calculus-based or numerical techniques can often be avoided. Perhaps more important, by avoiding a descent into difficult symbol pushing, a greater understanding of the problem's essentials can sometimes be gained and a valuable independent check on rigorous -- and often more error prone -- methods is obtained.

Chapter 1 is about dimensional analysis: the idea that by attaching dimension units (kg, m/s2, etc.) to quantities in calculations about the physical world, we gain some error checking and also some insight into the solution. Dimensional analysis is simple and highly effective and it should be second nature for all of us.
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25 of 26 people found the following review helpful By Rahul Sarpeshkar on May 20, 2010
Format: Paperback
This book is a treasure trove of intuitive, practical, and brilliant mathematical techniques. Every person with an interest in mathematics, science, or engineering will enjoy this highly stimulating and fun book. For example, beautiful pictorial proofs of the inequality between the arithmetic mean and geometric mean illustrate the power, clarity, speed, and insight of intuitive visual methods versus traditional symbolic grungy methods. The power of working with operators to perform complex series summations is explained so clearly that both the beginner and the expert can experience the `aha' joy that comes with true understanding. Fluid-mechanics calculations via methods of dimensional analysis and the method of `easy cases', methods for quick integration by `lumping' that are remarkably accurate, techniques of successive approximation to solve physics problems with insight, rapidly converging series for pi, and pictorial proofs of series summations are just some of the many gems in this book. Sanjoy is one of MIT's best teachers and his book, therefore, reads like a novel. This book breaks new ground in the teaching of mathematics and will make powerful mathematical street fighters of all of its readers.
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7 of 7 people found the following review helpful By Kaushik Basu on April 12, 2011
Format: Paperback Verified Purchase
Many years from now, when the name of Feynman and Woods are long uncorrelated, we are likely to come across a generation of scientists or science buffs who will reflect back to the nostalgic days when they learnt to perform many a magical mathematical sleight of hand. They will look back to formative influences, and they will often come up with a name that sounds like a Tariq Ali account of the 60's student movement. On further questioning, sources would be eagerly divulged, and there would pop up the name of Sanjoy Mahajan, and the book dubbed Street Fighting Mathematics. An even more rigorous analysis might reveal such luminaries as Mick Jagger, but the general drift of the book in question would be precisely the contrary - it shows us how to be dirty and pretty at once, without overdue analytical makeup. The author, in a related course he teaches at MIT, puts it succinctly - no eplisons or deltas were harmed by this book.

To not make things sound further oblique, Richard Feynman learnt the wonders of using the Liebniz's integral rule from a book by Woods, Advanced calculus when he was relegated to the back of the class to peruse it, as he was too 'bored' with the mundane (I'm assuming) plug and chug of high school calculus. He describes it in his witty account Surely You're Joking, Mr. Feynman! as a bag of tools he would use repeatedly to solve integrals other graduate students were stumped by.

If you think I'm taking this anecdotal analogy too far, you need look no further than the first chapter of street fighting math.
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