Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solvingby Sanjoy Mahajan, Carver A. Mead
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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.
- MIT Press
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What People are Saying About This
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
"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
Meet 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.
Most Helpful Customer Reviews
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This book was a thought-provoking read that brought up unique ideas about how to approach mathematics. There is an often unheard of view about how to consider common dilemmas in this book that reveals to not purely focus on rules when attempting to problem solve. This exemplifies an untraditional approach that reveals the need for estimations and not always exact answers that can often take too much time to solve and focus too strongly on calculations. One of my favorite aspects of this book was surprisingly the title, Street-Fighting Mathematics. This theme carried through the entire read and related to all points that Mahajan was presenting by connecting how rules often do not apply in situations and how one needs to be able to use reason in order to solve problems. Six tools were described that reveal how to “street-fight mathematics”: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. I thought that reasoning by analogy was the most effective tool and was presented the best. The advice was simply to find an easier problem similar to the one at hand and compare it to what is trying to be solved. This was most relatable to real life situations in my opinion because there are so many uses in being able to compare and utilize the information from a simple situation and apply it to a more complex one. Some aspects that I believe could have been improved upon would be the examples that were given in the book. There were plenty of examples given and they were all well explained, but I wish that some were given that applied to real-world situations instead of only academic problems. I believe that this would have helped to broaden my understanding of Mahajan’s points and allow me to utilize his advice better in my life. Overall, I would recommend this book because it was an easy to understand read that still gave a wealth of information as well as being well organized and the explanations were thorough.