StreetFighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving (Google eBook)In problem solving, as in street fighting, rules are for fools: do whatever worksdon'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 StreetFighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and downanddirty, opportunistic problem solving across diverse fields of knowledgefrom 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 toolthe general principlefrom the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. StreetFighting Mathematics grew out of a short course taught by the author at MIT for students ranging from firstyear 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.StreetFighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license. 
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Review: StreetFighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving
User Review  Daniel Wilson  GoodreadsA fantastic book which only requires some mathematical wherewithal. Covers various methods for estimation and informal proofs. I really liked the intuitive way he describes the topics, which range ... Read full review
Review: StreetFighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving
User Review  Tung  GoodreadsNot to brag, but I was a math whiz in high school and college, which is why I'm a fan of popmath books that frame real world issues through the lens of numbers. Given the title of this book (and its ... Read full review
Contents
1 Dimensions  1 
2 Easy cases  13 
3 Lumping  31 
4 Pictorial proofs  57 
5 Taking out the big part  77 
6 Analogy  99 
123  
127  
Common terms and phrases
aﬀect AM–GM inequality amplitude analogous arithmetic mean bisecting path bond angle calculation Carver Mead closed form coeﬃcient compute cone conjecture correction curve deﬁnite depth derivative diﬀerence diﬀerential equation diﬃcult dimensional analysis dimensionless constant dimensionless groups drag force easy easycases tests eﬀect error estimate Euler–MacLaurin summation evaluate exact example exponent factor ﬁnd ﬁrst ﬁrst term ﬁve ﬂow ﬂuid formula fractional change freefall function Gaussian integral geometric mean George Polya guess height hydrogens identical dimensions impact speed inﬁnite length linear logarithm lowentropy expressions lumping mathematics method Navier–Stokes equations operator overestimate period plane plausible polynomial prediction produces pyramid quadratic quantities ratio rectangle regions result rewriting Reynolds number roots roughly Section signiﬁcant change signiﬁcantchange simpliﬁes slope solution solve square Stefan–Boltzmann law Summary and further tanx Taylor series terminal velocity triangle underestimate velocity vertical volume width zero