## Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem SolvingIn 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. |

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#### LibraryThing Review

User Review - fpagan - LibraryThingSlim but college-level and technical, intriguingly covering dimensional analysis, easy-case method, lumping, pictorial proofs, big-part removal, and analogical reasoning. Read full review

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An exciting book written on educated guessing, problem solving and rough calculations by MIT Prof. Sanjoy Mahajan. This book is all about applying the mathematics principles in situations dominated by fear and pressure,like a street fighting perhaps. You don’t have to follow rules in street fighting, so why not do so in fast problem solving too?

Read full preview here: http://guruparan18.wordpress.com/2010/03/30/street-fighting-mathematics-preview/

### 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 | |

### Other editions - View all

Street-fighting Mathematics: The Art of Educated Guessing and Opportunistic ... Sanjoy Mahajan No preview available - 2010 |

### 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 easy-cases tests eﬀect error estimate Euler–MacLaurin summation evaluate exact example exponent factor ﬁnd ﬁrst ﬁrst term ﬁve ﬂow ﬂuid formula fractional change free-fall function Gaussian integral geometric mean George Polya guess height hydrogens identical dimensions impact speed inﬁnite length linear logarithm low-entropy 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 signiﬁcant-change simpliﬁes slope solution solve square Stefan–Boltzmann law Summary and further tanx Taylor series terminal velocity triangle underestimate velocity vertical volume width zero