Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem SolvingMIT Press, 5 במרץ 2010 - 152 עמודים This practical guide to educated guessing shows you how to find answers to partly-defined mathematical problems—without needing 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 6 tools: • Dimensional Analysis • Easy Cases • Lumping • Picture Proofs • Successive Approximation • 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. |
תוכן
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 | |
מהדורות אחרות - הצג הכל
Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic ... <span dir=ltr>Sanjoy Mahajan</span> אין תצוגה מקדימה זמינה - 2010 |
Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic ... <span dir=ltr>Sanjoy Mahajan</span> אין תצוגה מקדימה זמינה - 2010 |
מונחים וביטויים נפוצים
accurate alternative amplitude analogous angle apply approximation base becomes bond calculation circle closed coefficient combination Compare compute cone conjecture constant contains correction curve depends depth derivative difference differential equation dimensional analysis dimensionless dimensionless groups dimensions distance drag Draw easy equation error estimate evaluate exact example expansion explain expressions extreme factor fall find first force formula fractional change function Gaussian geometric George Polya gives guess height improved increase integral length limit lumping mathematics mean method operator path pattern pendulum period pictorial picture pieces plane plausible polynomial positive prediction Problem produces pyramid quadratic quantities ratio reasoning rectangle regions requires result roots roughly secant side simple slope solution solve speed square step summation taking tanx term tool triangle turns units volume width zero