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Street Fighting Mathematics

Street Fighting Mathematics Author Sanjoy Mahajan
ISBN-10 9780262265591
Release 2010-03-05
Pages 152
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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.

Street fighting Mathematics

Street fighting Mathematics Author Sanjoy Mahajan
ISBN-10 026251429X
Release 2010
Pages 134
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An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation.

The Art of Insight in Science and Engineering

The Art of Insight in Science and Engineering Author Sanjoy Mahajan
ISBN-10 9780262526548
Release 2014-11-07
Pages 408
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In this book, Sanjoy Mahajan shows us that the way to master complexity is through insight rather than precision. Precision can overwhelm us with information, whereas insight connects seemingly disparate pieces of information into a simple picture. Unlike computers, humans depend on insight. Based on the author's fifteen years of teaching at MIT, Cambridge University, and Olin College, The Art of Insight in Science and Engineering shows us how to build insight and find understanding, giving readers tools to help them solve any problem in science and engineering.To master complexity, we can organize it or discard it. The Art of Insight in Science and Engineering first teaches the tools for organizing complexity, then distinguishes the two paths for discarding complexity: with and without loss of information. Questions and problems throughout the text help readers master and apply these groups of tools. Armed with this three-part toolchest, and without complicated mathematics, readers can estimate the flight range of birds and planes and the strength of chemical bonds, understand the physics of pianos and xylophones, and explain why skies are blue and sunsets are red.The Art of Insight in Science and Engineering will appear in print and online under a Creative Commons Noncommercial Share Alike license.

How Many Licks

How Many Licks Author Aaron Santos
ISBN-10 9780762439188
Release 2009-08-25
Pages 176
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How many licks to the center of a Tootsie Pop? How many people are having sex at this moment? How long would it take a monkey on a typewriter to produce the plays of Shakespeare? For all those questions that keep you up at night, here's the way to answer them. And the beauty of it is that it's all approximate! Using Enrico Fermi's theory of approximation, Santos brings the world of numbers into perspective. For puzzle junkies and trivia fanatics, these 70 word puzzles will show the reader how to take a bit of information, add what they already know, and extrapolate an answer. Santos has done the impossible: make math and the multiple possibilities of numbers fun and informative. Can you really cry a river? Is it possible to dig your way out of jail with just a teaspoon and before your life sentence is up? Taking an academic subject and using it as the prism to view everyday off-the-wall questions as math problems to be solved is a natural step for the lovers of sudoku, cryptograms, word puzzles, and other thought-provoking games.

Guesstimation 2 0

Guesstimation 2 0 Author Lawrence Weinstein
ISBN-10 9781400844661
Release 2012-09-30
Pages 384
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Guesstimation 2.0 reveals the simple and effective techniques needed to estimate virtually anything--quickly--and illustrates them using an eclectic array of problems. A stimulating follow-up to Guesstimation, this is the must-have book for anyone preparing for a job interview in technology or finance, where more and more leading businesses test applicants using estimation questions just like these. The ability to guesstimate on your feet is an essential skill to have in today's world, whether you're trying to distinguish between a billion-dollar subsidy and a trillion-dollar stimulus, a megawatt wind turbine and a gigawatt nuclear plant, or parts-per-million and parts-per-billion contaminants. Lawrence Weinstein begins with a concise tutorial on how to solve these kinds of order of magnitude problems, and then invites readers to have a go themselves. The book features dozens of problems along with helpful hints and easy-to-understand solutions. It also includes appendixes containing useful formulas and more. Guesstimation 2.0 shows how to estimate everything from how closely you can orbit a neutron star without being pulled apart by gravity, to the fuel used to transport your food from the farm to the store, to the total length of all toilet paper used in the United States. It also enables readers to answer, once and for all, the most asked environmental question of our day: paper or plastic?

Back of the Envelope Physics

Back of the Envelope Physics Author Clifford Swartz
ISBN-10 9780801881640
Release 2004-12-01
Pages 176
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Covering such subjects as astronomy, magnetism, optics, sound, heat, mechanics, waves, and electricity, the book provides a rich source of material for teachers and anyone interested in the physics of everyday life.

Consider a Spherical Cow

Consider a Spherical Cow Author John Harte
ISBN-10 093570258X
Release 1988-01-01
Pages 283
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Challenging, real-world situations and worked-out solutions provide the means both for gaining insights into the process of problem solving and for thinking quantitatively and creatively about such environmental concerns as energy and water resources, food production, indoor air pollution, acid rain, and human influences on climate.

Collective Electrodynamics

Collective Electrodynamics Author Carver Mead
ISBN-10 0262632608
Release 2002
Pages 135
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Carver Mead offers a radically new approach to the standard problems of electromagnetic theory.

Chaotic Dynamics

Chaotic Dynamics Author Gregory L. Baker
ISBN-10 0521476852
Release 1996-01-26
Pages 256
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New edition of a very successful undergraduate text on chaos.

Scaling Self similarity and Intermediate Asymptotics

Scaling  Self similarity  and Intermediate Asymptotics Author G. I. Barenblatt
ISBN-10 0521435226
Release 1996-12-12
Pages 386
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Scaling (power-type) laws reveal the fundamental property of the phenomena--self similarity. Self-similar (scaling) phenomena repeat themselves in time and/or space. The property of self-similarity simplifies substantially the mathematical modeling of phenomena and its analysis--experimental, analytical and computational. The book begins from a non-traditional exposition of dimensional analysis, physical similarity theory and general theory of scaling phenomena. Classical examples of scaling phenomena are presented. It is demonstrated that scaling comes on a stage when the influence of fine details of initial and/or boundary conditions disappeared but the system is still far from ultimate equilibrium state (intermediate asymptotics). It is explained why the dimensional analysis as a rule is insufficient for establishing self-similarity and constructing scaling variables. Important examples of scaling phenomena for which the dimensional analysis is insufficient (self-similarities of the second kind) are presented and discussed. A close connection of intermediate asymptotics and self-similarities of the second kind with a fundamental concept of theoretical physics, the renormalization group, is explained and discussed. Numerous examples from various fields--from theoretical biology to fracture mechanics, turbulence, flame propagation, flow in porous strata, atmospheric and oceanic phenomena are presented for which the ideas of scaling, intermediate asymptotics, self-similarity and renormalization group were of decisive value in modeling.

Consider a Cylindrical Cow

Consider a Cylindrical Cow Author John Harte
ISBN-10 1891389173
Release 2001-01-01
Pages 211
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Following in the tradition of Consider a Spherical Cow, the Cylindrical Cow will help students achieve a whole new level of environmental modeling and problem solving. Featuring a new core set of 25 fully worked-out problems, this book uses real problems in environmental science rather than relying on the more traditional "cookbook" problems found in textbooks. It is organized according to five thematic sections on probability, optimization, scaling, differential equations, and stability and feedback. Each section begins with a general treatment of the relevant mathematical concepts, and concludes with a range of homework exercises to help students sharpen their modeling skills. Like its predecessor, this book will empower students with the mathematical skills needed to cut through the complexity of real-world problems.

Art School

Art School Author Steven Henry Madoff
ISBN-10 9780262134934
Release 2009
Pages 373
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Leading international artists and art educators consider the challenges of arteducation in today's dramatically changed art world.

An Engine Not a Camera

An Engine  Not a Camera Author Donald Mackenzie
ISBN-10 9780262250047
Release 2008-08-29
Pages 392
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In An Engine, Not a Camera, Donald MacKenzie argues that the emergence of modern economic theories of finance affected financial markets in fundamental ways. These new, Nobel Prize-winning theories, based on elegant mathematical models of markets, were not simply external analyses but intrinsic parts of economic processes.Paraphrasing Milton Friedman, MacKenzie says that economic models are an engine of inquiry rather than a camera to reproduce empirical facts. More than that, the emergence of an authoritative theory of financial markets altered those markets fundamentally. For example, in 1970, there was almost no trading in financial derivatives such as "futures." By June of 2004, derivatives contracts totaling $273 trillion were outstanding worldwide. MacKenzie suggests that this growth could never have happened without the development of theories that gave derivatives legitimacy and explained their complexities.MacKenzie examines the role played by finance theory in the two most serious crises to hit the world's financial markets in recent years: the stock market crash of 1987 and the market turmoil that engulfed the hedge fund Long-Term Capital Management in 1998. He also looks at finance theory that is somewhat beyond the mainstream -- chaos theorist Benoit Mandelbrot's model of "wild" randomness. MacKenzie's pioneering work in the social studies of finance will interest anyone who wants to understand how America's financial markets have grown into their current form.

Preference Belief and Similarity

Preference  Belief  and Similarity Author Amos Tversky
ISBN-10 026270093X
Release 2004
Pages 1023
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Selected works by the influential cognitive and mathematical psychologist and decision theorist Amos Tversky.

Complex Problem Solving

Complex Problem Solving Author Peter A. Frensch
ISBN-10 9781317781394
Release 2014-04-04
Pages 360
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This volume presents a state-of-the-science review of the most promising current European research -- and its historic roots of research -- on complex problem solving (CPS) in Europe. It is an attempt to close the knowledge gap among American scholars regarding the European approach to understanding CPS. Although most of the American researchers are well aware of the fact that CPS has been a very active research area in Europe for quite some time, they do not know any specifics about even the most important research. Part of the reason for this lack of knowledge is undoubtedly the fact that European researchers -- for the most part -- have been rather reluctant to publish their work in English-language journals. The book concentrates on European research because the basic approach European scholars have taken to studying CPS is very different from one taken by North American researchers. Traditionally, American scholars have been studying CPS in "natural" domains -- physics, reading, writing, and chess playing -- concentrating primarily on exploring novice-expert differences and the acquisition of a complex skill. European scholars, in contrast, have been primarily concerned with problem solving behavior in artificially generated, mostly computerized, complex systems. While the American approach has the advantage of high external validity, the European approach has the advantage of system variables that can be systematically manipulated to reveal the effects of system parameters on CPS behavior. The two approaches are thus best viewed as complementing each other. This volume contains contributions from four European countries -- Sweden, Switzerland, Great Britain, and Germany. As such, it accurately represents the bulk of empirical research on CPS which has been conducted in Europe. An international cooperation started two years ago with the goal of bringing the European research on complex problem solving to the awareness of American scholars. A direct result of that effort, the contributions to this book are both informative and comprehensive.

Cell Biology by the Numbers

Cell Biology by the Numbers Author Ron Milo
ISBN-10 9781317230694
Release 2015-12-01
Pages 400
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Very little in our human experience is truly comparable to the immensely crowded and bustling interior of a cell. Biological numeracy provides a new kind of understanding of the cellular world. This book brings together up-to-date quantitative data from the vast biological literature and uses the powerful tool of "back of the envelope" estimates to reveal fresh perspectives and insights from numbers commonly encountered in cell biology. Readers gain a feeling for the sizes, concentrations, energies, and rates that characterize the lives of cellsÑ thereby shedding new light on the microscopic realm.

Cybernetic Revolutionaries

Cybernetic Revolutionaries Author Eden Medina
ISBN-10 9780262016490
Release 2011-10-28
Pages 326
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A historical study of Chile's twin experiments with cybernetics and socialism, and what they tell us about the relationship of technology and politics.