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Street Fighting Mathematics

Author: Sanjoy Mahajan
Publisher: MIT Press
ISBN: 0262265591
Size: 14.61 MB
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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.

The Art Of Insight In Science And Engineering

Author: Sanjoy Mahajan
Publisher: MIT Press
ISBN: 0262526549
Size: 11.39 MB
Format: PDF, Mobi
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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.

Solving Everyday Problems With The Scientific Method Thinking Like A Scientist Second Edition

Author: Mak Don K
Publisher: World Scientific
ISBN: 9813145323
Size: 20.25 MB
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This book describes how one can use The Scientific Method to solve everyday problems including medical ailments, health issues, money management, traveling, shopping, cooking, household chores, etc. It illustrates how to exploit the information collected from our five senses, how to solve problems when no information is available for the present problem situation, how to increase our chances of success by redefining a problem, and how to extrapolate our capabilities by seeing a relationship among heretofore unrelated concepts. One should formulate a hypothesis as early as possible in order to have a sense of direction regarding which path to follow. Occasionally, by making wild conjectures, creative solutions can transpire. However, hypotheses need to be well-tested. Through this way, The Scientific Method can help readers solve problems in both familiar and unfamiliar situations. Containing real-life examples of how various problems are solved — for instance, how some observant patients cure their own illnesses when medical experts have failed — this book will train readers to observe what others may have missed and conceive what others may not have contemplated. With practice, they will be able to solve more problems than they could previously imagine. In this second edition, the authors have added some more theories which they hope can help in solving everyday problems. At the same time, they have updated the book by including quite a few examples which they think are interesting.

Mathematics Without Apologies

Author: Michael Harris
Publisher: Princeton University Press
ISBN: 1400885523
Size: 72.89 MB
Format: PDF, Kindle
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What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers—for the sake of truth, beauty, and practical applications—this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.

Mathematics Matters In Education

Author: Yeping Li
Publisher: Springer
ISBN: 3319614347
Size: 40.74 MB
Format: PDF
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This book is inspired by Roger E. Howe's contributions to the international communities of mathematics and mathematics education. Renowned for his research contributions in the fields of representation theory, automorphic forms, harmonic analysis, and invariant theory, Dr. Howe has also fundamentally deepened our understanding of the mathematics taught in the early school grades and has challenged and stimulated mathematicians and mathematics educators to work together to examine this part of the mathematical universe more critically and in imaginative new ways. This volume will help summarize and highlight Howe's contributions to several topic areas in mathematics education, demonstrating the possibility and importance of engaging mathematicians in high-impact research in mathematics education, and showcasing the importance of cross-disciplinary collaboration and exchange.

X And The City

Author: John A. Adam
Publisher: Princeton University Press
ISBN: 1400841690
Size: 42.73 MB
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X and the City, a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through tunnels? Can you predict whether a traffic light will stay green long enough for you to cross the intersection? And what is the likelihood that your city will be hit by an asteroid? Every math problem and equation in this book tells a story and examples are explained throughout in an informal and witty style. The level of mathematics ranges from precalculus through calculus to some differential equations, and any reader with knowledge of elementary calculus will be able to follow the materials with ease. There are also some more challenging problems sprinkled in for the more advanced reader. Filled with interesting and unusual observations about how cities work, X and the City shows how mathematics undergirds and plays an important part in the metropolitan landscape.