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Street Fighting Mathematics

Author : Sanjoy Mahajan
ISBN : 9780262265591
Genre : Mathematics
File Size : 41.34 MB
Format : PDF, Kindle
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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.
Category: Mathematics

Mathematics Without Apologies

Author : Michael Harris
ISBN : 9780691175836
Genre : Mathematics
File Size : 64.9 MB
Format : PDF
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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.
Category: Mathematics

Mathematics Matters In Education

Author : Yeping Li
ISBN : 9783319614342
Genre : Education
File Size : 32.20 MB
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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.
Category: Education


Author : Paul Dickson
ISBN : 9781936863570
Genre : Humor
File Size : 52.91 MB
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A comprehensive A-to-Z dictionary of journalistic buzzwords and phrases, this witty book is both a handy reference and a humorous look at the true absurdity of journalists' tired quips and cliches. With an irreverent tone, the authors present hundreds of entries, the majority of which are accompanied by real-world examples and well-phrased criticisms, on topics such as incendiary leads, double entendres, media shoptalk, teasers, hidden agendas, and tabloid-TV excesses. A go-to resource for journalists, students, and word lovers, this book is a vanguard for identifying the misled word-based methods employed by modern media outlets.
Category: Humor

The Art Of Insight In Science And Engineering

Author : Sanjoy Mahajan
ISBN : 9780262526548
Genre : Mathematics
File Size : 56.32 MB
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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.
Category: Mathematics

A Student S Guide To Newton S Laws Of Motion

Author : Sanjoy Mahajan
ISBN : 1108457193
Genre : Science
File Size : 37.37 MB
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Newton's laws of motion, which introduce force and describe how it affects motion, are the gateway to physics -- yet they are often misunderstood due to their many subtleties. Based on the author's twenty years of teaching physics and engineering, this intuitive guide to Newton's laws of motion corrects the many misconceptions surrounding this fundamental topic. Adopting an informal and pedagogical approach and a clear, accessible style, this concise text presents Newton's laws in a coherent story of force and motion. Carefully scaffolded everyday examples and full explanations of concepts and equations ensure that all students studying physics develop a deep understanding of Newton's laws of motion.
Category: Science

Sociocultural Research On Mathematics Education

Author : Bill Atweh
ISBN : 9781135653118
Genre : Education
File Size : 21.61 MB
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This volume--the first to bring together research on sociocultural aspects of mathematics education--presents contemporary and international perspectives on social justice and equity issues that impact mathematics education. In particular, it highlights the importance of three interacting and powerful factors--gender, social, and cultural dimensions. Sociocultural Research on Mathematics Education: An International Perspective is distinguished in several ways: * It is research based. Chapters report on significant research projects; present a comprehensive and critical summary of the research findings; and offer a critical discussion of research methods and theoretical perspectives undertaken in the area. * It is future oriented, presenting recommendations for practice and policy and identifying areas for further research. * It deals with all aspects of formal and informal mathematics education and applications and all levels of formal schooling. As the context of mathematics education rapidly changes-- with an increased demand for mathematically literate citizenship; an increased awareness of issues of equity, inclusivity, and accountability; and increased efforts for globalization of curriculum development and research-- questions are being raised more than ever before about the problems of teaching and learning mathematics from a non-cognitive science perspective. This book contributes significantly to addressing such issues and answering such questions. It is especially relevant for researchers, graduate students, and policymakers in the field of mathematics education.
Category: Education

How Math Explains The World

Author : James D. Stein
ISBN : UCSC:32106019539391
Genre : Mathematics
File Size : 37.93 MB
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In How Math Explains the World, mathematician Stein reveals how seemingly arcane mathematical investigations and discoveries have led to bigger, more world-shaking insights into the nature of our world. In the four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects of our universe. From their successes and failures, delusions, and even duels, the trajectories of their innovations—and their impact on society—are traced in this fascinating narrative. Quantum mechanics, space-time, chaos theory and the workings of complex systems, and the impossibility of a "perfect" democracy are all here. Stein's book is both mind-bending and practical, as he explains the best way for a salesman to plan a trip, examines why any thought you could have is imbedded in the number π , and—perhaps most importantly—answers one of the modern world's toughest questions: why the garage can never get your car repaired on time. Friendly, entertaining, and fun, How Math Explains the World is the first book by one of California's most popular math teachers, a veteran of both "math for poets" and Princeton's Institute for Advanced Studies. And it's perfect for any reader wanting to know how math makes both science and the world tick.
Category: Mathematics

The Silent Frontier

Author : Peter Watt
ISBN : 1742626041
Genre : Fiction
File Size : 49.81 MB
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Lachlan, John and Phoebe MacDonald, three young children tragically separated after the massacre at the Ballarat goldfields, try to make their way in a world filled with poverty and war. John is determined to find his lost siblings and meanwhile works hard to make a name for himself. A business partnership leads to riches and rewards that he never dreamed of. Lachlan has always known what it is to struggle for survival. But even a life of bare knuckle fighting and destitution cannot prepare him for the war he finds himself in against the Maori of New Zealand, nor the feelings he has for his commanding Officer's sister. Phoebe barely remembers what it is to have a family and yearns for a love that will make her feel complete, and a home to call her own. Three tales of courage, hope and forbidden love set against the backdrop of the New Zealand Maori wars and an emerging Australian nation.
Category: Fiction