To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok.In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing's role in breaking Germany's Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security.Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.

    An impassioned critique of K 12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here Lockhart offers the positive side of the math education story by showing us how math should be done. "Measurement "offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living.In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science.Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can do the math in a way that brings emotional and aesthetic rewards. "Measurement" is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work."

    If you've never had to survive on an income so small, it is hard to imagine. How would you put food on the table, afford a home, and educate your children? How would you handle emergencies and old age? Every day, more than a billion people around the world must answer these questions. Portfolios of the Poor is the first book to systematically explain how the poor find solutions to their everyday financial problems.The authors conducted year-long interviews with impoverished villagers and slum dwellers in Bangladesh, India, and South Africa--records that track penny by penny how specific households manage their money. The stories of these families are often surprising and inspiring. Most poor households do not live hand to mouth, spending what they earn in a desperate bid to keep afloat. Instead, they employ financial tools, many linked to informal networks and family ties. They push money into savings for reserves, squeeze money out of creditors whenever possible, run sophisticated savings clubs, and use microfinancing wherever available. Their experiences reveal new methods to fight poverty and ways to envision the next generation of banks for the "bottom billion."Indispensable for those in development studies, economics, and microfinance, Portfolios of the Poor will appeal to anyone interested in knowing more about poverty and what can be done about it.

    Our Big Bang, our distant future, parallel worlds, the sub-atomic and intergalactic - none of them are what they seem. But there is a way to understand this immense strangeness - mathematics. Seeking an answer to the fundamental puzzle of why our universe seems so mathematical, Tegmark proposes a radical idea: that our physical world not only is described by mathematics, but that it is mathematics. This may offer answers to our deepest questions: How large is reality? What is everything made of? Why is our universe the way it is?Table of ContentsPreface 1 What Is Reality? Not What It Seems • What’s the Ultimate Question? • The Journey Begins Part One: Zooming Out 2 Our Place in Space Cosmic Questions • How Big Is Space? • The Size of Earth • Distance to the Moon • Distance to the Sun and the Planets • Distance to the Stars • Distance to the Galaxies • What Is Space? 3 Our Place in TimeWhere Did Our Solar System Come From? • Where Did theGalaxies Come From? • Where Did the Mysterious MicrowavesCome From? • Where Did the Atoms Come From? 4 Our Universe by NumbersWanted: Precision Cosmology • Precision Microwave-Background Fluctuations • Precision Galaxy Clustering • The Ultimate Map of Our Universe • Where Did Our Big Bang Come From? 5 Our Cosmic Origins What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation 6 Welcome to the Multiverse The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup Part Two: Zooming In 7 Cosmic Legos Atomic Legos • Nuclear Legos • Particle-Physics Legos • Mathematical Legos • Photon Legos • Above the Law? • Quanta and Rainbows • Making Waves • Quantum Weirdness • The Collapse of Consensus • The Weirdness Can’t Be Confined • Quantum Confusion 8 The Level III Multiverse The Level III Multiverse • The Illusion of Randomness • Quantum Censorship • The Joys of Getting Scooped • Why Your Brain Isn’t a Quantum Computer • Subject, Object and Environment • Quantum Suicide • Quantum Immortality? • Multiverses Unified • Shifting Views: Many Worlds or Many Words? Part Three: Stepping Back 9 Internal Reality, External Reality and Consensus Reality External Reality and Internal Reality • The Truth, the Whole Truth and Nothing but the Truth • Consensus Reality • Physics: Linking External to Consensus Reality 10 Physical Reality and Mathematical Reality Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure? 11 Is Time an Illusion? How Can Physical Reality Be Mathematical? • What Are You? • Where Are You? (And What Do You Perceive?) • When Are You? 12 The Level IV Multiverse Why I Believe in the Level IV Multiverse • Exploring the Level IV Multiverse: What’s Out There? • Implications of the Level IV Multiverse • Are We Living in a Simulation? • Relation Between the MUH, the Level IV Multiverse and Other Hypotheses •Testing the Level IV Multiverse 13 Life, Our Universe and Everything How Big Is Our Physical Reality? • The Future of Physics • The Future of Our Universe—How Will It End? • The Future of Life •The Future of You—Are You Insignificant? Acknowledgments Suggestions for Further Reading Index

    In this book, a wealth of exercises are provided throughout each section, designed to reinforce learning and the logical comprehension of topics. The use of real data is incorporated much more extensively than in any other book on the market. Consist of strong coverage of computer-based methods, especially in the coverage of analysis of variance and regression. This text stresses mastery of methods most often used in medical research, with specific reference to actual medical literature and actual medical research. The approach minimizes mathematical formulation, yet gives complete explanations of all important concepts. Every new concept is systematically developed through completely worked-out examples from current medical research problems. Computer output is used to illustrate concepts when appropriate.

    Carlota Perez draws upon Schumpeter's theories of the clustering of innovations to explain why each technological revolution gives rise to a paradigm shift and a "New Economy" and how these "opportunity explosions", focused on specific industries, also lead to the recurrence of financial bubbles and crises. These findings are illustrated with examples from the past two centuries: the industrial revolution, the age of steam and railways, the age of steel and electricity, the emergence of mass production and automobiles, and the current information revolution/knowledge society. By analyzing the changing relationship between finance capital and production capital during the emergence, diffusion and assimilation of new technologies throughout the global economic system, this book sheds light on some of the most pressing economic problems of today.

    Out of Control chronicles the dawn of a new era in which the machines and systems that drive our economy are so complex and autonomous as to be indistinguishable from living things.

    The theme of Heisenberg's exposition is that words and concepts familiar in daily life can lose their meaning in the world of relativity and quantum physics. This in turn has profound philosophical implications for the nature of reality and for our total world view.

    With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader.

    The Sovereign Individual details strategies necessary for adapting financially to the next phase of Western civilization. Few observers of the late twentieth century have their fingers so presciently on the pulse of the global political and economic realignment ushering in the new millennium as do James Dale Davidson and Lord William Rees-Mogg. Their bold prediction of disaster on Wall Street in Blood in the Streets was borne out by Black Tuesday. In their ensuing bestseller, The Great Reckoning, published just weeks before the coup attempt against Gorbachev, they analyzed the pending collapse of the Soviet Union and foretold the civil war in Yugoslavia and other events that have proved to be among the most searing developments of the past few years. In The Sovereign Individual, Davidson and Rees-Mogg explore the greatest economic and political transition in centuries—the shift from an industrial to an information-based society. This transition, which they have termed "the fourth stage of human society," will liberate individuals as never before, irrevocably altering the power of government. This outstanding book will replace false hopes and fictions with new understanding and clarified values.

    Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

    An unprecedented redistribution of jobs, population, and wealth is under way in America, and it is likely to accelerate in the years to come. America’s new economic map shows growing differences, not just between people but especially between communities. In this important and persuasive book, U.C. Berkeley economist Enrico Moretti provides a fresh perspective on the tectonic shifts that are reshaping America’s labor market—from globalization and income inequality to immigration and technological progress—and how these shifts are affecting our communities. Drawing on a wealth of stimulating new studies, Moretti uncovers what smart policies may be appropriate to address the social challenges that are arising. We’re used to thinking of the United States in dichotomous terms: red versus blue, black versus white, haves versus have-nots. But today there are three Americas. At one extreme are the brain hubs—cities like San Francisco, Boston, Austin, and Durham—with a well-educated labor force and a strong innovation sector. Their workers are among the most productive, creative, and best paid on the planet. At the other extreme are cities once dominated by traditional manufacturing, which are declining rapidly, losing jobs and residents. In the middle are a number of cities that could go either way. For the past thirty years, the three Americas have been growing apart at an accelerating rate. This divergence is one the most important recent developments in the United States and is causing growing geographic disparities is all other aspects of our lives, from health and longevity to family stability and political engagement. But the winners and losers aren’t necessarily who you’d expect. Moretti’s groundbreaking research shows that you don’t have to be a scientist or an engineer to thrive in one of these brain hubs. Among the beneficiaries are the workers who support the "idea-creators"—the carpenters, hair stylists, personal trainers, lawyers, doctors, teachers and the like. In fact, Moretti has shown that for every new innovation job in a city, five additional non-innovation jobs are created, and those workers earn higher salaries than their counterparts in other cities. It wasn’t supposed to be this way. As the global economy shifted from manufacturing to innovation, geography was supposed to matter less. But the pundits were wrong. A new map is being drawn—the inevitable result of deep-seated but rarely discussed economic forces. These trends are reshaping the very fabric of our society. Dealing with this split—supporting growth in the hubs while arresting the decline elsewhere—will be the challenge of the century, and　The New Geography of Jobs　lights the way.

    This guide also helps you understand the many data-mining techniques in use today.Based on an MBA course Provost has taught at New York University over the past ten years, Data Science for Business provides examples of real-world business problems to illustrate these principles. You’ll not only learn how to improve communication between business stakeholders and data scientists, but also how participate intelligently in your company’s data science projects. You’ll also discover how to think data-analytically, and fully appreciate how data science methods can support business decision-making.Understand how data science fits in your organization—and how you can use it for competitive advantageTreat data as a business asset that requires careful investment if you’re to gain real valueApproach business problems data-analytically, using the data-mining process to gather good data in the most appropriate wayLearn general concepts for actually extracting knowledge from dataApply data science principles when interviewing data science job candidates

    Along the way we’ll learn how selection bias can explain why your boss doesn’t know he sucks (even when everyone else does); how to use Bayes’ Theorem to decide if your partner is cheating on you; and why Mark Zuckerberg should never be used as an example for anything. See the world in a whole new light, and make better decisions and judgements without ever going near a t-test. Think. Think Statistically.

    W. R. Dedekind. The first presents Dedekind's theory of the irrational number-the Dedekind cut idea-perhaps the most famous of several such theories created in the 19th century to give a precise meaning to irrational numbers, which had been used on an intuitive basis since Greek times. This paper provided a purely arithmetic and perfectly rigorous foundation for the irrational numbers and thereby a rigorous meaning of continuity in analysis.The second essay is an attempt to give a logical basis for transfinite numbers and properties of the natural numbers. It examines the notion of natural numbers, the distinction between finite and transfinite (infinite) whole numbers, and the logical validity of the type of proof called mathematical or complete induction.The contents of these essays belong to the foundations of mathematics and will be welcomed by those who are prepared to look into the somewhat subtle meanings of the elements of our number system. As a major work of an important mathematician, the book deserves a place in the personal library of every practicing mathematician and every teacher and historian of mathematics. Authorized translations by "Vooster " V. Beman.