While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.

    It is so important that it provides the fundamental underpinning of all modern sciences. Without it, we'd have no nuclear power or nuclear bombs, no lasers, no TV, no computers, no science of molecular biology, no understanding of DNA, no genetic engineering—at all. John Gribbin tells the complete story of quantum mechanics, a truth far stranger than any fiction. He takes us step-by-step into an ever more bizarre and fascinating place—requiring only that we approach it with an open mind. He introduces the scientists who developed quantum theory. He investigates the atom, radiation, time travel, the birth of the universe, superconductors and life itself. And in a world full of its own delights, mysteries and surprises, he searches for Schrödinger's Cat—a search for quantum reality—as he brings every reader to a clear understanding of the most important area of scientific study today—quantum physics.

    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 new translation of Volume One, the only volume to be completed and edited by Marx himself, avoids some of the mistakes that have marred earlier versions and seeks to do justice to the literary qualities of the work. The introduction is by Ernest Mandel, author of Late Capitalism, one of the only comprehensive attempts to develop the theoretical legacy of Capital.

    "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems."

    D. Williams wrote this entertaining, witty introduction for the nonscientist, game theory was still a somewhat mysterious subject familiar to very few scientists beyond those researchers, like himself, working for the military. Now, over thirty years after its original publication as a Rand Corporation research study, his light-hearted though thoroughly effective primer is the recognized classic introduction to an increasingly applicable discipline. Used by amateurs, professionals, and students throughout the world in the classroom, on the job, and for personal amusement, the book has been through ten printings, and has been translated into at least five languages (including Russian and Japanese).Revised, updated, and available for the first time in an inexpensive paperback edition, The Compleat Strategyst is a highly entertaining text essential for anyone interested in this provocative and engaging area of modern mathematics. In fully illustrated chapters complete with everyday examples and word problems, Williams offers readers a working understanding of the possible methods for selecting strategies in a variety of situations, simple to complex. With just a basic understanding of arithmetic, anyone can grasp all necessary aspects of two-, three-, four-, and larger strategy games with two or more sets of inimical interests and a limitless array of zero-sum payoffs.As research and study continues not only in this new discipline but in the related areas of statistics, probability and behavioral science, understanding of games, decision making, and the development of strategies will be increasingly important. In the areas of economics, sociology, politics, and the military, game theory is sure to have an even wider impact. For students and amateurs fascinated by game theory's implications there is no better, immediately applicable, or more entertaining introduction to the subject than this engaging text by the late J. D. Williams, Professor of Mathematics at Princeton University and a member of the Research Council of The Rand Corporation.

    Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

    of Wisconsin-Madison) and Wichern (Texas A&M U.) present the newest edition of this college text on the statistical methods for describing and analyzing multivariate data, designed for students who have taken two or more statistics courses. The fifth edition includes the addition of seve

    His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

    The average young person in the UK will spend 10,000 hours gaming by the age of twenty-one. What's causing this mass exodus? According to world-renowned game designer Jane McGonigal the answer is simple: videogames are fulfilling genuine human needs. Drawing on positive psychology, cognitive science and sociology, Reality is Broken shows how game designers have hit on core truths about what makes us happy, and utilized these discoveries to astonishing effect in virtual environments. But why, McGonigal asks, should we use the power of games for escapist entertainment alone? In this groundbreaking exploration of the power and future of gaming, she reveals how gamers have become expert problem solvers and collaborators, and shows how we can use the lessons of game design to socially positive ends, be it in our own lives, our communities or our businesses. Written for gamers and non-gamers alike, Reality is Broken sends a clear and provocative message: the future will belong to those who can understand, design and play games.

    The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo MCMC. Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

    But power is not merely shifting and dispersing. It is also decaying. Those in power today are more constrained in what they can do with it and more at risk of losing it than ever before. In The End of Power, award-winning columnist and former Foreign Policy editor Moisés Naím illuminates the struggle between once-dominant megaplayers and the new micropowers challenging them in every field of human endeavor. Drawing on provocative, original research, Naím shows how the antiestablishment drive of micropowers can topple tyrants, dislodge monopolies, and open remarkable new opportunities, but it can also lead to chaos and paralysis. Naím deftly covers the seismic changes underway in business, religion, education, within families, and in all matters of war and peace. Examples abound in all walks of life: In 1977, eighty-nine countries were ruled by autocrats while today more than half the world's population lives in democracies. CEO's are more constrained and have shorter tenures than their predecessors. Modern tools of war, cheaper and more accessible, make it possible for groups like Hezbollah to afford their own drones. In the second half of 2010, the top ten hedge funds earned more than the world's largest six banks combined. Those in power retain it by erecting powerful barriers to keep challengers at bay. Today, insurgent forces dismantle those barriers more quickly and easily than ever, only to find that they themselves become vulnerable in the process. Accessible and captivating, Naím offers a revolutionary look at the inevitable end of power—and how it will change your world.

    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.

    By the mid-1990s the old school grizzled traders had been replaced by a new breed of quantitative analysts, applying mathematics to the "art" of trading and making of it a science. A similar phenomenon is happening in poker. The grizzled "road gamblers" are being replaced by a new generation of players who have challenged many of the assumptions that underlie traditional approaches to the game. One of the most important features of this new approach is a reliance on quantitative analysis and the application of mathematics to the game. This book provides an introduction to quantitative techniques as applied to poker and to a branch of mathematics that is particularly applicable to poker, game theory, in a manner that makes seemingly difficult topics accessible to players without a strong mathematical background.

    You'll discover the power of storytelling and the way to make data a pivotal point in your story. The lessons in this illuminative text are grounded in theory, but made accessible through numerous real-world examples--ready for immediate application to your next graph or presentation.Storytelling is not an inherent skill, especially when it comes to data visualization, and the tools at our disposal don't make it any easier. This book demonstrates how to go beyond conventional tools to reach the root of your data, and how to use your data to create an engaging, informative, compelling story. Specifically, you'll learn how to:Understand the importance of context and audience Determine the appropriate type of graph for your situation Recognize and eliminate the clutter clouding your information Direct your audience's attention to the most important parts of your data Think like a designer and utilize concepts of design in data visualization Leverage the power of storytelling to help your message resonate with your audience Together, the lessons in this book will help you turn your data into high impact visual stories that stick with your audience. Rid your world of ineffective graphs, one exploding 3D pie chart at a time. There is a story in your data--Storytelling with Data will give you the skills and power to tell it!