Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    Simmons advocates a careful approach to the subject, covering such topics as the wave equation, Gauss's hypergeometric function, the gamma function and the basic problems of the calculus of variations in an explanatory fashions - ensuring that students fully understand and appreciate the topics.

    Raymond Serway, Robert Beichner, and contributing author John W. Jewett present a strong problem-solving approach that is further enhanced through increased realism in worked examples. Problem-solving strategies and hints allow students to develop a systematic approach to completing homework problems. The outstanding ancillary package includes full multimedia support, online homework, and a content-rich Web site that provides extensive support for instructors and students. The CAPA (Computer-assisted Personalized Approach), WebAssign, and University of Texas homework delivery systems give instructors flexibility in assigning online homework.

    How can we catch schools that cheat on standardized tests? How does Netflix know which movies you’ll like? What is causing the rising incidence of autism? As best-selling author Charles Wheelan shows us in Naked Statistics, the right data and a few well-chosen statistical tools can help us answer these questions and more.For those who slept through Stats 101, this book is a lifesaver. Wheelan strips away the arcane and technical details and focuses on the underlying intuition that drives statistical analysis. He clarifies key concepts such as inference, correlation, and regression analysis, reveals how biased or careless parties can manipulate or misrepresent data, and shows us how brilliant and creative researchers are exploiting the valuable data from natural experiments to tackle thorny questions.And in Wheelan’s trademark style, there’s not a dull page in sight. You’ll encounter clever Schlitz Beer marketers leveraging basic probability, an International Sausage Festival illuminating the tenets of the central limit theorem, and a head-scratching choice from the famous game show Let’s Make a Deal—and you’ll come away with insights each time. With the wit, accessibility, and sheer fun that turned Naked Economics into a bestseller, Wheelan defies the odds yet again by bringing another essential, formerly unglamorous discipline to life.

    Get a new and powerful understanding of the world around you. Save yourself from the nonsense spouted by politicians, TV pundits, right-wingers, left-wingers, shamans, uncles, and best friends.

    Linear Equations; Vector Spaces; Linear Transformations; Polynomials; Determinants; Elementary canonical Forms; Rational and Jordan Forms; Inner Product Spaces; Operators on Inner Product Spaces; Bilinear Forms For all readers interested in linear algebra.

    Employing an irresistible cast of dragon-riding Vikings, lizard-throwing giants, and feuding aliens, the renowned illustrator Grady Klein and the award-winning statistician Alan Dabney teach you how to collect reliable data, make confident statements based on limited information, and judge the usefulness of polls and the other numbers that you're bombarded with every day. If you want to go beyond the basics, they've created the ultimate resource: "The Math Cave," where they reveal the more advanced formulas and concepts.Timely, authoritative, and hilarious, The Cartoon Introduction to Statistics is an essential guide for anyone who wants to better navigate our data-driven world.

    . . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book ReviewThis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference."This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science

    And it’s getting worse. Since the turn of the twenty-first century, we’ve seen two massive value-destroying market meltdowns and a string of ethics breaches, including accounting scandals, options-backdating schemes, and the subprime mortgage debacle.Just what is going on here? Is it the inevitable decline of the American economy? Is it the new normal in a technology-enabled global marketplace? Or is it possible that the very theories we’ve embraced to underpin our capital markets are actually producing these crises?In Fixing the Game, Roger Martin reveals the culprit behind the sorry state of American capitalism: our deep and abiding commitment to the idea that the purpose of the firm is to maximize shareholder value. This theory has led to a massive growth in stock-based compensation for executives and, through this, to a naive and wrongheaded linking of the real market—the business of designing, making, and selling products and services—with the expectations market—the business of trading stocks, options, and complex derivatives. Martin shows how this tight coupling has been engineered and lays out its results: a single-minded focus on the expectations market that will continue driving us from crisis to crisis—unless we act now.Using the National Football League as his primary example, Martin illustrates that it is possible to take a much more thoughtful and effective approach than we now do to the intersection of the real and the expectations markets and to governance in general in the capital markets. Martin shows how we can act to end the destructive cycle, including:• Restructuring executive compensation to focus entirely on the real market, not the expectations market• Rethinking the meaning of board governance and role of board members• Reining in the power of hedge funds and monopoly pension fundsConcise, hard-hitting, and entertaining, Fixing the Game advocates seizing American capitalism from the jaws of the expectations market and planting it firmly in the real market—and it presents the steps we must take now to do so.

    Porter's Competitive Strategy has transformed the theory, practice, and teaching of business strategy throughout the world. Electrifying in its simplicity -- like all great breakthroughs -- Porter's analysis of industries captures the complexity of industry competition in five underlying forces. Porter introduces one of the most powerful competitive tools yet developed: his three generic strategies -- lowest cost, differentiation, and focus -- which bring structure to the task of strategic positioning. He shows how competitive advantage can be defined in terms of relative cost and relative prices, thus linking it directly to profitability, and presents a whole new perspective on how profit is created and divided. In the almost two decades since publication, Porter's framework for predicting competitor behavior has transformed the way in which companies look at their rivals and has given rise to the new discipline of competitor assessment. More than a million managers in both large and small companies, investment analysts, consultants, students, and scholars throughout the world have internalized Porter's ideas and applied them to assess industries, understand competitors,, and choose competitive positions. The ideas in the book address the underlying fundamentals of competition in a way that is independent of the specifics of the ways companies go about competing. Competitive Strategy has filled a void in management thinking. It provides an enduring foundation and grounding point on which all subsequent work can be built. By bringing a disciplined structure to the question of how firms achieve superior profitability, Porter's rich frameworks and deep insights comprise a sophisticated view of competition unsurpassed in the last quarter-century.

    A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.

    xn + yn = zn, where n represents 3, 4, 5, ...no solution"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

    Game Theory is the mathematical formalization of interactive decision-making - it assumes that each player's goal is to maximize his/her benefit, whatever it may be. Players may be friends, foes, political parties, states, or any entity that behaves interactively, whether collectively or individually. One of the problems with game analysis is the fact that, as a player, it's very hard to know what would benefit each of the other players; some of us are not even clear about our own goals or what might actually benefit us. Haim Shapira uses multiple examples to explain what Game Theory is and how the different interactions between decision-makers can play out. In this book you will: Meet the Nobel Laureate John F Nash and familiarize yourself with his celebrated equilibrium Learn the basic ideas of the art of negotiation Visit the gladiators' ring and apply for a coaching position Build an airport and divide inheritance Issue ultimatums and learn to trust

    The book's approach interweaves traditional topics with data analysis and reflects the use of the computer with close ties to the practice of statistics. The author stresses analysis of data, examines real problems with real data, and motivates the theory. The book's descriptive statistics, graphical displays, and realistic applications stand in strong contrast to traditional texts which are set in abstract settings.

    From that modest beginning, container shipping developed into a huge industry that made the boom in global trade possible. "The Box" tells the dramatic story of the container's creation, the decade of struggle before it was widely adopted, and the sweeping economic consequences of the sharp fall in transportation costs that containerization brought about.Published on the fiftieth anniversary of the first container voyage, this is the first comprehensive history of the shipping container. It recounts how the drive and imagination of an iconoclastic entrepreneur, Malcom McLean, turned containerization from an impractical idea into a massive industry that slashed the cost of transporting goods around the world and made the boom in global trade possible.But the container didn't just happen. Its adoption required huge sums of money, both from private investors and from ports that aspired to be on the leading edge of a new technology. It required years of high-stakes bargaining with two of the titans of organized labor, Harry Bridges and Teddy Gleason, as well as delicate negotiations on standards that made it possible for almost any container to travel on any truck or train or ship. Ultimately, it took McLean's success in supplying U.S. forces in Vietnam to persuade the world of the container's potential.Drawing on previously neglected sources, economist Marc Levinson shows how the container transformed economic geography, devastating traditional ports such as New York and London and fueling the growth of previously obscure ones, such as Oakland. By making shipping so cheap that industry could locate factories far from its customers, the container paved the way for Asia to become the world's workshop and brought consumers a previously unimaginable variety of low-cost products from around the globe.