Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

    In-depth explorations of the derivative, the differentiation and integration of the powers of x, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous drills, illustrative examples. 1967 edition. Solution guide available upon request.

    Myerson introduces, clarifies, and synthesizes the extraordinary advances made in the subject over the past fifteen years, presents an overview of decision theory, and comprehensively reviews the development of the fundamental models: games in extensive form and strategic form, and Bayesian games with incomplete information.Game Theory will be useful for students at the graduate level in economics, political science, operations research, and applied mathematics. Everyone who uses game theory in research will find this book essential.

     According to MSNBC, having a child makes you stupid. You actually lose IQ points. Good Morning America has announced that natural blondes will be extinct within two hundred years. Pundits estimated that there were more than a million demonstrators at a tea party rally in Washington, D.C., even though roughly sixty thousand were there. Numbers have peculiar powers-they can disarm skeptics, befuddle journalists, and hoodwink the public into believing almost anything. "Proofiness," as Charles Seife explains in this eye-opening book, is the art of using pure mathematics for impure ends, and he reminds readers that bad mathematics has a dark side. It is used to bring down beloved government officials and to appoint undeserving ones (both Democratic and Republican), to convict the innocent and acquit the guilty, to ruin our economy, and to fix the outcomes of future elections. This penetrating look at the intersection of math and society will appeal to readers of Freakonomics and the books of Malcolm Gladwell.

    Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction.In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more.By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.

    From the first lesson to the last, each chapter introduces games of increasing complexity and then teaches the game theoretical tools necessary to solve them. Inside, you will find: All the basics fully explained, including pure strategy Nash equilibrium, mixed strategy Nash equilibrium, the mixed strategy algorithm, how to calculate payoffs, strict dominance, weak dominance, iterated elimination of strictly dominated strategies, iterated elimination of weakly dominated strategies, and more! Dozens of games solved, including the prisoner's dilemma, stag hunt, matching pennies, zero sum games, battle of the sexes/Bach or Stravinsky, chicken/snowdrift, pure coordination, deadlock, and safety in numbers! Crystal clear, line-by-line calculations of every step, with more than 200 images so you don't miss a thing! Tons of applications: war, trade, game shows, and duopolistic competition. Quick, efficient, and to the point, Game Theory 101: The Basics is perfect for introductory game theory, intermediate microeconomics, and political science.

    From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's intriguing and illuminating look at how randomness, chance, and probability affect our daily lives will intrigue, awe, and inspire.

    He is a leader in applying computer modeling to social science problems. His book The Evolution of Cooperation has been hailed as a seminal contribution and has been translated into eight languages since its initial publication. The Complexity of Cooperation is a sequel to that landmark book. It collects seven essays, originally published in a broad range of journals, and adds an extensive new introduction to the collection, along with new prefaces to each essay and a useful new appendix of additional resources. Written in Axelrod's acclaimed, accessible style, this collection serves as an introductory text on complexity theory and computer modeling in the social sciences and as an overview of the current state of the art in the field.The articles move beyond the basic paradigm of the Prisoner's Dilemma to study a rich set of issues, including how to cope with errors in perception or implementation, how norms emerge, and how new political actors and regions of shared culture can develop. They use the shared methodology of agent-based modeling, a powerful technique that specifies the rules of interaction between individuals and uses computer simulation to discover emergent properties of the social system. The Complexity of Cooperation is essential reading for all social scientists who are interested in issues of cooperation and complexity.

    The other books in the series are The Black Swan, Antifragile,and The Bed of Procrustes.

    Now Wright attempts something even more ambitious: explaining the direction of evolution and human history–and discerning where history will lead us next.In Nonzero: The Logic of Human Destiny, Wright asserts that, ever since the primordial ooze, life has followed a basic pattern. Organisms and human societies alike have grown more complex by mastering the challenges of internal cooperation. Wright's narrative ranges from fossilized bacteria to vampire bats, from stone-age villages to the World Trade Organization, uncovering such surprises as the benefits of barbarian hordes and the useful stability of feudalism. Here is history endowed with moral significance–a way of looking at our biological and cultural evolution that suggests, refreshingly, that human morality has improved over time, and that our instinct to discover meaning may itself serve a higher purpose. Insightful, witty, profound, Nonzero offers breathtaking implications for what we believe and how we adapt to technology's ongoing transformation of the world.From the Trade Paperback edition.

    Albert-László Barabási, the nation’s foremost expert in the new science of networks and author of Bursts, takes us on an intellectual adventure to prove that social networks, corporations, and living organisms are more similar than previously thought. Grasping a full understanding of network science will someday allow us to design blue-chip businesses, stop the outbreak of deadly diseases, and influence the exchange of ideas and information. Just as James Gleick and the Erdos–Rényi model brought the discovery of chaos theory to the general public, Linked tells the story of the true science of the future and of experiments in statistical mechanics on the internet, all vital parts of what would eventually be called the Barabási–Albert model.

    Republished in book form shortly thereafter, it has since gone through four hardcover and sixteen paperback printings. It is a revolutionary work, astounding in its foresight and contemporaneity. The University of Illinois Press is pleased and honored to issue this commemorative reprinting of a classic.

    With boundless erudition and in delightfully clear prose, Surowiecki ranges across fields as diverse as popular culture, psychology, ant biology, behavioral economics, artificial intelligence, military history, and politics to show how this simple idea offers important lessons for how we live our lives, select our leaders, run our companies, and think about our world.

    Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be "computable," creating the field of computability theory in the process, a foundation of present-day computer programming.The book expands Turing's original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing's statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others.Interwoven into the narrative are the highlights of Turing's own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.

    That’s a mistake, Tim Harford says in The Data Detective. We shouldn’t be suspicious of statistics—we need to understand what they mean and how they can improve our lives: they are, at heart, human behavior seen through the prism of numbers and are often “the only way of grasping much of what is going on around us.” If we can toss aside our fears and learn to approach them clearly—understanding how our own preconceptions lead us astray—statistics can point to ways we can live better and work smarter.As “perhaps the best popular economics writer in the world” (New Statesman), Tim Harford is an expert at taking complicated ideas and untangling them for millions of readers. In The Data Detective, he uses new research in science and psychology to set out ten strategies for using statistics to erase our biases and replace them with new ideas that use virtues like patience, curiosity, and good sense to better understand ourselves and the world. As a result, The Data Detective is a big-idea book about statistics and human behavior that is fresh, unexpected, and insightful.