Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    Discovered by an 18th century mathematician and preacher, Bayes' rule is a cornerstone of modern probability theory. In this richly illustrated book, intuitive visual representations of real-world examples are used to show how Bayes' rule is actually a form of commonsense reasoning. The tutorial style of writing, combined with a comprehensive glossary, makes this an ideal primer for novices who wish to gain an intuitive understanding of Bayesian analysis. As an aid to understanding, online computer code (in MatLab, Python and R) reproduces key numerical results and diagrams.Stone's book is renowned for its visually engaging style of presentation, which stems from teaching Bayes' rule to psychology students for over 10 years as a university lecturer.

    

    Capturing the tone of students exchanging ideas among themselves, this unique guide also explains how calculus is taught, how to get the best teachers, what to study, and what is likely to be on exams—all the tricks of the trade that will make learning the material of first-semester calculus a piece of cake. Funny, irreverent, and flexible, How to Ace Calculus shows why learning calculus can be not only a mind-expanding experience but also fantastic fun.

    You multiply something by something, right? Or you're scratching your head, wondering how to compute the odds that your football team will take next Sunday's game. You're pretty sure that involved ratios. The problem is, you can't quite remember.Here you get an adult refresher and real-life context—with examples ranging from how to figure out how many shingles it takes to re-roof the garage to the formula for resizing Mom's tomato sauce recipe for your entire family.Forget higher calculus—you just need an open mind. And with this practical guide, math can stop being scary and start being useful.

    Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

     Two hot topics team up in The Baseball Economist, and the result is a refreshing, clear- eyed survey of a playing field that has changed radically in recent years. Utilizing the latest economic methods and statistical analysis, writer, economics professor, and popular blogger J. C. Bradbury dissects burning baseball topics with his original Sabernomic perspective, such as: • Did steroids have nothing to do with the recent home run records? Incredibly, Bradbury's research, reviewed by Stanford economists, reveals steroids had little statistical significance. • Is the big-city versus small-city competition really lopsided? Bradbury shows why the Marlins and Indians are likely to dominate big-city franchises in the coming years. • Which players are ridiculously overvalued? Bradbury lists all players by team with their revenue value to the team listed in dollars—including a dishonor role of those players with negative values. • Is major league baseball a monopoly that can't govern itself? Bradbury sets out what rules the owners really need to play by, and what the players' union should be doing. • Does it help to lobby for balls and strikes? How would Babe Ruth perform in today's game? And who killed all the left-handed catchers, anyway? The Baseball Economist knows. Providing far more than a mere collection of numbers, Bradbury shines the light of his economic thinking on baseball, exposing the power of tradeoffs, competition, and incentives. Statistics alone aren't enough anymore. Fans, fantasy buffs, and players, as well as coaches at all levels who want to grasp what is really happening on the field today and in the coming years, will use and enjoy Bradbury's brilliant new understanding of the national pastime.

    Readers of The Da Vinci Code were given a glimpse of the mysterious connections between math, science, and Leonardo's art. Math and the Mona Lisa picks up where The Da Vinci Code left off, illuminating Leonardo's life and work to uncover connections that, until now, have been known only to scholars.Following Leonardo's own unique model, Atalay searches for the internal dynamics of art and science, revealing to us the deep unity of the two cultures. He provides a broad overview of the development of science from the dawn of civilization to today's quantum mechanics. From this base of information, Atalay offers a fascinating view into Leonardo's restless intellect and modus operandi, allowing us to see the source of his ideas and to appreciate his art from a new perspective. William D. Phillips, who won the Nobel Prize in physics in 1997, writes of the author, "Atalay is indeed a modern renaissance man, and he invites us to tap the power of synthesis that is Leonardo's model."

    It moves beyond a mere study of algorithms without sacrificing the rigor that faculty desire. As in every edition, Winston reinforces the book's successful features and coverage with the most recent developments in the field. The Student Suite CD-ROM, which now accompanies every new copy of the text, contains the latest versions of commercial software for optimization, simulation, and decision analysis.

    Focused on helping students understand and construct proofs and expanding their mathematical maturity, this best-selling text is an accessible introduction to discrete mathematics. Johnsonbaugh's algorithmic approach emphasizes problem-solving techniques. The Seventh Edition reflects user and reviewer feedback on both content and organization.

    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.

    Virtually everything in our lives is digital, numerical, or quantified. The story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. Finding Zero is an adventure filled saga of Amir Aczel's lifelong obsession: to find the original sources of our numerals. Aczel has doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross examining so-called scholars who offered wildly differing sets of facts, and ultimately penetrating deep into a Cambodian jungle to find a definitive proof. Here, he takes the reader along for the ride.The history begins with the early Babylonian cuneiform numbers, followed by the later Greek and Roman letter numerals. Then Aczel asks the key question: where do the numbers we use today, the so-called Hindu-Arabic numerals, come from? It is this search that leads him to explore uncharted territory, to go on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero—the keystone of our entire system of numbers—on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures. While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves—who finally reveal where our numbers come from.

    Today, these paradoxes remain on the cutting edge of our investigations into the fabric of space and time. Zeno's Paradox uses the motion paradox as a jumping-off point for an exploration of the twenty-five-hundred-year quest to uncover the true nature of the universe. From Galileo to Einstein to Stephen Hawking, some of the greatest minds in history have tackled the problem and made spectacular breakthroughs, but through it all, the paradox of motion remains.

    It is based on the idea that everyone acts competitively and in his own best interest. With the help of mathematical models, it is possible to anticipate the actions of others in nearly all life's enterprises. This book includes down-to-earth examples and solutions, as well as charts and illustrations designed to help teach the concept. In The Complete Idiot's Guide® to Game Theory, Dr. Edward C. Rosenthal makes it easy to understand game theory with insights into:? The history of the disciple made popular by John Nash, the mathematician dramatized in the film A Beautiful Mind? The role of social behavior and psychology in this amazing discipline? How important game theory has become in our society and why

    Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.