Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: ..". all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999..". the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals."

    In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simplicity of the proofs for many theorems.Among the topics covered in this accessible, carefully designed introduction are multiplicativity-divisibility, including the fundamental theorem of arithmetic, combinatorial and computational number theory, congruences, arithmetic functions, primitive roots and prime numbers. Later chapters offer lucid treatments of quadratic congruences, additivity (including partition theory) and geometric number theory.Of particular importance in this text is the author's emphasis on the value of numerical examples in number theory and the role of computers in obtaining such examples. Exercises provide opportunities for constructing numerical tables with or without a computer. Students can then derive conjectures from such numerical tables, after which relevant theorems will seem natural and well-motivated..

    Endorsed by the National Institute for the Clinical Application of Behavioral Medicine, mindfulness is a simple way to gently help you become more present with the challenges you face and navigate difficulties with more clarity and courage.The guidance presented in Real-World Mindfulness for Beginners has been praised by today’s leading voices on mindfulness. Particularly helpful to those who are new to mindfulness, Real-World Mindfulness for Beginners offers knowledge that is easy to understand and techniques that can be applied immediately. Each chapter offers mindfulness practices that are specific to common challenges such as dealing with anxiety and stress, managing anger and hurt, and coping with grief and loss. In Real-World Mindfulness for Beginners, you’ll find: Mindfulness practices that are most applicable to your current need Easy mindfulness practices that take only minutes or even seconds Tips that modify mindfulness practices to inspire new experiences Through the practices in Real-World Mindfulness for Beginners you’ll unearth the quiet strength within to handle life’s curve balls as they come, wherever you may be.

    Early beginnings in antiquity, medieval contributions, and a century of anticipation lead up to a consideration of Newton and Leibniz, the period of indecison that followed them, and the final rigorous formulation that we know today.

    Their essays cover the spectrum of the hobby market, from role-playing games to collectible card games, miniatures games to wargames to board games, with titles both familiar and esoteric. Writers include such legendary designers as Gary Gygax, co-creator of Dungeons & Dragons; Richard Garfield, creator of Magic: The Gathering and Larry Harris, creator of Axis and Allies; best-selling authors R. A. Salvatore, Tracy Hickman, Ed Greenwood, and Michael Stackpole; computer industry notables Bruce Shelley of Ensemble Studios (Age of Empires) and Jack Emmert of Cryptic Studios (City of Heroes); as well as dozens of other noteworthy and award-winning creators. Hobby Games: The 100 Best also features a foreword by board game legend Reiner Knizia and an afterword by wargame legend James F. Dunnigan.

    But few people are aware of the bagel’s provenance, let alone its adventuresome history. This charming book tells the remarkable story of the bagel’s journey from the tables of seventeenth-century Poland to the freezers of middle America today, a story of often surprising connections between a cheap market-day snack and centuries of Polish, Jewish, and American history. Research in international archives and numerous personal interviews uncover the bagel’s links with the defeat of the Turks by Polish King Jan Sobieski in 1683, the Yiddish cultural revival of the late nineteenth century, and Jewish migration across the Atlantic to America. There the story moves from the bakeries of New York’s Lower East Side to the Bagel Bakers’ Local 388 Union of the 1960s, and the attentions of the mob. For all its modest size, the bagel has managed to bridge cultural gaps, rescue kings from obscurity, charge the emotions, and challenge received wisdom. Maria Balinska weaves together a rich, quirky, and evocative history of East European Jewry and the unassuming ring-shaped roll the world has taken to its heart.

    He sifts through over 30,000 survey submissions to uncover the world’s favourite number, and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India, and visits the engineer who designed the first roller-coaster loop. Get hooked on math as Alex delves deep into humankind’s turbulent relationship with numbers, and reveals how they have shaped the world we live in.

    The result is Act Natural, hilarious and deft dissection of the history of Western parenting, written with the signature biting wit and deep insights Traig has become known for.Moving from ancient Rome to Puritan New England to the Dr. Spock craze of mid-century America, Traig cheerfully explores historic and present-day parenting techniques ranging from the misguided, to the nonsensical, to the truly horrifying. Be it childbirth, breastfeeding, or the ways in which we teach children how to sleep, walk, eat, and talk, she leaves no stone unturned in her quest for answers: Have our techniques actually evolved into something better? Or are we still just scrambling in the dark?

    Julia Diggins masterfully recreates the atmosphere of ancient times, when men, using three simple tools, the string, the straightedge, and the shadow, discovered the basic principles and constructions of elementary geometry. Her book reveals how these discoveries related to the early civilizations of Mesopotamia, Egypt, and Greece.The fabric of the story is woven out of archeological and historical records and legends about the major men of mathematics. By reconstructing the events as they might have happened, Diggins enables the attentive reader to easily follow the pattern of reasoning that leads to an ingenious proof of the Pythagorean theorem, an appreciation of the significance of the Golden Mean in art and architecture, and the construction of the five regular solids.Out of print for 34 years, Julia Diggins' classic book is back and is a must-read for middle school students or for parents helping their children through their first geometry course. You will be fascinated with the graphic illustrations and written depiction of how the knowledge and wisdom of so many cultures helped shape our civilization today. This book is popular with teachers and parents who use Jamie York's Making Math Meaningful curriculum books.

    This book helps you even the odds. Using easy-to-understand explanations and examples, it demystifies probability -- and even offers savvy tips to boost your chances of gambling success Discover how to* Conquer combinations and permutations* Understand probability models from binomial to exponential* Make good decisions using probability* Play the odds in poker, roulette, and other games

    Aczel turns his sights on probability theory -- the branch of mathematics that measures the likelihood of a random event. He explains probability in clear, layman's terms, and shows its practical applications. What is commonly called luck has mathematical roots and in Chance, you'll learn to increase your odds of success in everything from true love to the stock market. For thousands of years, the twin forces of chance and mischance have beguiled humanity like none other. Why does fortune smile on some people, and smirk on others? What is luck, and why does it so often visit the undeserving? How can we predict the random events happening around us? Even better, how can we manipulate them? In this delightful and lucid voyage through the realm of the random, Dr. Aczel once again makes higher mathematics intelligible to us.

    “Why wouldn’t seaweeds be a protean life source for the lives that have evolved since?” On a planet facing environmental change and diminishing natural resources, seaweed is increasingly important as a source of food and as a fundamental part of our global ecosystem. In Seaweed Chronicles, Shetterly takes readers deep into the world of this essential organism by providing an immersive, often poetic look at life on the rugged shores of her beloved Gulf of Maine, where the growth and harvesting of seaweed is becoming a major industry. While examining the life cycle of seaweed and its place in the environment, she tells the stories of the men and women who farm and harvest it—and who are fighting to protect this critical species against forces both natural and man-made. Ideal for readers of such books as The Hidden Life of Trees and How to Read Water, Seaweed Chronicles is a deeply informative look at a little understood and too often unappreciated part of our habitat.

    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.

    But the way we talk about the brain is often rooted more in mystical conceptions of the soul than in scientific fact. This blinds us to the physical realities of mental function. We ignore bodily influences on our psychology, from chemicals in the blood to bacteria in the gut, and overlook the ways that the environment affects our behavior, via factors varying from subconscious sights and sounds to the weather. As a result, we alternately overestimate our capacity for free will or equate brains to inorganic machines like computers. But a brain is neither a soul nor an electrical network: it is a bodily organ, and it cannot be separated from its surroundings. Our selves aren't just inside our heads -- they're spread throughout our bodies and beyond. Only once we come to terms with this can we grasp the true nature of our humanity.

    In recent decades, hamburgers, hot dogs, and pizza have been thought to define the nation’s palate. Not so, says food historian Paul Freedman, who demonstrates that there is an exuberant and diverse, if not always coherent, American cuisine that reflects the history of the nation itself.Combining historical rigor and culinary passion, Freedman underscores three recurrent themes—regionality, standardization, and variety—that shape a completely novel history of the United States.From the colonial period until after the Civil War, there was a patchwork of regional cooking styles that produced local standouts, such as gumbo from southern Louisiana, or clam chowder from New England. Later, this kind of regional identity was manipulated for historical effect, as in Southern cookbooks that mythologized gracious “plantation hospitality,” rendering invisible the African Americans who originated much of the region’s food.As the industrial revolution produced rapid changes in every sphere of life, the American palate dramatically shifted from local to processed. A new urban class clamored for convenient, modern meals and the freshness of regional cuisine disappeared, replaced by packaged and standardized products—such as canned peas, baloney, sliced white bread, and jarred baby food.By the early twentieth century, the era of homogenized American food was in full swing. Bolstered by nutrition “experts,” marketing consultants, and advertising executives, food companies convinced consumers that industrial food tasted fine and, more importantly, was convenient and nutritious. No group was more susceptible to the blandishments of advertisers than women, who were made feel that their husbands might stray if not satisfied with the meals provided at home. On the other hand, men wanted women to be svelte, sporty companions, not kitchen drudges. The solution companies offered was time-saving recipes using modern processed helpers. Men supposedly liked hearty food, while women were portrayed as fond of fussy, “dainty,” colorful, but tasteless dishes—tuna salad sandwiches, multicolored Jell-O, or artificial crab toppings.The 1970s saw the zenith of processed-food hegemony, but also the beginning of a food revolution in California. What became known as New American cuisine rejected the blandness of standardized food in favor of the actual taste and pleasure that seasonal, locally grown products provided. The result was a farm-to-table trend that continues to dominate.“A book to be savored” (Stephen Aron), American Cuisine is also a repository of anecdotes that will delight food lovers: how dry cereal was created by William Kellogg for people with digestive and low-energy problems; that chicken Parmesan, the beloved Italian favorite, is actually an American invention; and that Florida Key lime pie goes back only to the 1940s and was based on a recipe developed by Borden’s condensed milk. More emphatically, Freedman shows that American cuisine would be nowhere without the constant influx of immigrants, who have popularized everything from tacos to sushi rolls.“Impeccably researched, intellectually satisfying, and hugely readable” (Simon Majumdar), American Cuisine is a landmark work that sheds astonishing light on a history most of us thought we never had.