Yet Eli Maor argues that music has influenced math at least as much as math has influenced music. Starting with Pythagoras, proceeding through the work of Schoenberg, and ending with contemporary string theory, Music by the Numbers tells a fascinating story of composers, scientists, inventors, and eccentrics who played a role in the age-old relationship between music, mathematics, and the sciences, especially physics and astronomy. Music by the Numbers explores key moments in this history, particularly how problems originating in music have inspired mathematicians for centuries. Perhaps the most famous of these problems is the vibrating string, which pitted some of the greatest mathematicians of the eighteenth century against each other in a debate that lasted more than fifty years and that eventually led to the development of post-calculus mathematics. Other highlights in the book include a comparison between meter in music and metric in geometry, complete with examples of rhythmic patterns from Bach to Stravinsky, and an exploration of a suggestive twentieth-century development: the nearly simultaneous emergence of Einstein's theory of relativity and Schoenberg's twelve-tone system.Weaving these compelling historical episodes with Maor's personal reflections as a mathematician and lover of classical music, Music by the Numbers will delight anyone who loves mathematics and music.

    No graduate student of quantum theory should leave it unread"--W.C Schieve, University of Texas

    Yet despite logic's widely acknowledged importance, it remains an unbroken seal for many, due to its heavy use of jargon and mathematical symbolism.This book follows the historical development of logic, explains the symbols and methods involved and explores the philosophical issues surrounding the topic in an easy-to-follow and friendly manner. It will take you through the influence of logic on scientific method and the various sciences from physics to psychology, and will show you why computers and digital technology are just another case of logic in action.

    But a dispute over its discovery sowed the seeds of discontent between two of the greatest scientific giants of all time - Sir Isaac Newton and Gottfried Wilhelm Leibniz." "Today Newton and Leibniz are generally considered the twin independent inventors of calculus. They are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret." This long and bitter dispute has been swept under the carpet by historians - perhaps because it reveals Newton and Leibniz in their worst light - but The Calculus Wars tells the full story in narrative form for the first time. This history ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad, and in the end completely human.

    At the pizzeria where he worked as a kid, he learned to substitute pork for veal in cutlets—which came in handy later when the bankroll was low. At thirteen, he got his first percentage from a local deli—that lost business when he started supplying the neighborhood wiseguys with his own heroes. And what great heroes they were… Once he entered Witness Protection, though, Hill found himself in places where prosciutto was impossible to get and gravy was something you put on mashed potatoes. So he learned to fake it when necessary (for example, Romano with white pepper took the place of real pecorino-siciliano cheese), and wherever he found himself, Hill managed to keep good Italian food on the table. He still brings this flair for improvisation to his cooking. No recipe is set in stone. And substitutions are listed in case you need them. Now, in his inimitable style, Hill tells some spicy stories of his life in the Mob and shows you how to whip up his favorite dishes, Sicilian style—even when you’re cooking on the run....

    These talks, coming during the last days of his life, were the culmination of the rarest teachings he had to give us; they were the summit of the heights of his wisdom.

    Through this three-dimensional, colorful explanation, you are introduced to a framework that will help you understand everything that an engineer does— enabling you to not only recognize what you like, but how to achieve it in your studio. Expand your recording techniques by learning what your recording equipment does and how it all works together in a simple, visual manner. From bluegrass to big band, new age to heavy metal, classical to hip-hop, jazz to rap, and alternative rock to techno, Gibson has mapped out everything that can be done to create various effects in all standard mixes. Once you have a perspective on what can be done, you have the power to be truly creative on your own: to make art out of technology.

    Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . Up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . . . But unlike its more celebrated colleagues π and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction. Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!). Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.-- "Notices of the American Mathematical Society"

    New in this edition: -- All new design, including two-color text-- Recipes with numbered steps for easy use-- Preparation and cooking times with each recipe-- Lighter versions of favorite recipes-- Timesaving tips to make recipes even quicker-- 200 all-new color photographs-- All-new line art to make learning techniques easy-- Complete nutrition information with each recipe, including percentage of calories from fat-- Back cover of the book shows sample pages of the interior, so you can see the design even though it is shrink-wrappedPeople really rely on Betty Crocker, and all the information they have come to expect is here, revised to be up-to-the-minute.-- Over 900 recipes, from how to make coffee to rolling a fajita-- Recipes that call for readily available ingredients-- Definitions of cooking terms-- Microwave basics and tips-- The best -- and easiest -- way to cook anything, from oysters to apple pie to spaghetti squash-- Photographs to help identify foods, such as types of mushrooms and pasta-- Step-by-step photographs illustrating cooking techniques-- Complete roasting, broiling and microwaving charts for meat and poultry-- Trouble-shooting guides for successful baking-- Food safety facts-- High altitude cooking informationTrust Betty Crocker to make cooking easy, fun, and up-to-the-minute!

    Birth of a Theorem is Villani’s own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career.But you don’t have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn’t simplify or overexplain; rather, it invites readers into collaboration. Villani’s diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You’re privy to the dining-hall conversations at the world’s greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker’s whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

    This language contains many subtle, but important nuances and is very different from human verbal communication, but it is nevertheless a language that can be learned. The Secret Language of Dogs shows you how to interpret what your canine is telling you through their behavior, and it explains how they, in turn, interpret our body language and attempts to communicate and interact with them.Known as “man’s best friend” for a reason, dogs are scientifically proven to enhance our quality of life. The Secret Language of Dogs helps return the favor by providing insights into why dogs act as they do. It also contains practical advice for training, addressing common health and behavioral problems, and strengthening the bond with your canine friend. Promptly and properly decoding canine communication is the key to both a contented dog and a confident owner. The Secret Language of Dogs takes the mysteries out of dog body language, giving you the insight to gain a better understanding of your much-loved pet.

    The distinguished director, Howard Hawks, discusses his techniques of filmmaking, analyzes the artistry of his movies, and portrays his experiences working in Hollywood.

    This recreational math book takes the reader on a fantastic voyage into the world of natural numbers. From the earliest discoveries of the ancient Greeks to various fundamental characteristics of the natural number sequence, Clawson explains fascinating mathematical mysteries in clear and easy prose. He delves into the heart of number theory to see and understand the exquisite relationships among natural numbers, and ends by exploring the ultimate mystery of mathematics: the Riemann hypothesis, which says that through a point in a plane, no line can be drawn parallel to a given line.While a professional mathematician's treatment of number theory involves the most sophisticated analytical tools, its basic ideas are surprisingly easy to comprehend. By concentrating on the meaning behind various equations and proofs and avoiding technical refinements, Mathematical Mysteries lets the common reader catch a glimpse of this wonderful and exotic world.

    This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

    Cited as an influence by such envelope-pushing directors as Spike Jonze and P. T. Anderson, Altman has created a genre all his own, notable for its improvised, overlapping dialogue and creative cinematography. One of the key moviemakers of the 1970s--commonly considered the heyday of American film--Altman's irrepressible combination of unorthodox vision and style is most clearly evidenced in the fourteen movies he released across that decade. By fine-tuning his talent in a diverse array of genres, including westerns, thrillers, and loopy, absurdist comedies--all subtly altered to fit his signature métier--he cemented his place as one of our most esteemed directors.In these conversations with David Thompson, Altman reflects on his start in industrial filmmaking, as well as his tenure in television directing Alfred Hitchcock Presents and Bonanza, and his big break in feature films as the director of the enormously popular M*A*S*H, a project for which he was the last possible resort behind fourteen other directors. The resulting portrait reveals a quixotic man whose films continue to delight and challenge audiences, both in the United States and beyond.