But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting." — Saturday Review of Literature.

    Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences--perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

    Written not from a post-crisis perspective – but from a preventative point of view – this book traces the development of financial derivatives from bonds to credit default swaps, and shows how mathematical formulas went beyond pricing to expand their use to the point where they dwarfed the real economy. You'll learn how the deadly allure of their ice-cold beauty has misled generations of economists and investors, and how continued reliance on these formulas can either assist future economic development, or send the global economy into the financial equivalent of a cardiac arrest. Rather than rehash tales of post-crisis fallout, this book focuses on preventing the next one. By exploring the heart of the shadow economy, you'll be better prepared to ride the rough waves of finance into the turbulent future. Delve into one of the world's least-understood but highest-impact industries Understand the key principles of quantitative finance and the evolution of the field Learn what quantitative finance has become, and how it affects us all Discover how the industry's next steps dictate the economy's future How do you create a quadrillion dollars out of nothing, blow it away and leave a hole so large that even years of "quantitative easing" can't fill it – and then go back to doing the same thing? Even amidst global recovery, the financial system still has the potential to seize up at any moment. The Money Formula explores the how and why of financial disaster, what must happen to prevent the next one.

    The author defines all terms, points out potential pitfalls in algebraic calculation, and makes problem solving a fun activity. New in this edition are painless approaches to understanding and graphing linear equations, solving systems of linear inequalities, and graphing quadratic equations. Barron’s popular Painless Series of study guides for middle school and high school students offer a lighthearted, often humorous approach to their subjects, transforming details that might once have seemed boring or difficult into a series of interesting and mentally challenging ideas. Most titles in the series feature many fun-to-solve “Brain Tickler” problems with answers at the end of each chapter.

    Many of these students are extremely intelligent and hardworking, but even the best will, at some point, struggle with the demands of making the transition to advanced mathematics. Some have difficulty adjusting to independent study and to learning from lectures. Other struggles, however, are more fundamental: the mathematics shifts in focus from calculation to proof, so students are expected to interact with it in different ways. These changes need not be mysterious - mathematics education research has revealed many insights into the adjustments that are necessary - but they are not obvious and they do need explaining.This no-nonsense book translates these research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics degree, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time. Part 1 provides an in-depth discussion of advanced mathematical thinking, and explains how a student will need to adapt and extend their existing skills in order to develop a good understanding of undergraduate mathematics. Part 2 covers study skills as these relate to the demands of a mathematics degree. It suggests practical approaches to learning from lectures and to studying for examinations while also allowing time for a fulfilling all-round university experience.The first subject-specific guide for students, this friendly, practical text will be essential reading for anyone studying mathematics at university.

    Haskell emerged in the last decade as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvellous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures.This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others.

    Topics include the development of counting and numbers systems, the emergence of zero, cultures that don’t have numbers, algebra, solid geometry, symmetry and beauty, perspective, riddles and problems, calculus, mathematical logic, friction force and displacement, subatomic particles, and the expansion of the universe. Great mathematical thinkers covered include Napier, Liu Hui, Aryabhata, Galileo, Newton, Russell, Einstein, Riemann, Euclid, Carl Friedrich Gauss, Charles Babbage, Montmort, Wittgenstein, and many more. The book is beautifully illustrated throughout in full color.

    Written by the 19th-century mathematician who also gave us "Alive in Wonderland", they are among the most entertaining logical works ever written, and contain some of the most thought-provoking puzzles ever devised.

    

    Indeed, numbers are part of every discipline in the sciences and the arts.With 350 illustrations, including diagrams, photographs and computer imagery, the book chronicles the centuries-long search for the meaning of numbers by famous and lesser-known mathematicians, and explains the puzzling aspects of the mathematical world. Topics include:The earliest ideas of numbers and counting Patterns, logic, calculating Natural, perfect, amicable and prime numbers Numerology, the power of numbers, superstition The computer, the Enigma Code Infinity, the speed of light, relativity Complex numbers The Big Bang and Chaos theories The Philosopher's Stone. The Book of Numbers shows enthusiastically that numbers are neither boring nor dull but rather involve intriguing connections, rivalries, secret documents and even mysterious deaths.

    Lorentz.

    As exciting as any action/adventure novel, this is actually the story of incredible individuals and engrossing tales behind the most profound, enduring mathematical theorems.Archimedes famously ran naked through the streets shouting, “Eureka, eureka!” after finding a method for measuring the volume of an irregular-shaped object. René Descartes was not only a great French mathematician, philosopher, physicist, and natural scientist; he was also an expert swordsman who traveled with European armies from town to town, dressed in green taffeta and accompanied by a valet. Georg Cantor grappled with mental illness as he explored the highly counterintuitive, bizarre properties of infinite sets and numbers. Emmy Noether struggled to find employment as she laid the mathematical groundwork for modern theoretical physics. And Alexander Grothendieck taught himself mathematics while interned in Nazi concentration camps, only to disappear into the Pyrenees at the zenith of his career.These are just a few stories recounted in this absorbing narrative. In probing the lives of the preeminent mathematicians in history, a Strange Wilderness will leave you entertained and enlightened, with a newfound appreciation of the tenacity, complexity, and brilliance of the mathematical genius.

    It presents in a unified manner an introduction to the mathematical theory underlying computer graphic applications. It covers topics of keen interest to students in engineering and computer science: transformations, projections, 2-D and 3-D curve definition schemes, and surface definitions. It also includes techniques, such as B-splines, which are incorporated as part of the software in advanced engineering workstations. A basic knowledge of vector and matrix algebra and calculus is required.

    

    Since its first appearance in 1956 there have been eight editions as well as translations from the original Russian into Ukrainian, Estonian, Lettish, and Lithuanian. Almost a million copies of the Russian version alone have been sold.Part of the reason for the book's success is its marvelously varied assortment of brainteasers ranging from simple "catch" riddles to difficult problems (none, however, requiring advanced mathematics). Many of the puzzles will be new to Western readers, while some familiar problems have been clothed in new forms. Often the puzzles are presented in the form of charming stories that provide non-Russian readers with valuable insights into contemporary Russian life and customs. In addition, Martin Gardner, former editor of the Mathematical Games Department, Scientific American, has clarified and simplified the book to make it as easy as possible for an English-reading public to understand and enjoy. He has been careful, moreover, to retain nearly all the freshness, warmth, and humor of the original.Lavishly illustrated with over 400 clear diagrams and amusing sketches, this inexpensive edition of the first English translation will offer weeks or even months of stimulating entertainment. It belongs in the library of every puzzlist or lover of recreational mathematics.