Nobel-Prize-winner Claude Cohen-Tannoudji and his colleagues have written this book to eliminate precisely these difficulties. Fourteen chapters provide a clarity of organization, careful attention to pedagogical details, and a wealth of topics and examples which make this work a textbook as well as a timeless reference, allowing to tailor courses to meet students' specific needs. Each chapter starts with a clear exposition of the problem which is then treated, and logically develops the physical and mathematical concept. These chapters emphasize the underlying principles of the material, undiluted by extensive references to applications and practical examples which are put into complementary sections. The book begins with a qualitative introduction to quantum mechanical ideas using simple optical analogies and continues with a systematic and thorough presentation of the mathematical tools and postulates of quantum mechanics as well as a discussion of their physical content. Applications follow, starting with the simplest ones like e.g. the harmonic oscillator, and becoming gradually more complicated (the hydrogen atom, approximation methods, etc.). The complementary sections each expand this basic knowledge, supplying a wide range of applications and related topics as well as detailed expositions of a large number of special problems and more advanced topics, integrated as an essential portion of the text.

    Stimulating, illuminating, and always surprising, The Big Questions challenges readers to re-evaluate their most fundamental beliefs and reveals the relationship between the loftiest philosophical quests and our everyday lives.

    As he did so masterfully in Prime Obsession, Derbyshire brings the evolution of mathematical thinking to dramatic life by focusing on the key historical players. Unknown Quantity begins in the time of Abraham and Isaac and moves from Abel's proof to the higher levels of abstraction developed by Galois through modern-day advances. Derbyshire explains how a simple turn of thought from this plus this equals this to this plus what equals this? gave birth to a whole new way of perceiving the world. With a historian's narrative authority and a beloved teacher's clarity and passion, Derbyshire leads readers on an intellectually satisfying and pleasantly challenging historical and mathematical journey.

    We often overlook the historical link between mathematics and technological advances, says Stewart—but this connection is integral to any complete understanding of human history.Equations are modeled on the patterns we find in the world around us, says Stewart, and it is through equations that we are able to make sense of, and in turn influence, our world. Stewart locates the origins of each equation he presents—from Pythagoras's Theorem to Newton's Law of Gravity to Einstein's Theory of Relativity—within a particular historical moment, elucidating the development of mathematical and philosophical thought necessary for each equation's discovery. None of these equations emerged in a vacuum, Stewart shows; each drew, in some way, on past equations and the thinking of the day. In turn, all of these equations paved the way for major developments in mathematics, science, philosophy, and technology. Without logarithms (invented in the early 17th century by John Napier and improved by Henry Briggs), scientists would not have been able to calculate the movement of the planets, and mathematicians would not have been able to develop fractal geometry. The Wave Equation is one of the most important equations in physics, and is crucial for engineers studying the vibrations in vehicles and the response of buildings to earthquakes. And the equation at the heart of Information Theory, devised by Claude Shannon, is the basis of digital communication today.An approachable and informative guide to the equations upon which nearly every aspect of scientific and mathematical understanding depends, In Pursuit of the Unknown is also a reminder that equations have profoundly influenced our thinking and continue to make possible many of the advances that we take for granted.

    This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. * The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.

    Without a doubt, the development of the computer was a massive leap forward in humankind's progress and will stand as one of the twentieth century's greatest achievements. But how many of us know how it really works? "Turing And The Computer" offers a brilliant encapsulation of the groundwork that led to the invention of the computer as we know it, and an absorbing account of the man who helped develop it, only to be largely forgotten after his death. Eccentric and principled, Turing would lay aside a brilliant career in mathematics to serve his country by breaking German codes during the Second World War. Openly homosexual, he would later be put on trial on indecency charges and forced to undergo hormone treatments that wrecked his body and his spirit. But the modern machine he helped create lives on.Concise and thoroughly compelling, "Turing And The Computer" is for all those curious about the philosophy and mechanics behind the now indispensable computer, and for anyone awed by the spark of invention that inspires its birth.

    Our inaugural effort is OpenIntro Statistics. Probability is optional, inference is key, and we feature real data whenever possible. Files for the entire book are freely available at openintro.org, and anybody can purchase a paperback copy from amazon.com for under $10.The future for OpenIntro depends on the involvement and enthusiasm of our community. Visit our website, openintro.org. We provide free course management tools, including an online question bank, utilities for creating course quizzes, and many other helpful resources.CERTAIN CONTENT THAT APPEARS ON THIS SITE COMES FROM AMAZON SERVICES LLC. THIS CONTENT IS PROVIDED ‘AS IS’ AND IS SUBJECT TO CHANGE OR REMOVAL AT ANY TIME.Can’t find it here? Search Amazon.com Search: All Products Apparel & AccessoriesBabyBeautyBooksCamera & PhotoCell Phones & ServiceClassical MusicComputersComputer & Video GamesDVDElectronicsGourmet FoodHome & GardenMiscellaneousHealth & Personal CareJewelry & WatchesKitchen & HousewaresMagazine SubscriptionsMusicMusical InstrumentsSoftwareSports & OutdoorsTools & HardwareToys & GamesVHS Keywords:

    Beginning millions of years ago with ancient “ant odometers” and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares from centuries ago, the discovery of pi and calculus, and the butterfly effect. Each topic gets a lavishly illustrated spread with stunning color art, along with formulas and concepts, fascinating facts about scientists’ lives, and real-world applications of the theorems.

    This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.

    Using a "physics first" approach to the subject, renowned relativist James B. Hartle provides a fluent and accessible introduction that uses a minimum of new mathematics and is illustrated with a wealth of exciting applications. KEY TOPICS: The emphasis is on the exciting phenomena of gravitational physics and the growing connection between theory and observation. The Global Positioning System, black holes, X-ray sources, pulsars, quasars, gravitational waves, the Big Bang, and the large scale structure of the universe are used to illustrate the widespread role of how general relativity describes a wealth of everyday and exotic phenomena. MARKET: For anyone interested in physics or general relativity.

    (The also-rans that year included Tom Wolfe, Verlyn Klinkenborg, and Oliver Sacks.) Hayes's work in this genre has also appeared in such anthologies as The Best American Magazine Writing, The Best American Science and Nature Writing, and The Norton Reader. Here he offers us a selection of his most memorable and accessible pieces--including "Clock of Ages"--embellishing them with an overall, scene-setting preface, reconfigured illustrations, and a refreshingly self-critical "Afterthoughts" section appended to each essay.

    They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide--more than 104,000 copies were bought of the prior edition--includes problems and examples using graphing calculators..

    Intended for undergraduate students with foundation skills in mathematics and a deep interest in physics, it systematically lays out the principles of mechanics: vectors, Newton's laws, momentum, energy, rotational motion, angular momentum and noninertial systems, and includes chapters on central force motion, the harmonic oscillator, and relativity. Numerous worked examples demonstrate how the principles can be applied to a wide range of physical situations, and more than 600 figures illustrate methods for approaching physical problems. The book also contains over 200 challenging problems to help the student develop a strong understanding of the subject. Password-protected solutions are available for instructors at www.cambridge.org/9780521198219.

    Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack ofadvanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicatedwith the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

    A modern classic by an accomplished mathematician and best-selling author has been updated to encompass and explain the recent headline-making advances in the field in non-technical terms.