Aiming to tell the dark secrets of computer arithmetic, this title is suitable for library developers, compiler writers, and lovers of elegant hacks.

    But was he right? Can the quantum theory of fields and Einstein's general theory of relativity, the two most accurate and successful theories in all of physics, be united in a single quantum theory of gravity? Can quantum and cosmos ever be combined? On this issue, two of the world's most famous physicists--Stephen Hawking ("A Brief History of Time") and Roger Penrose ("The Emperor's New Mind" and "Shadows of the Mind")--disagree. Here they explain their positions in a work based on six lectures with a final debate, all originally presented at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge.How could quantum gravity, a theory that could explain the earlier moments of the big bang and the physics of the enigmatic objects known as black holes, be constructed? Why does our patch of the universe look just as Einstein predicted, with no hint of quantum effects in sight? What strange quantum processes can cause black holes to evaporate, and what happens to all the information that they swallow? Why does time go forward, not backward?In this book, the two opponents touch on all these questions. Penrose, like Einstein, refuses to believe that quantum mechanics is a final theory. Hawking thinks otherwise, and argues that general relativity simply cannot account for how the universe began. Only a quantum theory of gravity, coupled with the no-boundary hypothesis, can ever hope to explain adequately what little we can observe about our universe. Penrose, playing the realist to Hawking's positivist, thinks that the universe is unbounded and will expand forever. The universe can be understood, he argues, in terms of the geometry of light cones, the compression and distortion of spacetime, and by the use of twistor theory. With the final debate, the reader will come to realize how much Hawking and Penrose diverge in their opinions of the ultimate quest to combine quantum mechanics and relativity, and how differently they have tried to comprehend the incomprehensible.

    Take in the spectacle of Machu Picchu at sunrise, treat your taste buds to Lima's famous ceviche, or try to solve the mystery of the Nazca Lines; all with your trusted travel companion. Discover the best of Peru and begin your journey now!Inside Lonely Planet Discover Peru: Full-color maps and images throughoutHighlights and itineraries show you the simplest way to tailor your trip to your own personal needs and interestsInsider tips save you time and money and help you get around like a local, avoiding crowds and trouble spotsEssential info at your fingertips - including hours of operation, phone numbers, websites, transit tips, and pricesHonest reviews for all budgets - including eating, sleeping, sight-seeing, going out, shopping, and hidden gems that most guidebooks missCultural insights give you a richer and more rewarding travel experience - including customs, history, art, literature, music, landscapes, outdoor activities, wildlife, food, drink, and moreOver 50 color local mapsUseful features - including Walking Tours, Month-by-Month (annual festival calendar), and Travel with KidsCoverage of Iquitos, the Amazon, Huaraz, Trujillo, the North, Cuzco, Machu Picchu, Lima, Lake Titicaca, Nazca, Arequipa, the South, and moreThe Perfect Choice: Lonely Planet Discover Peru, our easy-to-use guide, is perfect for travelers who seek the most popular attractions a destination has to offer. Filled with inspiring and colorful photos, this guide focuses on the best of the best.Looking for a comprehensive guide that recommends a wide range of experiences, both popular and offbeat, and extensively covers all the country has to offer? Check out Lonely Planet's Peru guide. Authors: Written and researched by Lonely Planet, Carolina A Miranda, Carolyn McCarthy, Kevin Raub, Brendan Sainsbury, and Luke Waterson.About Lonely Planet: Started in 1973, Lonely Planet has become the world's leading travel guide publisher with guidebooks to every destination on the planet, as well as an award-winning website, a suite of mobile and digital travel products, and a dedicated traveler community. Lonely Planet's mission is to enable curious travelers to experience the world and to truly get to the heart of the places they find themselves in.TripAdvisor Travelers' Choice Awards 2012 and 2013 winner in Favorite Travel Guide category'Lonely Planet guides are, quite simply, like no other.' - New York Times'Lonely Planet. It's on everyone's bookshelves; it's in every traveller's hands. It's on mobile phones. It's on the Internet. It's everywhere, and it's telling entire generations of people how to travel the world.' - Fairfax Media (Australia)

    And the best news? This book tells you how to do it without spending lots more time planning, researching and preparing out of this world lessons.All of the activities have been tried-and-tested in the classroom and are divided into three areas: ideas for embedding or preparing ''''by this time tomorrow'''', ''''by this time next month'''' and ''''by this time next term'''' so you can choose the activity you have time for. Each chapter focuses on a perennial issue in teaching and in inspection, such as differentiation, working with your Teaching Assistant and Assessment for Learning.There are dozens of starters and plenaries and useful websites, and the authors own website offers resources to save you even more time. A must for all primary school teachers who want to become outstanding, not just for the inspectors but for every child they teach.

    New in the Mountaineers Outdoor Expert Series: instruction for the beginning to intermediate rock climber by an internationally known guide.

    The authors are well-known for their clear presentation that makes the material accessible to a a broad audience and requires no special previous mathematical experience. KEY TOPICS: In this new edition, the authors incorporate a somewhat more informal, friendly writing style to present both classical and contemporary theories of computation. Algorithms, complexity analysis, and algorithmic ideas are introduced informally in Chapter 1, and are pursued throughout the book. Each section is followed by problems.

    A compendium of the world's most loved music. True to the spirit of the great composers, this volume fills the needs of students and teachers. Over 100 works, including Schubert's "Moment Musicale," Chopin's "Minute Waltz," Beethoven's "Rondo a Cappriccio," and much more. Spiral bound.

    Includes such gems as:? There are 42 eyes in a deck of cards, and 42 dots on a pair of dice ? In order to fill in a map so that neighboring regions never get the same color, one never needs more than four colors ? Hells Angels use the number 81 in their insignia because the initials H and A are the eighth and first numbers in the alphabet respectively

    It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.

    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.

    

    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.

    The new edition includes the most up-to-date research developments and many more examples and problems.

    Bringing together the best and most interesting science stories appearing in Quanta Magazine over the past five years, Alice and Bob Meet the Wall of Fire reports on some of the greatest scientific minds as they test the limits of human knowledge. Quanta, under editor-in-chief Thomas Lin, is the only popular publication that offers in-depth coverage of today's challenging, speculative, cutting-edge science. It communicates science by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves.In the title story, Alice and Bob--beloved characters of various thought experiments in physics--grapple with gravitational forces, possible spaghettification, and a massive wall of fire as Alice jumps into a black hole. Another story considers whether the universe is impossible, in light of experimental results at the Large Hadron Collider. We learn about quantum reality and the mystery of quantum entanglement; explore the source of time's arrow; and witness a eureka moment when a quantum physicist exclaims: "Finally, we can understand why a cup of coffee equilibrates in a room." We reflect on humans' enormous skulls and the Brain Boom; consider the evolutionary benefits of loneliness; peel back the layers of the newest artificial-intelligence algorithms; follow the "battle for the heart and soul of physics"; and mourn the disappearance of the "diphoton bump," revealed to be a statistical fluctuation rather than a revolutionary new particle. These stories from Quanta give us a front-row seat to scientific discovery.ContributorsPhilip Ball, K. C. Cole, Robbert Dijkgraaf, Dan Falk, Courtney Humphries, Ferris Jabr, Katia Moskvitch, George Musser, Michael Nielsen, Jennifer Ouellette, John Pavlus, Emily Singer, Andreas von Bubnoff, Frank Wilczek, Natalie Wolchover, Carl Zimmer

    Albert-László Barabási, the nation’s foremost expert in the new science of networks and author of Bursts, takes us on an intellectual adventure to prove that social networks, corporations, and living organisms are more similar than previously thought. Grasping a full understanding of network science will someday allow us to design blue-chip businesses, stop the outbreak of deadly diseases, and influence the exchange of ideas and information. Just as James Gleick and the Erdos–Rényi model brought the discovery of chaos theory to the general public, Linked tells the story of the true science of the future and of experiments in statistical mechanics on the internet, all vital parts of what would eventually be called the Barabási–Albert model.