Roger Penrose—one of the most innovative mathematicians of our time—turns around this predominant picture of the universe’s “heat death,” arguing how the expected ultimate fate of our accelerating, expanding universe can actually be reinterpreted as the “Big Bang” of a new one.Along the way to this remarkable cosmological picture, Penrose sheds new light on basic principles that underlie the behavior of our universe, describing various standard and nonstandard cosmological models, the fundamental role of the cosmic microwave background, and the key status of black holes. Ideal for both the amateur astronomer and the advanced physicist—with plenty of exciting insights for each—Cycles of Time is certain to provoke and challenge.Intellectually thrilling and accessible, this is another essential guide to the universe from one of our preeminent thinkers.

    The presentation is never awkward or dry, as it sometimes is in other "modern" textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all, this is an excellent work, of equally high value for both student and teacher." Zentralblatt f�r Mathematik

    The author has a direct style. His book presents detailed and intensive explanations. Many diagrams and key examples are used to aid understanding, as well as the application of calculus to physics and engineering and economics. The text is well organized, and it covers single variable and multivariable calculus in depth. An instructor's manual and student guide are available online at http: //ocw.mit.edu/ans7870/resources/Strang/....

    No less miraculous, the fundamental laws of the universe can be written in the language of advanced mathematics.Searching for these laws, physicists have found themselves developing ambitious mathematical ideas without experiment as their guide. In The Universe Speaks in Numbers, Graham Farmelo demonstrates how today's greatest scientific minds are working in a tradition that dates back to Newton. He takes us on an adventure from the Enlightenment, through the breakthroughs of Einstein and Dirac, to the contemporary physicists and mathematicians who are shedding fascinating light on each other's disciplines. As Farmelo shows, this blossoming relationship between mathematics and physics is responsible for huge, redefining advances in our understanding of reality, space and time. Always lively, vivid and authoritative, Farmelo guides the reader through the most thrilling and controversial developments in contemporary thought. LISTEN TO THE ACCOMPANYING PODCAST featuring interviews with leading scientists at www.grahamfarmelo.com 'A superbly written, riveting book. In elegant prose, and using virtually no equations, Farmelo describes the ongoing quest of great thinkers to understand the bedrock nature of reality' Martin Rees, Astronomer Royal, Emeritus Professor of Cosmology and Astrophysics at the University of Cambridge'I am overcome with admiration for this book's range and profundity ... An amazing achievement' Michael Frayn, award-winning writer of Copenhagen 'Masterful ... a riveting account of one of the greatest stories of our time' Nima Arkani-Hamed, Professor at the Institute of Advanced Study, Princeton

    In The Master Algorithm, Pedro Domingos lifts the veil to give us a peek inside the learning machines that power Google, Amazon, and your smartphone. He assembles a blueprint for the future universal learner--the Master Algorithm--and discusses what it will mean for business, science, and society. If data-ism is today's philosophy, this book is its bible.

    Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.

    

    Role of the unconscious in invention; the medium of ideas — do they come to mind in words? in pictures? in mathematical terms? Much more. "It is essential for the mathematician, and the layman will find it good reading." — Library Journal.

    You experience it passing every day when you watch clocks tick, bread toast, and children grow. But most physicists see things differently, from Newton to Einstein to today’s quantum theorists. For them, time isn’t real. You may think you experience time passing, but they say it’s just an illusion.Lee Smolin, author of the controversial bestseller The Trouble with Physics, argues this limited notion of time is holding physics back. It’s time for a major revolution in scientific thought. The reality of time could be the key to the next big breakthrough in theoretical physics.What if the laws of physics themselves were not timeless? What if they could evolve? Time Reborn offers a radical new approach to cosmology that embraces the reality of time and opens up a whole new universe of possibilties. There are few ideas that, like our notion of time, shape our thinking about literally everything, with major implications for physics and beyond—from climate change to the economic crisis. Smolin explains in lively and lucid prose how the true nature of time impacts our world.

    In How to Create a Mind, Kurzweil presents a provocative exploration of the most important project in human-machine civilization—reverse engineering the brain to understand precisely how it works and using that knowledge to create even more intelligent machines.Kurzweil discusses how the brain functions, how the mind emerges from the brain, and the implications of vastly increasing the powers of our intelligence in addressing the world’s problems. He thoughtfully examines emotional and moral intelligence and the origins of consciousness and envisions the radical possibilities of our merging with the intelligent technology we are creating.Certain to be one of the most widely discussed and debated science books of the year, How to Create a Mind is sure to take its place alongside Kurzweil’s previous classics which include Fantastic Voyage: Live Long Enough to Live Forever and The Age of Spiritual Machines.

    Although Einstein understood that black holes were mathematical solutions to his equations, he never accepted their physical reality--a viewpoint many shared. This all changed in the 1960s and 1970s, when a deeper conceptual understanding of black holes developed just as new observations revealed the existence of quasars and X-ray binary star systems, whose mysterious properties could be explained by the presence of black holes. Black holes have since been the subject of intense research--and the physics governing how they behave and affect their surroundings is stranger and more mind-bending than any fiction.After introducing the basics of the special and general theories of relativity, this book describes black holes both as astrophysical objects and theoretical "laboratories" in which physicists can test their understanding of gravitational, quantum, and thermal physics. From Schwarzschild black holes to rotating and colliding black holes, and from gravitational radiation to Hawking radiation and information loss, Steven Gubser and Frans Pretorius use creative thought experiments and analogies to explain their subject accessibly. They also describe the decades-long quest to observe the universe in gravitational waves, which recently resulted in the LIGO observatories' detection of the distinctive gravitational wave "chirp" of two colliding black holes--the first direct observation of black holes' existence.The Little Book of Black Holes takes readers deep into the mysterious heart of the subject, offering rare clarity of insight into the physics that makes black holes simple yet destructive manifestations of geometric destiny.

    Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical―that what is commonly called mathematics is simply later deductions from logical premises.His ideas have had a profound influence on twentieth-century work on logic and the foundations of mathematics.

    From the transistor to the laser, it s hard to find an aspect of modern life that hasn t been touched by Bell Labs. Why did so many transformative ideas come from Bell Labs? In "The Idea Factory," Jon Gertner traces the origins of some of the twentieth century s most important inventions and delivers a riveting and heretofore untold chapter of American history. At its heart this is a story about the life and work of a small group of brilliant and eccentric men Mervin Kelly, Bill Shockley, Claude Shannon, John Pierce, and Bill Baker who spent their careers at Bell Labs. Their job was to research and develop the future of communications. Small-town boys, childhood hobbyists, oddballs: they give the lie to the idea that Bell Labs was a grim cathedral of top-down command and control.Gertner brings to life the powerful alchemy of the forces at work behind Bell Labs inventions, teasing out the intersections between science, business, and society. He distills the lessons that abide: how to recruit and nurture young talent; how to organize and lead fractious employees; how to find solutions to the most stubbornly vexing problems; how to transform a scientific discovery into a marketable product, then make it even better, cheaper, or both. Today, when the drive to invent has become a mantra, Bell Labs offers us a way to enrich our understanding of the challenges and solutions to technological innovation. Here, after all, was where the foundational ideas on the management of innovation were born. "The Idea Factory" is the story of the origins of modern communications and the beginnings of the information age a deeply human story of extraordinary men who were given extraordinary means time, space, funds, and access to one another and edged the world into a new dimension."

    How to make sense of them? The answer lies in mathematical modeling, a science with applications in a host of biological systems. Soccermatics brings the two together in a fascinating, mind-bending synthesis.What's the similarity between an ant colony and Total Football, Dutch style? How is the Barcelona midfield linked geometrically? And how can we relate the mechanics of a Mexican Wave to the singing of cicadas in an Australian valley? Welcome to the world of mathematical modeling, expressed brilliantly by David Sumpter through the prism of soccer. Soccer is indeed more than a game and this book is packed with game theory. After reading it, you will forever watch the game with new eyes.

    Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.