According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

    This is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities.

    Contains 640 problems including solutions; additional practice problems with answers; explanations of complex variable theory; coverage of applications of complex variables in engineering, physics, and elsewhere, with accompanying sample problems and solutions.

    The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist)"No matter how gently one introduces students to the concept of Dirac's bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that there is nothing to be frightened of." (Physics Bulletin)Reviews of the Second Edition:"This massive text of 700 and odd pages has indeed an excellent get-up, is very verbal and expressive, and has extensively worked out calculational details---all just right for a first course. The style is conversational, more like a corridor talk or lecture notes, though arranged as a text. ... It would be particularly useful to beginning students and those in allied areas like quantum chemistry." (Mathematical Reviews)R. Shankar has introduced major additions and updated key presentations in this second edition of Principles of Quantum Mechanics. New features of this innovative text include an entirely rewritten mathematical introduction, a discussion of Time-reversal invariance, and extensive coverage of a variety of path integrals and their applications. Additional highlights include:- Clear, accessible treatment of underlying mathematics- A review of Newtonian, Lagrangian, and Hamiltonian mechanics- Student understanding of quantum theory is enhanced by separate treatment of mathematical theorems and physical postulates- Unsurpassed coverage of path integrals and their relevance in contemporary physicsThe requisite text for advanced undergraduate- and graduate-level students, Principles of Quantum Mechanics, Second Edition is fully referenced and is supported by many exercises and solutions. The book's self-contained chapters also make it suitable for independent study as well as for courses in applied disciplines.

    joyfully shows you how to make nature's numbers dance."--Bill Nye (the science guy)The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples-from ice-cream scoops and poker hands to measuring mountains and making magic squares-this book revels in key mathematical fields including arithmetic, algebra, geometry, and calculus, plus Fibonacci numbers, infinity, and, of course, mathematical magic tricks. Known throughout the world as the "mathemagician," Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand for math fan and math-phobic alike."A positively joyful exploration of mathematics."-Publishers Weekly, starred review"Each [trick] is more dazzling than the last."-Physics World

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    But for the past thirty-five years of his professional life, he has also been active as an investigator of the paranormal, occult, and supernatural claims that have impressed the thinking of the public for a generation: ESP, psychokinesis, psychic detectives, levitation, psychic surgery, UFOs, dowsing, astrology, and many others. Those of us unable to discriminate between geniune scientific research and the pseudoscientific nonsense that has resulted in fantastic theories and fancies have long needed James Randi and Flim-Flam!In this book, Randi explores and exposes what he believes to be the outrageous deception that has been promoted widely in the media. Unafraid to call researchers to account for their failures and impostures, Randi tells us that we have been badly served by scientists who have failed to follow the procedures required by their training and traditions. Here he shows us how what he views as sloppy research has been followed by rationalizations of evident failures, and we see these errors and misrepresentations clearly pointed out. Mr. Randi provides us with a compelling and convincing document that will certainly startle and enlighten all who read it.

    New to this third edition are expanded coverage of such important topics as surface boundary interfaces, improved discussions of such physical and mathematical laws as the Law of Biot and Savart and the Euler Momentum Integral. A very important new section on Computational Fluid Dynamics has been added for the very first time to this edition. Expanded and improved end-of-chapter problems will facilitate the teaching experience for students and instrutors alike. This book remains one of the most comprehensive and useful texts on fluid mechanics available today, with applications going from engineering to geophysics, and beyond to biology and general science. * Ample, useful end-of-chapter problems.* Excellent Coverage of Computational Fluid Dynamics.* Coverage of Turbulent Flows.* Solutions Manual available.

    From the sudden expansion of a cloud of gas to the cooling of hot metal--everything is moved or restrained by four simple laws. Written by Peter Atkins, one of the world's leading authorities on thermodynamics, this powerful and compact introduction explains what these four laws are and how they work, using accessible language and virtually no mathematics. Guiding the reader a step at a time, Atkins begins with Zeroth (so named because the first two laws were well established before scientists realized that a third law, relating to temperature, should precede them--hence the jocular name zeroth), and proceeds through the First, Second, and Third Laws, offering a clear account of concepts such as the availability of work and the conservation of energy. Atkins ranges from the fascinating theory of entropy (revealing how its unstoppable rise constitutes the engine of the universe), through the concept of free energy, and to the brink, and then beyond the brink, of absolute zero. About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    Plait created his popular web site: http://www.badastronomy.com/index.html, to debunk bad astronomy in popular culture. This website proved popular, which led to this first book by Plait, that carries on from the website and in a detailed and clear fashion criticises and disproves popular myths and misconceptions relating to astronomy, and promotes science as a means of explaining the skies. The work describes 24 common astronomical fallacies, including the beliefs that the Coriolis effect determines the direction that water drains in a bathtub, and that planetary alignments can cause disaster on Earth. The author sharply and convincingly dismisses astrology, creationism, and UFO sightings, and explains the principles behind basic general concepts (the Big Bang, why the sky is blue, etc.).

    Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.

    In Dataclysm, Christian Rudder uses it to show us who we truly are.   For centuries, we’ve relied on polling or small-scale lab experiments to study human behavior. Today, a new approach is possible. As we live more of our lives online, researchers can finally observe us directly, in vast numbers, and without filters. Data scientists have become the new demographers.   In this daring and original book, Rudder explains how Facebook "likes" can predict, with surprising accuracy, a person’s sexual orientation and even intelligence; how attractive women receive exponentially more interview requests; and why you must have haters to be hot. He charts the rise and fall of America’s most reviled word through Google Search and examines the new dynamics of collaborative rage on Twitter. He shows how people express themselves, both privately and publicly. What is the least Asian thing you can say? Do people bathe more in Vermont or New Jersey? What do black women think about Simon & Garfunkel? (Hint: they don’t think about Simon & Garfunkel.) Rudder also traces human migration over time, showing how groups of people move from certain small towns to the same big cities across the globe. And he grapples with the challenge of maintaining privacy in a world where these explorations are possible.   Visually arresting and full of wit and insight, Dataclysm is a new way of seeing ourselves—a brilliant alchemy, in which math is made human and numbers become the narrative of our time.

    However, once their predictions were compared to the results of experiments in the real world, it became clear that the principles of classical physics and mechanics were far from capable of explaining phenomena on the atomic scale. With this realization came the advent of quantum physics, one of the most important intellectual movements in human history. Today, quantum physics is everywhere: it explains how our computers work, how lasers transmit information across the Internet, and allows scientists to predict accurately the behavior of nearly every particle in nature. Its application continues to be fundamental in the investigation of the most expansive questions related to our world and the universe.However, while the field and principles of quantum physics are known to have nearly limitless applications, the fundamental reasons why this is the case are far less understood. In Quantum Physics: What Everyone Needs to Know, quantum physicist Michael G. Raymer distills the basic principles of such an abstract field, and addresses the many ways quantum physics is a key factor in today's science and beyond. The book tackles questions as broad as the meaning of quantum entanglement and as specific and timely as why governments worldwide are spending billions of dollars developing quantum technology research. Raymer's list of topics is diverse, and showcases the sheer range of questions and ideas in which quantum physics is involved. From applications like data encryption and quantum computing to principles and concepts like "quantum nonlocality" and Heisenberg's uncertainty principle, Quantum Physics: What Everyone Needs to Know is a wide-reaching introduction to a nearly ubiquitous scientific topic.

    Essentially, you are estimating a probability, but then updating that estimate based on other things that you know. This book is designed to give you an intuitive understanding of how to use Bayes Theorem. It starts with the definition of what Bayes Theorem is, but the focus of the book is on providing examples that you can follow and duplicate. Most of the examples are calculated in Excel, which is useful for updating probability if you have dozens or hundreds of data points to roll in.

    Composed of such luminaries as Kurt Gödel and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science.Exact Thinking in Demented Times tells the often outrageous, sometimes tragic, and never boring stories of the men who transformed scientific thought. A revealing work of history, this landmark book pays tribute to those who dared to reinvent knowledge from the ground up.