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.

    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.

    You'll find out how to unknot your DNA, how to count like a supercomputer and how to become famous for solving mathematics' most challenging problem.

    Victor Stenger reviews the key developments in the history of science that led to the current consensus view of astrophysicists, taking pains to explain essential concepts and discoveries in accessible terminology. The author shows that science’s emerging understanding of the multiverse—consisting of trillions upon trillions of galaxies—is fully explicable in naturalistic terms with no need for supernatural forces to explain its origin or ongoing existence. How can conceptions of God, traditional or otherwise, be squared with this new worldview? The author shows how long-held beliefs will need to undergo major revision or otherwise face eventual extinction.

    How to Destroy the Universe embraces thirty-five key physics ideas in a way that anyone can understand. Read this book and you will discover how to reverse the effects of global warming and fend off killer asteroids. You'll learn essential survival skills such as how to live through a lightning strike and how to fall into a black hole without being turned into spaghetti. You'll discover how to turn lead into gold, how to travel to the centre of the Earth and how to use physics to predict the stock market. How to Destroy the Universe will make you see the world through fresh eyes.

    His illuminating explanation is addressed to the person who wants to understand the place of mathematics in modern civilization but who has been intimidated by its supposed difficulty. Mathematics is the language of size, shape, and order—a language Hogben shows one can both master and enjoy.

    The objective here is to explain science in a simple, attractive and fun form that is open to all.The first axiom of this approach was set out as follows: “We believe in the magic of science. We hope to show you that sci-ence is not a secret art, accessible only to a dedicated few. It involves learning about nature and society, and aspects of our existence which affect us all, and which we should all therefore have the chance to understand. We shall interpret science for those who might not speak its language fluently, but want to understand its meaning. We don’t teach, we just tell stories about the beginnings of science, the natural phenomena and the underlying principles through which they occur, and the lives of the people who discovered them.”The aim of the writings collected in this series is to present some key scientific events, ideas and personalities in the form of short stories that are easy and fun to read. Scientific and philo-sophical concepts are explained in a way that anyone may under-stand. Each story may be read separately, but at the same time they all band together to form a wide-ranging introduction to the history of science and areas of contemporary scientific research, as well as some of the recurring problems science has encountered in history and the philosophical dilemmas it raises today.Review“If I were the only survivor on a remote island and all I had with me were this book, a Swiss army knife and a bottle, I would throw the bottle into the sea with the note: ‘Don’t worry, I have everything I need.’”— Ciril Horjak, alias Dr. Horowitz, a comic artist“The writing is understandable, but never simplistic. Instructive, but never patronizing. Straightforward, but never trivial. In-depth, but never too intense.”— Ali Žerdin, editor at Delo, the main Slovenian newspaper“Does science think? Heidegger once answered this question with a decisive No. The writings on modern science skillfully penned by Sašo Dolenc, these small stories about big stories, quickly convince us that the contrary is true. Not only does science think in hundreds of unexpected ways, its intellectual challenges and insights are an inexhaustible source of inspiration and entertainment. The clarity of thought and the lucidity of its style make this book accessible to anyone … in the finest tradition of popularizing science, its achievements, dilemmas and predicaments.”— Mladen Dolar, philosopher and author of A Voice and Nothing More“Sašo Dolenc is undoubtedly one of our most successful authors in the field of popular science, possessing the ability to explain complex scientific achievements to a broader audience in a clear and captivating way while remaining precise and scientific. His collection of articles is of particular importance because it encompasses all areas of modern science in an unassuming, almost light-hearted manner.”— Boštjan Žekš, physicist and former president of the Slovenian Academy of Sciences and Arts

    In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Godel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

    The Clay Mathematics Institute is offering a prize of $1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem.The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from some very deep--and often very mystifying--mathematical ideas. Using only basic algebra and calculus while presenting numerous eye-opening examples, Ash and Gross make these ideas accessible to general readers, and in the process venture to the very frontiers of modern mathematics. Along the way, they give an informative and entertaining introduction to some of the most profound discoveries of the last three centuries in algebraic geometry, abstract algebra, and number theory. They demonstrate how mathematics grows more abstract to tackle ever more challenging problems, and how each new generation of mathematicians builds on the accomplishments of those who preceded them. Ash and Gross fully explain how the Birch and Swinnerton-Dyer Conjecture sheds light on the number theory of elliptic curves, and how it provides a beautiful and startling connection between two very different objects arising from an elliptic curve, one based on calculus, the other on algebra.

    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.

    This ideal guide shows us how mathematics can illuminate the human condition.

    Readers will progress from building a basic physics engine to creating intelligent moving objects and complex systems, setting the foundation for further experiments in generative design. Subjects covered include forces, trigonometry, fractals, cellular automata, self-organization, and genetic algorithms. The book's examples are written in Processing, an open-source language and development environment built on top of the Java programming language. On the book's website (http://www.natureofcode.com), the examples run in the browser via Processing's JavaScript mode.

    She draws on conversations with hundreds of the world's top scientists and on her own work as a Pulitzer Prize-winning writer for the New York Times to create a thoroughly entertaining guide to scientific literacy. Angier's gifts are on full display in The Canon, an ebullient celebration of science that stands to become a classic. The Canon is vital reading for anyone who wants to understand the great issues of our time -- from stem cells and bird flu to evolution and global warming. And it's for every parent who has ever panicked when a child asked how the earth was formed or what electricity is. Angier's sparkling prose and memorable metaphors bring the science to life, reigniting our own childhood delight in discovering how the world works. "Of course you should know about science," writes Angier, "for the same reason Dr. Seuss counsels his readers to sing with a Ying or play Ring the Gack: These things are fun and fun is good." The Canon is a joyride through the major scientific disciplines: physics, chemistry, biology, geology, and astronomy. Along the way, we learn what is actually happening when our ice cream melts or our coffee gets cold, what our liver cells do when we eat a caramel, why the horse is an example of evolution at work, and how we're all really made of stardust. It's Lewis Carroll meets Lewis Thomas -- a book that will enrapture, inspire, and enlighten.

    Petr Beckmann holds up this mirror, giving the background of the times when pi made progress -- and also when it did not, because science was being stifled by militarism or religious fanaticism.

    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