From the early Greek influences to the Middle Ages and the Renaissance to the end of the 19th century, trace the fascinating foundation of mathematics as it developed through the ages. Aristotle, Galileo, Kepler, Newton: you know the names. Now here's what they really did, and the effect their discoveries had on our culture, all explained in a way the layperson can understand. Begin with the basis of arithmetic (Plato and the introduction of geometry), and discover why the use of Arabic numerals was critical to the development of both commerce and science. The development of calculus made space travel a reality, while the abacus prefigured the computer. The greats examined in depth include Leonardo da Vinci, a brilliant mathematician as well as artist; Pascal, who laid out the theory of probabilities; and Fermat, whose intriguing theory has only recently been solved.

    Earth, born in a nuclear explosion, is a radioactive planet; without radiation, life would not exist. And while radiation can be dangerous, it is also deeply misunderstood and often mistakenly feared. Now Robert Peter Gale, M.D,—the doctor to whom concerned governments turned in the wake of the Chernobyl and Fukushima disasters—in collaboration with medical writer Eric Lax draws on an exceptional depth of knowledge to correct myths and establish facts. Exploring what have become trigger words for anxiety—nuclear energy and nuclear weapons, uranium, plutonium, iodine-131, mammogram, X-ray, CT scan, threats to the food chain—the authors demystify the science and dangers of radiation, and examine its myriad benefits, from safely sterilizing our food to the relatively low-risk fuel alternative of nuclear energy. This is the book for all readers who have asked themselves questions such as: What kinds of radiation, and what degree of exposure, cause cancer? What aftereffects have nuclear accidents and bombs had? Does radiation increase the likelihood of birth defects? And how does radiation work? Hugely illuminating, Radiation is the definitive road map to our post-Chernobyl, post-Fukushima world.

    He was trying to find an equation that explained all physical reality - a theory of everything. He failed, but others have taken up the challenge in a remarkable quest that is shedding light on unsuspected secrets of the cosmos.Experimental physicist and award-winning educator Dr. Don Lincoln of the Fermi National Accelerator Laboratory takes you on this exciting journey in The Theory of Everything: The Quest to Explain All Reality. Suitable for the intellectually curious at all levels and assuming no background beyond basic high-school math, these 24 half-hour lectures cover recent developments at the forefront of particle physics and cosmology, while delving into the history of the centuries-long search for this holy grail of science.You trace the dream of a theory of everything through Newton, Maxwell, Einstein, Bohr, Schrödinger, Feynman, Gell-Mann, Weinberg, and other great physicists, charting their progress toward an all-embracing, unifying theory. Their resulting equations are the masterpieces of physics, which Dr. Lincoln explains in fascinating and accessible detail. Studying them is like touring a museum of great works of art - works that are progressing toward an ultimate, as-yet-unfinished masterpiece.Listening Length: 12 hours and 21 minutes

    Written not from a post-crisis perspective – but from a preventative point of view – this book traces the development of financial derivatives from bonds to credit default swaps, and shows how mathematical formulas went beyond pricing to expand their use to the point where they dwarfed the real economy. You'll learn how the deadly allure of their ice-cold beauty has misled generations of economists and investors, and how continued reliance on these formulas can either assist future economic development, or send the global economy into the financial equivalent of a cardiac arrest. Rather than rehash tales of post-crisis fallout, this book focuses on preventing the next one. By exploring the heart of the shadow economy, you'll be better prepared to ride the rough waves of finance into the turbulent future. Delve into one of the world's least-understood but highest-impact industries Understand the key principles of quantitative finance and the evolution of the field Learn what quantitative finance has become, and how it affects us all Discover how the industry's next steps dictate the economy's future How do you create a quadrillion dollars out of nothing, blow it away and leave a hole so large that even years of "quantitative easing" can't fill it – and then go back to doing the same thing? Even amidst global recovery, the financial system still has the potential to seize up at any moment. The Money Formula explores the how and why of financial disaster, what must happen to prevent the next one.

    The first half of the book deals with classical physical optics; the second principally with the quantum nature of light. Chapters 1 and 2 treat the propagation of light waves, including the concepts of phase and group velocities, and the vectorial nature of light. Chapter 3 applies the concepts of partial coherence and coherence length to the study of interference, and Chapter 4 takes up multiple-beam interference and includes Fabry-Perot interferometry and multilayer-film theory. Diffraction and holography are the subjects of Chapter 5, and the propagation of light in material media (including crystal and nonlinear optics) are central to Chapter 6. Chapters 7 and 8 introduce the quantum theory of light and elementary optical spectra, and Chapter 9 explores the theory of light amplification and lasers. Chapter 10 briefly outlines ray optics in order to introduce students to the matrix method for treating optical systems and to apply the ray matrix to the study of laser resonators.Many applications of the laser to the study of optics are integrated throughout the text. The author assumes students have had an intermediate course in electricity and magnetism and some advanced mathematics beyond calculus. For classroom use, a list of problems is included at the end of each chapter, with selected answers at the end of the book.

    This book will offer students a broad outline of essential mathematics and will help to fill in the gaps in their knowledge. The author explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The topics include linear algebra, vector calculus, differential and analytical geometry, real analysis, point-set topology, probability, complex analysis, set theory, algorithms, and more. An annotated bibliography offers a guide to further reading and to more rigorous foundations.

      “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.”—Nina MacLaughlin, Boston Globe “Engaging, eminently readable . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.”—Judith Goodstein, American Scientist  Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.

    Never before in history have we been able to acquire, record, communicate, and use information in so many different forms. Never before have we had access to such vast quantities of data of every kind. This revolution goes far beyond the limitless content that fills our lives, because information also underlies our understanding of ourselves, the natural world, and the universe. It is the key that unites fields as different as linguistics, cryptography, neuroscience, genetics, economics, and quantum mechanics. And the fact that information bears no necessary connection to meaning makes it a profound puzzle that people with a passion for philosophy have pondered for centuries.Table of ContentsLECTURE 1The Transformability of Information 4LECTURE 2Computation and Logic Gates 17LECTURE 3Measuring Information 26LECTURE 4Entropy and the Average Surprise 34LECTURE 5Data Compression and Prefix-Free Codes 44LECTURE 6Encoding Images and Sounds 57LECTURE 7Noise and Channel Capacity 69LECTURE 8Error-Correcting Codes 82LECTURE 9Signals and Bandwidth 94LECTURE 10Cryptography and Key Entropy 110LECTURE 11Cryptanalysis and Unraveling the Enigma 119LECTURE 12Unbreakable Codes and Public Keys 130LECTURE 13What Genetic Information Can Do 140LECTURE 14Life’s Origins and DNA Computing 152LECTURE 15Neural Codes in the Brain 169LECTURE 16Entropy and Microstate Information 185LECTURE 17Erasure Cost and Reversible Computing 198LECTURE 18Horse Races and Stock Markets 213LECTURE 19Turing Machines and Algorithmic Information 226LECTURE 20Uncomputable Functions and Incompleteness 239LECTURE 21Qubits and Quantum Information 253LECTURE 22Quantum Cryptography via Entanglement 266LECTURE 23It from Bit: Physics from Information 281LECTURE 24The Meaning of Information 293

    But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    Craig has done a great work, and it is marvelous that now the philosophy of religion is engaging with the philosophy of science to the great benefit of both.--John R. LucasFellow of Merton College, Oxford University Time and Eternity offers a comprehensive discussion of the problems in the concepts of time and eternity on the basis of an extraordinary familiarity with a vast number of recent contributions to this issue from scientists and philosophers. The argument is subtle and precise. Particularly important are the sections on the impact of the different versions of relativity theory on the concept of time.... The book offers a plausible argument for a realistic conception of temporal process and for God's involvement in the temporal distinctions and processes because of His presence in His creation.--Wolfhart PannenbergProfessor of Systematic TheologyLudwig Maximilliens Universitaet-Muenchen, Germany As a scientist doing theoretical research in gravitational physics and quantum cosmology, I found Dr. Craig's thoughtful book highly interesting. He has carefully given arguments defending several different viewpoints for each of the many issues about time that he discusses, followed by critiques in which he emphasizes his own opinion. Reading Time and Eternity has forced me to develop better arguments for my own opinions (which differ considerably from Craig's).... I am certain that Time and Eternity will also stimulate your thinking about this fascinating subject and your appreciation for the God who created time as part of the marvelous universe He has given us.--Don N. PageProfessor of Physics and Fellow of the Cosmology and Gravitation Program of the Canadian Institute for Advanced ResearchUniversity of Alberta, Edmonton, Alberta, Canada William Lane Craig is one the leading philosophers of religion and one of the leading philosophers of time. In this book, he combines his expertise in these areas to produce an original, erudite, and accessible theory of time and God that will be of great interest to both the general public and scholars. It is a rewarding experience to read through this brilliant and well-researched book by one of the most learned and creative thinkers of our era.--Quentin SmithProfessor of Philosophy, Western Michigan University In Time and Eternity, William Lane Craig defends the remarkable conclusion that "God is timeless without creation and temporal since creation." Craig argues his case philosophically by carefully weighing evidence for and against divine temporality and personhood in light of dynamic versus static theories of time and their warrants, in turn, in a Lorentzian interpretation of special relativity and an objective, mind-independent theory of becoming, including fascinating excursions into Big Bang cosmology and the philosophy of mathematics. As the latest in his series of ground-breaking books, Time and Eternity summarizes and extends Craig's previous technical arguments and conveys them to a more general audience. It is a must-read for anyone seriously interested in the problem of time and eternity in Christian philosophy.--Robert RussellProfessor of Theology and ScienceGraduate Theological Union, Berkeley, Calif. The nature of time is a continuing source of puzzlement both to science and in everyday life. It is also an important issue in theological understandings of the nature of God. In this interesting book, Professor Craig tackles this complex set of topics in a clear way. His discussion of the interrelated scientific, philosophical, and theological issues clears up many previous misconceptions and proposes a plausible understanding of the relation of God to time and eternity that many will find helpful.--George EllisProfessor of Mathematics and Applied MathematicsUniversity of Capetown

    But what about relativity? Physics professor Chad Orzel and his inquisitive canine companion, Emmy, tackle the concepts of general relativity in this irresistible introduction to Einstein’s physics. Through armchair ”and sometimes passenger-seat” conversations with Emmy about the relative speeds of dog and cat motion or the logistics of squirrel-chasing, Orzel translates complex Einsteinian ideas, i.e., ”the slowing of time for a moving observer, the shrinking of moving objects, the effects of gravity on light and time, black holes, the Big Bang, and of course, E=mc2” into examples simple enough for a dog to understand.A lively romp through one of the great theories of modern physics, How to Teach Relativity to Your Dog will teach you everything you ever wanted to know about space, time, and anything else you might have slept through in high school physics class.

    In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

    String Theory For Dummies offers an accessible introduction to this highly mathematical "theory of everything," which posits ten or more dimensions in an attempt to explain the basic nature of matter and energy. Written for both students and people interested in science, this guide explains concepts, discusses the string theory's hypotheses and predictions, and presents the math in an approachable manner. It features in-depth examples and an easy-to-understand style so that readers can understand this controversial, cutting-edge theory.

    Emphasizes the applications of theory, and contains new material on particle physics, electron-positron annihilation in solids and the Mossbauer effect. Includes new appendices on such topics as crystallography, Fourier Integral Description of a Wave Group, and Time-Independent Perturbation Theory.

    In question-and-answer format, Polkinghorne and his collaborator Nicholas Beale offer their highly informed opinions about some of the most frequently asked of these questions. Readers can follow their own paths through the book, selecting questions that interest them and looking at the additional material if they choose. This unique book will help Christians clarify their beliefs regarding difficult issues and better face challenges--from within and from others--to their faith.