Thoroughly updated, this edition offers new, faster techniques for solving differential equations generated by the emergence of high-speed computers.

    DLC: Quantum theory.

    In the mid-1970s, scientists began using DNA sequences to reexamine the history of all life. Perhaps the most startling discovery to come out of this new field—the study of life’s diversity and relatedness at the molecular level—is horizontal gene transfer (HGT), or the movement of genes across species lines. It turns out that HGT has been widespread and important. For instance, we now know that roughly eight percent of the human genome arrived not through traditional inheritance from directly ancestral forms, but sideways by viral infection—a type of HGT.David Quammen chronicles these discoveries through the lives of the researchers who made them—such as Carl Woese, the most important little-known biologist of the twentieth century; Lynn Margulis, the notorious maverick whose wild ideas about “mosaic” creatures proved to be true; and Tsutomu Wantanabe, who discovered that the scourge of antibiotic-resistant bacteria is a direct result of horizontal gene transfer, bringing the deep study of genome histories to bear on a global crisis in public health.

    Sympathetic yet balanced, Michael White's Isaac Newton offers a revelatory picture of Newton as a genius who stood at the point in history where magic ended and science began.

    Even when dealing with standard material, Stillwell manages to dramatize it and to make it worth rethinking. In short, his book is a splendid addition to the genre of works that build royal roads to mathematical culture for the many." (Mathematical Intelligencer)This second edition includes new chapters on Chinese and Indian number theory, on hypercomplex numbers, and on algebraic number theory. Many more exercises have been added, as well as commentary to the exercises explaining how they relate to the preceding section, and how they foreshadow later topics.

    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.

     Carl Sagan is considered one of the greatest scientific minds of our time. His remarkable ability to explain science in terms easily understandable to the layman in bestselling books such as Cosmos, The Dragons of Eden, and The Demon-Haunted World won him a Pulitzer Prize and placed him firmly next to Isaac Asimov, Stephen Jay Gould, and Oliver Sachs as one of the most important and enduring communicators of science. In December 2006 it will be the tenth anniversary of Sagan's death, and Ann Druyan, his widow and longtime collaborator, will mark the occasion by releasing Sagan's famous "Gifford Lectures in Natural Theology," The Varieties of Scientific Experience: A Personal View of the Search for God. The chance to give the Gifford Lectures is an honor reserved for the most distinguished scientists and philosophers of our civilization. In 1985, on the grand occasion of the centennial of the lectureship, Carl Sagan was invited to give them. He took the opportunity to set down in detail his thoughts on the relationship between religion and science as well as to describe his own personal search to understand the nature of the sacred in the vastness of the cosmos. The Varieties of Scientific Experience, edited, updated and with an introduction by Ann Druyan, is a bit like eavesdropping on a delightfully intimate conversation with the late great astronomer and astrophysicist. In his charmingly down-to-earth voice, Sagan easily discusses his views on topics ranging from manic depression and the possibly chemical nature of transcendance to creationism and so-called intelligent design to the likelihood of intelligent life on other planets to the likelihood of nuclear annihilation of our own to a new concept of science as "informed worship." Exhibiting a breadth of intellect nothing short of astounding, he illuminates his explanations with examples from cosmology, physics, philosophy, literature, psychology, cultural anthropology, mythology, theology, and more. Sagan's humorous, wise, and at times stunningly prophetic observations on some of the greatest mysteries of the cosmos have the invigorating effect of stimulating the intellect, exciting the imagination, and reawakening us to the grandeur of life in the cosmos.

    Simmons advocates a careful approach to the subject, covering such topics as the wave equation, Gauss's hypergeometric function, the gamma function and the basic problems of the calculus of variations in an explanatory fashions - ensuring that students fully understand and appreciate the topics.

    To shape debates over health care, energy policy, space travel, and other vital issues, ordinary citizens must engage directly with research rather than relying on pundits’ and politicians’ interpretations. Otherwise, fringe opinions that have been discredited in the scientific community can take hold in the public imagination. At the same time, scientists must understand their roles as communicators and ambassadors as well as researchers.Rees not only diagnoses this central problem but also explains how scientists and the general public can deploy a global, long-term perspective to address the new challenges we face. In the process, he reveals critical shortcomings in our current system—for example, the tendency to be overly anxious about minor hazards while underrating the risk of potential catastrophes. Offering a strikingly clear portrait of the future of science, Rees tackles such diverse topics as the human brain, the possibility that humans will colonize other planets, and the existence of extraterrestrial life in order to distinguish between what scientists can hope to discover and what will always lie beyond our grasp.A fresh perspective on science’s significance and potential, From Here to Infinity will inspire and enlighten.

    The Big Bang Cosmology is explored, looking at its observational successes in explaining the expansion of the Universe, the existence and properties of the cosmic microwave background, and the origin of light elements in the universe. Properties of the very early Universe are also covered, including the motivation for a rapid period of expansion known as cosmological inflation. The third edition brings this established undergraduate textbook up-to-date with the rapidly evolving observational situation. This fully revised edition of a bestseller takes an approach which is grounded in physics with a logical flow of chapters leading the reader from basic ideas of the expansion described by the Friedman equations to some of the more advanced ideas about the early universe. It also incorporates up-to-date results from the Planck mission, which imaged the anisotropies of the Cosmic Microwave Background radiation over the whole sky. The Advanced Topic sections present subjects with more detailed mathematical approaches to give greater depth to discussions. Student problems with hints for solving them and numerical answers are embedded in the chapters to facilitate the reader's understanding and learning. Cosmology is now part of the core in many degree programs. This current, clear and concise introductory text is relevant to a wide range of astronomy programs worldwide and is essential reading for undergraduates and Masters students, as well as anyone starting research in cosmology.

    Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations--as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.

    Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.

    Using a "physics first" approach to the subject, renowned relativist James B. Hartle provides a fluent and accessible introduction that uses a minimum of new mathematics and is illustrated with a wealth of exciting applications. KEY TOPICS: The emphasis is on the exciting phenomena of gravitational physics and the growing connection between theory and observation. The Global Positioning System, black holes, X-ray sources, pulsars, quasars, gravitational waves, the Big Bang, and the large scale structure of the universe are used to illustrate the widespread role of how general relativity describes a wealth of everyday and exotic phenomena. MARKET: For anyone interested in physics or general relativity.

    The rest is known as dark matter and dark energy, because their precise identities are unknown. "The Cosmic Cocktail" is the inside story of the epic quest to solve one of the most compelling enigmas of modern science--what is the universe made of?--told by one of today's foremost pioneers in the study of dark matter.Blending cutting-edge science with her own behind-the-scenes insights as a leading researcher in the field, acclaimed theoretical physicist Katherine Freese recounts the hunt for dark matter, from the discoveries of visionary scientists like Fritz Zwicky--the Swiss astronomer who coined the term "dark matter" in 1933--to the deluge of data today from underground laboratories, satellites in space, and the Large Hadron Collider. Theorists contend that dark matter consists of fundamental particles known as WIMPs, or weakly interacting massive particles. Billions of them pass through our bodies every second without us even realizing it, yet their gravitational pull is capable of whirling stars and gas at breakneck speeds around the centers of galaxies, and bending light from distant bright objects. Freese describes the larger-than-life characters and clashing personalities behind the race to identify these elusive particles.Many cosmologists believe we are on the verge of solving the mystery. "The Cosmic Cocktail" provides the foundation needed to fully fathom this epochal moment in humankind's quest to understand the universe.

    As he wanders the land year upon year, Raymo gathers the revelations embedded in the geological and cultural history of this wild and ancient place. "When I called out for the Absolute, I was answered by the wind," Raymo writes. "If it was God's voice in the wind, then I heard it." In poetic prose grounded in a mind trained to discover fact, Honey from Stone enters the wonder of the material world in search of our deepest nature.