Remarkable for his range of thought and his mastery of treatment, Archimedes addressed such topics as the famous problems of the ratio of the areas of a cylinder and an inscribed sphere; the measurement of a circle; the properties of conoids, spheroids, and spirals; and the quadrature of the parabola. This edition offers an informative introduction with many valuable insights into the ancient mathematician's life and thought as well as the views of his contemporaries. Modern mathematicians, physicists, science historians, and logicians will find this volume a source of timeless fascination.

    Beginning near the speed of light and proceeding to explorations of space-time and curved spaces, "Introducing Relativity" plots a visually accessible course through the thought experiments that have given shape to contemporary physics. Scientists from Newton to Hawking add their unique contributions to this story, as we encounter Einstein's astounding vision of gravity as the curvature of space-time and arrive at the breathtakingly beautiful field equations. Einstein's legacy is reviewed in the most advanced frontiers of physics today - black holes, gravitational waves, the accelerating universe and string theory. This is a superlative, fascinating graphic account of Einstein's strange world and how his legacy has been built upon since.

    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.

    Wolfram lets the world see his work in A New Kind of Science, a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modeling complex systems. On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple nonmathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day. Wolfram wrote the book in a distinct style meant to make it easy to read, even for nontechies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton

    Dark matter. These strange and invisible substances don't just sound mysterious: their unexpected appearance in the cosmic census is upending long-held notions about the nature of the Universe. Astronomers have long known that the Universe is expanding, but everything they could see indicated that gravity should be slowing this spread. Instead, it appears that the Universe is accelerating its expansion and that something stronger than gravity--dark energy--is at work. In Einstein's Telescope Evalyn Gates, a University of Chicago astrophysicist, transports us to the edge of contemporary science to explore the revolutionary tool that unlocks the secrets of these little-understood cosmic constituents. Based on Einstein's theory of general relativity, gravitational lensing, or "Einstein's Telescope," is enabling new discoveries that are taking us toward the next revolution in scientific thinking--one that may change forever our notions of where the Universe came from and where it is going.

    The issues that John Henry Newman raised—the place of religion and moral values in the university setting, the competing claims of liberal and professional education, the character of the academic community, the cultural role of literature, the relation of religion and science--have provoked discussion from Newman's time to our own.

    A truly landmark study, The Hour of Our Death reveals a pattern of gradually developing evolutionary stages in our perceptions of life in relation to death, each stage representing a virtual redefinition of human nature. Starting at the very foundations of Western culture, the eminent historian Phillipe Aries shows how, from Graeco-Roman times through the first ten centuries of the Common Era, death was too common to be frightening; each life was quietly subordinated to the community, which paid its respects and then moved on. Aries identifies the first major shift in attitude with the turn of the eleventh century when a sense of individuality began to rise and with it, profound consequences: death no longer meant merely the weakening of community, but rather the destruction of self. Hence the growing fear of the afterlife, new conceptions of the Last Judgment, and the first attempts (by Masses and other rituals) to guarantee a better life in the next world. In the 1500s attention shifted from the demise of the self to that of the loved one (as family supplants community), and by the nineteenth century death comes to be viewed as simply a staging post toward reunion in the hereafter. Finally, Aries shows why death has become such an unendurable truth in our own century--how it has been nearly banished from our daily lives--and points out what may be done to re-tame this secret terror. The richness of Aries's source material and investigative work is breathtaking. While exploring everything from churches, religious rituals, and graveyards (with their often macabre headstones and monuments), to wills and testaments, love letters, literature, paintings, diaries, town plans, crime and sanitation reports, and grave robbing complaints, Aries ranges across Europe to Russia on the one hand and to England and America on the other. As he sorts out the tangled mysteries of our accumulated terrors and beliefs, we come to understand the history--indeed the pathology--of our intellectual and psychological tensions in the face of death.

    Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.

    Though he is still best known for this finding, his partnership with his sister Caroline yielded groundbreaking work, including techniques that remain in use today. The duo pioneered comprehensive surveys of the night sky, carefully categorizing every visible object in the void. Caroline wrote an influential catalogue of nebulae, and William discovered infrared radiation. Celebrated science writer Michael Lemonick guides readers through the depths of the solar system and into his protagonists' private lives: William developed bizarre theories about inhabitants of the sun; he procured an unheard-of salary for Caroline even while haggling with King George III over the funding for an enormous, forty-foot telescope; the siblings feuded over William's marriage and eventually reconciled. Erudite and accessible, The Georgian Star is a lively portrait of the pair who invented modern astronomy.

      In the past few years, a handful of scientists have been in a race to explain a disturbing aspect of our universe: only 4 percent of it consists of the matter that makes up you, me, our books, and every planet, star, and galaxy. The rest—96 percent of the universe—is completely unknown.   Richard Panek tells the dramatic story of how scientists reached this conclusion, and what they’re doing to find this "dark" matter and an even more bizarre substance called dark energy. Based on in-depth, on-site reporting and hundreds of interviews—with everyone from Berkeley’s feisty Saul Perlmutter and Johns Hopkins’s meticulous Adam Riess to the quietly revolutionary Vera Rubin—the book offers an intimate portrait of the bitter rivalries and fruitful collaborations, the eureka moments and blind alleys, that have fueled their search, redefined science, and reinvented the universe.

    Psychology is the only branch of learning in which I am particularly versed. To the psychologist the religious propensities of man must be at least as interesting as any other of the facts pertaining to his mental constitution. It would seem, therefore, as a psychologist, the natural thing for me would be to invite you to a descriptive survey of those religious propensities." When William James went to the University of Edinburgh in 1901 to deliver a series of lectures on "natural religion," he defined religion as "the feelings, acts, and experiences of individual men in their solitude, so far as they apprehend themselves to stand in relation to whatever they may consider the divine." Considering religion, then, not as it is defined by--or takes place in--the churches, but as it is felt in everyday life, he undertook a project that, upon completion, stands not only as one of the most important texts on psychology ever written, not only as a vitally serious contemplation of spirituality, but for many critics one of the best works of nonfiction written in the 20th century. Reading The Varieties of Religious Experience, it is easy to see why. Applying his analytic clarity to religious accounts from a variety of sources, James elaborates a pluralistic framework in which "the divine can mean no single quality, it must mean a group of qualities, by being champions of which in alternation, different men may all find worthy missions." It's an intellectual call for serious religious tolerance--indeed, respect--the vitality of which has not diminished through the subsequent decades.

    Language is informal, examples are vivid and lively, and the perspectivie is fresh. Based on lectures delivered to engineering students, this work will also be valued by scientists, engineers, technicians, businessmen, anyone facing energy challenges of the future.

    Crease tells the stories behind ten of the greatest equations in human history. Was Nobel laureate Richard Feynman really joking when he called Maxwell's electromagnetic equations the most significant event of the nineteenth century? How did Newton's law of gravitation influence young revolutionaries? Why has Euler's formula been called "God's equation," and why did a mysterious ecoterrorist make it his calling card? What role do betrayal, insanity, and suicide play in the second law of thermodynamics?The Great Equations tells the stories of how these equations were discovered, revealing the personal struggles of their ingenious originators. From "1 + 1 = 2" to Heisenberg's uncertainty principle, Crease locates these equations in the panoramic sweep of Western history, showing how they are as integral to their time and place of creation as are great works of art.

    In The Constants of Nature, Cambridge Professor and bestselling author John D.Barrow takes us on an exploration of these governing principles. Drawing on physicists such as Einstein and Planck, Barrow illustrates with stunning clarity our dependence on the steadfastness of these principles. But he also suggests that the basic forces may have been radically different during the universe’s infancy, and suggests that they may continue a deeply hidden evolution. Perhaps most tantalizingly, Barrow theorizes about the realities that might one day be found in a universe with different parameters than our own.

    These sections together make an appropriate one-term advanced/graduate level course (mathematical prerequisites: vector analysis and simple partial-differential equations). The book is printed to make it easy for readers to identify these sections.• The remaining Track 2 material provides a wealth of advanced topics instructors can draw from to flesh out a two-term course, with Track 1 sections serving as prerequisites.