The complexity of nature's shapes differs in kind, not merely degree, from that of the shapes of ordinary geometry, the geometry of fractal shapes.Now that the field has expanded greatly with many active researchers, Mandelbrot presents the definitive overview of the origins of his ideas and their new applications. The Fractal Geometry of Nature is based on his highly acclaimed earlier work, but has much broader and deeper coverage and more extensive illustrations.

    In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions.

    However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers attain human intelligence. Gödel, Escher, Bach is a wonderful exploration of fascinating ideas at the heart of cognitive science: meaning, reduction, recursion, and much more.

    Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. Features include: The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated.Carefully chosen advanced topics that can be skipped in a standard one-semester course, but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence.An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text, DasGupta also offers a Solutions Manual, which is available on the Online Learning Center.Algorithms is an outstanding undergraduate text, equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel, it is a joy to read. Tim Roughgarden Stanford University

    How does Jane Goodall’s relationship with her dog Rusty inform her thinking about our relationship to other species? Which time and place would Jared Diamond most prefer to live in, in light of his work on the role of chance in history? What does driving a sports car have to do with Steven Weinberg’s quest for the “theory of everything”? Physicist and journalist Stefan Klein’s intimate conversations with nineteen of the world’s best-known scientists (including three Nobel Laureates) let us listen in as they talk about their paradigm-changing work—and how it is deeply rooted in their daily lives. • Cosmologist Martin Rees on the beginning and end of the world • Evolutionary biologist Richard Dawkins on egoism and selflessness • Neuroscientist V. S. Ramachandran on consciousness • Molecular biologist Elizabeth Blackburn on aging • Philosopher Peter Singer on morality • Physician and social scientist Nicholas Christakis on human relationships • Biochemist Craig Venter on the human genome • Chemist and poet Roald Hoffmann on beauty

    Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery. Dr. Michael Guillen is Instructor of Physics and Mathematics in the Core Curriculum Program at Harvard University.

    Seasoned researchers and educators Gregory G. Colomb and Joseph M. Williams present an updated third edition of their classic handbook, whose first and second editions were written in collaboration with the late Wayne C. Booth. The Craft of Research explains how to build an argument that motivates readers to accept a claim; how to anticipate the reservations of readers and to respond to them appropriately; and how to create introductions and conclusions that answer that most demanding question, “So what?” The third edition includes an expanded discussion of the essential early stages of a research task: planning and drafting a paper. The authors have revised and fully updated their section on electronic research, emphasizing the need to distinguish between trustworthy sources (such as those found in libraries) and less reliable sources found with a quick Web search. A chapter on warrants has also been thoroughly reviewed to make this difficult subject easier for researchers Throughout, the authors have preserved the amiable tone, the reliable voice, and the sense of directness that have made this book indispensable for anyone undertaking a research project.

    But ask what it means, and the result will be a brawl. For a century, most physicists have followed Niels Bohr's Copenhagen interpretation and dismissed questions about the reality underlying quantum physics as meaningless. A mishmash of solipsism and poor reasoning, Copenhagen endured, as Bohr's students vigorously protected his legacy, and the physics community favored practical experiments over philosophical arguments. As a result, questioning the status quo long meant professional ruin. And yet, from the 1920s to today, physicists like John Bell, David Bohm, and Hugh Everett persisted in seeking the true meaning of quantum mechanics. What Is Real? is the gripping story of this battle of ideas and of the courageous scientists who dared to stand up for truth.

    It may hide additional dimensions of space other than the familier three we recognize. There might even be another universe adjacent to ours, invisible and unattainable . . . for now.Warped Passages is a brilliantly readable and altogether exhilarating journey that tracks the arc of discovery from early twentieth-century physics to the razor's edge of modern scientific theory. One of the world's leading theoretical physicists, Lisa Randall provides astonishing scientific possibilities that, until recently, were restricted to the realm of science fiction. Unraveling the twisted threads of the most current debates on relativity, quantum mechanics, and gravity, she explores some of the most fundamental questions posed by Nature—taking us into the warped, hidden dimensions underpinning the universe we live in, demystifying the science of the myriad worlds that may exist just beyond our own.

    Everyday experience cannot prepare us for the sub-atomic world, where quantum effects become all-important. Here, particles can look like waves, and vice versa; electrons seem to lose their identity and instead take on a shifting, unpredictable appearance that depends on how they are being observed; and a single photon may sometimes behave as if it could be in two places at once. In the world of quantum mechanics, uncertainty and ambiguity become not just unavoidable, but essential ingredients of science -- a development so disturbing that to Einstein "it was as if God were playing dice with the universe." And there is no one better able to explain the quantum revolution as it approaches the century mark than David Lindley. He brings the quantum revolution full circle, showing how the familiar and trustworthy reality of the world around us is actually a consequence of the ineffable uncertainty of the subatomic quantum world -- the world we can't see.

    Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

    In the book, Sagan explores 15 billion years of cosmic evolution and the development of science and civilization. Cosmos traces the origins of knowledge and the scientific method, mixing science and philosophy, and speculates to the future of science. The book also discusses the underlying premises of science by providing biographical anecdotes about many prominent scientists throughout history, placing their contributions into the broader context of the development of modern science.The book covers a broad range of topics, comprising Sagan's reflections on anthropological, cosmological, biological, historical, and astronomical matters from antiquity to contemporary times. Sagan reiterates his position on extraterrestrial life—that the magnitude of the universe permits the existence of thousands of alien civilizations, but no credible evidence exists to demonstrate that such life has ever visited earth.

    Book by Weinberg, Robert A.

    They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide--more than 104,000 copies were bought of the prior edition--includes problems and examples using graphing calculators..

    Learn You a Haskell for Great Good! introduces programmers familiar with imperative languages (such as C++, Java, or Python) to the unique aspects of functional programming. Packed with jokes, pop culture references, and the author's own hilarious artwork, Learn You a Haskell for Great Good! eases the learning curve of this complex language, and is a perfect starting point for any programmer looking to expand his or her horizons. The well-known web tutorial on which this book is based is widely regarded as the best way for beginners to learn Haskell, and receives over 30,000 unique visitors monthly.