They speak of it in awed terms and consider it to be an even more difficult problem than Fermat's last theorem, which was finally proven by Andrew Wiles in 1995.In The Riemann Hypothesis, acclaimed author Karl Sabbagh interviews some of the world's finest mathematicians who have spent their lives working on the problem--and whose approaches to meeting the challenges thrown up by the hypothesis are as diverse as their personalities.Wryly humorous, lively, accessible and comprehensive, The Riemann Hypothesis is a compelling exploration of the people who do math and the ideas that motivate them to the brink of obsession--and a profound meditation on the ultimate meaning of mathematics.

    This book is an introduction to the concepts of computer programming within the context of the visual arts. It offers a comprehensive reference and text for Processing (www.processing.org), an open-source programming language that can be used by students, artists, designers, architects, researchers, and anyone who wants to program images, animation, and interactivity. The ideas in Processing have been tested in classrooms, workshops, and arts institutions, including UCLA, Carnegie Mellon, New York University, and Harvard University. Tutorial units make up the bulk of the book and introduce the syntax and concepts of software (including variables, functions, and object-oriented programming), cover such topics as photography and drawing in relation to software, and feature many short, prototypical example programs with related images and explanations. More advanced professional projects from such domains as animation, performance, and typography are discussed in interviews with their creators. "Extensions" present concise introductions to further areas of investigation, including computer vision, sound, and electronics. Appendixes, references to additional material, and a glossary contain additional technical details. Processing can be used by reading each unit in order, or by following each category from the beginning of the book to the end. The Processing software and all of the code presented can be downloaded and run for future exploration.Includes essays by Alexander R. Galloway, Golan Levin, R. Luke DuBois, Simon Greenwold, Francis Li, and Hernando Barragan and interviews with Jared Tarbell, Martin Wattenberg, James Paterson, Erik van Blockland, Ed Burton, Josh On, Jurg Lehni, Auriea Harvey and Michael Samyn, Mathew Cullen and Grady Hall, Bob Sabiston, Jennifer Steinkamp, Ruth Jarman and Joseph Gerhardt, Sue Costabile, Chris Csikszentmihalyi, Golan Levin and Zachary Lieberman, and Mark Hansen.Casey Reas is Associate Professor in the Design Media Arts Department at the University of California, Los Angeles. Ben Fry is Nierenburg Chair of Design in the School of Design at Carnegie Mellon University, 2006-2007."

    His yearly gatherings of short and inventive problems were easily his most anticipated math columns. Loyal readers would savor the wit and elegance of his explorations in physics, probability, topology, and chess, among others. Grouped by subject and arrayed from easiest to hardest, the puzzles gathered here, which complement the lengthier, more involved problems in The Colossal Book of Mathematics, have been selected by Gardner for their illuminating; and often bewildering; solutions. Filled with over 300 illustrations, this new volume even contains nine new mathematical gems that Gardner, now ninety, has been gathering for the last decade. No amateur or expert math lover should be without this indispensable volume; a capstone to Gardner's seventy-year career.

    Organized around the central concept of a vector space, the book includes numerous physical applications in the body of the text as well as many problems of a physical nature. It is also one of the purposes of this book to introduce the physicist to the language and style of mathematics as well as the content of those particular subjects with contemporary relevance in physics.Chapters 1 and 2 are devoted to the mathematics of classical physics. Chapters 3, 4 and 5 — the backbone of the book — cover the theory of vector spaces. Chapter 6 covers analytic function theory. In chapters 7, 8, and 9 the authors take up several important techniques of theoretical physics — the Green's function method of solving differential and partial differential equations, and the theory of integral equations. Chapter 10 introduces the theory of groups. The authors have included a large selection of problems at the end of each chapter, some illustrating or extending mathematical points, others stressing physical application of techniques developed in the text.Essentially self-contained, the book assumes only the standard undergraduate preparation in physics and mathematics, i.e. intermediate mechanics, electricity and magnetism, introductory quantum mechanics, advanced calculus and differential equations. The text may be easily adapted for a one-semester course at the graduate or advanced undergraduate level.

    Explaining why the whole is sometimes smarter than the sum of its parts, Johnson presents surprising examples of feedback, self-organization, and adaptive learning. How does a lively neighborhood evolve out of a disconnected group of shopkeepers, bartenders, and real estate developers? How does a media event take on a life of its own? How will new software programs create an intelligent World Wide Web? In the coming years, the power of self-organization -- coupled with the connective technology of the Internet -- will usher in a revolution every bit as significant as the introduction of electricity. Provocative and engaging, Emergence puts you on the front lines of this exciting upheaval in science and thought.

    With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.

    Each mini-chapter adds one feature to the ray tracer, and by the end the reader can produce the image on the book cover. Details of basic ray tracing code architecture and C++ classes are given.

    It shouldn't be like that. Learning calculus without mechanics is incredibly boring. Learning mechanics without calculus is missing the point. This textbook integrates both subjects and highlights the profound connections between them.This is the deal. Give me 350 pages of your attention, and I'll teach you everything you need to know about functions, limits, derivatives, integrals, vectors, forces, and accelerations. This book is the only math book you'll need for the first semester of undergraduate studies in science.With concise, jargon-free lessons on topics in math and physics, each section covers one concept at the level required for a first-year university course. Anyone can pick up this book and become proficient in calculus and mechanics, regardless of their mathematical background.Visit http://minireference.com for more details.

    Others may think of it as the last architectural treatise, for it provides a discursive container for ideas that would otherwise be lost. Whatever genre it belongs to, SITELESS is a new kind of architecture book that seems to have come out of nowhere. Its author, a young French architect practicing in Tokyo, admits he "didn't do this out of reverence toward architecture, but rather out of a profound boredom with the discipline, as a sort of compulsive reaction." What would happen if architects liberated their minds from the constraints of site, program, and budget? he asks. The result is a book that is saturated with forms, and as free of words as any architecture book the MIT Press has ever published.The 1001 building forms in SITELESS include structural parasites, chain link towers, ball bearing floors, corrugated corners, exponential balconies, radial facades, crawling frames, forensic housing--and other architectural ideas that may require construction techniques not yet developed and a relation to gravity not yet achieved. SITELESS presents an open-ended compendium of visual ideas for the architectural imagination to draw from. The forms, drawn freehand (to avoid software-specific shapes) but from a constant viewing angle, are presented twelve to a page, with no scale, order, or end to the series. After setting down 1001 forms in siteless conditions and embryonic stages, Blanciak takes one of the forms and performs a "scale test," showing what happens when one of these fantastic ideas is subjected to the actual constraints of a site in central Tokyo. The book ends by illustrating the potential of these shapes to morph into actual building proportions.

    Encompassing a grand sweep of human history, A History of the World in 100 Objects begins with one of the earliest surviving objects made by human hands, a chopping tool from the Olduvai gorge in Africa, and ends with objects which characterise the world we live in today. Seen through MacGregor's eyes, history is a kaleidoscope - shifting, interconnected, constantly surprising, and shaping our world today in ways that most of us have never imagined. A stone pillar tells us about a great Indian emperor preaching tolerance to his people; Spanish pieces of eight tell us about the beginning of a global currency; and an early Victorian tea-set speaks to us about the impact of empire. An intellectual and visual feast, this is one of the most engrossing and unusual history books published in years. 'Brilliant, engagingly written, deeply researched' Mary Beard, Guardian 'A triumph: hugely popular, and rightly lauded as one of the most effective and intellectually ambitious initiatives in the making of 'public history' for many decades' Sunday Telegraph 'Highly intelligent, delightfully written and utterly absorbing ' Timothy Clifford, Spectator 'This is a story book, vivid and witty, shining with insights, connections, shocks and delights' Gillian Reynolds Daily Telegraph

    The work is predicated on the idea that studying mathematics can generate the same enthusiasm as playing a team sport - without necessarily being competitive.

    "One of today's best popularizers of science." —Kirkus Reviews.Loyal readers of the monthly "Universe" essays in Natural History magazine have long recognized Neil deGrasse Tyson's talent for guiding them through the mysteries of the cosmos with stunning clarity and almost childlike enthusiasm. Here, Tyson compiles his favorite essays across a myriad of cosmic topics. The title essay introduces readers to the physics of black holes by explaining the gory details of what would happen to your body if you fell into one. "Holy Wars" examines the needless friction between science and religion in the context of historical conflicts. "The Search for Life in the Universe" explores astral life from the frontiers of astrobiology. And "Hollywood Nights" assails the movie industry's feeble efforts to get its night skies right. Known for his ability to blend content, accessibility, and humor, Tyson is a natural teacher who simplifies some of the most complex concepts in astrophysics while simultaneously sharing his infectious excitement about our universe.

    In this book, William Cook takes readers on a mathematical excursion, picking up the salesman's trail in the 1800s when Irish mathematician W. R. Hamilton first defined the problem, and venturing to the furthest limits of today's state-of-the-art attempts to solve it. He also explores its many important applications, from genome sequencing and designing computer processors to arranging music and hunting for planets.In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

    New problems added throughout.

    This brief, accessible introduction describes some of the most interesting research in the field and also enables readers to implement and experiment with genetic algorithms on their own. It focuses in depth on a small set of important and interesting topics--particularly in machine learning, scientific modeling, and artificial life--and reviews a broad span of research, including the work of Mitchell and her colleagues.The descriptions of applications and modeling projects stretch beyond the strict boundaries of computer science to include dynamical systems theory, game theory, molecular biology, ecology, evolutionary biology, and population genetics, underscoring the exciting general purpose nature of genetic algorithms as search methods that can be employed across disciplines.An Introduction to Genetic Algorithms is accessible to students and researchers in any scientific discipline. It includes many thought and computer exercises that build on and reinforce the reader's understanding of the text. The first chapter introduces genetic algorithms and their terminology and describes two provocative applications in detail. The second and third chapters look at the use of genetic algorithms in machine learning (computer programs, data analysis and prediction, neural networks) and in scientific models (interactions among learning, evolution, and culture; sexual selection; ecosystems; evolutionary activity). Several approaches to the theory of genetic algorithms are discussed in depth in the fourth chapter. The fifth chapter takes up implementation, and the last chapter poses some currently unanswered questions and surveys prospects for the future of evolutionary computation.