Heath's translation of the thirteen books of Euclid's Elements. In keeping with Green Lion's design commitment, diagrams have been placed on every spread for convenient reference while working through the proofs; running heads on every page indicate both Euclid's book number and proposition numbers for that page; and adequate space for notes is allowed between propositions and around diagrams. The all-new index has built into it a glossary of Euclid's Greek terms.Heath's translation has stood the test of time, and, as one done by a renowned scholar of ancient mathematics, it can be relied upon not to have inadvertantly introduced modern concepts or nomenclature. We have excised the voluminous historical and scholarly commentary that swells the Dover edition to three volumes and impedes classroom use of the original text. The single volume is not only more convenient, but less expensive as well.

    These vignettes serve as springboards to many telling perspectives: simple arithmetic puts life-long habits in a dubious new light; higher dimensional geometry helps us see that we're all rather peculiar; nonlinear dynamics explains the narcissism of small differences cascading into very different siblings; logarithms and exponentials yield insight on why we tend to become bored and jaded as we age; and there are tricks and jokes, probability and coincidences, and much more.For fans of Paulos or newcomers to his work, this witty commentary on his life--and yours--is fascinating reading.From the Trade Paperback edition.

    Tobias Dantzig shows that the development of math—from the invention of counting to the discovery of infinity—is a profoundly human story that progressed by “trying and erring, by groping and stumbling.” He shows how commerce, war, and religion led to advances in math, and he recounts the stories of individuals whose breakthroughs expanded the concept of number and created the mathematics that we know today.

    It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.

    You experience it passing every day when you watch clocks tick, bread toast, and children grow. But most physicists see things differently, from Newton to Einstein to today’s quantum theorists. For them, time isn’t real. You may think you experience time passing, but they say it’s just an illusion.Lee Smolin, author of the controversial bestseller The Trouble with Physics, argues this limited notion of time is holding physics back. It’s time for a major revolution in scientific thought. The reality of time could be the key to the next big breakthrough in theoretical physics.What if the laws of physics themselves were not timeless? What if they could evolve? Time Reborn offers a radical new approach to cosmology that embraces the reality of time and opens up a whole new universe of possibilties. There are few ideas that, like our notion of time, shape our thinking about literally everything, with major implications for physics and beyond—from climate change to the economic crisis. Smolin explains in lively and lucid prose how the true nature of time impacts our world.

    Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria. Worse, these "too good to not be true" theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.

    Many of these students are extremely intelligent and hardworking, but even the best will, at some point, struggle with the demands of making the transition to advanced mathematics. Some have difficulty adjusting to independent study and to learning from lectures. Other struggles, however, are more fundamental: the mathematics shifts in focus from calculation to proof, so students are expected to interact with it in different ways. These changes need not be mysterious - mathematics education research has revealed many insights into the adjustments that are necessary - but they are not obvious and they do need explaining.This no-nonsense book translates these research-based insights into practical advice for a student audience. It covers every aspect of studying for a mathematics degree, from the most abstract intellectual challenges to the everyday business of interacting with lecturers and making good use of study time. Part 1 provides an in-depth discussion of advanced mathematical thinking, and explains how a student will need to adapt and extend their existing skills in order to develop a good understanding of undergraduate mathematics. Part 2 covers study skills as these relate to the demands of a mathematics degree. It suggests practical approaches to learning from lectures and to studying for examinations while also allowing time for a fulfilling all-round university experience.The first subject-specific guide for students, this friendly, practical text will be essential reading for anyone studying mathematics at university.

    It covers all relevant areas, including molecular spectroscopy, electronic structure computations, molecular beam methods and time-resolved measurements of chemical systems.

    Today Nash's beautiful math has become a universal language for research in the social sciences and has infiltrated the realms of evolutionary biology, neuroscience, and even quantum physics. John Nash won the 1994 Nobel Prize in economics for pioneering research published in the 1950s on a new branch of mathematics known as game theory. At the time of Nash's early work, game theory was briefly popular among some mathematicians and Cold War analysts. But it remained obscure until the 1970s when evolutionary biologists began applying it to their work. In the 1980s economists began to embrace game theory. Since then it has found an ever expanding repertoire of applications among a wide range of scientific disciplines. Today neuroscientists peer into game players' brains, anthropologists play games with people from primitive cultures, biologists use games to explain the evolution of human language, and mathematicians exploit games to better understand social networks. A common thread connecting much of this research is its relevance to the ancient quest for a science of human social behavior, or a Code of Nature, in the spirit of the fictional science of psychohistory described in the famous Foundation novels by the late Isaac Asimov. In A Beautiful Math, acclaimed science writer Tom Siegfried describes how game theory links the life sciences, social sciences, and physical sciences in a way that may bring Asimov's dream closer to reality.

    Bardon employs helpful illustrations and keeps technical language to a minimum in bringing the resources of over 2500 years of philosophy and science to bear on some of humanity's most fundamental and enduring questions.

    What do these have to do with the birth of a universe and with your need for meaning? Everything, as you’re about to see. How does the cosmos do something it has long been thought only gods could achieve? How does an inanimate universe generate stunning new forms and unbelievable new powers without a creator? How does the cosmos create? That’s the central question of this book, which finds clues in strange places. Why A does not equal A. Why one plus one does not equal two. How the Greeks used kickballs to reinvent the universe. And the reason that Polish-born Benoît Mandelbrot—the father of fractal geometry—rebelled against his uncle.You’ll take a scientific expedition into the secret heart of a cosmos you’ve never seen. Not just any cosmos. An electrifyingly inventive cosmos. An obsessive-compulsive cosmos. A driven, ambitious cosmos. A cosmos of colossal shocks. A cosmos of screaming, stunning surprise. A cosmos that breaks five of science’s most sacred laws. Yes, five. And you’ll be rewarded with author Howard Bloom’s provocative new theory of the beginning, middle, and end of the universe—the Bloom toroidal model, also known as the big bagel theory—which explains two of the biggest mysteries in physics: dark energy and why, if antimatter and matter are created in equal amounts, there is so little antimatter in this universe.Called "truly awesome" by Nobel Prize–winner Dudley Herschbach, The God Problem will pull you in with the irresistible attraction of a black hole and spit you out again enlightened with the force of a big bang. Be prepared to have your mind blown.

    When the boy's eyes were healed they removed the bandages and, waving a hand in front of the child's physically perfect eyes, asked him what he saw. "I don't know," was his only reply. What he saw was only a varying brightness in front of him. However, when allowed to touch the hand as it began to move, he cried out in a voice of triumph, "It's moving!" He could feel it move, but he still needed laboriously to learn to see it move. Light and eyes were not enough to grant him sight. How, then, do we see? What's the difference between seeing and perception? What is light?From ancient times to the present, from philosophers to quantum physicists, nothing has so perplexed, so fascinated, so captivated the mind as the elusive definition of light. In Catching the Light, Arthur Zajonc takes us on an epic journey into history, tracing how humans have endeavored to understand the phenomenon of light. Blending mythology, religion, science, literature, and painting, Zajonc reveals in poetic detail the human struggle to identify the vital connection between the outer light of nature and the inner light of the human spirit. He explains the curiousness of the Greeks' blue and green "color blindness": Odysseus gazing longingly at the "wine-dark sea"; the use of chloros (green) as the color of honey in Homer's Odessey; and Euripides' use of the color green to describe the hue of tears and blood. He demonstrates the complexity of perception through the work of Paul Cézanne--the artist standing on the bank of a river, painting the same scene over and over again, the motifs multiplying before his eyes. And Zajonc goes on to show how our quest for an understanding of light, as well as the conclusions we draw, reveals as much about the nature of our own psyche as it does about the nature of light itself. For the ancient Egyptians the nature of light was clear--it simply was the gaze of God. In the hands of the ancient Greeks, light had become the luminous inner fire whose ethereal effluence brought sight. In our contemporary world of modern quantum physics, science plays the greatest part in our theories of light's origin--from scientific perspectives such as Sir Isaac Newton's "corpuscular theory of light" and Michael Faraday's "lines of force" to such revolutionary ideas as Max Planck's "discrete motion of a pendulum" (the basis of quantum mechanics), Albert Einstein's "particles of light" and "theory of relativity," and Niels Bohr's "quantum jumps." Yet the metaphysical aspects of the scientific search, Zajonc shows, still loom large. For the physicist Richard Feynman, a quantum particle travels all paths, eventually distilling to one path whose action is least--the most beautiful path of all. Whatever light is, here is where we will find it.With rare clarity and unmatched lyricism, Zajonc illuminates the profound implications of the relationships between the multifaceted strands of human experience and scientific endeavor. A fascinating search into our deepest scientific mystery, Catching the Light is a brilliant synthesis

    Contains 640 problems including solutions; additional practice problems with answers; explanations of complex variable theory; coverage of applications of complex variables in engineering, physics, and elsewhere, with accompanying sample problems and solutions.

    The book begins with an excerpt from Maxwell Bennett and Peter Hacker's Philosophical Foundations of Neuroscience (Blackwell, 2003), which questions the conceptual commitments of cognitive neuroscientists. Their position is then criticized by Daniel Dennett and John Searle, two philosophers who have written extensively on the subject, and Bennett and Hacker in turn respond.Their impassioned debate encompasses a wide range of central themes: the nature of consciousness, the bearer and location of psychological attributes, the intelligibility of so-called brain maps and representations, the notion of qualia, the coherence of the notion of an intentional stance, and the relationships between mind, brain, and body. Clearly argued and thoroughly engaging, the authors present fundamentally different conceptions of philosophical method, cognitive-neuroscientific explanation, and human nature, and their exchange will appeal to anyone interested in the relation of mind to brain, of psychology to neuroscience, of causal to rational explanation, and of consciousness to self-consciousness.In his conclusion Daniel Robinson (member of the philosophy faculty at Oxford University and Distinguished Professor Emeritus at Georgetown University) explains why this confrontation is so crucial to the understanding of neuroscientific research. The project of cognitive neuroscience, he asserts, depends on the incorporation of human nature into the framework of science itself. In Robinson's estimation, Dennett and Searle fail to support this undertaking; Bennett and Hacker suggest that the project itself might be based on a conceptual mistake. Exciting and challenging, Neuroscience and Philosophy is an exceptional introduction to the philosophical problems raised by cognitive neuroscience.

    It contains many puzzles and their solutions and aims to attract many readers in an age where computer science, logic, and mathematics are becoming increasingly important and popular.