In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy.In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

    Featuring many striking photos, this Very Short Introduction offers a fascinating portrait of the unique world of each planet as well as an illuminating discussion of moons, asteroids, and Trans-Neptunian objects. Leading planetary scientist David A. Rothery, who has chaired the European Space Agency's Mercury surface and composition working group since 2007, gives a stimulating overview of the origin, nature, and evolution of our Solar System, including the controversial issues of what qualifies as a planet, and what conditions are required for a planetary body to support life. He explains how the surfaces of planets and moons have been sculpted by geology, weather, and impacts by meteors and asteroids. Rothery shows how our knowledge has advanced over the centuries, and how it has expanded at a dramatic rate in recent years, going far beyond our Solar System to explore planets orbiting distant stars.

    The authors introduce the general reader to some of the most important basic findings, concepts, and procedures of evolutionary biology, as it has developed since the first publications of Darwin and Wallace on the subject, over 140 years ago. They show how evolution provides a unifying set of principles for the whole of biology and sheds light on the relation of human beings to the universe and each other.

    In this Very Short Introduction, Michael Newman seeks to place the idea of socialism in a modern context for today's readers. He explains socialist ideas in the framework of its historical evolution, from the French Revolution to the present day, and examines practical attempts to implement socialism.Not just another history of socialist ideas, this book aims for a different approach that looks at practice as well as theory--centering on the contrast between Communism and Social Democracy. The relationship between socialism and notions of democracy, freedom, and equality is also discussed. Newman brings the subject entirely up to date by tackling contemporary forms of socialism. While the book's focus is on Europe and the Soviet Union, it is set in a broader geographical context. Newman's fresh approach to the subject enables the reader to re-evaluate socialism.About the Series: Combining authority with wit, accessibility, and style, Very Short Introductions offer an introduction to some of life's most interesting topics. Written by experts for the newcomer, they demonstrate the finest contemporary thinking about the central problems and issues in hundreds of key topics, from philosophy to Freud, quantum theory to Islam.

    Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack ofadvanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicatedwith the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

    Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life. In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!

    Why do we recognize patterns? Is there such a thing as positive stress? Are we genetically programmed to be in conflict with each other? Those are just some of the 150 questions that the world's best scientific minds answer with elegant simplicity.With contributions from Jared Diamond, Richard Dawkins, Nassim Taleb, Brian Eno, Steven Pinker, and more, everything is explained in fun, uncomplicated terms that make the most complex concepts easy to comprehend.

    Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.

    Suppose, instead of thinking about organisms using genes to reproduce themselves, as we had since Mendel's work was rediscovered, we turn it around and imagine that "our" genes build and maintain us in order to make more genes. That simple reversal seems to answer many puzzlers which had stumped scientists for years, and we haven't thought of evolution in the same way since. Drawing fascinating examples from every field of biology, he paved the way for a serious re-evaluation of evolution. He also introduced the concept of self-reproducing ideas, or memes, which (seemingly) use humans exclusively for their propagation. If we are puppets, he says, at least we can try to understand our strings.

    “I walk with a new spring in my step and I look at life through physics-colored eyes,” wrote one such fan. When Lewin’s lectures were made available online, he became an instant YouTube celebrity, and The New York Times declared, “Walter Lewin delivers his lectures with the panache of Julia Child bringing French cooking to amateurs and the zany theatricality of YouTube’s greatest hits.” For more than thirty years as a beloved professor at the Massachusetts Institute of Technology, Lewin honed his singular craft of making physics not only accessible but truly fun, whether putting his head in the path of a wrecking ball, supercharging himself with three hundred thousand volts of electricity, or demonstrating why the sky is blue and why clouds are white. Now, as Carl Sagan did for astronomy and Brian Green did for cosmology, Lewin takes readers on a marvelous journey in For the Love of Physics, opening our eyes as never before to the amazing beauty and power with which physics can reveal the hidden workings of the world all around us. “I introduce people to their own world,” writes Lewin, “the world they live in and are familiar with but don’t approach like a physicist—yet.” Could it be true that we are shorter standing up than lying down? Why can we snorkel no deeper than about one foot below the surface? Why are the colors of a rainbow always in the same order, and would it be possible to put our hand out and touch one? Whether introducing why the air smells so fresh after a lightning storm, why we briefly lose (and gain) weight when we ride in an elevator, or what the big bang would have sounded like had anyone existed to hear it, Lewin never ceases to surprise and delight with the extraordinary ability of physics to answer even the most elusive questions. Recounting his own exciting discoveries as a pioneer in the field of X-ray astronomy—arriving at MIT right at the start of an astonishing revolution in astronomy—he also brings to life the power of physics to reach into the vastness of space and unveil exotic uncharted territories, from the marvels of a supernova explosion in the Large Magellanic Cloud to the unseeable depths of black holes. “For me,” Lewin writes, “physics is a way of seeing—the spectacular and the mundane, the immense and the minute—as a beautiful, thrillingly interwoven whole.” His wonderfully inventive and vivid ways of introducing us to the revelations of physics impart to us a new appreciation of the remarkable beauty and intricate harmonies of the forces that govern our lives.

    Drawing on studies of social class, crime and deviance, work in bureaucracies, and changes in religious and political organizations, this Very Short Introduction explores the tension between the individual's role in society and society's role in shaping the individual, and demonstrates the value of sociology as a perspective for understanding the modern world.

    Focusing on the leading figures of existentialism, including Sartre, Nietzsche, Heidegger, Kierkegaard, de Beauvoir, Merleau-Ponty, and Camus, Thomas Flynn offers a concise account of existentialism, explaining the key themes of individuality, free will, and personal responsibility, which marked the movement as a way of life, not just a way of thinking. Flynn sets the philosophy of existentialism in context, from the early phenomenologists, to its rise in the 40's and 50's, and the connections with National Socialism, Communism, and Feminism. He identifies the original definition of "existentialism," which tends to be obscured by misappropriation, and highlights how the philosophy is still relevant in our world today.

    Witty and accessible, Paul Lockhart’s controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever.Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann’s School in Brooklyn, New York.

    "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.

    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.