Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics.Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts.Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved.Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

    The book has been stimulating creativity in millions of readers, translated into eleven languages, and used in seminars around the world.Now Roger von Oech's fully illustrated and updated volume is filled with even more provocative puzzles, anecdotes, exercises, metaphors, cartoons, questions, quotations, stories, and tips designed to systematically break through your mental blocks and unlock your mind for creative thinking. This new edition will attract an entire new generation of readers with updated and mind-stretching material.

    An invaluable resource for any manager or professional, this book offers a collection of proven, practical methods for simplifying any problem and making faster, better decisions every time.

    Now, in his first book, written more than two decades after the web was created, Lanier offers this provocative and cautionary look at the way it is transforming our lives for better and for worse.The current design and function of the web have become so familiar that it is easy to forget that they grew out of programming decisions made decades ago. The web’s first designers made crucial choices (such as making one’s presence anonymous) that have had enormous—and often unintended—consequences. What’s more, these designs quickly became “locked in,” a permanent part of the web’s very structure. Lanier discusses the technical and cultural problems that can grow out of poorly considered digital design and warns that our financial markets and sites like Wikipedia, Facebook, and Twitter are elevating the “wisdom” of mobs and computer algorithms over the intelligence and judgment of individuals. Lanier also shows:How 1960s antigovernment paranoia influenced the design of the online world and enabled trolling and trivialization in online discourseHow file sharing is killing the artistic middle class;How a belief in a technological “rapture” motivates some of the most influential technologistsWhy a new humanistic technology is necessary. Controversial and fascinating, You Are Not a Gadget is a deeply felt defense of the individual from an author uniquely qualified to comment on the way technology interacts with our culture.

    The long-anticipated revision of this best-selling text offers the most comprehensive, up-to-date introduction to the theory and practice of artificial intelligence. *NEW-Nontechnical learning material-Accompanies each part of the book. *NEW-The Internet as a sample application for intelligent systems-Added in several places including logical agents, planning, and natural language. *NEW-Increased coverage of material - Includes expanded coverage of: default reasoning and truth maintenance systems, including multi-agent/distributed AI and game theory; probabilistic approaches to learning including EM; more detailed descriptions of probabilistic inference algorithms. *NEW-Updated and expanded exercises-75% of the exercises are revised, with 100 new exercises. *NEW-On-line Java software. *Makes it easy for students to do projects on the web using intelligent agents. *A unified, agent-based approach to AI-Organizes the material around the task of building intelligent agents. *Comprehensive, up-to-date coverage-Includes a unified view of the field organized around the rational decision making pa

    It had a decisive impact on twentieth century philosophy and is one of few works to have influenced both continental and analytic philosophy.This is the first time both volumes have been available in paperback. They include a new introduction by Dermot Moran, placing the Investigations in historical context and bringing out their contemporary philosophical importance.These editions include a new preface by Sir Michael Dummett.

    Philosophy starts with questions, but attempts at answers are just as important, and these answers require reasoned argument. Cutting through dense philosophical prose, 100 famous and influential arguments are presented in their essence, with premises, conclusions and logical form plainly identified. Key quotations provide a sense of style and approach. Just the Arguments is an invaluable one-stop argument shop. A concise, formally structured summation of 100 of the most important arguments in Western philosophy The first book of its kind to present the most important and influential philosophical arguments in a clear premise/conclusion format, the language that philosophers use and students are expected to know Offers succinct expositions of key philosophical arguments without bogging them down in commentary Translates difficult texts to core arguments Designed to provides a quick and compact reference to everything from Aquinas' "Five Ways" to prove the existence of God, to the metaphysical possibilities of a zombie world

     If you've been on social media lately, or turned on your TV, you may have noticed a lot of dumb ideas floating around."We know when history will repeat and when it won't.""We can tell the difference between evidence and coincidences.""The simplest explanation is usually true."Wrong, wrong, and dangerous!If we're not careful, loserthink would have us believe that every Trump supporter is a bigoted racist, addicts should be responsible for fixing the opioid epidemic, and that your relationship fell apart simply because you chewed with your mouth open.Even the smartest people can slip into loserthink's seductive grasp. This book will teach you how to spot and avoid it--and will give you scripts to respond when hollow arguments are being brandished against you, whether by well-intentioned friends, strangers on the internet, or political pundits. You'll also learn how to spot the underlying causes of loserthink, like the inability to get ego out of your decisions, thinking with words instead of reasons, failing to imagine alternative explanations, and making too much of coincidences.Your bubble of reality doesn't have to be a prison. This book will show you how to break free--and, what's more, to be among the most perceptive and respected thinkers in every conversation.

    Mirroring his theory, Minsky boldly casts The Society of Mind as an intellectual puzzle whose pieces are assembled along the way. Each chapter -- on a self-contained page -- corresponds to a piece in the puzzle. As the pages turn, a unified theory of the mind emerges, like a mosaic. Ingenious, amusing, and easy to read, The Society of Mind is an adventure in imagination.

    Some modern thinkers view it as the first work dealing with the social sciences of sociology, demography, and cultural history. The Muqaddimah also deals with Islamic theology, historiography, the philosophy of history, economics, political theory, and ecology. It has also been described as an early representative of social Darwinism.

    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!

    He solidified his standing as the nation's foremost political forecaster with his near perfect prediction of the 2012 election. Silver is the founder and editor in chief of FiveThirtyEight.com. Drawing on his own groundbreaking work, Silver examines the world of prediction, investigating how we can distinguish a true signal from a universe of noisy data. Most predictions fail, often at great cost to society, because most of us have a poor understanding of probability and uncertainty. Both experts and laypeople mistake more confident predictions for more accurate ones. But overconfidence is often the reason for failure. If our appreciation of uncertainty improves, our predictions can get better too. This is the "prediction paradox": The more humility we have about our ability to make predictions, the more successful we can be in planning for the future.In keeping with his own aim to seek truth from data, Silver visits the most successful forecasters in a range of areas, from hurricanes to baseball, from the poker table to the stock market, from Capitol Hill to the NBA. He explains and evaluates how these forecasters think and what bonds they share. What lies behind their success? Are they good-or just lucky? What patterns have they unraveled? And are their forecasts really right? He explores unanticipated commonalities and exposes unexpected juxtapositions. And sometimes, it is not so much how good a prediction is in an absolute sense that matters but how good it is relative to the competition. In other cases, prediction is still a very rudimentary-and dangerous-science.Silver observes that the most accurate forecasters tend to have a superior command of probability, and they tend to be both humble and hardworking. They distinguish the predictable from the unpredictable, and they notice a thousand little details that lead them closer to the truth. Because of their appreciation of probability, they can distinguish the signal from the noise.

    Good stories are full of life: they engage our emotions and have subtlety and nuance, but they lack rigor and the truths they tell are elusive and subject to debate. As ways of understanding the world around us, numbers and stories seem almost completely incompatible. Once Upon a Number shows that stories and numbers aren't as different as you might imagine, and in fact they have surprising and fascinating connections. The concepts of logic and probability both grew out of intuitive ideas about how certain situations would play out. Now, logicians are inventing ways to deal with real world situations by mathematical means -- by acknowledging, for instance, that items that are mathematically interchangeable may not be interchangeable in a story. And complexity theory looks at both number strings and narrative strings in remarkably similar terms. Throughout, renowned author John Paulos mixes numbers and narratives in his own delightful style. Along with lucid accounts of cutting-edge information theory we get hilarious anecdotes and jokes; instructions for running a truly impressive pyramid scam; a freewheeling conversation between Groucho Marx and Bertrand Russell (while they're stuck in an elevator together); explanations of why the statistical evidence against OJ Simpson was overwhelming beyond doubt and how the Unabomber's thinking shows signs of mathematical training; and dozens of other treats. This is another winner from America's favorite mathematician.

    In Feeling Good, eminent psychiatrist, David D. Burns, M.D., outlines the remarkable, scientifically proven techniques that will immediately lift your spirits and help you develop a positive outlook on life. Now, in this updated edition, Dr. Burns adds an All-New Consumer′s Guide To Anti-depressant Drugs as well as a new introduction to help answer your questions about the many options available for treating depression.- Recognise what causes your mood swings- Nip negative feelings in the bud- Deal with guilt- Handle hostility and criticism- Overcome addiction to love and approval- Build self-esteem- Feel good everyday

    But our fears are misplaced, according to Yale early childhood expert Erika Christakis. Children are powerful and inventive; and the tools to reimagine their learning environment are right in front of our eyes.           Children are hardwired to learn in any setting, but they don’t get the support they need when “learning” is defined by strict lessons and dodgy metrics that devalue children’s intelligence while placing unfit requirements on their developing brains. We have confused schooling with learning, and we have altered the very habitat young children occupy. The race for successful outcomes has blinded us to how young children actually process the world, acquire skills, and grow, says Christakis, who powerfully defends the preschool years as a life stage of inherent value and not merely as preparation for a demanding or uncertain future.           In her pathbreaking book, Christakis explores what it’s like to be a young child in America today, in a world designed by and for adults. With school-testing mandates run amok, playfulness squeezed, and young children increasingly pathologized for old-fashioned behaviors like daydreaming and clumsiness, it’s easy to miss what’s important about the crucial years of three to six, and the kind of guidance preschoolers really need. Christakis provides a forensic and far-reaching analysis of today’s whole system of early learning, exploring pedagogy, history, science, policy, and politics. She also offers a wealth of proven strategies about what to do to reimagine the learning environment to suit the child’s real, but often invisible, needs. The ideas range from accommodating children’s sense of time, to decluttering classrooms, to learning how to better observe and listen as children express themselves in pictures and words.           With her strong foundation in the study of child development and early education and her own in-the-trenches classroom experience, Christakis peels back the mystery of early childhood, revealing a place that’s rich with possibility. Her message is energizing and reassuring: Parents have more power (and more knowledge) than they think they do, and young children are inherently creative and will flourish, if we can learn new ways to support them and restore their vital learning habitat.