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.

    We secretly want to know: could it happen to me? Amanda Montell’s argument is that, on some level, it already has . . .Our culture tends to provide pretty flimsy answers to questions of cult influence, mostly having to do with vague talk of “brainwashing.” But the true answer has nothing to do with freaky mind-control wizardry or Kool-Aid. In Cultish, Montell argues that the key to manufacturing intense ideology, community, and us/them attitudes all comes down to language. In both positive ways and shadowy ones, cultish language is something we hear—and are influenced by—every single day.Through juicy storytelling and cutting original research, Montell exposes the verbal elements that make a wide spectrum of communities “cultish,” revealing how they affect followers of groups as notorious as Heaven’s Gate, but also how they pervade our modern start-ups, Peloton leaderboards, and Instagram feeds. Incisive and darkly funny, this enrapturing take on the curious social science of power and belief will make you hear the fanatical language of “cultish” everywhere.

    D. Williams wrote this entertaining, witty introduction for the nonscientist, game theory was still a somewhat mysterious subject familiar to very few scientists beyond those researchers, like himself, working for the military. Now, over thirty years after its original publication as a Rand Corporation research study, his light-hearted though thoroughly effective primer is the recognized classic introduction to an increasingly applicable discipline. Used by amateurs, professionals, and students throughout the world in the classroom, on the job, and for personal amusement, the book has been through ten printings, and has been translated into at least five languages (including Russian and Japanese).Revised, updated, and available for the first time in an inexpensive paperback edition, The Compleat Strategyst is a highly entertaining text essential for anyone interested in this provocative and engaging area of modern mathematics. In fully illustrated chapters complete with everyday examples and word problems, Williams offers readers a working understanding of the possible methods for selecting strategies in a variety of situations, simple to complex. With just a basic understanding of arithmetic, anyone can grasp all necessary aspects of two-, three-, four-, and larger strategy games with two or more sets of inimical interests and a limitless array of zero-sum payoffs.As research and study continues not only in this new discipline but in the related areas of statistics, probability and behavioral science, understanding of games, decision making, and the development of strategies will be increasingly important. In the areas of economics, sociology, politics, and the military, game theory is sure to have an even wider impact. For students and amateurs fascinated by game theory's implications there is no better, immediately applicable, or more entertaining introduction to the subject than this engaging text by the late J. D. Williams, Professor of Mathematics at Princeton University and a member of the Research Council of The Rand Corporation.

    From the movement of flocks of birds to the Internet, environmental sustainability, and market regulation, the study and understanding of complex non-linear systems has become highly influential over the last 30 years.In this Very Short Introduction, one of the leading figures in the field, John Holland, introduces the key elements and conceptual framework of complexity. From complex physical systems such as fluid flow and the difficulties of predicting weather, to complex adaptive systems such as the highly diverse and interdependent ecosystems of rainforests, he combines simple, well-known examples -- Adam Smith's pin factory, Darwin's comet orchid, and Simon's 'watchmaker' -- with an account of the approaches, involving agents and urn models, taken by complexity theory.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

    Writing with dazzling elegance and clarity, he retraces the steps that have led modern scientists from relativity and quantum mechanics to the notion of superstrings and the idea that our universe may coexist with others.But Weinberg asks as many questions as he answers, among them: Why does each explanation of the way nature works point to the other, deeper explanations? Why are the best theories not only logical but beautiful? And what implications will a final theory have for our philosophy and religious faith?Intellectually daring, rich in anecdote and aphorism, Dreams of a Final Theory launches us into a new cosmos and helps us make sense of what we find there.“This splendid book is as good reading about physics and physicists as this reviewer can name…clear, honest, and brilliantly instructive.”—Philip Morrison, Scientific American

    But have you ever felt like you are too busy "discerning" to actually decide? True decision-making is more than just thinking about something . . . decisions involve taking action.YouTube star, Fr. Mike Schmitz, gives you the tools to decide what to do with your life today, tomorrow, and in the future with clarity and confidence. In this little book you will learn to:• know when God is speaking,• how to recognize the "signs,"• and make wise decisions for your life.Fate is when you're fixed; you don't have a choice. Destiny is your destination . . . Know your destiny.

    Why do living things and physical phenomena take the forms they do? Analyzing the mathematical and physical aspects of biological processes, this historic work, first published in 1917, has become renowned as well for the poetry of is descriptions.

    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.

    Individual chapters discuss the representativeness and availability heuristics, problems in judging covariation and control, overconfidence, multistage inference, social perception, medical diagnosis, risk perception, and methods for correcting and improving judgments under uncertainty. About half of the chapters are edited versions of classic articles; the remaining chapters are newly written for this book. Most review multiple studies or entire subareas of research and application rather than describing single experimental studies. This book will be useful to a wide range of students and researchers, as well as to decision makers seeking to gain insight into their judgments and to improve them.

    Si todos debemos movernos para sobrevivir, vale la pena preguntarse: ¿qué factores de nuestro entorno nos impulsan a movernos y cuáles, por el contrario, nos detienen? ¿Por qué algunas personas tienen la oportunidad de moverse hacia donde quieren y otras no? ¿Por qué ciertas sociedades evolucionan y otras no? Para responder a estas interrogantes, los autores del libro estudiaron los códigos culturales y el comportamiento Bio-Lógico de 71 países para desarrollar un índice de que permite medir la movilidad social dentro de estas sociedades.Andrés Roemer y Clotaire Rapaille señalan que las culturas más exitosas son aquellas que han sabido preservar los mejores aspectos de su tradición, al mismo tiempo que han estado dispuestas a innovar y buscar nuevos horizontes. Se trata de sociedades abiertas al cambio y sin temor al statu quo. Otra clave del éxito evolutivo de las sociedades es el equilibrio entre el aspecto biológico (determinado por cuatro factores: supervivencia, sexo, seguridad y superación) y el aspecto cultural. El reto, concluyen los autores, es aprender a armonizar nuestros instintos (nuestro cerebro reptiliano) con nuestras emociones (nuestro cerebro límbico) y nuestra lógica (el neocórtex).ENGLISH DESCRIPTION If we all know we must move to survive, shouldn’t we ask ourselves which factors in our environment propel us and which halt us? Why do certain societies evolve while others don’t? In this book, Andrés Roemer and Clotaire Rapaille point out that the most successful cultures are those that are not afraid of the status quo: they have learned to preserve the best qualities of their traditions while being open to innovation and to uncovering new horizons. Another key to the success of these societies is the equilibrium between biological and the cultural aspects. The challenge is to harmonize our instincts, our emotions, and our logic.

    Composed of such luminaries as Kurt Gödel and Rudolf Carnap, and stimulated by the works of Ludwig Wittgenstein and Karl Popper, the Vienna Circle left an indelible mark on science.Exact Thinking in Demented Times tells the often outrageous, sometimes tragic, and never boring stories of the men who transformed scientific thought. A revealing work of history, this landmark book pays tribute to those who dared to reinvent knowledge from the ground up.

    . . brilliantly integrat[es] science, literature, and pop culture into elegant and insightful commentaries on the most interesting and important questions of our time. A delightful read.”—Michael Shermer, author of The Science of Good and Evil“Entertaining and thought-provoking.”—Steven Pinker, author of The Blank SlateIf we are, in part, a product of our genes, can free will exist? Incisive and engaging, this indispensable tour of evolutionary biology runs the gamut of contemporary debates, from science and religion to our place in the universe.David Barash is the author of The Myth of Monogamy and Madame Bovary’s Ovaries. He lives in Redmond, Washington.

    It is a ‘ must’ book for those in every branch of science . . . in addition, economists, politicians, statesmen, and businessmen cannot afford to overlook cybernetics and its tremendous, even terrifying implications. "It is a beautifully written book, lucid, direct, and despite its complexity, as readable by the layman as the trained scientist." -- John B. Thurston, "The Saturday Review of Literature" Acclaimed one of the "seminal books . . . comparable in ultimate importance to . . . Galileo or Malthus or Rousseau or Mill," "Cybernetics" was judged by twenty-seven historians, economists, educators, and philosophers to be one of those books published during the "past four decades", which may have a substantial impact on public thought and action in the years ahead." -- Saturday Review

    Thinking Physics is a perfect beginner’s guide to an amazingly wide range of physics-related questions. The book targets topics that science teachers and students spend time wondering about, like wing lift. Epstein elucidates the familiar but misunderstood — such as how tides work — along with more obscure but fascinating phenomena like the “Bernoulli sub” and the “artificial aurora” created by hydrogen bombs. Broken into many short sections and peppered with Epstein’s own playful hand-drawn illustrations, the book does not simply give the right answer: It also goes into the answers that seem right but are wrong and shows why they are wrong — a rarity in science books. Thinking Physics is a rigorously correct, lighthearted, and cleverly designed Q and A book for physicists of all ages.

    Monk's life of Wittgenstein is such a one."--"The Christian Science Monitor."