Then, attempting to break a Nazi code during World War II, he successfully designed and built one, thus ensuring the Allied victory. Turing became a champion of artificial intelligence, but his work was cut short. As an openly gay man at a time when homosexuality was illegal in England, he was convicted and forced to undergo a humiliating "treatment" that may have led to his suicide.With a novelist's sensitivity, David Leavitt portrays Turing in all his humanity—his eccentricities, his brilliance, his fatal candor—and elegantly explains his work and its implications.

    

    Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

    

    During dessert, the other guests do not mind their manners, each one taking half of the remaining cake as it is passed around. By the time it reaches Ant, barely a crumb is left for her to share with the King! She promises to make up for it by baking another cake for the King, and not to be outdone, all the other animals in turn offer to make twice as many cakes as the next. By the time the hippo speaks up, he's to bake 256 peanut butter cakes! With McElligott's signature humor and gorgeous mixed-media art, the math concepts of halving and doubling have never been so much fun.

    Historian Jacqueline Stedall shows that mathematical ideas are far from being fixed, but are adapted and changed by their passage across periods and cultures. The book illuminates some of the varied contexts in which people have learned, used, and handed on mathematics, drawing on fascinating case studies from a range of times and places, including early imperial China, the medieval Islamic world, and nineteenth-century Britain. By drawing out some common threads, Stedall provides an introduction not only to the mathematics of the past but to the history of mathematics as a modern academic discipline.

    . . full of intellectual treats and tricks, of whimsy and deep scientific philosophy. It is highbrow entertainment at its best, a teasing challenge to all who aspire to think about the universe." — New York Herald TribuneOne of the world's foremost nuclear physicists (celebrated for his theory of radioactive decay, among other accomplishments), George Gamow possessed the unique ability of making the world of science accessible to the general reader.He brings that ability to bear in this delightful expedition through the problems, pleasures, and puzzles of modern science. Among the topics scrutinized with the author's celebrated good humor and pedagogical prowess are the macrocosm and the microcosm, theory of numbers, relativity of space and time, entropy, genes, atomic structure, nuclear fission, and the origin of the solar system.In the pages of this book readers grapple with such crucial matters as whether it is possible to bend space, why a rocket shrinks, the "end of the world problem," excursions into the fourth dimension, and a host of other tantalizing topics for the scientifically curious. Brimming with amusing anecdotes and provocative problems, One Two Three . . . Infinity also includes over 120 delightful pen-and-ink illustrations by the author, adding another dimension of good-natured charm to these wide-ranging explorations.Whatever your level of scientific expertise, chances are you'll derive a great deal of pleasure, stimulation, and information from this unusual and imaginative book. It belongs in the library of anyone curious about the wonders of the scientific universe. "In One Two Three . . . Infinity, as in his other books, George Gamow succeeds where others fail because of his remarkable ability to combine technical accuracy, choice of material, dignity of expression, and readability." — Saturday Review of Literature

    Or you have persistent pain you and your doctor can't explain. Man or woman, you may be fighting fluctuating hormone levels. Or maybe you snore like a freight train.Anything that narrows the throat and interrupts sleep, particularly breathing problems brought on by sleep position, illness, life changes, or your anatomy, may be key to understanding a host of common health issues. In this groundbreaking book, Dr. Steven Park outlines a simple, rational explanation for what s making you sick, and provides guidance for treatment options that address specific health problems.

    A basic idea that proved elusive for hundreds of years and bent the minds of the greatest thinkers in the world, the algorithm is what made the modern world possible. Without the algorithm, there would have been no computer, no Internet, no virtual reality, no e-mail, or any other technological advance that we rely on every day.In The Advent of the Algorithm, David Berlinski combines science, history, and math to explain and explore the intriguing story of how the algorithm was finally discovered by a succession of mathematicians and logicians, and how this paved the way for the digital age. Beginning with Leibniz and culminating in the middle of the twentieth century with the groundbreaking work of Gödel and Turing, The Advent of the Algorithm is an epic tale told with clarity and imaginative brilliance.

    The New Keto-Friendly South Beach Diet combines the good fats and healthy carbs of the world-famous heart-healthy program with the advanced nutrition science of keto-all in a doctor-approved plan that is easier than strict keto diets.The original South Beach Diet defined the cutting edge of healthy weight loss. Now the creator of the classic plan combines his signature diet with the latest, most cutting-edge advances in healthy eating that are the basis for the ketogenic diet. With a new emphasis on good carbs, healthy fats, and quality proteins, The New Keto-Friendly South Beach Diet takes the powerful fundamentals of the original South Beach Diet and adds the fat-burning principles of keto. Dr. Arthur Agatston cuts through the confusion around keto and low carb diets and gives readers a step-by-step 28-day eating plan that increases satisfaction, decreases appetite, and makes it easy to lose weight and keep it off. He also explains why strict ketosis is not necessary to achieve results; the effectiveness of intermittent fasting; and the relationship between yo-yo-dieting and sugar addiction.This plan offers the benefits of keto and low carb without the pitfalls. As this new book reveals, you can boost your metabolism and put your body safely into fat-burning mode with a diet that's more flexible and more sustainable than traditional keto. And that's not all: in addition to long-term weight loss, the South Beach Keto-Friendly plan can boost mental sharpness, reduce inflammation and pain, increase your energy, and improve diabetes and heart health. Includes around 100 recipes, full-color photos, and an easy-to-follow 28-day meal plan.

    It's an empowering and sometimes challenging guide to living a joyful, productive and ambitious life.

    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.

    Aczel's compelling narrative that blends a story of infinity with the tragic tale of a tormented and brilliant mathematician.From the Pythagoreans, the Greek cult of mathematics, to the mystical Jewish numerology found in the Kabbalah, The Mystery Of The Aleph follows the search for an answer that may never truly be trusted.

    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.

    Frighteningly often, the influence of technology in and on our lives goes completely unchallenged by citizens and governments. We comfort ourselves with the soothing refrain that technology has no morals and can display no prejudice, and it's only the users of technology who distort certain aspects of it.But is this statement actually true? Dr Robert Smith thinks it is dangerously untrue in the modern era.Having worked in the field of artificial intelligence for over 30 years, Smith reveals the mounting evidence that the mechanical actors in our lives do indeed have, or at least express, morals: they're just not the morals of the progressive modern society that we imagined we were moving towards. Instead, as we are just beginning to see – in the US elections and Brexit to name but a few – there are increasing incidences of machine bigotry, greed and the crass manipulation of our basest instincts.It is easy to assume that these are the result of programmer prejudices or the product of dark forces manipulating the masses through the network of the Internet. But what if there is something more fundamental and explicitly mechanical at play, something inherent within technology itself?This book demonstrates how non-scientific ideas have been encoded deep into our technological infrastructure. Offering a rigorous, fresh perspective on how technology has brought us to this place, Rage Inside the Machine challenges the long-held assumption that technology is an apolitical and amoral force. Shedding light on little-known historical stories and investigating the complex connections between scientific philosophy, institutional prejudice and new technology, this book offers a new, honest and more truly scientific vision of ourselves.