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.

    These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The Fifth Edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject. True to the Fourth Edition, the text-specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed. The book is appropriate for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite.

    I always have. To me it’s very simple: If you’re going to be thinking anyway, you might as well think big.”—Donald J. Trump  Here is Trump in action—how he runs his business and how he runs his life—as he meets the people he needs to meet, chats with family and friends, clashes with enemies, and changes the face of the New York City skyline. But even a maverick plays by rules, and Trump has formulated eleven guidelines for success. He isolates the common elements in his greatest deals; he shatters myths; he names names, spells out the zeros, and fully reveals the deal-maker’s art. And throughout, Trump talks—really talks—about how he does it. Trump: The Art of the Deal is an unguarded look at the mind of a brilliant entrepreneur and an unprecedented education in the practice of deal-making. It’s the most streetwise business book there is—and the ultimate read for anyone interested in achieving money and success, and knowing the man behind the spotlight.

    You’ll learn how to combine social web data, analysis techniques, and visualization to find what you’ve been looking for in the social haystack—as well as useful information you didn’t know existed.Each standalone chapter introduces techniques for mining data in different areas of the social Web, including blogs and email. All you need to get started is a programming background and a willingness to learn basic Python tools.Get a straightforward synopsis of the social web landscapeUse adaptable scripts on GitHub to harvest data from social network APIs such as Twitter, Facebook, LinkedIn, and Google+Learn how to employ easy-to-use Python tools to slice and dice the data you collectExplore social connections in microformats with the XHTML Friends NetworkApply advanced mining techniques such as TF-IDF, cosine similarity, collocation analysis, document summarization, and clique detectionBuild interactive visualizations with web technologies based upon HTML5 and JavaScript toolkits"A rich, compact, useful, practical introduction to a galaxy of tools, techniques, and theories for exploring structured and unstructured data." --Alex Martelli, Senior Staff Engineer, Google

    Rucker acquaints us with Godel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations.Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Godel's incompleteness theorems. His personal encounters with Godel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism.

    Meanwhile, people with important ideas--entrepreneurs, teachers, politicians, and journalists--struggle to make them "stick."In Made to Stick, Chip and Dan Heath reveal the anatomy of ideas that stick and explain ways to make ideas stickier, such as applying the human scale principle, using the Velcro Theory of Memory, and creating curiosity gaps. Along the way, we discover that sticky messages of all kinds--from the infamous "kidney theft ring" hoax to a coach's lessons on sportsmanship to a vision for a new product at Sony--draw their power from the same six traits.Made to Stick will transform the way you communicate. It's a fast-paced tour of success stories (and failures): the Nobel Prize-winning scientist who drank a glass of bacteria to prove a point about stomach ulcers; the charities who make use of the Mother Teresa Effect; the elementary-school teacher whose simulation actually prevented racial prejudice.Provocative, eye-opening, and often surprisingly funny, Made to Stick shows us the vital principles of winning ideas--and tells us how we can apply these rules to making our own messages stick.

    In Turing’s Cathedral, George Dyson focuses on a small group of men and women, led by John von Neumann at the Institute for Advanced Study in Princeton, New Jersey, who built one of the first computers to realize Alan Turing’s vision of a Universal Machine. Their work would break the distinction between numbers that mean things and numbers that do things—and our universe would never be the same. Using five kilobytes of memory (the amount allocated to displaying the cursor on a computer desktop of today), they achieved unprecedented success in both weather prediction and nuclear weapons design, while tackling, in their spare time, problems ranging from the evolution of viruses to the evolution of stars. Dyson’s account, both historic and prophetic, sheds important new light on how the digital universe exploded in the aftermath of World War II. The proliferation of both codes and machines was paralleled by two historic developments: the decoding of self-replicating sequences in biology and the invention of the hydrogen bomb. It’s no coincidence that the most destructive and the most constructive of human inventions appeared at exactly the same time.  How did code take over the world? In retracing how Alan Turing’s one-dimensional model became John von Neumann’s two-dimensional implementation, Turing’s Cathedral offers a series of provocative suggestions as to where the digital universe, now fully three-dimensional, may be heading next.

    Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.

    Hailed as the father of modern anatomy and neurobiology, he was largely responsible for the modern conception of the brain. His groundbreaking works were New Ideas on the Structure of the Nervous System and Histology of the Nervous System in Man and Vertebrates. In addition to leaving a legacy of unparalleled scientific research, Cajal sought to educate the novice scientist about how science was done and how he thought it should be done. This recently rediscovered classic, first published in 1897, is an anecdotal guide for the perplexed new investigator as well as a refreshing resource for the old pro.Cajal was a pragmatist, aware of the pitfalls of being too idealistic--and he had a sense of humor, particularly evident in his diagnoses of various stereotypes of eccentric scientists. The book covers everything from valuable personality traits for an investigator to social factors conducive to scientific work.

    James Paul Gee begins his new book with 'I want to talk about vide games- yes, even violent video games - and say some positive things about them'. With this simple but explosive beginning, one of America's most well-respected professors of education looks seriously at the good that can come from playing video games. Gee is interested in the cognitive development that can occur when someone is trying to escape a maze, find a hidden treasure and, even, blasting away an enemy with a high-powered rifle. Talking about his own video-gaming experience learning and using games as diverse as Lara Croft and Arcanum, Gee looks at major specific cognitive activities: How individuals develop a sense of identity; How one grasps meaning; How one evaluates and follows a command; How one picks a role model; How one perceives the world.

    But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like nonparametric curve estimation, bootstrapping, and clas- sification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analyzing data. For some time, statistics research was con- ducted in statistics departments while data mining and machine learning re- search was conducted in computer science departments. Statisticians thought that computer scientists were reinventing the wheel. Computer scientists thought that statistical theory didn't apply to their problems. Things are changing. Statisticians now recognize that computer scientists are making novel contributions while computer scientists now recognize the generality of statistical theory and methodology. Clever data mining algo- rithms are more scalable than statisticians ever thought possible. Formal sta- tistical theory is more pervasive than computer scientists had realized.

    Now this instant classic has been completely updated, outfitted with a whole new arsenal of indispensable knowledge on global affairs, popular culture, economic trends, scientific principles, and modern arts. Here's your chance to brush up on all those subjects you slept through in school, reacquaint yourself with all the facts you once knew (then promptly forgot), catch up on major developments in the world today, and become the Renaissance man or woman you always knew you could be! How do you tell the Balkans from the Caucasus? What's the difference between fission and fusion? Whigs and Tories? Shiites and Sunnis? Deduction and induction? Why aren't all Shakespearean comedies necessarily thigh-slappers? What are transcendental numbers and what are they good for? What really happened in Plato's cave? Is postmodernism dead or just having a bad hair day? And for extra credit, when should you use the adjective continual and when should you use continuous? An Incomplete Education answers these and thousands of other questions with incomparable wit, style, and clarity. American Studies, Art History, Economics, Film, Literature, Music, Philosophy, Political Science, Psychology, Religion, Science, and World History: Here's the bottom line on each of these major disciplines, distilled to its essence and served up with consummate flair.

    It is universally recognized as the standard English version of Aristotle. This revised edition contains the substance of the original translation, slightly emended in light of recent scholarship; three of the original versions have been replaced by new translations; and a new and enlarged selection of Fragments has been added. The aim of the translation remains the same: to make the surviving works of Aristotle readily accessible to English speaking readers.

    It’s time we stand face-to-digital-face with the true powers and limitations of the algorithms that already automate important decisions in healthcare, transportation, crime, and commerce. Hello World is indispensable preparation for the moral quandaries of a world run by code, and with the unfailingly entertaining Hannah Fry as our guide, we’ll be discussing these issues long after the last page is turned.

    Economists Ivan and Tuvana Pastine explain why, in these situations, we sometimes cooperate, sometimes clash, and sometimes act in a way that seems completely random.Stylishly brought to life by award-winning cartoonist Tom Humberstone, Game Theory will help readers understand behaviour in everything from our social lives to business, global politics to evolutionary biology. It provides a thrilling new perspective on the world we live in.