"A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    What began more than sixty years ago as a modest proposal that a mathematician and an economist write a short paper together blossomed, in 1944, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.This sixtieth anniversary edition includes not only the original text but also an introduction by Harold Kuhn, an afterword by Ariel Rubinstein, and reviews and articles on the book that appeared at the time of its original publication in the New York Times, tthe American Economic Review, and a variety of other publications. Together, these writings provide readers a matchless opportunity to more fully appreciate a work whose influence will yet resound for generations to come.

    Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

    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.

    It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.

    

      “An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.”—Nina MacLaughlin, Boston Globe “Engaging, eminently readable . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.”—Judith Goodstein, American Scientist  Harvard geometer and Fields medalist Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems. With complicated ideas explained for a broad audience, this book offers readers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.

    Never again will you order the Poisson Distribution in a French restaurant!This updated version features all new material.

    Virtually every choice we make hinges on how someone generates data . . . and how someone else interprets it--whether we realize it or not.Where do you send your child for the best education? Big Data. Which airline should you choose to ensure a timely arrival? Big Data. Who will you vote for in the next election? Big Data.The problem is, the more data we have, the more difficult it is to interpret it. From world leaders to average citizens, everyone is prone to making critical decisions based on poor data interpretations.In Numbersense, expert statistician Kaiser Fung explains when you should accept the conclusions of the Big Data experts--and when you should say, Wait . . . what? He delves deeply into a wide range of topics, offering the answers to important questions, such as:How does the college ranking system really work?Can an obesity measure solve America's biggest healthcare crisis?Should you trust current unemployment data issued by the government?How do you improve your fantasy sports team?Should you worry about businesses that track your data?Don't take for granted statements made in the media, by our leaders, or even by your best friend. We're on information overload today, and there's a lot of bad information out there.Numbersense gives you the insight into how Big Data interpretation works--and how it too often doesn't work. You won't come away with the skills of a professional statistician. But you will have a keen understanding of the data traps even the best statisticians can fall into, and you'll trust the mental alarm that goes off in your head when something just doesn't seem to add up.Praise for NumbersenseNumbersense correctly puts the emphasis not on the size of big data, but on the analysis of it. Lots of fun stories, plenty of lessons learned--in short, a great way to acquire your own sense of numbers!Thomas H. Davenport, coauthor of Competing on Analytics and President's Distinguished Professor of IT and Management, Babson CollegeKaiser's accessible business book will blow your mind like no other. You'll be smarter, and you won't even realize it. Buy. It. Now.Avinash Kaushik, Digital Marketing Evangelist, Google, and author, Web Analytics 2.0Each story in Numbersense goes deep into what you have to think about before you trust the numbers. Kaiser Fung ably demonstrates that it takes skill and resourcefulness to make the numbers confess their meaning.John Sall, Executive Vice President, SAS InstituteKaiser Fung breaks the bad news--a ton more data is no panacea--but then has got your back, revealing the pitfalls of analysis with stimulating stories from the front lines of business, politics, health care, government, and education. The remedy isn't an advanced degree, nor is it common sense. You need Numbersense.Eric Siegel, founder, Predictive Analytics World, and author, Predictive AnalyticsI laughed my way through this superb-useful-fun book and learned and relearned a lot. Highly recommended! Tom Peters, author of In Search of Excellence

    Previously undocumented, these 23 patterns allow designers to create more flexible, elegant, and ultimately reusable designs without having to rediscover the design solutions themselves.The authors begin by describing what patterns are and how they can help you design object-oriented software. They then go on to systematically name, explain, evaluate, and catalog recurring designs in object-oriented systems. With Design Patterns as your guide, you will learn how these important patterns fit into the software development process, and how you can leverage them to solve your own design problems most efficiently. Each pattern describes the circumstances in which it is applicable, when it can be applied in view of other design constraints, and the consequences and trade-offs of using the pattern within a larger design. All patterns are compiled from real systems and are based on real-world examples. Each pattern also includes code that demonstrates how it may be implemented in object-oriented programming languages like C++ or Smalltalk.

    In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings.

    Topics covered in the book include the properties of arithmetic, exponents, primes and divisors, fractions, equations and inequalities, decimals, ratios and proportions, unit conversions and rates, percents, square roots, basic geometry (angles, perimeter, area, triangles, and quadrilaterals), statistics, counting and probability, and more! The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, giving the student a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which algebraic techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains well over 1000 problems. The solutions manual (sold separately) contains full solutions to all of the problems, not just answers. This book can serve as a complete Prealgebra course. This text is supplemented by free videos and a free learning system at the publisher's website.

    Lewis Carroll’s Symbolic logic : part I, Elementary, 1896, fifth edition, part II, Advanced, never previously published : together with letters from Lewis Carroll to eminent nineteenth-century logicians and to his "logical sister," and eight versions of the Barber-shop paradox / edited, with annotations and an introd., by William Warren Bartley, III.

    This concise introduction shows you how to perform statistical analysis computationally, rather than mathematically, with programs written in Python.You'll work with a case study throughout the book to help you learn the entire data analysis process—from collecting data and generating statistics to identifying patterns and testing hypotheses. Along the way, you'll become familiar with distributions, the rules of probability, visualization, and many other tools and concepts.Develop your understanding of probability and statistics by writing and testing codeRun experiments to test statistical behavior, such as generating samples from several distributionsUse simulations to understand concepts that are hard to grasp mathematicallyLearn topics not usually covered in an introductory course, such as Bayesian estimationImport data from almost any source using Python, rather than be limited to data that has been cleaned and formatted for statistics toolsUse statistical inference to answer questions about real-world data

    The patterns apply to the development process as well as to architecture and coding practices. The content is based on a presentation developed by Scott Guthrie and delivered by him at the Norwegian Developers Conference (NDC) in June of 2013 (part 1, part 2), and at Microsoft Tech Ed Australia in September 2013 (part 1, part 2). Many others updated and augmented the content while transitioning it from video to written form. Who should read this book Developers who are curious about developing for the cloud, are considering a move to the cloud, or are new to cloud development will find here a concise overview of the most important concepts and practices they need to know. The concepts are illustrated with concrete examples, and each chapter includes links to other resources that provide more in-depth information. The examples and the links to additional resources are for Microsoft frameworks and services, but the principles illustrated apply to other web development frameworks and cloud environments as well. Developers who are already developing for the cloud may find ideas here that will help make them more successful. Each chapter in the series can be read independently, so you can pick and choose topics that you're interested in. Anyone who watched Scott Guthrie's "Building Real World Cloud Apps with Windows Azure" presentation and wants more details and updated information will find that here. Assumptions This ebook expects that you have experience developing web applications by using Visual Studio and ASP.NET. Familiarity with C# would be helpful in places.