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.

    Most of the time this math works quietly behind the scenes . . . until it doesn't. All sorts of seemingly innocuous mathematical mistakes can have significant consequences.Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean.Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun.

    The book has been designed to offer maximal accessibility to the widest range of students (not only those majoring in philosophy) and assumes no formal training in elementary symbolic logic. It offers a comprehensive course covering all basic definitions of induction and probability, and considers such topics as decision theory, Bayesianism, frequency ideas, and the philosophical problem of induction. The key features of the book are: * A lively and vigorous prose style* Lucid and systematic organization and presentation of the ideas* Many practical applications* A rich supply of exercises drawing on examples from such fields as psychology, ecology, economics, bioethics, engineering, and political science* Numerous brief historical accounts of how fundamental ideas of probability and induction developed.* A full bibliography of further reading Although designed primarily for courses in philosophy, the book could certainly be read and enjoyed by those in the social sciences (particularly psychology, economics, political science and sociology) or medical sciences such as epidemiology seeking a reader-friendly account of the basic ideas of probability and induction. Ian Hacking is University Professor, University of Toronto. He is Fellow of the Royal Society of Canada, Fellow of the British Academy, and Fellow of the American Academy of Arts and Sciences. he is author of many books including five previous books with Cambridge (The Logic of Statistical Inference, Why Does Language Matter to Philosophy?, The Emergence of Probability, Representing and Intervening, and The Taming of Chance).

    Illuminating overviews and a selection of readings from both traditional and contemporary sources make even complex philosophical concepts reader friendly. Comprehensive, clear-sighted introductions to general and specific areas of ethical debate cover major ethical theories, including feminist ethics, contract theory, and ethical relativism, before delving into issues ranging from euthanasia and sexual morality to war and globalization. A broader range of voices and philosophical traditions in this edition includes continental and non-Western philosophers, with new readings from prominent ethicists. Increased coverage of contemporary dilemmas highlights issues of widespread interest, including torture and terrorism, "partial birth" abortion, cloning, same-sex marriage, and global distributive justice. An innovative online resource center offers, among other things, animated simulations. These simulations allows you to personally engage with dilemmas and thought experiments commonly presented in introduction to ethics classes and provide instructors with a way to seamlessly integrate online assignments into the class.

    It demonstrates how to encourage, develop, and foster the processes which seem to come naturally to mathematicians.

    As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

    Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. Features include: The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated.Carefully chosen advanced topics that can be skipped in a standard one-semester course, but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence.An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text, DasGupta also offers a Solutions Manual, which is available on the Online Learning Center.Algorithms is an outstanding undergraduate text, equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel, it is a joy to read. Tim Roughgarden Stanford University

    No graduate student of quantum theory should leave it unread"--W.C Schieve, University of Texas

    Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.

    The heart of this creative process lies in an analogy between proving mathematical theorems by induction and designing combinatorial algorithms. The book contains hundreds of problems and examples. It is designed to enhance the reader's problem-solving abilities and understanding of the principles behind algorithm design.

    By staying current, remaining relevant, and adapting to emerging course needs, this market-leading text has continued to define the operating systems course. This Seventh Edition not only presents the latest and most relevant systems, it also digs deeper to uncover those fundamental concepts that have remained constant throughout the evolution of today's operation systems. With this strong conceptual foundation in place, students can more easily understand the details related to specific systems. New Adaptations * Increased coverage of user perspective in Chapter 1. * Increased coverage of OS design throughout. * A new chapter on real-time and embedded systems (Chapter 19). * A new chapter on multimedia (Chapter 20). * Additional coverage of security and protection. * Additional coverage of distributed programming. * New exercises at the end of each chapter. * New programming exercises and projects at the end of each chapter. * New student-focused pedagogy and a new two-color design to enhance the learning process.

    This book develops statistical thinking over rote drill and practice. The Nature of Statistics; Organizing Data; Descriptive Measures; Probability Concepts; Discrete Random Variables; The Normal Distribution; The Sampling Distribution of the Sample Menu; Confidence Intervals for One Population Mean; Hypothesis Tests for One Population Mean; Inferences for Two Population Means; Inferences for Population Standard Deviations; Inferences for Population Proportions; Chi-Square Procedures; Descriptive Methods in Regression and Correlation; Inferential Methods in Regression and Correlation; Analysis of Variance (ANOVA) For all readers interested in Introductory Statistics.

    This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. * The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.

    When it comes to creating websites, the PHP scripting language is truly a red-hot property. In fact, PHP is currently used on more than 19 million websites, surpassing Microsoft's ASP .NET technology in popularity. Programmers love its flexibility and speed; designers love its accessibility and convenience. As the industry standard book on PHP, all of the essentials are covered in a clear and concise manner. Language syntax and programming techniques are coupled with numerous examples that illustrate both correct usage and common idioms. With style tips and practical programming advice, this book will help you become not just a PHP programmer, but a good PHP programmer. Programming PHP, Second Edition covers everything you need to know to create effective web applications with PHP. Contents include: Detailed information on the basics of the PHP language, including data types, variables, operators, and flow control statements Chapters outlining the basics of functions, strings, arrays, and objects Coverage of common PHP web application techniques, such as form processing and validation, session tracking, and cookies Material on interacting with relational databases, such as MySQL and Oracle, using the database-independent PEAR DB library and the new PDO Library Chapters that show you how to generate dynamic images, create PDF files, and parse XML files with PHP Advanced topics, such as creating secure scripts, error handling, performance tuning, and writing your own C language extensions to PHP A handy quick reference to all the core functions in PHP and all the standard extensions that ship with PHP Praise for the first edition: "If you are just getting into the dynamic Web development world or you are considering migrating from another dynamic web product to PHP, Programming PHP is the book of choice to get you up, running, and productive in a short time."--Peter MacIntrye, eWeek "I think this is a great book for programmers who want to start developing dynamic websites with PHP. It gives a detailed overview of PHP, lots of valuable tips, and a good sense of PHP's strengths."--David Dooling, Slashdot.org

    To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok.In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing's role in breaking Germany's Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security.Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.