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 framework of probabilistic graphical models, presented in this book, provides a general approach for this task. The approach is model-based, allowing interpretable models to be constructed and then manipulated by reasoning algorithms. These models can also be learned automatically from data, allowing the approach to be used in cases where manually constructing a model is difficult or even impossible. Because uncertainty is an inescapable aspect of most real-world applications, the book focuses on probabilistic models, which make the uncertainty explicit and provide models that are more faithful to reality.Probabilistic Graphical Models discusses a variety of models, spanning Bayesian networks, undirected Markov networks, discrete and continuous models, and extensions to deal with dynamical systems and relational data. For each class of models, the text describes the three fundamental cornerstones: representation, inference, and learning, presenting both basic concepts and advanced techniques. Finally, the book considers the use of the proposed framework for causal reasoning and decision making under uncertainty. The main text in each chapter provides the detailed technical development of the key ideas. Most chapters also include boxes with additional material: skill boxes, which describe techniques; case study boxes, which discuss empirical cases related to the approach described in the text, including applications in computer vision, robotics, natural language understanding, and computational biology; and concept boxes, which present significant concepts drawn from the material in the chapter. Instructors (and readers) can group chapters in various combinations, from core topics to more technically advanced material, to suit their particular needs.

    His Contemporary Abstract Algebra, 6/e, includes challenging topics in abstract algebra as well as numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings that give the subject a current feel and makes the content interesting and relevant for students.

    Since that time, this text has been revised, tweaked, and enhanced to account for the changes found within each release of the .NET platform (1.1, 2.0, 3.0 and now 3.5)..NET 3.0 was more of an augmentative release, essentially providing three new APIs: Windows Presentation Foundation (WPF), Windows Communication Foundation (WCF) and Windows Workflow Foundation (WF). As you would expect, coverage of the "W's" has been expanded a great deal in this version of the book from the previous Special Edition text.Unlike .NET 3.0, .NET 3.5 provides dozens of C# language features and .NET APIs. This edition of the book will walk you through all of this material using the same readable approach as was found in previous editions. Rest assured, you'll find detailed coverage of Language Integrated Query (LINQ), the C# 2008 language changes (automatic properties, extension methods, anonymous types, etc.) and the numerous bells and whistles of Visual Studio 2008. What you'll learn Everything you need to knowget up to speed with C# 2008 quickly and efficiently. Discover all the new .NET 3.5 featuresLanguage Integrated Query, anonymous types, extension methods, automatic properties, and more. Get a professional footholdtargeted to appeal to experienced software professionals, this book gives you the facts you need the way you need to see them. A rock-solid foundationfocuses on everything you need to be a successful .NET 3.5 programmer, not just the new features. Get comfortable with all the core aspects of the platform including assemblies, remoting, Windows Forms, Web Forms, ADO.NET, XML web services, and much more. Who this book is forIf you're checking out this book for the first time, understand that it targets experienced software professionals and/or students of computer science (so please don't expect three chapters devoted to "for" loops). The mission of this text is to provide you with a rock-solid foundation to the C# 2008 programming language and the core aspects of the .NET platform (object-oriented programming, assemblies, file IO, Windows Forms/WPF, ASP.NET, ADO.NET, WCF, WF, etc.). Once you digest the information presented in these 33 chapters, you'll be in a perfect position to apply this knowledge to your specific programming assignments, and you'll be well equipped to explore the .NET universe on your own terms. "

    This introduction is ideal for beginners: it requires no previous programming experience and all concepts are explained from first principles via carefully chosen examples. Each chapter includes exercises that range from the straightforward to extended projects, plus suggestions for further reading on more advanced topics. The author is a leading Haskell researcher and instructor, well-known for his teaching skills. The presentation is clear and simple, and benefits from having been refined and class-tested over several years. The result is a text that can be used with courses, or for self-learning. Features include freely accessible Powerpoint slides for each chapter, solutions to exercises and examination questions (with solutions) available to instructors, and a downloadable code that's fully compliant with the latest Haskell release.

    Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach.The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package—PMTK (probabilistic modeling toolkit)—that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

    Using his one-of-a-kind conversational style, Todd gives you clear and concise information on crucial networking topics through practical examples and insights drawn from his real-world experience. This Study Guide thoroughly covers all exam objectives for the CompTIA Network+ exam (N10-004), including key topics such as network technologies, media and topologies, devices, management, tools, and security. Along with the book you get a CD-ROM featuring a custom test engine with chapter review questions, two practice exams, flashcards, and the book as a searchable PDF.Note: CD-ROM/DVD and other supplementary materials are not included as part of eBook file.For Instructors: Teaching supplements are available for this title.

    A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.

    After introducing the basic concepts, the book examines techniques for modeling probability density functions and the properties and merits of the multi-layerperceptron and radial basis function network models. Also covered are various forms of error functions, principal algorithms for error function minimalization, learning and generalization in neural networks, and Bayesian techniques and their applications. Designed as a text, with over 100exercises, this fully up-to-date work will benefit anyone involved in the fields of neural computation and pattern recognition.

    A well-rounded balance of hard skills (HTML5, XHTML, CSS, JavaScript) and soft skills (Web Design, e-commerce, Web site promotion strategies) presents everything beginning Web developers need to know to build and promote successful Web sites.

    Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by "doing," writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site, codingthematrix.com provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant "xkcd" comics. Chapters: "The Function," "The Field," "The Vector," "The Vector Space," "The Matrix," "The Basis," "Dimension," "Gaussian Elimination," "The Inner Product," "Special Bases," "The Singular Value Decomposition," "The Eigenvector," "The Linear Program"

    Several things make this one stand out. Here's the most important: Linux Administration Handbook is designed for administrators working in industrial-strength production environments. It never glosses over the "subtleties" that can get you in big trouble. It doesn't stint on technical detail. It's never satisfied with restating the man pages. And it's full of war stories from folks who've been there. Evi Nemeth and her coauthors: Boy, have they ever been there. (Just ask any gray-bearded Unix sysadmin about their earlier, legendary Unix System Administration Handbook.) There's only been one downside to Linux Administration Handbook: It's been nearly five years since it was written. Well, that flaw's just been remedied. The new Second Edition has been systematically revised for the latest administration tools (think Nagios and LVM). It's carefully targeted at today's five most widely used distributions: Red Hat Enterprise Linux 4.3, Fedora Core 5, SUSE Linux 10.2, Debian 3.2 "Etch," and Ubuntu 6.06. The result: a book you can rely on for the next five years. Rely on to do what? Just about everything. You'll find chapters on booting and shutting down; "rootly" powers; controlling processes; the Linux filesystem; on adding new users. You'll learn the most efficient ways to perform backups. How to make sense of syslogs and log files. Everything you need to know about drivers, the kernel, networking, NFS -- and Internet services, from web hosting to email. Nemeth & Company bring their experience to bear on troubleshooting, performance optimization, print management, security, Windows interoperability, even "policies and politics." Whatever Linux books you already own, if you depend on Linux to run efficiently and reliably, you need this one, too. Bill Camarda, from the December 2006 href="http://www.barnesandnoble.com/newslet... Only

    David Peat explains the development and meaning of this Superstring Theory in a thoroughly readable, dramatic manner accessible to lay readers with no knowledge of mathematics. The consequences of the Superstring Theory are nothing less than astonishing.

    With problems and solutions. Includes 99 illustrations.

    K. Dewdney's The Turing Omnibus.Updated and expanded, The Turing Omnibus offers 66 concise, brilliantly written articles on the major points of interest in computer science theory, technology, and applications. New for this tour: updated information on algorithms, detecting primes, noncomputable functions, and self-replicating computers--plus completely new sections on the Mandelbrot set, genetic algorithms, the Newton-Raphson Method, neural networks that learn, DOS systems for personal computers, and computer viruses.Contents:1 Algorithms 2 Finite Automata 3 Systems of Logic 4 Simulation 5 Godel's Theorem 6 Game Trees 7 The Chomsky Hierarchy 8 Random Numbers 9 Mathematical Research 10 Program Correctness 11 Search Trees 12 Error-Corecting Codes 13 Boolean Logic 14 Regular Languages 15 Time and Space Complexity 16 Genetic Algorithms 17 The Random Access Machine 18 Spline Curves 19 Computer Vision 20 Karnaugh Maps 21 The Newton-Raphson Method 22 Minimum Spanning Trees 23 Generative Grammars 24 Recursion 25 Fast Multiplication 26 Nondeterminism 27 Perceptrons 28 Encoders and Multiplexers 29 CAT Scanning 30 The Partition Problem 31 Turing Machines 32 The Fast Fourier Transform 33 Analog Computing 34 Satisfiability 35 Sequential Sorting 36 Neural Networks That Learn 37 Public Key Cryptography 38 Sequential Cirucits 39 Noncomputerable Functions 40 Heaps and Merges 41 NP-Completeness 42 Number Systems for Computing 43 Storage by Hashing 44 Cellular Automata 45 Cook's Theorem 46 Self-Replicating Computers 47 Storing Images 48 The SCRAM 49 Shannon's Theory 50 Detecting Primes 51 Universal Turing Machines 52 Text Compression 53 Disk Operating Systems 54 NP-Complete Problems 55 Iteration and Recursion 56 VLSI Computers 57 Linear Programming 58 Predicate Calculus 59 The Halting Problem 60 Computer Viruses 61 Searching Strings 62 Parallel Computing 63 The Word Problem 64 Logic Programming 65 Relational Data Bases 66 Church's Thesis