It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.

    Covering number theory, algebra, analysis, Euclidean geometry, and analytic geometry, Solving Mathematical Problems includes numerous exercises and model solutions throughout. Assuming only a basic level of mathematics, the text is ideal for students of 14 years and above in pure mathematics.

    Haskell emerged in the last decade as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvellous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures.This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others.

    The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo MCMC. Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment.

    We nevertheless muddle through even in the absence of theories of how to act. But how do we do it?In Probably Approximately Correct, computer scientist Leslie Valiant presents a masterful synthesis of learning and evolution to show how both individually and collectively we not only survive, but prosper in a world as complex as our own. The key is “probably approximately correct” algorithms, a concept Valiant developed to explain how effective behavior can be learned. The model shows that pragmatically coping with a problem can provide a satisfactory solution in the absence of any theory of the problem. After all, finding a mate does not require a theory of mating. Valiant’s theory reveals the shared computational nature of evolution and learning, and sheds light on perennial questions such as nature versus nurture and the limits of artificial intelligence.Offering a powerful and elegant model that encompasses life’s complexity, Probably Approximately Correct has profound implications for how we think about behavior, cognition, biological evolution, and the possibilities and limits of human and machine intelligence.

    The applications and computations in operations research are emphasized. Significantly revised, this text streamlines the coverage of the theory, applications, and computations of operations research. Numerical examples are effectively used to explain complex mathematical concepts. A separate chapter of fully analyzed applications aptly demonstrates the diverse use of OR. The popular commercial and tutorial software AMPL, Excel, Excel Solver, and Tora are used throughout the book to solve practical problems and to test theoretical concepts. New materials include Markov chains, TSP heuristics, new LP models, and a totally new simplex-based approach to LP sensitivity analysis.

    Aiming to tell the dark secrets of computer arithmetic, this title is suitable for library developers, compiler writers, and lovers of elegant hacks.

    Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics — profusely illustrated — include: Mathematical Models, Elementary Concepts of Graph Theory, Transportation Problems, Connection Problems, Party Problems, Digraphs and Mathematical Models, Games and Puzzles, Graphs and Social Psychology, Planar Graphs and Coloring Problems, and Graphs and Other Mathematics. A useful Appendix covers Sets, Relations, Functions, and Proofs, and a section devoted to exercises — with answers, hints, and solutions — is especially valuable to anyone encountering graph theory for the first time. Undergraduate mathematics students at every level, puzzlists, and mathematical hobbyists will find well-organized coverage of the fundamentals of graph theory in this highly readable and thoroughly enjoyable book.

    The field is ready for a text that not only demonstrates how to use the algorithms that make up machine learning methods, but also provides the background needed to understand how and why these algorithms work. Machine Learning: An Algorithmic Perspective is that text.Theory Backed up by Practical ExamplesThe book covers neural networks, graphical models, reinforcement learning, evolutionary algorithms, dimensionality reduction methods, and the important area of optimization. It treads the fine line between adequate academic rigor and overwhelming students with equations and mathematical concepts. The author addresses the topics in a practical way while providing complete information and references where other expositions can be found. He includes examples based on widely available datasets and practical and theoretical problems to test understanding and application of the material. The book describes algorithms with code examples backed up by a website that provides working implementations in Python. The author uses data from a variety of applications to demonstrate the methods and includes practical problems for students to solve.Highlights a Range of Disciplines and ApplicationsDrawing from computer science, statistics, mathematics, and engineering, the multidisciplinary nature of machine learning is underscored by its applicability to areas ranging from finance to biology and medicine to physics and chemistry. Written in an easily accessible style, this book bridges the gaps between disciplines, providing the ideal blend of theory and practical, applicable knowledge."

    With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader.

    Thoroughly updated to include Java 6, the Third Edition of Horstmann's bestselling text helps you absorb computing concepts and programming principles, develop strong problem-solving skills, and become a better programmer, all while exploring the elements of Java that are needed to write real-life programs. A top-notch introductory text for beginners, Big Java, Third Edition is also a thorough reference for students and professionals alike to Java technologies, Internet programming, database access, and many other areas of computer science.Features of the Third Edition: The 'Objects Gradual' approach leads you into object-oriented thinking step-by-step, from using classes, implementing simple methods, all the way to designing your own object-oriented programs. A strong emphasis on test-driven development encourages you to consider outcomes as you write programming code so you design better, more usable programs Helpful "Testing Track" introduces techniques and tools step by step, ensuring that you master one before moving on to the next New teaching and learning tools in WileyPLUS--including a unique assignment checker that enables you to test your programming problems online before you submit them for a grade Graphics topics are developed gradually throughout the text, conveniently highlighted in separate color-coded sections Updated coverage is fully compatible with Java 5 and includes a discussion of the latest Java 6 features

    As author Jeffrey Needham points out in this eye-opening book, big data can provide unprecedented insight into user habits, giving enterprises a huge market advantage. It will also inspire organizations to change the way they function."Disruptive Possibilities: How Big Data Changes Everything" takes you on a journey of discovery into the emerging world of big data, from its relatively simple technology to the ways it differs from cloud computing. But the big story of big data is the disruption of enterprise status quo, especially vendor-driven technology silos and budget-driven departmental silos. In the highly collaborative environment needed to make big data work, silos simply don't fit.Internet-scale computing offers incredible opportunity and a tremendous challenge--and it will soon become standard operating procedure in the enterprise. This book shows you what to expect.

    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.

    Hundreds of thousands of Python developers around the world rely on Python for general-purpose tasks, Internet scripting, systems programming, user interfaces, and product customization. Available on all major computing platforms, including commercial versions of Unix, Linux, Windows, and Mac OS X, Python is portable, powerful and remarkable easy to use.With its convenient, quick-reference format, "Python Pocket Reference," 3rd Edition is the perfect on-the-job reference. More importantly, it's now been refreshed to cover the language's latest release, Python 2.4. For experienced Python developers, this book is a compact toolbox that delivers need-to-know information at the flip of a page. This third edition also includes an easy-lookup index to help developers find answers fast!Python 2.4 is more than just optimization and library enhancements; it's also chock full of bug fixes and upgrades. And these changes are addressed in the "Python Pocket Reference," 3rd Edition. New language features, new and upgraded built-ins, and new and upgraded modules and packages--they're all clarified in detail.The "Python Pocket Reference," 3rd Edition serves as the perfect companion to "Learning Python" and "Programming Python."

    This bookpresents an introductory survey of computer science. It explores thebreadth of the subject while including enough depth to convey anhonest appreciation for the topics involved. The new edition includesreorganization of some key material for enhanced clarity (SoftwareEngineering and Artificial Intelligence chapters), new and expandedmaterial on Security and Data Abstractions, more on ethics anddifferent ethical theories in Chapter 0. Anyone interested in gaining athorough introduction to Computer Science.