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Includes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.

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A unique approach to analysis that lets you apply mathematics across a range of subjects This innovative text sets forth a thoroughly rigorous modern account of the theoretical underpinnings of calculus: continuity, differentiability, and convergence. Using a constructive approach, every proof of every result is direct and ultimately computationally verifiable. In particular, existence is never established by showing that the assumption of non-existence leads to a contradiction. The ultimate consequence of this method is that it makes sense—not just to math majors but also to students from all branches of the sciences. The text begins with a construction of the real numbers beginning with the rationals, using interval arithmetic. This introduces readers to the reasoning and proof-writing skills necessary for doing and communicating mathematics, and it sets the foundation for the rest of the text, which includes: Early use of the Completeness Theorem to prove a helpful Inverse Function Theorem Sequences, limits and series, and the careful derivation of formulas and estimates for important functions Emphasis on uniform continuity and its consequences, such as boundedness and the extension of uniformly continuous functions from dense subsets Construction of the Riemann integral for functions uniformly continuous on an interval, and its extension to improper integrals Differentiation, emphasizing the derivative as a function rather than a pointwise limit Properties of sequences and series of continuous and differentiable functions Fourier series and an introduction to more advanced ideas in functional analysis Examples throughout the text demonstrate the application of new concepts. Readers can test their own skills with problems and projects ranging in difficulty from basic to challenging. This book is designed mainly for an undergraduate course, and the author understands that many readers will not go on to more advanced pure mathematics. He therefore emphasizes an approach to mathematical analysis that can be applied across a range of subjects in engineering and the sciences.

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Elements of Financial Time Series fills a gap in the market in the area of financial time series analysis by giving both conceptual and practical illustrations. Examples and discussions in the later chapters of the book make recent developments in time series more accessible. Examples from finance are maximized as much as possible throughout the book. * Full set of exercises is displayed at the end of each chapter. * First seven chapters cover standard topics in time series at a high-intensity level. * Recent and timely developments in nonstandard time series techniques are illustrated with real finance examples in detail. * Examples are systemically illustrated with S-plus with codes and data available on an associated Web site.

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An Introduction to Machine Learning in Finance, With Mathematical Background, Data Visualization, and R Nonparametric function estimation is an important part of machine learning, which is becoming increasingly important in quantitative finance. Nonparametric Finance provides graduate students and finance professionals with a foundation in nonparametric function estimation and the underlying mathematics. Combining practical applications, mathematically rigorous presentation, and statistical data analysis into a single volume, this book presents detailed instruction in discrete chapters that allow readers to dip in as needed without reading from beginning to end. Coverage includes statistical finance, risk management, portfolio management, and securities pricing to provide a practical knowledge base, and the introductory chapter introduces basic finance concepts for readers with a strictly mathematical background. Economic significance is emphasized over statistical significance throughout, and R code is provided to help readers reproduce the research, computations, and figures being discussed. Strong graphical content clarifies the methods and demonstrates essential visualization techniques, while deep mathematical and statistical insight backs up practical applications. Written for the leading edge of finance, Nonparametric Finance: • Introduces basic statistical finance concepts, including univariate and multivariate data analysis, time series analysis, and prediction • Provides risk management guidance through volatility prediction, quantiles, and value-at-risk • Examines portfolio theory, performance measurement, Markowitz portfolios, dynamic portfolio selection, and more • Discusses fundamental theorems of asset pricing, Black-Scholes pricing and hedging, quadratic pricing and hedging, option portfolios, interest rate derivatives, and other asset pricing principles • Provides supplementary R code and numerous graphics to reinforce complex content Nonparametric function estimation has received little attention in the context of risk management and option pricing, despite its useful applications and benefits. This book provides the essential background and practical knowledge needed to take full advantage of these little-used methods, and turn them into real-world advantage. Jussi Klemelä, PhD, is Adjunct Professor at the University of Oulu. His research interests include nonparametric function estimation, density estimation, and data visualization. He is the author of Smoothing of Multivariate Data: Density Estimation and Visualization and Multivariate Nonparametric Regression and Visualization: With R and Applications to Finance.

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This 1971 classic on linear models is once again available–as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.

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Learn rigorous statistical methods to ensure valid clinical trials This Second Edition of the critically hailed Clinical Trials builds on the text's reputation as a straightforward and authoritative presentation of statistical methods for clinical trials. Readers are introduced to the fundamentals of design for various types of clinical trials and then skillfully guided through the complete process of planning the experiment, assembling a study cohort, assessing data, and reporting results. Throughout the process, the author alerts readers to problems that may arise during the course of the trial and provides commonsense solutions. The author bases the revisions and updates on his own classroom experience, as well as feedback from students, instructors, and medical and statistical professionals involved in clinical trials. The Second Edition greatly expands its coverage, ranging from statistical principles to controversial topics, including alternative medicine and ethics. At the same time, it offers more pragmatic advice for issues such as selecting outcomes, sample size, analysis, reporting, and handling allegations of misconduct. Readers familiar with the First Edition will discover completely new chapters, including: * Contexts for clinical trials * Statistical perspectives * Translational clinical trials * Dose-finding and dose-ranging designs Each chapter is accompanied by a summary to reinforce the key points. Revised discussion questions stimulate critical thinking and help readers understand how they can apply their newfound knowledge, and updated references are provided to direct readers to the most recent literature. This text distinguishes itself with its accessible and broad coverage of statistical design methods–the crucial building blocks of clinical trials and medical research. Readers learn to conduct clinical trials that produce valid qualitative results backed by rigorous statistical methods.

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The first systematic, book-length treatment of the subject. Begins with a general introduction and the formal mathematical background behind qualitative and quantitative robustness. Stresses concepts. Provides selected numerical algorithms for computing robust estimates, as well as convergence proofs. Tables contain quantitative robustness information for a variety of estimates.

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The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. «Books such as this that bring together, clarify, and summarize recent research can lead to a great increase of interest in the area. . . . a major achievement in describing many aspects of spatial data and discussing, with examples, different methods of analysis.» –Royal Statistical Society «Dr. Ripley’s book is an excellent survey of the spatial statistical methodology. It is very well illustrated with examples [that] give a clear view of the wide scope of the subject, the way in which techniques often have to be tailored to particular applications, and the different sorts of spatial data that arise.» –The Bulletin of the London Mathematics Society Spatial Statistics provides a comprehensive guide to the analysis of spatial data. Each chapter covers a particular data format and the associated class of problems, introducing theory, giving computational suggestions, and providing examples. Methods are illustrated by computer-drawn figures. The book serves as an introduction to this rapidly growing research area for mathematicians and statisticians, and as a reference to new computer methods for researchers in ecology, geology, archaeology, and the earth sciences.

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This is the first book-length treatment of statistical surveillance methods used in financial analysis. It contains carefully selected chapters written by specialists from both fields and strikes a balance between the financial and statistical worlds, enhancing future collaborations between the two areas, and enabling more successful prediction of financial market trends. The book discusses, in detail, schemes for different control charts and different linear and nonlinear time series models and applies methods to real data from worldwide markets, as well as including simulation studies.

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There have been many advances in the theory and applications of discrete distributions in recent years. They can be applied to a wide range of problems, particularly in the health sciences, although a good understanding of their properties is very important. Discrete Distributions: Applications in the Health Sciences describes a number of new discrete distributions that arise in the statistical examination of real examples. For each example, an understanding of the issues surrounding the data provides the motivation for the subsequent development of the statistical models. Provides an overview of discrete distributions and their applications in the health sciences. Focuses on real examples, giving readers an insight into the utility of the models. Describes the properties of each distribution, and the methods that led to their development. Presents a range of examples from the health sciences, including cancer, epidemiology, and demography. Features discussion of software implementation – in SAS, Fortran and R – enabling readers to apply the methods to their own problems. Written in an accessible style, suitable for applied statisticians and numerate health scientists. Software and data sets are made available on the Web. Discrete Distributions: Applications in the Health Sciences provides a practical introduction to these powerful statistical tools and their applications, suitable for researchers and graduate students from statistics and biostatistics. The focus on applications, and the accessible style of the book, make it an excellent practical reference source for practitioners from the health sciences.

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