This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations. The subject originated in the 1950s with the work of Kleene, Kreisel and others, and has since expanded in many different directions under the influence of workers from both mathematical logic and computer science. The ideas of higher-order computability have proved valuable both for elucidating the constructive content of logical systems, and for investigating the expressive power of various higher-order programming languages. In contrast to the well-known situation for first-order functions, it turns out that at higher types there are several different notions of computability competing for our attention, and each of these has given rise to its own strand of research. In this book, the authors offer an integrated treatment that draws together many of these strands within a unifying framework, revealing not only the range of possible computability concepts but the relationships between them. The book will serve as an ideal introduction to the field for beginning graduate students, as well as a reference for advanced researchers
This book proves some important new theorems in the theory of canonical inner models for large cardinal hypotheses, a topic of central importance in modern set theory. In particular, the author 'completes' the theory of Fine Structure and Iteration Trees (FSIT) by proving a comparison theorem for mouse pairs parallel to the FSIT comparison theorem for pure extender mice, and then using the underlying comparison process to develop a fine structure theory for strategy mice. Great effort has been taken to make the book accessible to non-experts so that it may also serve as an introduction to the higher reaches of inner model theory. It contains a good deal of background material, some of it unpublished folklore, and includes many references to the literature to guide further reading. An introductory essay serves to place the new results in their broader context. This is a landmark work in inner model theory that should be in every set theorist's library.
An indespensable companion to The Norton Shakespeare, Based on the Oxford Edition, this is the most comprehensive reference work on Shakespearean textual problems ever compiled in a single volume. William Shakespeare: A Textual Companion provides a wealth of information about the problems presented by texts and the processes by which editorial decisions are reached. The General Introduction discusses the critical and theoretical issues raised by different kinds of editions, the nature of early manuscripts, printed texts, and the evidence for the canon and chronology of Shakespeare's works. It also offers a concise history of the editing of Shakespeare and sets forth the editorial principles of the Oxford Edition. Included for each work, are an introduction, textual notes, press variants, discussions of emendations and problems of modernization, plausible alternative readings, and a letter-by-letter reprint of the stage directions in the control text, among other materials. --
This is the first volume of a comprehensive two-volume treatment of mechanics intended for students of civil and mechanical engineering. Used for several years in courses at Bradley University, the text presents statics in a clear and straightforward way and emphasizes problem solving. More than 350 examples clarify the discussion. The diskette included with the book contains EnSolve, a program written by the authors for solving problems in engineering mechanics. The program runs on Macintosh and PC-DOS computers and includes the following: - a unit converter for SI to US units and vice versa - a graphics program for plotting functions and data - a set of numerical subroutines The graphics module will, among other features, fit smooth splines between data, plot regression lines and curves, and change scales -- including from arithmetic to log and log-log. The numerical routines will, for example, find roots of polynomials, solve systems of equations, invert matrices, differentiate and integrate, and solve boundary-value problems.
Accessible to anyone with a good general background in mathematics, but it nonetheless gets right to the cutting edge of active research. Some results appear here for the first time, while others have hitherto only been given in preprints.
Discusses theories of atmospheric circulation, covering such topics as atmospheric structure, vorticity, atmospheric wave motion, models of the wind, and moisture processes.
Continuing in the rich tradition of this popular handbook series, The Washington Manual® of Hematopathology provides concise, high-yield content that reflects today’s fast-changing advances in the field. Edited by Drs. Brooj Abro, John L. Frater, Louis P. Dehner, John D. Pfeifer, and Anjum Hassan, this all-new volume focuses on the essential information you need to know, using a concise format, along with numerous figures, tables, algorithms, and images throughout. In one convenient, portable resource, you’ll find complete coverage of hematopathology—both benign and malignant entities—all at your fingertips for quick review and reference.
This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.
In 1989 the first edition of this book set out Gittins' pioneering index solution to the multi-armed bandit problem and his subsequent investigation of a wide of sequential resource allocation and stochastic scheduling problems. Since then there has been a remarkable flowering of new insights, generalizations and applications, to which Glazebrook and Weber have made major contributions. This second edition brings the story up to date. There are new chapters on the achievable region approach to stochastic optimization problems, the construction of performance bounds for suboptimal policies, Whittle's restless bandits, and the use of Lagrangian relaxation in the construction and evaluation of index policies. Some of the many varied proofs of the index theorem are discussed along with the insights that they provide. Many contemporary applications are surveyed, and over 150 new references are included. Over the past 40 years the Gittins index has helped theoreticians and practitioners to address a huge variety of problems within chemometrics, economics, engineering, numerical analysis, operational research, probability, statistics and website design. This new edition will be an important resource for others wishing to use this approach.
Includes various mathematical papers of H J S Smith in chronological order. This book features Smith's work on geometry, theory of numbers, and elliptic functions.
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