This book presents the theory of dynamical systems with nonzero Lyapunov exponents, offering a rigorous mathematical foundation for deterministic chaos - the appearance of "chaotic" motions in pure deterministic dynamical systems. These ideas and methods are used in many areas of mathematics as well as in physics, biology, and engineering. Despite the substantial amount of research on the subject, there have been relatively few attempts to summarize and unify results in a single manuscript. This comprehensive book can be used as a reference or as a supplement to an advanced course on...

This updated edition will continue to meet the needs for an authoritative comprehensive analysis of the rapidly growing field of basic hypergeometric series, or q-series. It includes deductive proofs, exercises, and useful appendices. Three new chapters have been added to this edition covering q-series in two and more variables: linear- and bilinear-generating functions for basic orthogonal polynomials; and summation and transformation formulas for elliptic hypergeometric series. In addition, the text and bibliography have been expanded to reflect recent developments. First Edition Hb (1990):...

Researchers, teachers and graduate students in algebra and topology--familiar with the very basic notions of category theory--will welcome this categorical introduction to some of the key areas of modern mathematics, without being forced to study category theory. Rather, each of the eight largely independent chapters analyzes a particular subject, revealing the power and applicability of the categorical foundations in each case.

A series of important applications of combinatorics on words has emerged with the development of computerized text and string processing. The aim of this volume, the third in a trilogy, is to present a unified treatment of some of the major fields of applications. After an introduction that sets the scene and gathers together the basic facts, there follow chapters in which applications are considered in detail. The areas covered include core algorithms for text processing, natural language processing, speech processing, bioinformatics, and areas of applied mathematics such as combinatorial...

Dynamic data assimilation is the assessment, combination and synthesis of observational data, scientific laws and mathematical models to determine the state of a complex physical system, for instance as a preliminary step in making predictions about the system's behaviour. The topic has assumed increasing importance in fields such as numerical weather prediction where conscientious efforts are being made to extend the term of reliable weather forecasts beyond the few days that are presently feasible. This book is designed to be a basic one-stop reference for graduate students and researchers....

Some of the most beautiful mathematical objects found in the last forty years are the sporadic simple groups. However, gaining familiarity with these groups presents problems for two reasons. First, they were discovered in many different ways, so to understand their constructions in depth one needs to study lots of different techniques. Second, since each of them is in a sense recording some exceptional symmetry in spaces of certain dimensions, they are by their nature highly complicated objects with a rich underlying combinatorial structure. Motivated by initial results which showed that the...

Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. The subject overlaps with convex geometry and employs many tools from that area, including some formulas from integral geometry. It also has connections to discrete tomography, geometric probing in robotics and to stereology. This comprehensive study provides a rigorous treatment of the subject. Although...

Spline functions are universally recognized as highly effective tools in approximation theory, computer-aided geometric design, image analysis, and numerical analysis. The theory of univariate splines is well known but this text is the first comprehensive treatment of the analogous bivariate theory. A detailed mathematical treatment of polynomial splines on triangulations is outlined, providing a basis for developing practical methods for using splines in numerous application areas. The detailed treatment of the Bernstein-Bezier representation of polynomials will provide a valuable source for...

Sylvia Scribner's contributions to the emergent field of cultural psychology have been monumental. Her studies of reasoning and thinking within contexts of culture and activity added new concepts, methods, and findings to what many now consider a distinctive branch of psychology. Mind and Social Practice brings together published and unpublished work from Sylvia Scribner's wide-ranging and prolific career. The book is arranged chronologically and includes five section introductions by the editors, placing Scribner's work in the context of her life, her commitments, and the political and...