Mathematica, Maple, and similar software packages provide programs that carry out sophisticated mathematical operations. Applying the ideas introduced in Computer Algebra and Symbolic Computation: Elementary Algorithms, this book explores the application of algorithms to such methods as automatic simplification, polynomial decomposition, and polyno

This book provides a systematic approach for the algorithmic formulation and implementation of mathematical operations in computer algebra programming languages. The viewpoint is that mathematical expressions, represented by expression trees, are the data objects of computer algebra programs, and by using a few primitive operations that analyze and

This book is not a conventional political narrative of Carolingian history shaped by narrative sources, capitularies, and charter material. It is structured, instead, by numismatic, diplomatic, liturgical, and iconographic sources and deals with political signs, images, and fixed formulas in them as interconnected elements in a symbolic language that was used in the indirect negotiation and maintenance of Carolingian authority. Building on the comprehensive analysis of royal liturgy, intitulature, iconography, and graphic signs and responding to recent interpretations of early medieval politics, this book offers a fresh view of Carolingian political culture and of corresponding roles that royal/imperial courts, larger monasteries, and human agents played there.

This extensive library of computer programs-written in C language-allows readers to solve numerical problems in areas of linear algebra, ordinary and partial differential equations, optimization, parameter estimation, and special functions of mathematical physics. The library is based on NUMAL, the program assemblage developed and used at the Centre for Mathematics and Computer Science in Amsterdam, one of the world's leading research centers. The important characteristic of the library is its modular structure. Because it is highly compact, it is well-suited for use on personal computers. The library offers the expert a prodigious collection of procedures for implementing numerical methods. The novice can experiment with the worked examples provided and use the more comprehensive procedures to perform mathematical computations. The library provides a powerful research tool for computer scientists, engineers, and applied mathematicians. Applicable materials can be downloaded from the CRC Press website.

Latest Edition: Applied Symbolic Dynamics and Chaos (2nd Edition)Symbolic dynamics is a coarse-grained description of dynamics. It provides a rigorous way to understand the global systematics of periodic and chaotic motion in a system. In the last decade it has been applied to nonlinear systems described by one- and two-dimensional maps as well as by ordinary differential equations. This book will help practitioners in nonlinear science and engineering to master that powerful tool.

This book explores the use and development of man's symbolizing capacities-those qualities that make him distinctly human. Dr. Whitmont describes the symbolic approach to a dream, which takes into account a symptom's meaning in reference to an unfolding wholeness of personality. He then presents the view that the instinctual urge for meaning is served by the symbolizing capacities, and that this urge has been repressed in our time. In the field of psychology, this symbolic approach is most fully exemplified by the theories of C. G. Jung. The author's contribution includes many differentiations and speculations, especially concerning the problems of relatedness.

This book explores why, regarding practical reasoning, humans are sometimes still faster than artificial intelligence systems. It is the first to offer a self-contained presentation of neural network models for many computer science logics.

Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, tilings and stringology. It will also interest biologists using text algorithms.