Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

Books Journals

Chaos and Fractals

1st Edition
August 3, 1998
C.A. Pickover
English
eBook
9 7 8 0 0 8 0 5 2 8 8 6 1

These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art.Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art.Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.

Handbook of Proof Theory

1st Edition
Volume 137
July 9, 1998
S.R. Buss
English
Hardback
9 7 8 0 4 4 4 8 9 8 4 0 1
eBook
9 7 8 0 0 8 0 5 3 3 1 8 6

This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

Regression Analysis for Social Sciences

1st Edition
June 25, 1998
Alexander von Eye + 1 more
English
eBook
9 7 8 0 0 8 0 5 5 0 8 2 4

Regression Analysis for Social Sciences presents methods of regression analysis in an accessible way, with each method having illustrations and examples. A broad spectrum of methods are included: multiple categorical predictors, methods for curvilinear regression, and methods for symmetric regression. This book can be used for courses in regression analysis at the advanced undergraduate and beginning graduate level in the social and behavioral sciences. Most of the techniques are explained step-by-step enabling students and researchers to analyze their own data. Examples include data from the social and behavioral sciences as well as biology, making the book useful for readers with biological and biometrical backgrounds. Sample command and result files for SYSTAT are included in the text.

Vector Calculus

1st Edition
May 1, 1998
William Cox
English
eBook
9 7 8 0 0 8 0 5 7 2 9 5 6

Building on previous texts in the Modular Mathematics series, in particular 'Vectors in Two or Three Dimensions' and 'Calculus and ODEs', this book introduces the student to the concept of vector calculus. It provides an overview of some of the key techniques as well as examining functions of more than one variable, including partial differentiation and multiple integration.Undergra... who already have a basic understanding of calculus and vectors, will find this text provides tools with which to progress onto further studies; scientists who need an overview of higher order differential equations will find it a useful introduction and basic reference.

Stream Ciphers and Number Theory

1st Edition
Volume 55
April 20, 1998
T.W. Cusick + 2 more
English
eBook
9 7 8 0 0 8 0 5 4 1 8 4 6

This book is almost entirely concerned with stream ciphers, concentrating on a particular mathematical model for such ciphers which are called additive natural stream ciphers. These ciphers use a natural sequence generator to produce a periodic keystream. Full definitions of these concepts are given in Chapter 2.This book focuses on keystream sequences which can be analysed using number theory. It turns out that a great deal of information can be deducted about the cryptographic properties of many classes of sequences by applying the terminology and theorems of number theory. These connections can be explicitly made by describing three kinds of bridges between stream ciphering problems and number theory problems. A detailed summary of these ideas is given in the introductory Chapter 1.Many results in the book are new, and over seventy percent of these results described in this book are based on recent research results.

Parallel Computational Fluid Dynamics '97

1st Edition
April 17, 1998
D. Emerson + 4 more
English
eBook
9 7 8 0 0 8 0 5 3 8 3 7 2

Computational Fluid Dynamics (CFD) is a discipline that has always been in the vanguard of the exploitation of emerging and developing technologies. Advances in both algorithms and computers have rapidly been absorbed by the CFD community in its quest for more accurate simulations and reductions in the time to solution. Within this context, parallel computing has played an increasingly important role. Moreover, the uptake of parallel computing has brought the CFD community into ever-closer contact with hardware vendors and computer scientists. The multidisciplinary subject of parallel CFD and its rapidly evolving nature, in terms of hardware and software, requires a regular international meeting of this nature to keep abreast of the most recent developments.Paralle... CFD '97 is part of an annual conference series dedicated to the discussion of recent developments and applications of parallel computing in the field of CFD and related disciplines. This was the 9th in the series, and since the inaugural conference in 1989, many new developments and technologies have emerged. The intervening years have also proved to be extremely volatile for many hardware vendors and a number of companies appeared and then disappeared. However, the belief that parallel computing is the only way forward has remained undiminished. Moreover, the increasing reliability and acceptance of parallel computers has seen many commercial companies now offering parallel versions of their codes, many developed within the EC funded EUROPORT activity, but generally for more modest numbers of processors. It is clear that industry has not moved to large scale parallel systems but it has shown a keen interest in more modest parallel systems recognising that parallel computing will play an important role in the future. This book forms the proceedings of the CFD '97 conference, which was organised by the the Computational Engineering Group at Daresbury Laboratory and held in Manchester, England, on May 19-21 1997. The sessions involved papers on many diverse subjects including turbulence, reactive flows, adaptive schemes, unsteady flows, unstructured mesh applications, industrial applications, developments in software tools and environments, climate modelling, parallel algorithms, evaluation of computer architectures and a special session devoted to parallel CFD at the AEREA research centres. This year's conference, like its predecessors, saw a continued improvement in both the quantity and quality of contributed papers.Since the conference series began many significant milestones have been acheived. For example in 1994, Massively Parallel Processing (MPP) became a reality with the advent of Cray T3D. This, of course, has brought with it the new challenge of scalability for both algorithms and architectures. In the 12 months since the 1996 conference, two more major milestones were achieved: microprocessors with a peak performance of a Gflop/s became available and the world's first Tflop/s calculation was performed. In the 1991 proceedings, the editors indicated that a Tflop/s computer was likely to be available in the latter half of this decade. On December 4th 1996, Intel achieved this breakthrough on the Linpack benchmark using 7,264 (200MHz) Pentium Pro microprocessors as part of the ASCI Red project. With the developments in MPP, the rapid rise of SMP architectures and advances in PC technology, the future for parallel CFD looks both promising and challenging.

Visualization of Categorical Data

1st Edition
February 9, 1998
Jörg Blasius + 1 more
English
eBook
9 7 8 0 0 8 0 5 4 3 6 2 8

A unique and timely monograph, Visualization of Categorical Data contains a useful balance of theoretical and practical material on this important new area. Top researchers in the field present the books four main topics: visualization, correspondence analysis, biplots and multidimensional scaling, and contingency table models.This volume discusses how surveys, which are employed in many different research areas, generate categorical data. It will be of great interest to anyone involved in collecting or analyzing categorical data.

Experimental Design Techniques in Statistical Practice

1st Edition
January 1, 1998
William P Gardiner + 1 more
English
eBook
9 7 8 0 8 5 7 0 9 9 7 8 5

Provides an introduction to the diverse subject area of experimental design, with many practical and applicable exercises to help the reader understand, present and analyse the data. The pragmatic approach offers technical training for use of designs and teaches statistical and non-statistical skills in design and analysis of project studies throughout science and industry.

Linear Algebra, Rational Approximation and Orthogonal Polynomials

1st Edition
Volume 6
November 17, 1997
A. Bultheel + 1 more
English
eBook
9 7 8 0 0 8 0 5 3 5 5 2 4

Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padé tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algorithms for structured problems and shows how they deal with singular situations.Links are made with more applied subjects such as linear system theory and signal processing, and with more advanced topics and recent results such as general bi-orthogonal polynomials, minimal Padé approximation, polynomial root location problems in the complex plane, very general rational interpolation problems, and the lifting scheme for wavelet transform computation. The text serves as a supplement to existing books on structured linear algebra problems, rational approximation and orthogonal polynomials.Features of this book:• provides a unifying approach to linear algebra, rational approximation and orthogonal polynomials• requires an elementary knowledge of calculus and linear algebra yet introduces advanced topics.The book will be of interest to applied mathematicians and engineers and to students and researchers.

Inequalities for Differential and Integral Equations

1st Edition
Volume 197
November 12, 1997
William F. Ames + 1 more
English
eBook
9 7 8 0 0 8 0 5 3 4 6 4 0

Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course.

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