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

Surface Topology

3rd Edition
June 1, 2001
P A Firby + 1 more
English
Hardback
9 7 8 1 8 9 8 5 6 3 7 7 8
eBook
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This updated and revised edition of a widely acclaimed and successful text for undergraduates examines topology of recent compact surfaces through the development of simple ideas in plane geometry. Containing over 171 diagrams, the approach allows for a straightforward treatment of its subject area. It is particularly attractive for its wealth of applications and variety of interactions with branches of mathematics, linked with surface topology, graph theory, group theory, vector field theory, and plane Euclidean and non-Euclidean geometry.

Dynamical Models in Biology

1st Edition
May 23, 2001
Miklós Farkas
English
eBook
9 7 8 0 0 8 0 5 3 0 6 0 4

Dynamic Models in Biology offers an introduction to modern mathematical biology. This book provides a short introduction to modern mathematical methods in modeling dynamical phenomena and treats the broad topics of population dynamics, epidemiology, evolution, immunology, morphogenesis, and pattern formation. Primarily employing differential equations, the author presents accessible descriptions of difficult mathematical models. Recent mathematical results are included, but the author's presentation gives intuitive meaning to all the main formulae. Besides mathematicians who want to get acquainted with this relatively new field of applications, this book is useful for physicians, biologists, agricultural engineers, and environmentalists. Key Topics Include: Chaotic dynamics of populations The spread of sexually transmitted diseases Problems of the origin of life Models of immunology Formation of animal hide patterns The intuitive meaning of mathematical formulae explained with many figures Applying new mathematical results in modeling biological phenomena Miklos Farkas is a professor at Budapest University of Technology where he has researched and instructed mathematics for over thirty years. He has taught at universities in the former Soviet Union, Canada, Australia, Venezuela, Nigeria, India, and Columbia. Prof. Farkas received the 1999 Bolyai Award of the Hungarian Academy of Science and the 2001 Albert Szentgyorgyi Award of the Hungarian Ministry of Education.

An Introduction to Non-Harmonic Fourier Series, Revised Edition, 93

2nd Edition
May 16, 2001
Robert M. Young
English
Hardback
9 7 8 0 1 2 7 7 2 9 5 5 8
eBook
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An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

Banach Spaces

1st Edition
Volume 1
April 30, 2001
Corneliu Constantinescu
English
eBook
9 7 8 0 0 8 0 5 2 8 3 7 3

Graphs of Groups on Surfaces

1st Edition
Volume 188
April 27, 2001
A.T. White
English
eBook
9 7 8 0 0 8 0 5 0 7 5 8 3

The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English church-bell music. The latter is facilitated by imbedding the right graph of the right group on an appropriate surface, with suitable symmetries. Throughout the emphasis is on Cayley maps: imbeddings of Cayley graphs for finite groups as (possibly branched) covering projections of surface imbeddings of loop graphs with one vertex. This is not as restrictive as it might sound; many developments in topological graph theory involve such imbeddings.The approach aims to make all this interconnected material readily accessible to a beginning graduate (or an advanced undergraduate) student, while at the same time providing the research mathematician with a useful reference book in topological graph theory. The focus will be on beautiful connections, both elementary and deep, within mathematics that can best be described by the intuitively pleasing device of imbedding graphs of groups on surfaces.

Codes on Euclidean Spheres

1st Edition
Volume 63
April 27, 2001
T. Ericson + 1 more
English
eBook
9 7 8 0 0 8 0 5 0 2 1 6 8

Codes on Euclidean spheres are often referred to as spherical codes. They are of interest from mathematical, physical and engineering points of view. Mathematically the topic belongs to the realm of algebraic combinatorics, with close connections to number theory, geometry, combinatorial theory, and - of course - to algebraic coding theory. The connections to physics occur within areas like crystallography and nuclear physics. In engineering spherical codes are of central importance in connection with error-control in communication systems. In that context the use of spherical codes is often referred to as "coded modulation." The book offers a first complete treatment of the mathematical theory of codes on Euclidean spheres. Many new results are published here for the first time. Engineering applications are emphasized throughout the text. The theory is illustrated by many examples. The book also contains an extensive table of best known spherical codes in dimensions 3-24, including exact constructions.

Swarm Intelligence

1st Edition
March 26, 2001
Russell C. Eberhart + 2 more
English
Hardback
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eBook
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Traditional methods for creating intelligent computational systems haveprivileged private "internal" cognitive and computational processes. Incontrast, Swarm Intelligence argues that humanintelligence derives from the interactions of individuals in a social worldand further, that this model of intelligence can be effectively applied toartificially intelligent systems. The authors first present the foundations ofthis new approach through an extensive review of the critical literature insocial psychology, cognitive science, and evolutionary computation. Theythen show in detail how these theories and models apply to a newcomputational intelligence methodology—particle swarms—which focuseson adaptation as the key behavior of intelligent systems. Drilling downstill further, the authors describe the practical benefits of applying particleswarm optimization to a range of engineering problems. Developed bythe authors, this algorithm is an extension of cellular automata andprovides a powerful optimization, learning, and problem solving method. This important book presents valuable new insights by exploring theboundaries shared by cognitive science, social psychology, artificial life,artificial intelligence, and evolutionary computation and by applying theseinsights to the solving of difficult engineering problems. Researchers andgraduate students in any of these disciplines will find the materialintriguing, provocative, and revealing as will the curious and savvycomputing professional.

Handbook of Process Algebra

1st Edition
March 16, 2001
J.A. Bergstra + 2 more
English
eBook
9 7 8 0 0 8 0 5 3 3 6 7 4

Process Algebra is a formal description technique for complex computer systems, especially those involving communicating, concurrently executing components. It is a subject that concurrently touches many topic areas of computer science and discrete math, including system design notations, logic, concurrency theory, specification and verification, operational semantics, algorithms, complexity theory, and, of course, algebra.This Handbook documents the fate of process algebra since its inception in the late 1970's to the present. It is intended to serve as a reference source for researchers, students, and system designers and engineers interested in either the theory of process algebra or in learning what process algebra brings to the table as a formal system description and verification technique. The Handbook is divided into six parts spanning a total of 19 self-contained Chapters. The organization is as follows. Part 1, consisting of four chapters, covers a broad swath of the basic theory of process algebra. Part 2 contains two chapters devoted to the sub-specialization of process algebra known as finite-state processes, while the three chapters of Part 3 look at infinite-state processes, value-passing processes and mobile processes in particular. Part 4, also three chapters in length, explores several extensions to process algebra including real-time, probability and priority. The four chapters of Part 5 examine non-interleaving process algebras, while Part 6's three chapters address process-algebra tools and applications.

Nonlinear Equations and Optimisation

1st Edition
Volume 4
March 14, 2001
L.T. Watson + 2 more
English
eBook
9 7 8 0 0 8 0 9 2 9 5 4 5

/homepage/sac/cam/na... Set now available at special set price !In one of the papers in this collection, the remark that "nothing at all takes place in the universe in which some rule of maximum of minimum does not appear" is attributed to no less an authority than Euler. Simplifying the syntax a little, we might paraphrase this as Everything is an optimization problem. While this might be something of an overstatement, the element of exaggeration is certainly reduced if we consider the extended form: Everything is an optimization problem or a system of equations. This observation, even if only partly true, stands as a fitting testimonial to the importance of the work covered by this volume.Since the 1960s, much effort has gone into the development and application of numerical algorithms for solving problems in the two areas of optimization and systems of equations. As a result, many different ideas have been proposed for dealing efficiently with (for example) severe nonlinearities and/or very large numbers of variables. Libraries of powerful software now embody the most successful of these ideas, and one objective of this volume is to assist potential users in choosing appropriate software for the problems they need to solve. More generally, however, these collected review articles are intended to provide both researchers and practitioners with snapshots of the 'state-of-the-art' with regard to algorithms for particular classes of problem. These snapshots are meant to have the virtues of immediacy through the inclusion of very recent ideas, but they also have sufficient depth of field to show how ideas have developed and how today's research questions have grown out of previous solution attempts.The most efficient methods for local optimization, both unconstrained and constrained, are still derived from the classical Newton approach.As well as dealing in depth with the various classical, or neo-classical, approaches, the selection of papers on optimization in this volume ensures that newer ideas are also well represented.Solving nonlinear algebraic systems of equations is closely related to optimization. The two are not completely equivalent, however, and usually something is lost in the translation.Algorith... for nonlinear equations can be roughly classified as locally convergent or globally convergent. The characterization is not perfect.Locally convergent algorithms include Newton's method, modern quasi-Newton variants of Newton's method, and trust region methods. All of these approaches are well represented in this volume.

Stochastic Processes: Theory and Methods

1st Edition
Volume 19
March 8, 2001
D N Shanbhag
English
Hardback
9 7 8 0 4 4 4 5 0 0 1 4 4

J. Neyman, one of the pioneers in laying the foundations of modern statistical theory, stressed the importance of stochastic processes in a paper written in 1960 in the following terms: Currently in the period of dynamic indeterminism in science, there is hardly a serious piece of research, if treated realistically, does not involve operations on stochastic processes. Arising from the need to solve practical problems, several major advances have taken place in the theory of stochastic processes and their applications. Books by Doob (1953; J. Wiley and Sons), Feller (1957, 1966; J. Wiley and Sons) and Loeve (1960; D. van Nostrand and Col., Inc.) among others, have created growing awareness and interest in the use of stochastic processes in scientific and technological studies.The literature on stochastic processes is very extensive and is distributed in several books and journals.

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