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Elsevier

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.

  • The Infinite-Dimensional Topology of Function Spaces

    • 1st Edition
    • Volume 64
    • J. van Mill
    • English
    In this book we study function spaces of low Borel complexity.Technique... from general topology, infinite-dimensional topology, functional analysis and descriptive set theoryare primarily used for the study of these spaces. The mix ofmethods from several disciplines makes the subjectparticularly interesting. Among other things, a complete and self-contained proof of the Dobrowolski-Marcisze... Theorem that all function spaces of low Borel complexity are topologically homeomorphic, is presented.In order to understand what is going on, a solid background ininfinite-dimension... topology is needed. And for that a fair amount of knowledge of dimension theory as well as ANR theory is needed. The necessary material was partially covered in our previous book `Infinite-dimensiona... topology, prerequisites and introduction'. A selection of what was done there can be found here as well, but completely revised and at many places expanded with recent results. A `scenic' route has been chosen towards theDobrowolski-Marci... Theorem, linking theresults needed for its proof to interesting recent research developments in dimension theory and infinite-dimensional topology.The first five chapters of this book are intended as a text forgraduate courses in topology. For a course in dimension theory, Chapters 2 and 3 and part of Chapter 1 should be covered. For a course in infinite-dimensional topology, Chapters 1, 4 and 5. In Chapter 6, which deals with function spaces, recent research results are discussed. It could also be used for a graduate course in topology but its flavor is more that of a research monograph than of a textbook; it is thereforemore suitable as a text for a research seminar. The bookconsequently has the character of both textbook and a research monograph. In Chapters 1 through 5, unless statedotherwise, all spaces under discussion are separable andmetrizable. In Chapter 6 results for more general classes of spaces are presented.In Appendix A for easy reference and some basic facts that are important in the book have been collected. The book is not intended as a basis for a course in topology; its purpose is to collect knowledge about general topology.The exercises in the book serve three purposes: 1) to test the reader's understanding of the material 2) to supply proofs of statements that are used in the text, but are not proven there3) to provide additional information not covered by the text.Solutions to selected exercises have been included in Appendix B.These exercises are important or difficult.

  • Multivariate Polysplines

    Applications to Numerical and Wavelet Analysis
    • 1st Edition
    • Ognyan Kounchev
    • English
    Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design of surfaces and "smoothing" that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effective than well-established methods, such as kKriging, radial basis functions, thin plate splines and minimum curvature.

  • Surface Topology

    • 3rd Edition
    • P A Firby + 1 more
    • English
    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
    • Miklós Farkas
    • English
    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.

  • Computable Calculus

    • 1st Edition
    • Oliver Aberth
    • English
    Computable Calculus treats the fundamental topic of calculus in a novel way that is more in tune with today's computer age. Comprising 11 chapters and an accompanying CD-ROM, the book presents mathematical analysis that has been created to deal with constructively defined concepts. The book's "show your work" approach makes it easier to understand the pitfalls of various computations and, more importantly, how to avoid these pitfalls. The accompanying CD-ROM has self-contained programs that interact with the text, providing for easy grasp of the new concepts and enabling readers to write their own demonstration programs.

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

    • 2nd Edition
    • Robert M. Young
    • English
    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
    • English

  • Graphs of Groups on Surfaces

    Interactions and Models
    • 1st Edition
    • Volume 188
    • A.T. White
    • English
    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.

  • Banach Algebras and Compact Operators

    • 1st Edition
    • Volume 2
    • English

  • Codes on Euclidean Spheres

    • 1st Edition
    • Volume 63
    • T. Ericson + 1 more
    • English
    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.

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