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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.

  • Intensional Mathematics

    • 1st Edition
    • Volume 113
    • January 1, 1985
    • S. Shapiro
    • English
    ``Platonism and intuitionism are rival philosophies of Mathematics, the former holding that the subject matter of mathematics consists of abstract objects whose existence is independent of the mathematician, the latter that the subject matter consists of mental construction... both views are implicitly opposed to materialistic accounts of mathematics which take the subject matter of mathematics to consist (in a direct way) of material objects...'' FROM THE INTRODUCTIONAmong the aims of this book are: - The discussion of some important philosophical issues using the precision of mathematics. - The development of formal systems that contain both classical and constructive components. This allows the study of constructivity in otherwise classical contexts and represents the formalization of important intensional aspects of mathematical practice. - The direct formalization of intensional concepts (such as computability) in a mixed constructive/classic... context.

  • Graphs, Groups and Surfaces

    • 2nd Edition
    • Volume 8
    • January 1, 1985
    • A.T. White
    • English
    The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'' and 9 as ``unsolved''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''.

  • Eigenvalues in Riemannian Geometry

    • 2nd Edition
    • Volume 115
    • November 7, 1984
    • Isaac Chavel
    • English
    The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and results, currently used in the subject, to those working in it, and (iii) to present some of the results that are attractive in their own right, and which lend themselves to a presentation not overburdened with technical machinery.

  • Topics on Perfect Graphs

    • 1st Edition
    • Volume 21
    • November 1, 1984
    • V. Chvátal + 1 more
    • English
    The purpose of this book is to present selected results on perfect graphs in a single volume. These take the form of reprinted classical papers, survey papers or new results.

  • Mathematical Methods for Wave Phenomena

    • 1st Edition
    • July 27, 1984
    • Norman Bleistein
    • English
    Computer Science and Applied Mathematics: Mathematical Methods for Wave Phenomena focuses on the methods of applied mathematics, including equations, wave fronts, boundary value problems, and scattering problems. The publication initially ponders on first-order partial differential equations, Dirac delta function, Fourier transforms, asymptotics, and second-order partial differential equations. Discussions focus on prototype second-order equations, asymptotic expansions, asymptotic expansions of Fourier integrals with monotonic phase, method of stationary phase, propagation of wave fronts, and variable index of refraction. The text then examines wave equation in one space dimension, as well as initial boundary value problems, characteristics for the wave equation in one space dimension, and asymptotic solution of the Klein-Gordon equation. The manuscript offers information on wave equation in two and three dimensions and Helmholtz equation and other elliptic equations. Topics include energy integral, domain of dependence, and uniqueness, scattering problems, Green's functions, and problems in unbounded domains and the Sommerfeld radiation condition. The asymptotic techniques for direct scattering problems and the inverse methods for reflector imaging are also elaborated. The text is a dependable reference for computer science experts and mathematicians pursuing studies on the mathematical methods of wave phenomena.

  • Groups & Geometric Analysis

    Radon Transforms, Invariant Differential Operators and Spherical Functions: Volume 1
    • 1st Edition
    • Volume 113
    • June 30, 1984
    • English

  • Markov Chains

    • 1st Edition
    • Volume 11
    • May 1, 1984
    • D. Revuz
    • English
    This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail.The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.

  • The Smith Conjecture

    • 1st Edition
    • Volume 112
    • May 1, 1984
    • English

  • The Umbral Calculus

    • 1st Edition
    • Volume 111
    • March 21, 1984
    • English

  • Probability Theory with Applications

    • 1st Edition
    • February 1, 1984
    • M. M. Rao
    • English
    The material in this book is designed for a standard graduate course on probability theory, including some important applications. It was prepared from the sets of lecture notes for a course that I have taught several times over the past 20 years. The present version reflects the reactions of my audiences as well as some of the textbooks that I used.

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