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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.

BooksJournals

    • Fundamental Concepts of Mathematics

      • 2nd Edition
      • July 14, 2014
      • R. L. Goodstein
      • I. N. Sneddon
      • English
      • Paperback
        9 7 8 1 4 8 3 1 2 1 6 3 5
      • eBook
        9 7 8 1 4 8 3 1 5 4 0 5 3
      Fundamental Concepts of Mathematics, 2nd Edition provides an account of some basic concepts in modern mathematics. The book is primarily intended for mathematics teachers and lay people who wants to improve their skills in mathematics. Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. Unlike in the first edition, the second edition provides detailed solutions to exercises contained in the text. Mathematics teachers and people who want to gain a thorough understanding of the fundamental concepts of mathematics will find this book a good reference.

    • Introduction to Calculus

      • 2nd Edition
      • Volume 17
      • July 14, 2014
      • Kazimierz Kuratowski
      • A. J. Lohwater
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 9 1 9 7
      • eBook
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      The English edition does not differ essentially from the Polish one. Among the more important supplements I should mention § 6.5 containing elementary information on the notation of mathematical logic. To this supplement I was inclined by the experience of many years. For many students (not for all, perhaps) the notation of definitions of certain notions by means of the logical symbols makes it easier to understand these notions (e.g. the notions of uniform continuity or uniform convergence). Besides that, this supplement is included in the book in such a manner that it can be omitted in reading the whole book. Among other changes introduced in the English text, I should mention the addition of a number of exercises and problems; in the second English edition, many of them have been collected in the Supplement. I am glad also to mention the simplification of certain proofs, and finally the removal of mistakes which were found in the primary text

    • Analytic Properties of Automorphic L-Functions

      • 1st Edition
      • Volume 6
      • July 14, 2014
      • Stephen Gelbart + 1 more
      • J. Coates + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 3 9 3 0 9
      • eBook
        9 7 8 1 4 8 3 2 6 1 0 3 4
      Analytic Properties of Automorphic L-Functions is a three-chapter text that covers considerable research works on the automorphic L-functions attached by Langlands to reductive algebraic groups. Chapter I focuses on the analysis of Jacquet-Langlands methods and the Einstein series and Langlands’ so-called “Euler products”. This chapter explains how local and global zeta-integrals are used to prove the analytic continuation and functional equations of the automorphic L-functions attached to GL(2). Chapter II deals with the developments and refinements of the zeta-inetgrals for GL(n). Chapter III describes the results for the L-functions L (s, ?, r), which are considered in the constant terms of Einstein series for some quasisplit reductive group. This book will be of value to undergraduate and graduate mathematics students.

    • Huygens' Principle and Hyperbolic Equations

      • 1st Edition
      • Volume 5
      • July 14, 2014
      • Gunther Paul
      • J. Coates + 1 more
      • English
      • eBook
        9 7 8 1 4 8 3 2 6 2 2 2 2
      Huygens' Principle and Hyperbolic Equations is devoted to certain mathematical aspects of wave propagation in curved space-times. The book aims to present special nontrivial Huygens' operators and to describe their individual properties and to characterize these examples of Huygens' operators within certain more or less comprehensive classes of general hyperbolic operators. The materials covered in the book include a treatment of the wave equation for p-forms over a space of constant sectional curvature, the Riesz distributions, the Euler-Poisson-Darbou... over a Riemannian manifold, and plane wave manifolds. Physicists will find the book invaluable.

    • Non-Linear Differential Equations

      • 1st Edition
      • Volume 67
      • July 14, 2014
      • G. Sansone + 1 more
      • I. N. Sneddon + 2 more
      • English
      • Paperback
        9 7 8 1 4 8 3 1 6 9 2 4 8
      • eBook
        9 7 8 1 4 8 3 1 8 5 0 5 7
      Non-Linear Differential Equations covers the general theorems, principles, solutions, and applications of non-linear differential equations. This book is divided into nine chapters. The first chapters contain detailed analysis of the phase portrait of two-dimensional autonomous systems. The succeeding chapters deal with the qualitative methods for the discovery of periodic solutions in periodic systems. The remaining chapters describe a synthetical approach to the study of asymptotic properties, especially stability properties, of the solutions of general n-dimensional systems. This book will be of great value to mathematicians, researchers, and students.

    • Recent Topics in Differential and Analytic Geometry

      • 1st Edition
      • Volume 18
      • July 14, 2014
      • T. Ochiai
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 1 2 5 2
      • eBook
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      Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains. Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters consider the most recognized non-standard examples of compact homogeneous Einstein manifolds constructed via Riemannian submersions. This book discusses as well the natural compactification of the moduli space of polarized Einstein–Kähler orbitfold with a given Hilbert polynomials. The final chapter deals with solving a degenerate Monge–Ampère equation by constructing a family of Einstein–Kähler metrics on the smooth part of minimal varieties of general kind. This book is a valuable resource for graduate students and pure mathematicians.

    • Automorphic Forms and Geometry of Arithmetic Varieties

      • 1st Edition
      • July 14, 2014
      • K. Hashimoto + 1 more
      • English
      • Paperback
        9 7 8 1 4 8 3 2 0 4 6 4 2
      • eBook
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      Automorphic Forms and Geometry of Arithmetic Varieties deals with the dimension formulas of various automorphic forms and the geometry of arithmetic varieties. The relation between two fundamental methods of obtaining dimension formulas (for cusp forms), the Selberg trace formula and the index theorem (Riemann-Roch's theorem and the Lefschetz fixed point formula), is examined. Comprised of 18 sections, this volume begins by discussing zeta functions associated with cones and their special values, followed by an analysis of cusps on Hilbert modular varieties and values of L-functions. The reader is then introduced to the dimension formula of Siegel modular forms; the graded rings of modular forms in several variables; and Selberg-Ihara's zeta function for p-adic discrete groups. Subsequent chapters focus on zeta functions of finite graphs and representations of p-adic groups; invariants and Hodge cycles; T-complexes and Ogata's zeta zero values; and the structure of the icosahedral modular group. This book will be a useful resource for mathematicians and students of mathematics.

    • The Boundary Element Method for Plate Analysis

      • 1st Edition
      • July 11, 2014
      • John T. Katsikadelis
      • English
      • Paperback
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      • Hardback
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      • eBook
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      Boundary Element Method for Plate Analysis offers one of the first systematic and detailed treatments of the application of BEM to plate analysis and design. Aiming to fill in the knowledge gaps left by contributed volumes on the topic and increase the accessibility of the extensive journal literature covering BEM applied to plates, author John T. Katsikadelis draws heavily on his pioneering work in the field to provide a complete introduction to theory and application. Beginning with a chapter of preliminary mathematical background to make the book a self-contained resource, Katsikadelis moves on to cover the application of BEM to basic thin plate problems and more advanced problems. Each chapter contains several examples described in detail and closes with problems to solve. Presenting the BEM as an efficient computational method for practical plate analysis and design, Boundary Element Method for Plate Analysis is a valuable reference for researchers, students and engineers working with BEM and plate challenges within mechanical, civil, aerospace and marine engineering.

    • Introduction to Set Theory and Topology

      • 2nd Edition
      • July 10, 2014
      • Kazimierz Kuratowski
      • I. S. Sneddon + 1 more
      • English
      • Paperback
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      • eBook
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      Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.

    • Boundary Value Problems

      • 1st Edition
      • July 10, 2014
      • F. D. Gakhov
      • I. N. Sneddon + 2 more
      • English
      • Paperback
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      • eBook
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      Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems, emphasis is on linear problems with one unknown function. The definition of the Cauchy type integral, examples, limiting values, behavior, and its principal value are explained. The Riemann boundary value problem is emphasized in considering the theory of boundary value problems of analytic functions. The book then analyzes the application of the Riemann boundary value problem as applied to singular integral equations with Cauchy kernel. A second fundamental boundary value problem of analytic functions is the Hilbert problem with a Hilbert kernel; the application of the Hilbert problem is also evaluated. The use of Sokhotski's formulas for certain integral analysis is explained and equations with logarithmic kernels and kernels with a weak power singularity are solved. The chapters in the book all end with some historical briefs, to give a background of the problem(s) discussed. The book will be very valuable to mathematicians, students, and professors in advanced mathematics and geometrical functions.

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