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Books in Mathematics general

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Fundamental Concepts of Mathematics

  • 2nd Edition
  • July 14, 2014
  • R. L. Goodstein
  • I. N. Sneddon
  • English
  • 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.

Recent Topics in Differential and Analytic Geometry

  • 1st Edition
  • Volume 18
  • July 14, 2014
  • T. Ochiai
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 1 4 6 8 - 9
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.

Analytic Properties of Automorphic L-Functions

  • 1st Edition
  • Volume 6
  • July 14, 2014
  • Stephen Gelbart + 1 more
  • J. Coates + 1 more
  • English
  • 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-Darboux-equations over a Riemannian manifold, and plane wave manifolds. Physicists will find the book invaluable.

Automorphic Forms and Geometry of Arithmetic Varieties

  • 1st Edition
  • July 14, 2014
  • K. Hashimoto + 1 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 1 8 0 7 - 6
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.

Introduction to Calculus

  • 2nd Edition
  • Volume 17
  • July 14, 2014
  • Kazimierz Kuratowski
  • A. J. Lohwater
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 2 2 6 2 - 2
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

Calculus of Variations

  • 1st Edition
  • Volume 19
  • July 10, 2014
  • L. E. Elsgolc
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 3 7 5 6 - 8
Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter is illustrated by a large number of problems some of which are taken from existing textbooks. The solutions to the problems in each chapter are provided at the end of the book.

Foundations of Galois Theory

  • 1st Edition
  • July 10, 2014
  • M.M. Postnikov
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 5 6 4 7 - 7
Foundations of Galois Theory is an introduction to group theory, field theory, and the basic concepts of abstract algebra. The text is divided into two parts. Part I presents the elements of Galois Theory, in which chapters are devoted to the presentation of the elements of field theory, facts from the theory of groups, and the applications of Galois Theory. Part II focuses on the development of general Galois Theory and its use in the solution of equations by radicals. Equations that are solvable by radicals; the construction of equations solvable by radicals; and the unsolvability by radicals of the general equation of degree n ? 5 are discussed as well. Mathematicians, physicists, researchers, and students of mathematics will find this book highly useful.

Boundary Value Problems

  • 1st Edition
  • July 10, 2014
  • F. D. Gakhov
  • I. N. Sneddon + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 1 - 6 4 9 8 - 4
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.