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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.

  • An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics

    • 1st Edition
    • Volume 41
    • English

  • The Kleene Symposium

    • 1st Edition
    • J. Barwise + 2 more
    • English

  • Cohomology of Completions

    • 1st Edition
    • Volume 42
    • English

  • Some Applications of Topological K-Theory

    • 1st Edition
    • Volume 45
    • English

  • Functional Analysis: Surveys and Recent Results II

    • 1st Edition
    • Volume 38
    • K.-D. Bierstedt + 1 more
    • English

  • Introduction to Algebraic Geometry and Algebraic Groups

    • 1st Edition
    • Volume 39
    • English

  • Nonlinear Partial Differential Equations

    Sequential and weak solutions
    • 1st Edition
    • Volume 44
    • English

  • Graphs and Questionnaires

    • 1st Edition
    • Volume 32
    • English

  • Topics in Arithmetical Functions

    Asymptotic formulae for sums of reciprocals of arithmetical functions and related results
    • 1st Edition
    • Volume 43
    • English

  • Algebra for College Students

    • 1st Edition
    • Bernard Kolman + 1 more
    • English

  • Asymptotic Theory of Statistical Tests and Estimation

    In Honor of Wassily Hoeffding
    • 1st Edition
    • I. M. Chakravarti
    • English

  • New Developments in Boundary Elements Method

    Proceedings of the Second International Seminar on Recent Advances in Boundary Element Methods, held at the University of Southampton, March 1980
    • 1st Edition
    • C. A. Brebbia
    • English

  • Beginning Algebra

    • 1st Edition
    • Charles P. McKeague
    • English

  • Introduction to Metamathematics

    • 1st Edition
    • S.C. Kleene
    • English
    Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Gadel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic, at least a turning point after which nothing was ever the same. Kleene was an important figure in logic, and lived a long full life of scholarship and teaching. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of philosophical speculation to the realm of science. This was accomplished by the work of Kurt Gade1, Alan Turing, and Alonzo Church, who gave three apparently different precise definitions of computable. When they all turned out to be equivalent, there was a collective realization that this was indeed the right notion. Kleene played a key role in this process. One could say that he was there at the beginning of modern logic. He showed the equivalence of lambda calculus with Turing machines and with Gadel's recursion equations, and developed the modern machinery of partial recursive functions. This textbook played an invaluable part in educating the logicians of the present. It played an important role in their own logical education.

  • Multivariate Analysis

    • 1st Edition
    • Kanti V. Mardia + 2 more
    • English
    Multivariate Analysis deals with observations on more than one variable where there is some inherent interdependence between the variables. With several texts already available in this area, one may very well enquire of the authors as to the need for yet another book. Most of the available books fall into two categories, either theoretical or data analytic. The present book not only combines the two approaches but it also has been guided by the need to give suitable matter for the beginner as well as illustrating some deeper aspects of the subject for the research worker. Practical examples are kept to the forefront and, wherever feasible, each technique is motivated by such an example.

  • Functional Integration and Quantum Physics

    • 1st Edition
    • Volume 86
    • English
    It is fairly well known that one of Hilbert’s famous list of problems is that of developing an axiomatic theory of mathematical probability theory (this problem could be said to have been solved by Khintchine, Kolmogorov, andLevy), and also among the list is the “axiomatization of physics.” What is not so well known is that these are two parts of one and the same problem, namely, the sixth, and that the axiomatics of probability are discussed in the context of the foundations of statistical mechanics. Although Hilbert could not have known it when he formulated his problems, probability theory is also central to the foundations of quantum theory. In this book, I wish to describe a very different interface between probability and mathematical physics, namely, the use of certain notions of integration in function spaces as technical tools in quantum physics. Although Nelson has proposed some connection between these notions and foundational questions, we shall deal solely with their use to answer a variety of questions inconventional quantum theory.

  • Stochastic Models: Estimation and Control: v. 1

    • 1st Edition
    • Volume 141A
    • Maybeck
    • English

  • Introduction to Homological Algebra, 85

    • 1st Edition
    • Joseph J. Rotman
    • English
    An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and often, this involves yet another language: spectral sequences. Homological algebra is an accessible subject to those who wish to learn it, and this book is the author’s attempt to make it lovable. This book comprises 11 chapters, with an introductory chapter that focuses on line integrals and independence of path, categories and functors, tensor products, and singular homology. Succeeding chapters discuss Hom and Ⓧ; projectives, injectives, and flats; specific rings; extensions of groups; homology; Ext; Tor; son of specific rings; the return of cohomology of groups; and spectral sequences, such as bicomplexes, Kunneth Theorems, and Grothendieck Spectral Sequences. This book will be of interest to practitioners in the field of pure and applied mathematics.

  • III: Scattering Theory

    • 1st Edition
    • Volume 3
    • Michael Reed + 1 more
    • English
    Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second, one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example, in x-ray crystallography (which led to the discovery of DNA), tomography, and the detection of underwater objects by sonar, the underlying dynamics is well understood. What one would like to construct are correspondences that link, via the dynamics, the position, shape, and internal structure of the object to the scattering data. Ideally, the correspondence should be an explicit formula which allows one to reconstruct, at least approximately, the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton, had he bothered to ask the right question, its calculation is generally attributed to Rutherford more than two hundred years later. Of course, Rutherford's calculation was in connection with the first experiment in nuclear physics.

  • Differential Geometry, Lie Groups, and Symmetric Spaces

    • 1st Edition
    • Volume 80
    • Sigurdur Helgason
    • English
    The present book is intended as a textbook and reference work on three topics in the title. Together with a volume in progress on "Groups and Geometric Analysis" it supersedes my "Differential Geometry and Symmetric Spaces," published in 1962. Since that time several branches of the subject, particularly the function theory on symmetric spaces, have developed substantially. I felt that an expanded treatment might now be useful.

  • Developing Mathematics in Third World Countries

    Proceedings of the international conference held in Khartoum, March 6-9, 1978
    • 1st Edition
    • Volume 33
    • English

  • Transmutation and Operator Differential Equations

    • 1st Edition
    • Volume 37
    • English

  • Approximation Theory and Functional Analysis

    Proceedings of the International Symposium on Approximation Theory, Universidade Estadual de Campinas (UNICAMP) Brazil, August 1-5, 1977
    • 1st Edition
    • Volume 35
    • English

  • Rings of Differential Operators

    • 1st Edition
    • Volume 21
    • J.-E. Björk
    • English

  • Bifurcation of Maps and Applications

    • 1st Edition
    • Volume 36
    • English

  • Probabilities and Potential, A

    • 1st Edition
    • Volume 29
    • C. Dellacherie + 1 more
    • English

  • Set Theory

    • 1st Edition
    • Volume 79
    • English

  • Formal Groups and Applications

    • 1st Edition
    • Volume 78
    • English

  • Functional Analysis

    • 1st Edition
    • Volume 81
    • English

  • General lattice theory

    • 1st Edition
    • Volume 75
    • English

  • Locally Solid Riesz Spaces

    • 1st Edition
    • Volume 76
    • English

  • IV: Analysis of Operators

    • 1st Edition
    • Volume 4
    • Michael Reed + 1 more
    • English
    BESTSELLER of the XXth Century in Mathematical Physics voted on by participants of the XIIIth International Congress on Mathematical PhysicsThis revision will make this book mroe attractive as a textbook in functional analysis. Further refinement of coverage of physical topics will also reinforce its well-established use as a course book in mathemtical physics.

  • Invariant Variational Principles

    • 1st Edition
    • Volume 138
    • Logan
    • English

  • Moving Boundary Problems

    • 1st Edition
    • D. G. Wilson + 2 more
    • English

  • Contemporary Developments in Continuum Mechanics and Partial Differential Equations

    Proceedings of the International Symposium on Continuum Mechanics and Partial Differential Equations, Rio de Janeiro, August 1977
    • 1st Edition
    • Volume 30
    • English

  • Asymptotic Analysis for Periodic Structures

    • 1st Edition
    • Volume 5
    • G. Papanicolau + 2 more
    • English

  • Differential Equations and Applications

    Proceedings of the Third Scheveningen Conference on Differential Equations, the Netherlands, August 29-September 2, 1977
    • 1st Edition
    • Volume 31
    • English

  • Studies in Foundations and Combinatorics

    • 1st Edition
    • Gian-Carlo Rota
    • English

  • Algorithmic Aspects of Combinatorics

    • 1st Edition
    • B. Alspach + 2 more
    • English

  • Nonlinearity and Functional Analysis

    Lectures on Nonlinear Problems in Mathematical Analysis
    • 1st Edition
    • Melvyn S. Berger
    • English
    Nonlinearity and Functional Analysis is a collection of lectures that aim to present a systematic description of fundamental nonlinear results and their applicability to a variety of concrete problems taken from various fields of mathematical analysis. For decades, great mathematical interest has focused on problems associated with linear operators and the extension of the well-known results of linear algebra to an infinite-dimensional context. This interest has been crowned with deep insights, and the substantial theory that has been developed has had a profound influence throughout the mathematical sciences. This volume comprises six chapters and begins by presenting some background material, such as differential-geometr... sources, sources in mathematical physics, and sources from the calculus of variations, before delving into the subject of nonlinear operators. The following chapters then discuss local analysis of a single mapping and parameter dependent perturbation phenomena before going into analysis in the large. The final chapters conclude the collection with a discussion of global theories for general nonlinear operators and critical point theory for gradient mappings. This book will be of interest to practitioners in the fields of mathematics and physics, and to those with interest in conventional linear functional analysis and ordinary and partial differential equations.

  • Functional Analysis in Modern Applied Mathematics

    • 1st Edition
    • Volume 132
    • English
    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.

  • Elements of Set Theory

    • 1st Edition
    • Herbert B. Enderton
    • English
    This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

  • Probability Methods for Approximations in Stochastic Control and for Elliptic Equations

    • 1st Edition
    • Volume 129
    • Kushner
    • English

  • Modular Representations of Finite Groups

    • 1st Edition
    • Volume 73
    • English

  • System Identification Advances and Case Studies

    • 1st Edition
    • Volume 126
    • English
    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.

  • Statistical Methods for Social Scientists

    • 1st Edition
    • Eric A. Hanushek + 1 more
    • Peter H. Rossi
    • English
    The aspects of this text which we believe are novel, at least in degree, include: an effort to motivate different sections with practical examples and an empirical orientation; an effort to intersperse several easily motivated examples throughout the book and to maintain some continuity in these examples; and the extensive use of Monte Carlo simulations to demonstrate particular aspects of the problems and estimators being considered. In terms of material being presented, the unique aspects include the first chapter which attempts to address the use of empirical methods in the social sciences, the seventh chapter which considers models with discrete dependent variables and unobserved variables. Clearly these last two topics in particular are quite advanced--more advanced than material that is currently available on the subject. These last two topics are also currently experiencing rapid development and are not adequately described in most other texts.

  • Introduction to the Theory of Infiniteseimals

    • 1st Edition
    • Volume 72
    • English

  • Singular and Degenerate Cauchy Problems

    • 1st Edition
    • Volume 127
    • English
    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.

  • Functional Analysis: Surveys and Recent Results

    Proceedings of the Conference on Functional Analysis, Paderborn, Germany, November 17-21, 1976
    • 1st Edition
    • Volume 27
    • English

  • Infinite Dimensional Holomorphy and Applications

    • 1st Edition
    • Volume 12
    • English

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