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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.

  • Practical Studies in Systematic Design

    • 1st Edition
    • Vladimir Hubka + 2 more
    • English

  • BASIC Surveying

    • 1st Edition
    • W M Barnes
    • English

  • BASIC Forecasting Techniques

    • 1st Edition
    • David Johnson + 1 more
    • English

  • CD-ROM

    Fundamentals to Applications
    • 1st Edition
    • Charles Oppenheim
    • English

  • Using Ability on the Amstrad PC

    • 1st Edition
    • Samuel Kennington
    • English

  • Successful Spreadsheets Using Supercalc

    • 1st Edition
    • P.K. McBride
    • English

  • Mathematical Visions

    The Pursuit of Geometry in Victorian England
    • 1st Edition
    • Joan L. Richards
    • English

  • Graph Theory and Applications

    • 1st Edition
    • Volume 38
    • J. Akiyama + 2 more
    • English

  • Investigations in Number Theory

    • 1st Edition
    • T. Kubota
    • English

  • Recent Results in the Theory of Graph Spectra

    • 1st Edition
    • Volume 36
    • D.M. Cvetkovic + 3 more
    • English
    The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978.The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1.The study of various combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2.Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.

  • Operators and Representation Theory

    Canonical Models for Algebras of Operators Arising in Quantum Mechanics
    • 1st Edition
    • Volume 147
    • P.E.T. Jorgensen
    • English
    Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly elegant manner by the use of Lie algebras, extensions, and projective representations. In several cases, this Lie algebraic approach to questions in mathematical physics and C*-algebra theory is new; for example, the Lie algebraic treatment of the spectral theory of curved magnetic field Hamiltonians, the treatment of irrational rotation type algebras, and the Virasoro algebra.Also examined are C*-algebraic methods used (in non-traditional ways) in the study of representations of infinite-dimensional Lie algebras and their extensions, and the methods developed by A. Connes and M.A. Rieffel for the study of the Yang-Mills problem.Cutting across traditional separations between fields of specialization, the book addresses a broad audience of graduate students and researchers.

  • Generalized Solutions of Nonlinear Partial Differential Equations

    • 1st Edition
    • Volume 146
    • E.E. Rosinger
    • English
    During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concerning existence, uniqueness regularity, etc., of generalized solutions for nonlinear partial differential equations can be reduced to elementary calculus in Euclidean spaces, combined with elementary algebra in quotient rings of families of smooth functions on Euclidean spaces, all of that joined by certain asymptotic interpretations. In this way, one avoids the complexities and difficulties of the customary functional analytic methods which would involve sophisticated topologies on various function spaces. The result is a rather elementary yet powerful and far-reaching method which can, among others, give generalized solutions to linear and nonlinear partial differential equations previously unsolved or even unsolvable within distributions or hyperfunctions.Part 1 of the volume discusses the basic limitations of the linear theory of distributions when dealing with linear or nonlinear partial differential equations, particularly the impossibility and degeneracy results. Part 2 examines the way Colombeau constructs a nonlinear theory of generalized functions and then succeeds in proving quite impressive existence, uniqueness, regularity, etc., results concerning generalized solutions of large classes of linear and nonlinear partial differential equations. Finally, Part 3 is a short presentation of the nonlinear theory of Rosinger, showing its connections with Colombeau's theory, which it contains as a particular case.

  • Numerical Modelling: Applications to Marine Systems

    • 1st Edition
    • Volume 145
    • J. Noye
    • English
    The thirteen papers presented in this book are based on talks given at the workshop on Numerical Modelling of Marine Systems held at the University of Adelaide, South Australia in February 1986. Several of the articles are a direct outcome of two special sessions held on modelling of Open Boundary Conditions and on the Transport of Pollutants.Other articles in the book cover topics such as numerical modelling of wind-driven flow in shallow seas, sediment transport in estuaries, internal tides and comparison of numerical methods for solving tidal and pollutant transport problems.

  • Geometry of Numbers

    • 2nd Edition
    • Volume 37
    • C.G. Lekkerkerker + 1 more
    • English
    This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definite advantage of showing clearly where recent progress has taken place and in what areas interesting results may be expected in the future.

  • Difference Schemes

    An Introduction to the Underlying Theory
    • 1st Edition
    • Volume 19
    • S.K. Godunov + 1 more
    • English
    Much applied and theoretical research in natural sciences leads to boundary-value problems stated in terms of differential equations. When solving these problems with computers, the differential problems are replaced approximately by difference schemes.This book is an introduction to the theory of difference schemes, and was written as a textbook for university mathematics and physics departments and for technical universities. Some sections of the book will be of interest to computations specialists.While stressing a mathematically rigorous treatment of model problems, the book also demonstrates the relation between theory and computer experiments, using difference schemes created for practical computations.

  • The Algebraic Structure of Crossed Products

    • 1st Edition
    • Volume 142
    • G. Karpilovsky
    • English
    In the past 15 years, the theory of crossed products has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings.The purpose of this monograph is to give, in a self-contained manner, an up-to-date account of various aspects of this development, in an effort to convey a comprehensive picture of the current state of the subject. It is assumed that the reader has had the equivalent of a standard first-year graduate course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, which briefly surveys topics required later in the book.

  • Foundations of Analysis over Surreal Number Fields

    • 1st Edition
    • Volume 141
    • N.L. Alling
    • English
    In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway's field of surreal numbers is also given.Throughout the manuscript, great efforts have been made to make the volume fairly self-contained. Much exposition is given. Many references are cited. While experts may want to turn quickly to new results, students should be able to find the explanation of many elementary points of interest. On the other hand, many new results are given, and much mathematics is brought to bear on the problems at hand.

  • The Jacobson Radical of Group Algebras

    • 1st Edition
    • Volume 135
    • G. Karpilovsky
    • English
    Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J(FG) of FG is of fundamental importance. During the last two decades the subject has been pursued by a number of researchers and many interesting results have been obtained. This volume examines these results.The main body of the theory is presented, giving the central ideas, the basic results and the fundamental methods. It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, providing a survey of topics needed later in the book. There is a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest.

  • Inverse Spectral Theory

    • 1st Edition
    • Volume 130
    • Jurgen Poschel
    • English

  • Barrelled Locally Convex Spaces

    • 1st Edition
    • Volume 131
    • P. Pérez Carreras + 1 more
    • English
    This book is a systematic treatment of barrelled spaces, and of structures in which barrelledness conditions are significant. It is a fairly self-contained study of the structural theory of those spaces, concentrating on the basic phenomena in the theory, and presenting a variety of functional-analytic techniques.Beginning with some basic and important results in different branches of Analysis, the volume deals with Baire spaces, presents a variety of techniques, and gives the necessary definitions, exploring conditions on discs to ensure that they are absorbed by the barrels of the space. The abstract theory of barrelled spaces is then presented, as well as local completeness and its applications to the inheritance of the Mackey topology to subspaces. Further discussed is the abstract study of bornological and ultrabornological spaces; B- and Br-completeness; inductive limits; strong barrelledness conditions; characterizations of barrelled, bornological and (DF)-spaces in the context of spaces of type C(X); the stability of barrelledness conditions of topological tensor products and the related questions of commutability of inductive limits and tensor products; and the holomorphically significant properties of locally convex spaces as developed by Nachbin and others.

  • Obstacle Problems in Mathematical Physics

    • 1st Edition
    • Volume 134
    • J.-F. Rodrigues
    • English
    The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics.The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitati... problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.

  • Theory of Linear Operations

    • 1st Edition
    • Volume 38
    • S. Banach
    • English
    This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.

  • Numerical Approximation of Partial Differential Equations

    • 1st Edition
    • Volume 133
    • E.L. Ortiz
    • English
    This selection of papers is concerned with problems arising in the numerical solution of differential equations, with an emphasis on partial differential equations. There is a balance between theoretical studies of approximation processes, the analysis of specific numerical techniques and the discussion of their application to concrete problems relevant to engineering and science. Special consideration has been given to innovative numerical techniques and to the treatment of three-dimensional and singular problems. These topics are discussed in several of the invited papers.The contributed papers are divided into five parts: techniques of approximation theory which are basic to the numerical treatment of differential equations; numerical techniques based on discrete processes; innovative methods based on polynomial and rational approximation; variational inequalities, conformal transformation and asymptotic techniques; and applications of differential equations to problems in science and engineering.

  • Descriptive Set Theory

    • 1st Edition
    • Volume 100
    • Y.N. Moschovakis
    • English
    Now available in paperback, this monograph is a self-contained exposition of the main results and methods of descriptive set theory. It develops all the necessary background material from logic and recursion theory, and treats both classical descriptive set theory and the effective theory developed by logicians.

  • Digital Logic Design

    • 2nd Edition
    • B. Holdsworth
    • English

  • János Bolyai Appendix

    The Theory of Space
    • 1st Edition
    • Volume 138
    • F. Kárteszi + 1 more
    • English
    The epoch-making work of János Bolyai is presented here, together with a supplement outlining Hungarian political and science history to help the reader to get acquainted with the miserable fate of János Bolyai and with his intellectual world. A facsimile of a copy of Bolyai's original 1831 Scientia Spatii (also known as the Appendix) is included, together with a translation. Comments and notes, and a survey of the effects of his work, complete the volume.

  • Logic Colloquium '85

    • 1st Edition
    • Volume 122
    • The Paris Logic The Paris Logic Group
    • English
    The bulk of this volume consists of invited addresses presented at the Colloquium. These contributions report on recent or ongoing research in some of the mainstream areas of mathematical logic: model theory, both pure and in its applications (to group theory and real algebraic geometry); and proof theory, applied to set theory and diophantine equations.The major novel aspect of the book is the important place accorded to the connections of mathematical logic with the neighboring disciplines: mathematical foundations of computer science, and philosophy of mathematics.

  • Digital Logic Design

    • 2nd Edition
    • B. Holdsworth
    • English

  • Using GEM Paint on the Amstrad PC1512/1640

    • 2nd Edition
    • Stephen Morris
    • English

  • Decompositions of Manifolds

    • 1st Edition
    • Volume 124
    • English

  • Real-variable Methods in Harmonic Analysis

    • 1st Edition
    • Volume 123
    • English

  • Approximation of Continuously Differentiable Functions

    • 1st Edition
    • Volume 130
    • J.G. Llavona
    • English
    This self-contained book brings together the important results of a rapidly growing area.As a starting point it presents the classic results of the theory. The book covers such results as: the extension of Wells' theorem and Aron's theorem for the fine topology of order m; extension of Bernstein's and Weierstrass' theorems for infinite dimensional Banach spaces; extension of Nachbin's and Whitney's theorem for infinite dimensional Banach spaces; automatic continuity of homomorphisms in algebras of continuously differentiable functions, etc.

  • Boole's Logic and Probability

    A Critical Exposition from the Standpoint of Contemporary Algebra, Logic and Probability Theory
    • 2nd Edition
    • Volume 85
    • T. Hailperin
    • English
    Since the publication of the first edition in 1976, there has been a notable increase of interest in the development of logic. This is evidenced by the several conferences on the history of logic, by a journal devoted to the subject, and by an accumulation of new results. This increased activity and the new results - the chief one being that Boole's work in probability is best viewed as a probability logic - were influential circumstances conducive to a new edition.Chapter 1, presenting Boole's ideas on a mathematical treatment of logic, from their emergence in his early 1847 work on through to his immediate successors, has been considerably enlarged. Chapter 2 includes additional discussion of the ``uninterpretable'' notion, both semantically and syntactically. Chapter 3 now includes a revival of Boole's abandoned propositional logic and, also, a discussion of his hitherto unnoticed brush with ancient formal logic. Chapter 5 has an improved explanation of why Boole's probability method works. Chapter 6, Applications and Probability Logic, is a new addition. Changes from the first edition have brought about a three-fold increase in the bibliography.

  • A Mathematical Introduction to Dirac's Formalism

    • 1st Edition
    • Volume 36
    • S.J.L. van Eijndhoven + 1 more
    • English
    This monograph contains a functional analytic introduction to Dirac's formalism. The first part presents some new mathematical notions in the setting of triples of Hilbert spaces, mentioning the concept of Dirac basis. The second part introduces a conceptually new theory of generalized functions, integrating the notions of the first part.The last part of the book is devoted to a mathematical interpretation of the main features of Dirac's formalism. It involves a pairing between distributional bras and kets, continuum expansions and continuum matrices.

  • Recent Topics in Nonlinear PDE II

    • 1st Edition
    • K. Masuda + 1 more
    • English
    This volume is the result of lectures delivered at the second meeting on the subject of nonlinear partial differential equations, held at Tohoku University, 27-29 February 1984. The topics presented at the conference range over various fields of mathematical physics.

  • Introduction to Lie Groups and Lie Algebra, 51

    • 1st Edition
    • Arthur A. Sagle + 1 more
    • English

  • Nonstandard Methods in Stochastic Analysis and Mathematical Physics

    • 1st Edition
    • Volume 122
    • English

  • Fundamentals of the Theory of Operator Algebras. V2

    Advanced Theory
    • 1st Edition
    • Volume 100II
    • English

  • Matching Theory

    • 1st Edition
    • Volume 29
    • M.D. Plummer + 1 more
    • English
    This study of matching theory deals with bipartite matching, network flows, and presents fundamental results for the non-bipartite case. It goes on to study elementary bipartite graphs and elementary graphs in general. Further discussed are 2-matchings, general matching problems as linear programs, the Edmonds Matching Algorithm (and other algorithmic approaches), f-factors and vertex packing.

  • A Theory of Sets

    • 2nd Edition
    • Volume 108
    • English
    This book provides graduate students and professional mathematicians with a formal unified treatment of logic and set theory. The formalization can be used without change to build just about any mathematical structure on some suitable foundation of definitions and axioms. In addition to most of the topics considered standard fare for set theory several special ones are treated. This book will be found useful as a text for a substantial one-semester course in set theory and that the student will find continuing use for the formal and highly flexible language

  • Complex Cobordism and Stable Homotopy Groups of Spheres

    • 1st Edition
    • Volume 121
    • English

  • Number Theory

    • 1st Edition
    • Volume 20
    • English
    This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of the methods that are used. We have avoided that style which gives a systematic development of the apparatus and have used instead a freer style, in which the problems and the methods of solution are closely interwoven. We start from concrete problems in number theory. General theories arise as tools for solving these problems. As a rule, these theories are developed sufficiently far so that the reader can see for himself their strength and beauty, and so that he learns to apply them. Most of the questions that are examined in this book are connected with the theory of diophantine equations - that is, with the theory of the solutions in integers of equations in several variables. However, we also consider questions of other types; for example, we derive the theorem of Dirichlet on prime numbers in arithmetic progressions and investigate the growth of the number of solutions of congruences.

  • Logic, Methodology and Philosophy of Science VII

    • 1st Edition
    • Volume 114
    • R. Barcan Marcus + 2 more
    • English

  • Complex Analysis, Functional Analysis and Approximation Theory

    • 1st Edition
    • Volume 125
    • J. Mujica
    • English
    This proceedings volume contains papers of research of expository nature, and is addressed to research workers and advanced graduate students in mathematics. Some of the papers are the written and expanded texts of lectures delivered at the conference, whereas others have been included by invitation.

  • An Introduction to Differentiable Manifolds and Riemannian Geometry

    • 2nd Edition
    • Volume 120
    • English

  • Stability of Functional Differential Equations

    • 1st Edition
    • English
    This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.

  • Cubic Forms

    Algebra, Geometry, Arithmetic
    • 2nd Edition
    • Volume 4
    • Yu.I. Manin
    • English
    Since this book was first published in English, there has been important progress in a number of related topics. The class of algebraic varieties close to the rational ones has crystallized as a natural domain for the methods developed and expounded in this volume. For this revised edition, the original text has been left intact (except for a few corrections) and has been brought up to date by the addition of an Appendix and recent references.The Appendix sketches some of the most essential new results, constructions and ideas, including the solutions of the Luroth and Zariski problems, the theory of the descent and obstructions to the Hasse principle on rational varieties, and recent applications of K-theory to arithmetic.

  • Handbook of Mathematical Economics

    • 1st Edition
    • Volume 3
    • English
    The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970's the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field. Volume I deals with Mathematical Methods in Economics, including reviews of the concepts and techniques that have been most useful for the mathematical development of economic theory. Volume II elaborates on Mathematical Approaches to Microeconomic Theory, including consumer, producer, oligopoly, and duality theory, as well as Mathematical Approaches to Competitive Equilibrium including such aspects of competitive equilibrium as existence, stability, uncertainty, the computation of equilibrium prices, and the core of an economy.

  • Mathematical Models and Finite Elements for Reservoir Simulation

    Single Phase, Multiphase and Multicomponent Flows through Porous Media
    • 1st Edition
    • Volume 17
    • G. Chavent + 1 more
    • English
    Numerical simulators for oil reservoirs have been developed over the last twenty years and are now widely used by oil companies. The research, however, has taken place largely within the industry itself, and has remained somewhat inaccessible to the scientific community. This book hopes to remedy the situation by means of its synthesized presentation of the models used in reservoir simulation, in a form understandable to both mathematicians and engineers.The book aims to initiate a rigorous mathematical study of the immiscible flow models, partly by using the novel `global pressure' approach in treating incompressible two-phase problems. A finite element approximation technique based on the global pressure variational model is presented, and new approaches to the modelling of various kinds of multiphase flow through porous media are introduced.Much of the material is highly original, and has not been presented elsewhere. The mathematical and numerical models should be of great interest to applied mathematicians, and to engineers seeking an alternative approach to reservoir modelling.

  • Aspects of Mathematics and its Applications

    • 1st Edition
    • J.A. Barroso
    • English

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