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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.

  • Introductory Statistics

    • 2nd Edition
    • Sheldon M. Ross
    • English

  • Probability and Random Variables

    • 1st Edition
    • G P Beaumont
    • English
    This undergraduate text distils the wisdom of an experienced teacher and yields, to the mutual advantage of students and their instructors, a sound and stimulating introduction to probability theory. The accent is on its essential role in statistical theory and practice, built on the use of illustrative examples and the solution of problems from typical examination papers. Mathematically-frien... for first and second year undergraduate students, the book is also a reference source for workers in a wide range of disciplines who are aware that even the simpler aspects of probability theory are not simple.

  • Landmark Writings in Western Mathematics 1640-1940

    • 1st Edition
    • Ivor Grattan-Guinness
    • English
    This book contains around 80 articles on major writings in mathematics published between 1640 and 1940. All aspects of mathematics are covered: pure and applied, probability and statistics, foundations and philosophy. Sometimes two writings from the same period and the same subject are taken together. The biography of the author(s) is recorded, and the circumstances of the preparation of the writing are given. When the writing is of some lengths an analytical table of its contents is supplied. The contents of the writing is reviewed, and its impact described, at least for the immediate decades. Each article ends with a bibliography of primary and secondary items.

  • Applications of Functional Analysis and Operator Theory

    • 2nd Edition
    • Volume 200
    • V. Hutson + 2 more
    • English
    Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations. The present book provides, by careful selection of material, a collection of concepts and techniques essential for the modern practitioner. Emphasis is placed on the solution of equations (including nonlinear and partial differential equations). The assumed background is limited to elementary real variable theory and finite-dimensional vector spaces.

  • Fast Multipole Methods for the Helmholtz Equation in Three Dimensions

    • 1st Edition
    • Nail A Gumerov + 1 more
    • English
    This volume in the Elsevier Series in Electromagnetism presents a detailed, in-depth and self-contained treatment of the Fast Multipole Method and its applications to the solution of the Helmholtz equation in three dimensions. The Fast Multipole Method was pioneered by Rokhlin and Greengard in 1987 and has enjoyed a dramatic development and recognition during the past two decades. This method has been described as one of the best 10 algorithms of the 20th century. Thus, it is becoming increasingly important to give a detailed exposition of the Fast Multipole Method that will be accessible to a broad audience of researchers. This is exactly what the authors of this book have accomplished. For this reason, it will be a valuable reference for a broad audience of engineers, physicists and applied mathematicians.

  • Bitopological Spaces: Theory, Relations with Generalized Algebraic Structures and Applications

    • 1st Edition
    • Volume 199
    • Badri Dvalishvili
    • English
    This monograph is the first and an initial introduction to the theory of bitopological spaces and its applications. In particular, different families of subsets of bitopological spaces are introduced and various relations between two topologies are analyzed on one and the same set; the theory of dimension of bitopological spaces and the theory of Baire bitopological spaces are constructed, and various classes of mappings of bitopological spaces are studied. The previously known results as well the results obtained in this monograph are applied in analysis, potential theory, general topology, and theory of ordered topological spaces. Moreover, a high level of modern knowledge of bitopological spaces theory has made it possible to introduce and study algebra of new type, the corresponding representation of which brings one to the special class of bitopological spaces. It is beyond any doubt that in the nearest future the areas of essential applications will be the theories of linear topological spaces and topological groups, algebraic and differential topologies, the homotopy theory, not to mention other fundamental areas of modern mathematics such as geometry, mathematical logic, the probability theory and many other areas, including those of applied nature. Key Features:- First monograph is "Generalized Lattices"

  • Universal Spaces and Mappings

    • 1st Edition
    • Volume 198
    • S.D. Iliadis
    • English
    Universal Spaces and Mappings is devoted to universality problems. A new approach to these problems is given using some specific spaces. Since the construction of these specific spaces is set-theoretical, the given theory can be applied to different topics of Topology such as: universal mappings, dimension theory, action of groups, inverse spectra, isometrical embeddings, and so on.

  • Theories of Generalised Functions

    Distributions, Ultradistributions and Other Generalised Functions
    • 1st Edition
    • R F Hoskins + 1 more
    • English
    Explaining and comparing the various standard types of generalised functions which have been developed during the 20th Century, this text also contains accounts of recent non-standard theories of distributions, ultradistributions and Stato-hyperfunctions... The book could readily be used as a main text on generalised functions for mathematical undergraduates in final year analysis courses, as it presupposes little more than a general mathematical background. It also makes a valuable reference text for non-specific applied mathematics students, such as physicists or electrical engineers, needing to gain expertise in the application of generalised functions to physical problems, without any prior acquaintance of the specialised subject matter. An ideal companion book to Delta Functions, also by Professor Hoskins.

  • Build and Upgrade Your Own PC

    • 4th Edition
    • Ian Sinclair
    • English
    Ian Sinclair's Build Your Own books have established themselves as authoritative and highly practical guides for home and small business PC users and IT technicians alike. All aspects of building and upgrading a PC are covered, making this the book computer retailers don't want you to read! Build and Upgrade Your Own PC, 4th edition is based around building and upgrading to the latest systems, such as Pentium 4 or AMD Athlon XP motherboards running Windows XP and Windows 2000 Professional. As well as guiding you round the inside of your PC base unit Ian Sinclair also covers setup and security issues and peripherals, including: • Monitors, printers and scanners • Video capture • DVD drives • Small-scale networking solutions (wired and wireless)• Security technologies, including Firewall • Troubleshooting installation CD-ROMs

  • Parameter Estimation and Inverse Problems

    • 1st Edition
    • Richard C. Aster + 2 more
    • English
    Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. It promotes a fundamental understanding of parameter estimation and inverse problem philosophy and methodology. It introduces readers to Classical and Bayesian approaches to linear and nonlinear problems, with particular attention to computational, mathematical, and statistical issues related to their application to geophysical problems. Four appendices review foundational concepts in linear algebra, statistics, vector calculus, and notation. Pedagogy includes hundreds of highlighted equations, examples, and definitions; introductory chapter synopses; end-of-chapter exercises, both programming and theoretical; and suggestions for further reading. The text is designed to be accessible to graduate students and professionals in physical sciences without an extensive mathematical background.

  • Introduction to Robust Estimation and Hypothesis Testing

    • 2nd Edition
    • Rand R. Wilcox
    • English
    This revised book provides a thorough explanation of the foundation of robust methods, incorporating the latest updates on R and S-Plus, robust ANOVA (Analysis of Variance) and regression. It guides advanced students and other professionals through the basic strategies used for developing practical solutions to problems, and provides a brief background on the foundations of modern methods, placing the new methods in historical context. Author Rand Wilcox includes chapter exercises and many real-world examples that illustrate how various methods perform in different situations.Introduct... to Robust Estimation and Hypothesis Testing, Second Edition, focuses on the practical applications of modern, robust methods which can greatly enhance our chances of detecting true differences among groups and true associations among variables.

  • Real Analysis with an Introduction to Wavelets and Applications

    • 1st Edition
    • Don Hong + 2 more
    • English
    Real Analysis with an Introduction to Wavelets and Applications is an in-depth look at real analysis and its applications, including an introduction to wavelet analysis, a popular topic in "applied real analysis". This text makes a very natural connection between the classic pure analysis and the applied topics, including measure theory, Lebesgue Integral, harmonic analysis and wavelet theory with many associated applications.

  • Mathematics and the Divine

    A Historical Study
    • 1st Edition
    • Teun Koetsier + 1 more
    • English
    Mathematics and the Divine seem to correspond to diametrically opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn’t the Divine that which is immeasurable ?The present book shows that the domains of mathematics and the Divine, which may seem so radically separated, have throughout history and across cultures, proved to be intimately related. Religious activities such as the building of temples, the telling of ritual stories or the drawing of enigmatic figures all display distinct mathematical features. Major philosophical systems dealing with the Absolute and theological speculations focussing on our knowledge of the Ultimate have been based on or inspired by mathematics. A series of chapters by an international team of experts highlighting key figures, schools and trains of thought is presented here. Chinese number mysticism, the views of Pythagoras and Plato and their followers, Nicholas of Cusa's theological geometry, Spinozism and intuitionism as a philosophy of mathematics are treated side by side among many other themes in an attempt at creating a global view on the relation of mathematics and Man’s quest for the Absolute in the course of history.

  • Handbook of Complex Analysis

    Geometric Function Theory
    • 1st Edition
    • Reiner Kuhnau
    • English
    Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem. There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane).

  • Control and Optimal Control Theories with Applications

    • 1st Edition
    • D N Burghes + 1 more
    • English
    This sound introduction to classical and modern control theory concentrates on fundamental concepts. Employing the minimum of mathematical elaboration, it investigates the many applications of control theory to varied and important present-day problems, e.g. economic growth, resource depletion, disease epidemics, exploited population, and rocket trajectories. An original feature is the amount of space devoted to the important and fascinating subject of optimal control. The work is divided into two parts. Part one deals with the control of linear time-continuous systems, using both transfer function and state-space methods. The ideas of controllability, observability and minimality are discussed in comprehensible fashion. Part two introduces the calculus of variations, followed by analysis of continuous optimal control problems. Each topic is individually introduced and carefully explained with illustrative examples and exercises at the end of each chapter to help and test the reader’s understanding. Solutions are provided at the end of the book.

  • Functional Equations in Applied Sciences

    • 1st Edition
    • Volume 199
    • Enrique Castillo + 2 more
    • English
    The book provides the reader with the different types of functional equations that s/he can find in practice, showing, step by step, how they can be solved.A general methodology for solving functional equations is provided in Chapter 2. The different types of functional equations are described and solved in Chapters 3 to 8. Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, help the reader to change his/her mind in order to state problems as functional equations as an alternative to differential equations, and to state new problems in terms of functional equations or systems.An interesting feature of the book is that it deals with functional networks, a powerful generalization of neural networks that allows solving many practical problems. The second part of the book, Chapters 9 to 13, is devoted to the applications of this important paradigm.The book contains many examples and end of chapter exercises, that facilitates the understanding of the concepts and applications.

  • An Introduction to Measure-theoretic Probability

    • 1st Edition
    • George G. Roussas
    • English
    This book provides in a concise, yet detailed way, the bulk of the probabilistic tools that a student working toward an advanced degree in statistics,probabili... and other related areas, should be equipped with. The approach is classical, avoiding the use of mathematical tools not necessary for carrying out the discussions. All proofs are presented in full detail.

  • Handbook of Mathematical Fluid Dynamics

    • 1st Edition
    • Volume 3
    • S. Friedlander + 1 more
    • English
    The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

  • Random Matrices

    • 3rd Edition
    • Volume 142
    • Madan Lal Mehta
    • English
    Random Matrices gives a coherent and detailed description of analytical methods devised to study random matrices. These methods are critical to the understanding of various fields in in mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other zeta functions. More generally they apply to the characteristic energies of any sufficiently complicated system and which have found, since the publication of the second edition, many new applications in active research areas such as quantum gravity, traffic and communications networks or stock movement in the financial markets. This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time.

  • Coherent Systems

    • 1st Edition
    • Volume 2
    • Karl Schlechta
    • English
    One aspect of common sense reasoning is reasoning about normal cases, e.g. a physician will first try to interpret symptoms by a common disease, and will take more exotic possibilities only later into account. Such "normality" can be encoded, e.g. by a relation, where case A is considered more normal than case B. This gives a standard semantics or interpretation to nonmonotonic reasoning (a branch of common sense reasoning), or, more formally, to nonmonotonic logics. We consider in this book the repercussions such normality relations and similar constructions have on the resulting nonmonotonic logics, i.e. which types of logic are adequate for which kind of relation, etc. We show in this book that some semantics correspond nicely to some logics, but also that other semantics do not correspond to any logics of the usual form.

  • Working Analysis

    • 1st Edition
    • Jeffery Cooper
    • English
    Working Analysis is for a two semester course in advanced calculus. It develops the basic ideas of calculus rigorously but with an eye to showing how mathematics connects with other areas of science and engineering. In particular, effective numerical computation is developed as an important aspect of mathematical analysis.

  • Stochastic Local Search

    Foundations and Applications
    • 1st Edition
    • Holger H. Hoos + 1 more
    • English
    Stochastic local search (SLS) algorithms are among the most prominent and successful techniques for solving computationally difficult problems in many areas of computer science and operations research, including propositional satisfiability, constraint satisfaction, routing, and scheduling. SLS algorithms have also become increasingly popular for solving challenging combinatorial problems in many application areas, such as e-commerce and bioinformatics.Hoos and Stützle offer the first systematic and unified treatment of SLS algorithms. In this groundbreaking new book, they examine the general concepts and specific instances of SLS algorithms and carefully consider their development, analysis and application. The discussion focuses on the most successful SLS methods and explores their underlying principles, properties, and features. This book gives hands-on experience with some of the most widely used search techniques, and provides readers with the necessary understanding and skills to use this powerful tool.

  • Krylov Solvers for Linear Algebraic Systems

    Krylov Solvers
    • 1st Edition
    • Volume 11
    • Charles George Broyden + 1 more
    • English
    The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples ofthe block conjugate-gradient algorithm and it is this observation thatpermits the unification of the theory. The two major sub-classes of thosemethods, the Lanczos and the Hestenes-Stiefel, are developed in parallel asnatural generalisations of the Orthodir (GCR) and Orthomin algorithms. Theseare themselves based on Arnoldi's algorithm and a generalised Gram-Schmidtalgorith... and their properties, in particular their stability properties,are determined by the two matrices that define the block conjugate-gradiental... These are the matrix of coefficients and the preconditioningmatri... Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms.In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM.Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices.

  • Handbook of MRI Pulse Sequences

    • 1st Edition
    • Matt A. Bernstein + 2 more
    • English
    Magnetic Resonance Imaging (MRI) is among the most important medical imaging techniques available today. There is an installed base of approximately 15,000 MRI scanners worldwide. Each of these scanners is capable of running many different "pulse sequences", which are governed by physics and engineering principles, and implemented by software programs that control the MRI hardware. To utilize an MRI scanner to the fullest extent, a conceptual understanding of its pulse sequences is crucial. Handbook of MRI Pulse Sequences offers a complete guide that can help the scientists, engineers, clinicians, and technologists in the field of MRI understand and better employ their scanner.

  • Handbook of Differential Equations: Evolutionary Equations

    • 1st Edition
    • Volume 1
    • C.M. Dafermos + 1 more
    • English
    This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations. The main objective is to present clear, rigorous,and in depth surveys on the most important aspects of the present theory. The table of contents includes: W.Arendt: Semigroups and evolution equations: Calculus, regularity and kernel estimatesA.Bressan: The front tracking method for systems of conservation lawsE.DiBenedetto, J.M.Urbano,V.Vespri: Current issues on singular and degenerate evolution equations;L.Hsiao, S.Jiang: Nonlinear hyperbolic-parabolic coupled systemsA.Lunardi: Nonlinear parabolic equations and systemsD.Serre:L1-st... of nonlinear waves in scalar conservation laws B.Perthame:Kinetic formulations of parabolic and hyperbolic PDE’s: from theory to numerics

  • Handbook of Differential Equations: Ordinary Differential Equations

    • 1st Edition
    • Volume 1
    • A. Canada + 2 more
    • English
    The book contains seven survey papers about ordinary differential equations.The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling - nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations.The purpose of this volume is to inform the mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations, about some of these methods and possible applications.

  • Functional Analysis and its Applications

    Proceedings of the International Conference on Functional Analysis and its Applications dedicated to the 110th Anniversary of Stefan Banach, May 28-31, 2002, Lviv, Ukraine
    • 1st Edition
    • Volume 197
    • Vladimir Kadets + 1 more
    • English
    The conference took place in Lviv, Ukraine and was dedicated to a famous Polish mathematician Stefan Banach Æ’{ the most outstanding representative of the Lviv mathematical school. Banach spaces, introduced by Stefan Banach at the beginning of twentieth century, are familiar now to every mathematician. The book contains a short historical article and scientific contributions of the conference participants, mostly in the areas of functional analysis, general topology, operator theory and related topics.

  • Reliable Methods for Computer Simulation

    Error Control and Posteriori Estimates
    • 1st Edition
    • Volume 33
    • Pekka Neittaanmäki + 1 more
    • English
    Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods ofreliable computations. In general, a reliable numerical method must solve two basic problems: (a) generate a sequence of approximations that converges to a solution and (b) verify the accuracy of these approximations. A computer code for such a method must consist of two respective blocks: solver and checker.In this book, we are chiefly concerned with the problem (b) and try to present the main approaches developed for a posteriori error estimation in various problems.The authors try to retain a rigorous mathematical style, however, proofs are constructive whenever possible and additional mathematical knowledge is presented when necessary. The book contains a number of new mathematical results and lists a posteriori error estimation methods that have been developed in the very recent time.

  • Advances in Computers

    Advances in Software Engineering
    • 1st Edition
    • Volume 62
    • Marvin Zelkowitz
    • English
    Advances in Computers covers new developments in computer technology. Most chapters present an overview of a current subfield within computer science, with many citations, and often include new developments in the field by the authors of the individual chapters. Topics include hardware, software, theoretical underpinnings of computing, and novel applications of computers. This volume emphasizes software engineering issues in the design of new software systems. The use of the new emerging agile methods is presented as well as timeboxing and model based software engineering (MBASE) as techniques to manage large scale developments. The book series is a valuable addition to university courses that emphasize the topics under discussion in that particular volume as well as belonging on the bookshelf of industrial practitioners who need to implement many of the technologies that are described.

  • Computational Models for the Human Body: Special Volume

    • 1st Edition
    • Volume 12
    • Nicholas Philippe Ayache
    • English
    Provides a better understanding of the physiological and mechanical behaviour of the human body and the design of tools for their realistic numerical simulations, including concrete examples of such computational models. This book covers a large range of methods and an illustrative set of applications.

  • Handbook of Differential Equations: Stationary Partial Differential Equations

    • 1st Edition
    • Michel Chipot + 1 more
    • English
    The book could be a good companion for any graduate student in partial differential equations or in applied mathematics. Each chapter brings indeed new ideas and new techniques which can be used in these fields. The differents chapters can be read independently and are of great pedagogical value. The advanced researcher will find along the book the most recent achievements in various fields.

  • Stochastic Processes

    Estimation, Optimisation and Analysis
    • 1st Edition
    • Kaddour Najim + 2 more
    • English
    A ‘stochastic’ process is a ‘random’ or ‘conjectural’ process, and this book is concerned with applied probability and statistics. Whilst maintaining the mathematical rigour this subject requires, it addresses topics of interest to engineers, such as problems in modelling, control, reliability maintenance, data analysis and engineering involvement with insurance.This book deals with the tools and techniques used in the stochastic process – estimation, optimisation and recursive logarithms – in a form accessible to engineers and which can also be applied to Matlab. Amongst the themes covered in the chapters are mathematical expectation arising from increasing information patterns, the estimation of probability distribution, the treatment of distribution of real random phenomena (in engineering, economics, biology and medicine etc), and expectation maximisation. The latter part of the book considers optimization algorithms, which can be used, for example, to help in the better utilization of resources, and stochastic approximation algorithms, which can provide prototype models in many practical applications.

  • Principles of Mathematical Modeling

    • 2nd Edition
    • Clive Dym
    • English
    Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making. Prospective students should have already completed courses in elementary algebra, trigonometry, and first-year calculus and have some familiarity with differential equations and basic physics.

  • Nonmeasurable Sets and Functions

    • 1st Edition
    • Volume 195
    • Alexander Kharazishvili
    • English
    The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics:1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces;2. The theory of non-real-valued-meas... cardinals;3. The theory of invariant (quasi-invariant)ext... of invariant (quasi-invariant) measures.These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions.

  • Parallel Computational Fluid Dynamics 2003

    Advanced Numerical Methods, Software and Applications
    • 1st Edition
    • Boris Chetverushkin + 3 more
    • English
    The book is devoted to using of parallel multiprocessor computer systems for numerical simulation of the problems which can be described by the equations of continuum mechanics. Parallel algorithms and software, the problems of meta-computing are discussed in details, some results of high performance simulation of modern gas dynamic problems, combustion phenomena, plasma physics etc are presented.

  • Infinitesimal Methods of Mathematical Analysis

    • 1st Edition
    • J S Pinto
    • English
    This modern introduction to infinitesimal methods is a translation of the book Métodos Infinitesimais de Análise Matemática by José Sousa Pinto of the University of Aveiro, Portugal and is aimed at final year or graduate level students with a background in calculus. Surveying modern reformulations of the infinitesimal concept with a thoroughly comprehensive exposition of important and influential hyperreal numbers, the book includes previously unpublished material on the development of hyperfinite theory of Schwartz distributions and its application to generalised Fourier transforms and harmonic analysis. This translation by Roy Hoskins was also greatly assisted by the comments and constructive criticism of Professor Victor Neves, of the University of Aveiro.

  • Advances in Computers

    Information Security
    • 1st Edition
    • Volume 60
    • Marvin Zelkowitz
    • English
    Advances in Computers covers new developments in computer technology. Most chapters present an overview of a current subfield within computers, with many citations, and often include new developments in the field by the authors of the individual chapters. Topics include hardware, software, theoretical underpinnings of computing, and novel applications of computers. This current volume emphasizes information security issues and includes topics like certifying computer professionals, non-invasive attacks ("cognitive hacking"), computer files as legal evidence ("computer forensics") and the use of processors on plastic ("smartcards"). The book series is a valuable addition to university courses that emphasize the topics under discussion in that particular volume as well as belonging on the bookshelf of industrial practitioners who need to implement many of the technologies that are described.

  • Mathematics of Optimization: Smooth and Nonsmooth Case

    • 1st Edition
    • Giorgio Giorgi + 2 more
    • English
    The book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces). It contains a lot of material, from basic tools of convex analysis to optimality conditions for smooth optimization problems, for non smooth optimization problems and for vector optimization problems.The development of the subjects are self-contained and the bibliographical references are usually treated in different books (only a few books on optimization theory deal also with vector problems), so the book can be a starting point for further readings in a more specialized literature.Assuming only a good (even if not advanced) knowledge of mathematical analysis and linear algebra, this book presents various aspects of the mathematical theory in optimization problems. The treatment is performed in finite-dimensional spaces and with no regard to algorithmic questions. After two chapters concerning, respectively, introductory subjects and basic tools and concepts of convex analysis, the book treats extensively mathematical programming problems in the smmoth case, in the nonsmooth case and finally vector optimization problems.

  • The Rise of Modern Logic: from Leibniz to Frege

    • 1st Edition
    • Volume 3
    • Dov M. Gabbay + 1 more
    • English
    With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegcl make clear. Of the two, Hcgel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic - a development that will be covered in a further volume, British Logic in the Nineteenth Century.

  • Encyclopedia of Mathematical Physics

    • 1st Edition
    • Jean-Pierre Françoise + 2 more
    • English
    The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher’s own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originating from work in mathematical physics by providing them with focused high quality background information. Editorial Board: Jean-Pierre Françoise, Université Pierre et Marie Curie, Paris, FranceGregory L. Naber, Drexel University, Philadelphia, PA, USATsou Sheung Tsun, University of Oxford, UK Also available online via ScienceDirect (2006) – featuring extensive browsing, searching, and internal cross-referencing between articles in the work, plus dynamic linking to journal articles and abstract databases, making navigation flexible and easy. For more information, pricing options and availability visit www.info.sciencedire...

  • Actuaries' Survival Guide

    How to Succeed in One of the Most Desirable Professions
    • 1st Edition
    • Fred Szabo
    • English
    This unique book is a guide for students and graduates of mathematics, statistics, economics, finance, and other number-based disciplines contemplating a career in actuarial science. Given the comprehensive range of the cases that are analyzed in the book, the Actuaries' Survival Guide can serve as a companion to existing study material for all courses designed to prepare students for actuarial examinations.

  • Stream Ciphers and Number Theory

    • 1st Edition
    • Volume 66
    • Thomas W. Cusick + 2 more
    • English
    This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researchers in related fields.

  • Infinite Words

    Automata, Semigroups, Logic and Games
    • 1st Edition
    • Volume 141
    • Dominique Perrin + 1 more
    • English
    Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic.Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Büchi, McNaughton and Schützenberger.

  • Greek, Indian and Arabic Logic

    • 1st Edition
    • Volume 1
    • Dov M. Gabbay + 1 more
    • English
    Greek, Indian and Arabic Logic marks the initial appearance of the multi-volume Handbook of the History of Logic. Additional volumes will be published when ready, rather than in strict chronological order. Soon to appear are The Rise of Modern Logic: From Leibniz to Frege. Also in preparation are Logic From Russell to Gödel, Logic and the Modalities in the Twentieth Century, and The Many-Valued and Non-Monotonic Turn in Logic. Further volumes will follow, including Mediaeval and Renaissance Logic and Logic: A History of its Central.In designing the Handbook of the History of Logic, the Editors have taken the view that the history of logic holds more than an antiquarian interest, and that a knowledge of logic's rich and sophisticated development is, in various respects, relevant to the research programmes of the present day. Ancient logic is no exception. The present volume attests to the distant origins of some of modern logic's most important features, such as can be found in the claim by the authors of the chapter on Aristotle's early logic that, from its infancy, the theory of the syllogism is an example of an intuitionistic, non-monotonic, relevantly paraconsistent logic. Similarly, in addition to its comparative earliness, what is striking about the best of the Megarian and Stoic traditions is their sophistication and originality.Logic is an indispensably important pivot of the Western intellectual tradition. But, as the chapters on Indian and Arabic logic make clear, logic's parentage extends more widely than any direct line from the Greek city states. It is hardly surprising, therefore, that for centuries logic has been an unfetteredly international enterprise, whose research programmes reach to every corner of the learned world.Like its companion volumes, Greek, Indian and Arabic Logic is the result of a design that gives to its distinguished authors as much space as would be needed to produce highly authoritative chapters, rich in detail and interpretative reach. The aim of the Editors is to have placed before the relevant intellectual communities a research tool of indispensable value.Together with the other volumes, Greek, Indian and Arabic Logic, will be essential reading for everyone with a curiosity about logic's long development, especially researchers, graduate and senior undergraduate students in logic in all its forms, argumentation theory, AI and computer science, cognitive psychology and neuroscience, linguistics, forensics, philosophy and the history of philosophy, and the history of ideas.

  • Mathematica Navigator

    Mathematics, Statistics, and Graphics
    • 2nd Edition
    • Heikki Ruskeepaa
    • English
    Mathematica Navigator is the only book you need to understand and use the new Mathematica. Part tutorial and part handbook, this updated guidebook provides a thorough introduction to the software plus practical information and tips for using Mathematica on a daily basis to solve mathematical problems. The book emphasizes the use of graphics, methods of applied mathematics and statistics, and programming. While no previous experience with Mathematica is required, most chapters also include advanced material so that the book will be a valuable resource for beginners and experienced users. You'll want to keep it close by your computer for easy reference.

  • Algorithmic Graph Theory and Perfect Graphs

    • 2nd Edition
    • Volume 57
    • Martin Charles Golumbic
    • English
    Algorithmic Graph Theory and Perfect Graphs, first published in 1980, has become the classic introduction to the field. This new Annals edition continues to convey the message that intersection graph models are a necessary and important tool for solving real-world problems. It remains a stepping stone from which the reader may embark on one of many fascinating research trails. The past twenty years have been an amazingly fruitful period of research in algorithmic graph theory and structured families of graphs. Especially important have been the theory and applications of new intersection graph models such as generalizations of permutation graphs and interval graphs. These have lead to new families of perfect graphs and many algorithmic results. These are surveyed in the new Epilogue chapter in this second edition.

  • Differential Equations with Mathematica

    • 3rd Edition
    • Martha L. Abell + 1 more
    • English
    The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.

  • Advances in Survival Analysis

    • 1st Edition
    • Volume 23
    • Narayanaswamy Balakrishnan + 1 more
    • English
    Handbook of Statistics: Advances in Survival Analysis covers all important topics in the area of Survival Analysis. Each topic has been covered by one or more chapters written by internationally renowned experts. Each chapter provides a comprehensive and up-to-date review of the topic. Several new illustrative examples have been used to demonstrate the methodologies developed. The book also includes an exhaustive list of important references in the area of Survival Analysis.

  • Discrete Mathematics with Applications

    • 1st Edition
    • Thomas Koshy
    • English
    This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.

  • Nonlinear Theory of Pseudodifferential Equations on a Half-line

    • 1st Edition
    • Volume 194
    • Nakao Hayashi + 1 more
    • English
    This book is the first attempt to develop systematically a general theory of the initial-boundary value problems for nonlinear evolution equations with pseudodifferential operators Ku on a half-line or on a segment. We study traditionally important problems, such as local and global existence of solutions and their properties, in particular much attention is drawn to the asymptotic behavior of solutions for large time. Up to now the theory of nonlinear initial-boundary value problems with a general pseudodifferential operator has not been well developed due to its difficulty. There are many open natural questions. Firstly how many boundary data should we pose on the initial-boundary value problems for its correct solvability? As far as we know there are few results in the case of nonlinear nonlocal equations. The methods developed in this book are applicable to a wide class of dispersive and dissipative nonlinear equations, both local and nonlocal.

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