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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.

  • Quantum Theoretic Machines

    What is thought from the point of view of Physics?
    • 1st Edition
    • A. Stern
    • English
    Making Sense of Inner Sense'Terra cognita' is terra incognita. It is difficult to find someone not taken abackand fascinated by the incomprehensible but indisputable fact: there are material systems which are aware of themselves. Consciousness is self-cognizing code. During homo sapiens's relentness and often frustrated search for self-understanding various theories of consciousness have been and continue to be proposed. However, it remains unclear whether and at what level the problems of consciousness and intelligent thought can be resolved. Science's greatest challenge is to answer the fundamental question: what precisely does a cognitive state amount to in physical terms?Albert Einstein insisted that the fundamental ideas of science are essentially simple and can be expressed in a language comprehensible to everyone. When one thinks about the complexities which present themselves in modern physics and even more so in the physics of life, one may wonder whether Einstein really meant what he said. Are we to consider the fundamental problem of the mind, whose understanding seems to lie outside the limits of the mind, to be essentially simple too? Knowledge is neither automatic nor universally deductive. Great new ideas are typically counterintuitive and outrageous, and connecting them by simple logical steps to existing knowledge is often a hard undertaking. The notion of a tensor was needed to provide the general theory of relativity; the notion of entropy had to be developed before we could get full insight into the laws of thermodynamics; the notice of information bit is crucial for communication theory, just as the concept of a Turing machine is instrumental in the deep understanding of a computer. To understand something, consciousness must reach an adequate intellectual level, even more so in order to understand itself. Reality is full of unending mysteries, the true explanation of which requires very technical knowledge, often involving notions not given directly to intuition. Even though the entire content and the results of this study are contained in the eight pages of the mathematical abstract, it would be unrealistic and impractical to suggest that anyone can gain full insight into the theory that presented here after just reading abstract.In our quest for knowledge we are exploring the remotest areas of the macrocosm and probing the invisible particles of the microcosm, from tiny neutrinos and strange quarks to black holes and the Big Bang. But the greatest mystery is very close to home: the greatest mystery is human consciousness. The question before us is whether the logical brain has evolved to a conceptual level where it is able to understand itself.

  • Game Theory

    Mathematical Models of Conflict
    • 1st Edition
    • A. J. Jones
    • English
    Written engagingly and with agreeable humour, this book balances a light touch with a rigorous yet economical account of the theory of games and bargaining models. It provides a precise interpretation, discussion and mathematical analysis for a wide range of “game-like” problems in economics, sociology, strategic studies and war.There is first an informal introduction to game theory, which can be understood by non-mathematicians, which covers the basic ideas of extensive form, pure and mixed strategies and the minimax theorem. The general theory of non-cooperative games is then given a detailed mathematical treatment in the second chapter. Next follows a “first class” account of linear programming, theory and practice, terse, rigorous and readable, which is applied as a tool to matrix games and economics from duality theory via the equilibrium theorem, with detailed explanations of computational aspects of the simplex algorithm.The remaining chapters give an unusually comprehensive but concise treatment of cooperative games, an original account of bargaining models, with a skillfully guided tour through the Shapley and Nash solutions for bimatrix games and a carefully illustrated account of finding the best threat strategies.

  • Topological Algebras

    • 1st Edition
    • Volume 185
    • V.K. Balachandran
    • English
    This book consists of nine chapters. Chapter 1 is devoted to algebraic preliminaries. Chapter 2 deals with some of the basic definition and results concerning topological groups, topological linear spaces and topological algebras. Chapter 3 considered some generalizations of the norm. Chapter 4 is concerned with a generalization of the notion of convexity called p-convexity. In Chapter 5 some differential and integral analysis involving vector valued functions is developed. Chapter 6 is concerned with spectral analysis and applications. The Gelfand representation theory is the subject-matter of Chapter 7. Chapter 8 deals with commutative topological algebras. Finally in Chapter 9 an exposition of the norm uniqueness theorems of Gelfand and Johnson (extended to p-Banach algebras) is given.

  • From Peirce to Skolem

    A Neglected Chapter in the History of Logic
    • 1st Edition
    • Volume 4
    • Geraldine Brady
    • English
    This book is an account of the important influence on the development of mathematical logic of Charles S. Peirce and his student O.H. Mitchell, through the work of Ernst Schröder, Leopold Löwenheim, and Thoralf Skolem. As far as we know, this book is the first work delineating this line of influence on modern mathematical logic.

  • Handbook of Numerical Analysis

    • 1st Edition
    • Volume 7
    • Philippe G. Ciarlet
    • English
    These volumes cover all the major aspects of numerical analysis. This particular volume discusses the solution of equations in Rn, Gaussian elimination, techniques of scientific computer, the analysis of multigrid methods, wavelet methods, and finite volume methods.

  • Multigrid

    • 1st Edition
    • Ulrich Trottenberg + 2 more
    • English
    Multigrid presents both an elementary introduction to multigrid methods for solving partial differential equations and a contemporary survey of advanced multigrid techniques and real-life applications.Multigr... methods are invaluable to researchers in scientific disciplines including physics, chemistry, meteorology, fluid and continuum mechanics, geology, biology, and all engineering disciplines. They are also becoming increasingly important in economics and financial mathematics.Readers are presented with an invaluable summary covering 25 years of practical experience acquired by the multigrid research group at the Germany National Research Center for Information Technology. The book presents both practical and theoretical points of view.

  • A Course in Probability Theory

    • 3rd Edition
    • Kai Lai Chung
    • English
    Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses. While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication.

  • Handbook of Mathematical Formulas and Integrals

    • 2nd Edition
    • Alan Jeffrey
    • English
    This Second Edition follows the original pattern of presenting of presenting the most frequently used integrals, mathematical formulas, and results in a form convenient for the user. The Handbook provides an essential reference work for students and researchers in applied mathematics, engineering, and physics. The most important formulas, functions, and results used in applications of mathematics are covered.New material includes proof by mathematical induction, properties of spherical Bessel functions, more detailed results on orthogonal polynomials, interpolation and Pade approximation, and a section on the z-transform. The original thumb-tab indexing has been retained, as it provides an easy reference system that supplements the contents listing and extensive index.

  • Linear Algebra with Mathematica, Student Solutions Manual

    An Introduction Using Mathematica
    • 1st Edition
    • Fred Szabo
    • English
    This book introduces interested readers, practitioners, and researchers to Mathematica<$> methods for solving practical problems in linear algebra. It contains step-by-step solutions of problems in computer science, economics, engineering, mathematics, statistics, and other areas of application. Each chapter contains both elementary and more challenging problems, grouped by fields of application, and ends with a set of exercises. Selected answers are provided in an appendix. The book contains a glossary of definitions and theorem, as well as a summary of relevant Mathematica<$> tools. Applications of Linear Algebra<$> can be used both in laboratory sessions and as a source of take-home problems and projects.

  • Table of Integrals, Series, and Products

    • 6th Edition
    • Daniel Zwillinger + 1 more
    • English
    The Table of Integrals, Series, and Products is the major reference source for integrals in the English language.It is designed for use by mathematicians, scientists, and professional engineers who need to solve complex mathematical problems.

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