Skip to main content
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.

  • Algorithmically Specialized Parallel Computers

    • 1st Edition
    • Lawrence Snyder + 2 more
    • English
    Algorithmically Specialized Parallel Computers focuses on the concept and characteristics of an algorithmically specialized computer. This book discusses the algorithmically specialized computers, algorithmic specialization using VLSI, and innovative architectures. The architectures and algorithms for digital signal, speech, and image processing and specialized architectures for numerical computations are also elaborated. Other topics include the model for analyzing generalized inter-processor, pipelined architecture for search tree maintenance, and specialized computer organization for raster graphics display. The data base applications of the FETCH-AND-ADD instruction, distributed parallel architecture for speech understanding, and two parallel formulations of particle-in-cell models are likewise covered in this text. This publication is suitable for students, researchers and professionals concerned with algorithmically specialized computers.

  • Handbook of Mathematical Formulas

    • 1st Edition
    • Hans-Jochen Bartsch
    • English
    Handbook of Mathematical Formulas presents a compilation of formulas to provide the necessary educational aid. This book covers the whole field from the basic rules of arithmetic, via analytic geometry and infinitesimal calculus through to Fourier's series and the basics of probability calculus. Organized into 12 chapters, this book begins with an overview of the fundamental notions of set theory. This text then explains linear expression wherein the variables are only multiplied by constants and added to constants or expressions of the same kind. Other chapters consider a variety of topics, including matrices, statistics, linear optimization, Boolean algebra, and Laplace's transforms. This book discusses as well the various systems of coordinates in analytical geometry. The final chapter deals with algebra of logic and its development into a two-value Boolean algebra as switching algebra. This book is intended to be suitable for students of technical schools, colleges, and universities.

  • Representations of Finite Groups

    • 1st Edition
    • Hirosi Nagao + 1 more
    • English
    Representations of Finite Groups provides an account of the fundamentals of ordinary and modular representations. This book discusses the fundamental theory of complex representations of finite groups. Organized into five chapters, this book begins with an overview of the basic facts about rings and modules. This text then provides the theory of algebras, including theories of simple algebras, Frobenius algebras, crossed products, and Schur indices with representation-theor... versions of them. Other chapters include a survey of the fundamental theory of modular representations, with emphasis on Brauer characters. This book discusses as well the module-theoretic representation theory due to Green and includes some topics such as Burry–Carlson's theorem and Scott modules. The final chapter deals with the fundamental results of Brauer on blocks and Fong's theory of covering, and includes some approaches to them. This book is a valuable resource for readers who are interested in the various approaches to the study of the representations of groups.

  • Multiple Time Scales

    • 1st Edition
    • Jeremiah U. Brackbill + 1 more
    • English
    Multiple Time Scales presents various numerical methods for solving multiple-time-scale problems. The selection first elaborates on considerations on solving problems with multiple scales; problems with different time scales; and nonlinear normal-mode initialization of numerical weather prediction models. Discussions focus on analysis of observations, nonlinear analysis, systems of ordinary differential equations, and numerical methods for problems with multiple scales. The text then examines the diffusion-synthetic acceleration of transport iterations, with application to a radiation hydrodynamics problem and implicit methods in combustion and chemical kinetics modeling. The publication ponders on molecular dynamics and Monte Carlo simulations of rare events; direct implicit plasma simulation; orbit averaging and subcycling in particle simulation of plasmas; and hybrid and collisional implicit plasma simulation models. Topics include basic moment method, electron subcycling, gyroaveraged particle simulation, and the electromagnetic direct implicit method. The selection is a valuable reference for researchers interested in pursuing further research on the use of numerical methods in solving multiple-time-scale problems.

  • Computability, Complexity, and Languages

    Fundamentals of Theoretical Computer Science
    • 1st Edition
    • Martin D. Davis + 1 more
    • Werner Rheinboldt
    • English
    Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science provides an introduction to the various aspects of theoretical computer science. Theoretical computer science is the mathematical study of models of computation. This text is composed of five parts encompassing 17 chapters, and begins with an introduction to the use of proofs in mathematics and the development of computability theory in the context of an extremely simple abstract programming language. The succeeding parts demonstrate the performance of abstract programming language using a macro expansion technique, along with presentations of the regular and context-free languages. Other parts deal with the aspects of logic that are important for computer science and the important theory of computational complexity, as well as the theory of NP-completeness. The closing part introduces the advanced recursion and polynomial-time computability theories, including the priority constructions for recursively enumerable Turing degrees. This book is intended primarily for undergraduate and graduate mathematics students.

  • Metric Affine Geometry

    • 1st Edition
    • Ernst Snapper + 1 more
    • English
    Metric Affine Geometry focuses on linear algebra, which is the source for the axiom systems of all affine and projective geometries, both metric and nonmetric. This book is organized into three chapters. Chapter 1 discusses nonmetric affine geometry, while Chapter 2 reviews inner products of vector spaces. The metric affine geometry is treated in Chapter 3. This text specifically discusses the concrete model for affine space, dilations in terms of coordinates, parallelograms, and theorem of Desargues. The inner products in terms of coordinates and similarities of affine spaces are also elaborated. The prerequisites for this publication are a course in linear algebra and an elementary course in modern algebra that includes the concepts of group, normal subgroup, and quotient group. This monograph is suitable for students and aspiring geometry high school teachers.

  • Handbook of Neural Computing Applications

    • 1st Edition
    • Alianna J. Maren + 2 more
    • English
    Handbook of Neural Computing Applications is a collection of articles that deals with neural networks. Some papers review the biology of neural networks, their type and function (structure, dynamics, and learning) and compare a back-propagating perceptron with a Boltzmann machine, or a Hopfield network with a Brain-State-in-a-Box network. Other papers deal with specific neural network types, and also on selecting, configuring, and implementing neural networks. Other papers address specific applications including neurocontrol for the benefit of control engineers and for neural networks researchers. Other applications involve signal processing, spatio-temporal pattern recognition, medical diagnoses, fault diagnoses, robotics, business, data communications, data compression, and adaptive man-machine systems. One paper describes data compression and dimensionality reduction methods that have characteristics, such as high compression ratios to facilitate data storage, strong discrimination of novel data from baseline, rapid operation for software and hardware, as well as the ability to recognized loss of data during compression or reconstruction. The collection can prove helpful for programmers, computer engineers, computer technicians, and computer instructors dealing with many aspects of computers related to programming, hardware interface, networking, engineering or design.

  • Science, Computers, and the Information Onslaught

    A Collection of Essays
    • 1st Edition
    • Donald M. Kerr + 2 more
    • English
    Science, Computers, and the Information Onslaught: A Collection of Essays covers the proceedings of the 1981 meeting on “Science and the Information Onslaught”, held at Los Alamos, New Mexico. This book is organized into five parts encompassing 19 chapters. The first part deals with the problems of measurement and the uses of information in decisions concerning national security. This part also emphasizes the dependence of survival on technological progress. The next part examines the foundations of information theory, the interaction between psychological concepts and the mathematical theories of automata, and the major problems in robotics. These topics are followed by discussions of the efforts to codify languages in formal grammatical systems and the past misuse of irrelevantly detailed information in decision making, specifically the use and misuse of information in government decisions about technological projects. The remaining parts consider the project of enhancing human abilities by the insertion of silicon chips in the body. These parts also assess the implications of a microelectronic technology capable of producing chips bearing millions of logically active circuit elements. Accounts of cryptanalytic successes in World War II are also included. This book will be of value to mathematicians, physicists, linguistics, and computer scientists.

  • Software for Roundoff Analysis of Matrix Algorithms

    • 1st Edition
    • Webb Miller + 1 more
    • English
    Computer Science and Applied Mathematics: A Series of Monographs and Textbooks: Software for Roundoff Analysis of Matrix Algorithms focuses on the presentation of techniques and software tools for analyzing the propagation of rounding error in matrix algorithms. The publication looks into some elements of error analysis, concepts from linear algebra and analysis, and directed graphs. Discussions focus on arithmetic graphs, sums of path products, linear transformations, Minkowski sums and Cartesian products, and elementary concepts from analysis. The text then examines software for roundoff analysis, including rounding and perturbations of the computational problem, comparing rounding errors with problem sensitivity, reverse condition numbers, and comparing two algorithms. The book ponders on case studies, as well as Gaussian elimination with iterative improvement, Cholesky factorization, Gauss-Jordan elimination, variants of the Gram-Schmidt method, and Cholesky factors after rank-one modifications. The text is a valuable reference for researchers interested in the techniques and software tools involved in the analysis of the propagation of rounding error in matrix algorithms.

  • Locking Performance in Centralized Databases

    • 1st Edition
    • Y.C. Tay
    • W. Rheinboldt + 1 more
    • English
    Perspectives in Computing: Locking Performance in Centralized Databases reports some results from a project whose aim was the development of a performance model for concurrency control algorithms. This book proposes a model that is powerful enough to help users understand, compare, and control the performance of the algorithms. Organized into four chapters, this book begins with an overview of the model in its simplest form. This text then explains locking, which uses a combination of blocking and restarts to achieve correctness. Other chapters test the model and the method of analysis by comparing the model's predictions to simulation results wherein the prediction and simulations indicate that restarts can cause thrashing. This book discusses as well the formula for throughput and for the restart rate. The final chapter deals with the adaptation of the model to timestamping and distributed algorithms. This book is a valuable resource for mathematicians and research workers.

Related subjects