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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.

  • Discrete Computational Structures

    • 1st Edition
    • Robert R. Korfhage
    • Werner Rheinboldt
    • English
    Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasizes combinatorics and probability. Examples show different techniques of the general process of enumerating objects. Combinatorics cover permutations, enumerators for combinations, Stirling numbers, cycle classes of permutations, partitions, and compositions. The book cites as example the interplay between discrete mathematics and computing using a system of distinct representatives (SDR) problem. The problem, originating from group theory, graph theory, and set theory can be worked out by the student with a network model involving computers to generate and analyze different scenarios. The book is intended for sophomore or junior level, corresponding to the course B3, "Introduction to Discrete Structures," in the ACM Curriculum 68, as well as for mathematicians or professors of computer engineering and advanced mathematics.

  • Handbook of Differential Equations

    • 2nd Edition
    • Daniel Zwillinger
    • English
    Handbook of Differential Equations, Second Edition is a handy reference to many popular techniques for solving and approximating differential equations, including numerical methods and exact and approximate analytical methods. Topics covered range from transformations and constant coefficient linear equations to Picard iteration, along with conformal mappings and inverse scattering. Comprised of 192 chapters, this book begins with an introduction to transformations as well as general ideas about differential equations and how they are solved, together with the techniques needed to determine if a partial differential equation is well-posed or what the "natural" boundary conditions are. Subsequent sections focus on exact and approximate analytical solution techniques for differential equations, along with numerical methods for ordinary and partial differential equations. This monograph is intended for students taking courses in differential equations at either the undergraduate or graduate level, and should also be useful for practicing engineers or scientists who solve differential equations on an occasional basis.

  • Methodologies of Pattern Recognition

    • 1st Edition
    • Satosi Watanabe
    • English
    Methodologies of Pattern Recognition is a collection of papers that deals with the two approaches to pattern recognition (geometrical and structural), the Robbins-Monro procedures, and the implications of interactive graphic computers for pattern recognition methodology. Some papers describe non-supervised learning in statistical pattern recognition, parallel computation in pattern recognition, and statistical analysis as a tool to make patterns emerge from data. One paper points out the importance of cluster processing in visual perception in which proximate points of similar brightness values form clusters. At higher levels of mental activity humans are efficient in clumping complex items into clusters. Another paper suggests a recognition method which combines versatility and an efficient noise-proofness in dealing with the two main problems in the field of recognition. These difficulties are the presence of a large variety of observed signals and the presence of interference. One paper reports on a possible feature selection for pattern recognition systems employing the minimization of population entropy. Electronic engineers, physicists, physiologists, psychologists, logicians, mathematicians, and philosophers will find great rewards in reading the above collection.

  • Robustness in Statistics

    • 1st Edition
    • Robert L. Launer + 1 more
    • English
    Robustness in Statistics contains the proceedings of a Workshop on Robustness in Statistics held on April 11-12, 1978, at the Army Research Office in Research Triangle Park, North Carolina. The papers review the state of the art in statistical robustness and cover topics ranging from robust estimation to the robustness of residual displays and robust smoothing. The application of robust regression to trajectory data reduction is also discussed. Comprised of 14 chapters, this book begins with an introduction to robust estimation, paying particular attention to iteration schemes and error structure of estimators. Sensitivity and influence curves as well as their connection with jackknife estimates are described. The reader is then introduced to a simple analog of trimmed means that can be used for studying residuals from a robust point-of-view; a class of robust estimators (called P-estimators) based on the location and scale-invariant Pitman estimators of location; and robust estimation in the presence of outliers. Subsequent chapters deal with robust regression and its use to reduce trajectory data; tests for censoring of extreme values, especially when population distributions are incompletely defined; and robust estimation for time series autoregressions. This monograph should be of interest to mathematicians and statisticians.

  • Algebraic Methods of Mathematical Logic

    • 1st Edition
    • Ladislav Rieger
    • English
    Algebraic Methods of Mathematical Logic focuses on the algebraic methods of mathematical logic, including Boolean algebra, mathematical language, and arithmetization. The book first offers information on the dialectic of the relation between mathematical and metamathematical aspects; metamathematico-math... parallelism and its natural limits; practical applications of methods of mathematical logic; and principal mathematical tools of mathematical logic. The text then elaborates on the language of mathematics and its symbolization and recursive construction of the relation of consequence. Discussions focus on recursive construction of the relation of consequence, fundamental descriptively-semant... rules, mathematical logic and mathematical language as a material system of signs, and the substance and purpose of symbolization of mathematical language. The publication examines expressive possibilities of symbolization; intuitive and mathematical notions of an idealized axiomatic mathematical theory; and the algebraic theory of elementary predicate logic. Topics include the notion of Boolean algebra based on joins, meets, and complementation, logical frame of a language and mathematical theory, and arithmetization and algebraization. The manuscript is a valuable reference for mathematicians and researchers interested in the algebraic methods of mathematical logic.

  • Computer Capacity Planning

    Theory and Practice
    • 1st Edition
    • Shui F. Lam + 1 more
    • English
    Computer Capacity Planning: Theory and Practice deals with the theory and practice of computer capacity planning. Topics covered range from the tasks involved in computer capacity planning (inventory, workload measures and characterization, performance measurement, etc.) to environmental influences on computer capacity planning practices. An empirical study of computer capacity planning practices is also discussed, and the component approach is compared with the system modeling approach. Comprised of six chapters, this book begins with an introduction to the theories and techniques on computer capacity planning, along with the significance of computer capacity planning and the major elements in the process of computer capacity planning. The functions of each element are explained and the various techniques and tools for carrying out these functions are presented. The next chapter shows how these elements can be tied together to achieve the objective of computer capacity planning, that is, matching computer resources to computer workload in a cost-effective manner. The second part of the book examines how different organizations may adopt different capacity planning methods and how to improve the applicability of the theory and the quality of the practice on computer capacity planning. This monograph should be of interest to researchers, data processing managers, and analysts including those in charge of computer capacity planning and performance evaluation; auditors and quality assurance personnel; equipment manufacturers and software developers; and students in information sciences.

  • Calculus and Its Applications

    • 1st Edition
    • P. Mainardi + 1 more
    • English
    Calculus and its Applications provides information pertinent to the applications of calculus. This book presents the trapping technique in defining geometrical and physical entities that are usually regarded as limits of sums. Organized into 20 chapters, this book begins with an overview of the notion of average speed that seems to appear first as a qualitative concept. This text then presents the concepts of external and internal parameters to increase the appreciation of parametric functions. Other chapters consider separable differential equations with more detail than usual with their suitability in describing physical laws. This book discusses as well the study of variable quantities whose magnitude is determined by the magnitudes of several other variables. The final chapter deals with a homogeneous differential equation and auxiliary equations consisting imaginary roots. This book is a valuable resource for mathematicians and students. Readers whose interests span a variety of fields will also find this book useful.

  • A Course in Ordinary and Partial Differential Equations

    • 1st Edition
    • Zalman Rubinstein
    • English
    A Course in Ordinary and Partial Differential Equations discusses ordinary differential equations and partial differential equations. The book reviews the solution of elementary first-order differential equations, existence theorems, singular solutions, and linear equations of arbitrary order. It explains the solutions of linear equations with constant coefficients, operational calculus, and the solutions of linear differential equations. It also explores the techniques of computing for the solution of systems of linear differential equations, which is similar to the solutions of linear equations of arbitrary order. The text proves that if the coefficients of some differential equations possess certain restricted types of singularities, the solution will have Taylor series expansions about the singular points. The investigator can calculate a divergent series whose partial sums numerically approximate the solution for large x if the point in question is infinity, of which the series will be a Taylor series of negative powers of x. The book also explains the Fourier transform, its applications to partial differential equations, as well as the Hilbert space approach to partial differential equations. The book is a stimulating material for mathematicians, for professors, or for students of pure and applied mathematics, physics, or engineering.

  • Microprocessor Architectures and Systems

    RISC, CISC and DSP
    • 1st Edition
    • Steve Heath
    • English
    Microprocessor Architectures and Systems: RISC, CISC, and DSP focuses on the developments of Motorola's CISC, RISC, and DSP processors and the advancements of the design, functions, and architecture of microprocessors. The publication first ponders on complex instruction set computers and 32-bit CISC processors. Discussions focus on MC68881 and MC68882 floating point coprocessors, debugging support, MC68020 32-bit performance standard, bus interfaces, MC68010 SUPERVISOR resource, and high-level language support. The manuscript then covers the RISC challenge, digital signal processing, and memory management and caches. Topics include implementing memory systems, multitasking and user/supervisor conflicts, partitioning the system, cache size and organization, DSP56000 family, MC88100 programming model, M88000 family, and the 80/20 rule. The text examines the selection of a microprocessor architecture, changing design cycle, semiconductor technology, multiprocessing, and real-time software, interrupts, and exceptions. Concerns include locating associated tasks, MC88100 interrupt service routines, single- and multiple-threaded operating systems, and the MC68300 family. The publication is a valuable reference for computer engineers and researchers interested in microprocessor architectures and systems.

  • Topology

    Volume II
    • 1st Edition
    • K. Kuratowski
    • English
    Topology, Volume II deals with topology and covers topics ranging from compact spaces and connected spaces to locally connected spaces, retracts, and neighborhood retracts. Group theory and some cutting problems are also discussed, along with the topology of the plane. Comprised of seven chapters, this volume begins with a discussion on the compactness of a topological space, paying particular attention to Borel, Lebesgue, Riesz, Cantor, and Bolzano-Weierstrass conditions. Semi-continuity and topics in dimension theory are also considered. The reader is then introduced to the connectedness of a space, with emphasis on the general properties and monotone mappings of connected spaces; local connectedness of a topological space; absolute retracts and contractible spaces; and general properties of commutative groups. Qualitative problems related to polygonal arcs are also examined, together with cohomotopic multiplication and duality theorems. The final chapter is devoted to the topology of a plane and evaluates the concept of the Janiszewski space. This monograph will be helpful to students and practitioners of algebra and mathematics.

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