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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.

  • Elementary Functions and Analytic Geometry

    • 1st Edition
    • Harley Flanders
    • English
    Elementary Functions and Analytic Geometry is an introduction to college mathematics, with emphasis on elementary functions and analytic geometry. It aims to provide a working knowledge of basic functions (polynomial, rational, exponential, logarithmic, and trigonometric); graphing techniques and the numerical aspects and applications of functions; two- and three-dimensional vector methods; and complex numbers, mathematical induction, and the binomial theorem. Comprised of 13 chapters, this book begins with a discussion on functions and graphs, paying particular attention to quantities measured in the real number system. The next chapter deals with linear and quadratic functions as well as some of their applications. Tips on graphing are offered. Subsequent chapters focus on polynomial functions, along with graphs of factored polynomials; rational functions; exponential and logarithm functions; and trigonometric functions. Identities and inverse functions, vectors, and trigonometry are also explored, together with complex numbers and solid analytic geometry. The book concludes by considering mathematical induction, binomial coefficients, and the binomial theorem. This monograph will be a useful resource for undergraduate students of mathematics and algebra.

  • Introduction to Discrete Linear Controls

    Theory and Application
    • 1st Edition
    • Albert B. Bishop
    • J. William Schmidt
    • English
    Introduction to Discrete Linear Controls: Theory and Applications focuses on the design, analysis, and operation of discrete-time decision processes. The publication first offers information on systems theory and discrete linear control systems, discrete control-system models, and the calculus of finite differences. Discussions focus on the calculus of finite differences and linear difference equations, summations, control of cylinder diameter, generalized discrete process controller with sampling, difference equations, control theory, and system models. The text then examines classical solution of linear difference equations with constant, inverse transformation, and measures and environmental effects of system performance. The manuscript takes a look at parameter selection in first-order systems considering sampling and instrumentation errors, second-order systems, and system instability, including responses of the generalized second-order process controller; criterion for stability of discrete linear systems; and proportional-plus-di... control. The publication is a valuable source of information for engineers, operations researchers, and systems analysts.

  • Nonlinear Programming 4

    Proceedings of the Nonlinear Programming Symposium 4 Conducted by the Computer Sciences Department at the University of Wisconsin–Madison, July 14-16, 1980
    • 1st Edition
    • Olvi L. Mangasarian + 2 more
    • English
    Nonlinear Programming, 4 focuses on linear, quadratic, and nonlinear programming, unconstrained minimization, nonsmooth and discrete optimization, ellipsoidal methods, linear complementarity problems, and software evaluation. The selection first elaborates on an upper triangular matrix method for quadratic programming, solving quadratic programs by an exact penalty function, and QP-based methods for large-scale nonlinearly constrained optimization. Discussions focus on large-scale linearly constrained optimization, search direction for superbasic variables, finite convergence, basic properties, comparison of three active set methods, and QP-based methods for dense problems. The book then examines an iterative linear programming algorithm based on an augmented Lagrangian and iterative algorithms for singular minimization problems. The publication ponders on the derivation of symmetric positive definite secant updates, preconditioned conjugate gradient methods, and finding the global minimum of a function of one variable using the method of constant signed higher order derivatives. Topics include effects of calculation errors, application to polynomial minimization, using moderate additional storage, updating Cholesky factors, and utilizing sparse second order information. The selection is a valuable source of data for researchers interested in nonlinear programming.

  • 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.

  • Statistical Computation

    • 1st Edition
    • Roy C. Milton + 1 more
    • English
    Statistical Computation covers the proceedings of a conference held at the University of Wisconsin in Madison, Wisconsin on April 28-30, 1969. The book focuses on the methodologies, techniques, principles, and approaches involved in statistical computation. The selection first elaborates on the description of data structures for statistical computing, autocodes for the statistician, and an experimental data structure for statistical computing. Discussions focus on data-system organization, data structures, autocode requirements, data matrix, structure formulas, and structure formulas in data processing and output. The text then examines statistics and computers in relation to large data bases, statistical data language, facilities in a statistical program system for analysis of multiply-indexed data, and language design and the needs of statisticians. The book takes a look at time sharing and interactive statistics, an approach to conversational statistics, use of APL in statistics, and continuing development of a statistical system. Topics include arithmetic operations and branching statements, ASCOP system, application to statistics, semantics, pragmatics, and implementation. The selection is a valuable reference for statisticians and researchers interested in statistical computation.

  • 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.

  • 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.

  • Capacity Planning for Computer Systems

    • 1st Edition
    • Tim Browning
    • English
    Capacity Planning for Computer Systems covers the principles, concepts, and practical application of capacity planning to computer systems. This book is divided into nine chapters and begins with an introduction to the foundation and metrics of capacity planning. The subsequent chapters deal with the business elements, service levels, forecasting, and predictions of capacity planning, along with the regression techniques, forecast monitoring, and revision for the field. The remaining chapters highlight the applications of capacity planning, including in systems optimization, computer disk, tape, and tape drive. These chapters also provide the charting and graphics presentations for capacity planning. This book will be of value to computer scientists and researchers.

  • Zero-Symmetric Graphs

    Trivalent Graphical Regular Representations of Groups
    • 1st Edition
    • H. S. M. Coxeter + 2 more
    • English
    Zero-Symmetric Graphs: Trivalent Graphical Regular Representations of Groups describes the zero-symmetric graphs with not more than 120 vertices.The graphs considered in this text are finite, connected, vertex-transitive and trivalent. This book is organized into three parts encompassing 25 chapters. The first part reviews the different classes of zero-symmetric graphs, according to the number of essentially different edges incident at each vertex, namely, the S, T, and Z classes. The remaining two parts discuss the theorem and characteristics of type 1Z and 3Z graphs. These parts explore Cayley graphs of specific groups, including the parameters of Cayley graphs of groups. This book will prove useful to mathematicians, computer scientists, and researchers.

  • Numerical Algebra

    • 1st Edition
    • John Todd
    • Ch. Blanc + 2 more
    • English
    Basic Numerical Mathematics, Volume II: Numerical Algebra focuses on numerical algebra, with emphasis on the ideas of "controlled computational experiments" and "bad examples". The existence of an orthogonal matrix which diagonalizes a real symmetric matrix is highlighted, and partitioned or block matrices are discussed, along with induced norms and inversion problems. Comprised of 12 chapters, this volume begins with an overview of the manipulation of vectors and matrices, followed by an analysis of induced norms. The reader is then introduced to the direct solution of the inversion problem, first in the context of theoretical arithmetic (that is, when round-off is disregarded) and second in the context of practical computation. Various methods of handling the characteristic value problems are also considered, together with several iterative methods for the solution of a system of linear equations. Two applications are described: the solution of a two-point boundary value problem and the solution of least squares curve fitting. The book concludes with an account of the singular value decomposition and pseudo-inverses. This monograph will be of interest to mathematicians and students of mathematics.

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