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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.

  • Numerical Analysis

    A Second Course
    • 1st Edition
    • James M. Ortega
    • Werner Rheinboldt
    • English
    Computer Science and Applied Mathematics: Numerical Analysis: A Second Course presents some of the basic theoretical results pertaining to the three major problem areas of numerical analysis—rounding error, discretization error, and convergence error. This book is organized into four main topics: mathematical stability and ill conditioning, discretization error, convergence of iterative methods, and rounding error. In these topics, this text specifically discusses the systems of linear algebraic equations, eigenvalues and eigenvectors, and differential and difference equations. The discretization error for initial and boundary value problems, systems of linear and nonlinear equations, and rounding error for Gaussian elimination are also elaborated. This publication is recommended for undergraduate level students and students taking a one-semester first-year graduate course for computer science and mathematics majors.

  • Recent Developments in Clustering and Data Analysis

    Développements Récents en Classification Automatique et Analyse des Données: Proceedings of the Japanese-French Scientific Seminar March 24–26, 1987
    • 1st Edition
    • Chikio Hayashi + 2 more
    • English
    Recent Developments in Clustering and Data Analysis presents the results of clustering and multidimensional data analysis research conducted primarily in Japan and France. This book focuses on the significance of the data itself and on the informatics of the data. Organized into four sections encompassing 35 chapters, this book begins with an overview of the quantification of qualitative data as a method of analyzing statistically multidimensional data. This text then examines the rules of interpretation of correspondence cluster analysis by selecting classes and explaining variables involved in the algorithm of hierarchical classification. Other chapters consider the bootstrap and cross-validation methods, which are applied to the logistic ad nonparametric regression analyses of ordered categorical responses. The final chapter deals with a simpler treatment to classify the sleep state. This book is a valuable resource for researchers and workers in the fields from the behavioral sciences, biological sciences, medicine, and industrial sciences.

  • Associative Networks

    Representation and Use of Knowledge by Computers
    • 1st Edition
    • Nicholas V. Findler
    • English
    Associative Networks: Representation and Use of Knowledge by Computers is a collection of papers that deals with knowledge base of programs exhibiting some operational aspects of understanding. One paper reviews network formalism that utilizes unobstructed semantics, independent of the domain to which it is applied, that is also capable of handling significant epistemological relationships of concept structuring, attribute/value inheritance, multiple descriptions. Another paper explains network notations that encode taxonomic information; general statements involving quantification; information about processes and procedures; the delineation of local contexts, as well as the relationships between syntactic units and their interpretations. One paper shows that networks can be designed to be intuitively and formally interpretable. Network formalisms are computer-oriented logics which become distinctly significant when access paths from concepts to propositions are built into them. One feature of a topical network organization is its potential for learning. If one topic is too large, it could be broken down where groupings of propositions under the split topics are then based on "co-usage" statistics. As an example, one paper cites the University of Maryland artificial intelligence (AI) group which investigates the control and interaction of a meaning-based parser. The group also analyzes the inferences and predictions from a number of levels based on mundane inferences of actions and causes that can be used in AI. The collection can be useful for computer engineers, computer programmers, mathematicians, and researchers who are working on artificial intelligence.

  • Artificial Intelligence

    • 1st Edition
    • Earl B. Hunt
    • Edward C. Carterette + 1 more
    • English
    Artificial Intelligence provides information pertinent to the fundamental aspects of artificial intelligence. This book presents the basic mathematical and computational approaches to problems in the artificial intelligence field. Organized into four parts encompassing 16 chapters, this book begins with an overview of the various fields of artificial intelligence. This text then attempts to connect artificial intelligence problems to some of the notions of computability and abstract computing devices. Other chapters consider the general notion of computability, with focus on the interaction between computability theory and artificial intelligence. This book discusses as well the concepts of pattern recognition, problem solving, and machine comprehension. The final chapter deals with the study of machine comprehension and reviews the fundamental mathematical and computing techniques underlying artificial intelligence research. This book is a valuable resource for seniors and graduate students in any of the computer-related sciences, or in experimental psychology. Psychologists, general systems theorists, and scientists will also find this book useful.

  • Projective Geometry and Algebraic Structures

    • 1st Edition
    • R. J. Mihalek
    • English
    Projective Geometry and Algebraic Structures focuses on the relationship of geometry and algebra, including affine and projective planes, isomorphism, and system of real numbers. The book first elaborates on euclidean, projective, and affine planes, including axioms for a projective plane, algebraic incidence bases, and self-dual axioms. The text then ponders on affine and projective planes, theorems of Desargues and Pappus, and coordination. Topics include algebraic systems and incidence bases, coordinatization theorem, finite projective planes, coordinates, deletion subgeometries, imbedding theorem, and isomorphism. The publication examines projectivities, harmonic quadruples, real projective plane, and projective spaces. Discussions focus on subspaces and dimension, intervals and complements, dual spaces, axioms for a projective space, ordered fields, completeness and the real numbers, real projective plane, and harmonic quadruples. The manuscript is a dependable reference for students and researchers interested in projective planes, system of real numbers, isomorphism, and subspaces and dimensions.

  • Contributions to Probability

    A Collection of Papers Dedicated to Eugene Lukacs
    • 1st Edition
    • J. Gani + 1 more
    • English
    Contributions to Probability: A Collection of Papers Dedicated to Eugene Lukacs is a collection of papers that reflect Professor Eugene Lukacs’ broad range of research interests. This text celebrates the 75th birthday of Eugene Lukacs, mathematician, teacher, and research worker in probability and mathematical statistics. This book is organized into two parts encompassing 23 chapters. Part I consists of papers in probability theory, limit theorems, and stochastic processes. This part also deals with the continuation and arithmetic of distribution functions, the arc sine law, Fourier transform methods, and nondifferentiality of the Wiener sheet. Part II includes papers in information and statistical theories. This book will prove useful to statisticians, mathematicians, and advance mathematics students.

  • Singular Perturbations and Asymptotics

    Proceedings of an Advanced Seminar Conducted by the Mathematics Research Center, the University of Wisconsin—Madison, May 28-30, 1980
    • 1st Edition
    • Richard E. Meyer + 1 more
    • English
    Mathematics Research Center Symposia and Advanced Seminar Series: Singular Perturbations and Asymptotics covers the lectures presented at an Advanced Seminar on Singular Perturbation and Asymptotics, held in Madison, Wisconsin on May 28-30, 1980 under the auspices of the Mathematics Research Center of the University of Wisconsin—Madison. The book focuses on the processes, methodologies, reactions, and principles involved in singular perturbations and asymptotics, including boundary value problems, equations, perturbations, water waves, and gas dynamics. The selection first elaborates on basic concepts in the analysis of singular perturbations, limit process expansions and approximate equations, and results on singularly perturbed boundary value problems. Discussions focus on quasi-linear and nonlinear problems, semilinear systems, water waves, expansion in gas dynamics, asymptotic matching principles, and classical perturbation analysis. The text then takes a look at multiple solutions of singularly perturbed systems in the conditionally stable case and singular perturbations, stochastic differential equations, and applications. The book ponders on connection problems in the parameterless case; general connection-formula problem for linear differential equations of the second order; and turning-point problems for ordinary differential equations of hydrodynamic type. Topics include the comparison equation method, boundary layer flows, compound matrix method, asymptotic solution of the connection-formula problem, and higher order equations. The selection is a valuable source of information for researchers interested in singular perturbations and asymptotics.

  • Mathematics Applied to Science

    In Memoriam Edward D. Conway
    • 1st Edition
    • Jerome Goldstein + 2 more
    • English
    Mathematics Applied to Science: In Memoriam Edward D. Conway presents a compilation of articles as a lasting tribute to Edward Conway III. This book covers a variety of topics, including molecular electronic energies, partial differential equations, density matrix, electron density functional, and climate change. Organized into 13 chapters, this book begins with an overview of the large-time behavior of one-dimensional motion in a model gas whose particles have a discrete set of allowed velocities. This text then explores the operator splitting techniques for the solution of time dependent differential equations. Other chapters describe a Monte Carlo simulation procedure for evaluating the relaxation rate of an excited state vibrational population of a diatomic in a simple solvent. This book discusses as well the numerical solution of nonlinear differential equations. The final chapter deals with the physical, thermal, and dynamical properties near the surface of the Earth. This book is a valuable resource for mathematicians.

  • Introductory Statistics for the Behavioral Sciences

    Workbook
    • 1st Edition
    • Robert B. Ewen
    • English
    Introductory Statistics for the Behavioral Sciences is a workbook on statistical procedures and formulas that are relevant to research and field work. The book explains frequency distributions, graphs, and measures of central tendency. The workbook uses as example hypothetical scores of a test given to students in four universities. The book then has sections on reminders and problems to guide the reader. Other topics the book discusses include measures of variability, transformed scores, probability, and general strategy of inferential statistics. Other subjects the book also covers include inferences about the mean of a single population and testing hypotheses about the differences between the means of two populations. The workbook also includes practice problems on linear correlation, prediction, and other correlational techniques such as the Spearmen rank-order correlation coefficient or the point biserial correlation coefficient. The book also includes review chapters on normal curves, standard error procedures, and inferential statistics. The workbook can be a great aid for students of behavioral and physical sciences where statistics is applied in research and analysis.

  • Statistical Decision Theory and Related Topics

    • 1st Edition
    • Shanti S. Gupta + 1 more
    • English
    Statistical Decision Theory and Related Topics is a collection of the papers presented at the Symposium on Statistical Decision Theory and Related Topics which was held on November 23-25, 1970 at Purdue University. The conference brought together research workers in decision theory and related topics. This volume contains twenty papers presented during the symposium and includes works on molecular studies of evolution, globally optimal procedure for one-sided comparisons, multiple decision theory, outlier detection, empirical Bayes slippage tests, and non-optimality of likelihood ratio tests for sequential detection of signals in Gaussian noise. Mathematicians and statisticians will find the book highly insightful.

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