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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.

  • Traveling Wave Analysis of Partial Differential Equations

    Numerical and Analytical Methods with Matlab and Maple
    • 1st Edition
    • Graham Griffiths + 1 more
    • English
    Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors’ intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs. The Matlab and Maple software will be available for download from this website shortly. www.pdecomp.net

  • Computability Theory

    An Introduction to Recursion Theory
    • 1st Edition
    • Herbert B. Enderton
    • English
    Computability Theory: An Introduction to Recursion Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The text includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable way.

  • Essential Computational Modeling for the Human Body

    • 1st Edition
    • Philippe G. Ciarlet
    • English
    Essential Computational Modeling for the Human Body presents key contributions selected from the volume in the Handbook of Numerical Analysis: Computational Modeling for the Human Body Vol. 12 (2005). Computational (Mathematical) Modeling is used by scientists and researchers with various applications in chemical, biological, behavioral, environmental sciences, etc. This guide presents essential research techniques for analysis and essential concrete examples of computational models, while supplying a wide range of commonly used methods and applications, followed by various numerical simulations.

  • Essential Computational Modeling in Chemistry

    • 1st Edition
    • Philippe G. Ciarlet
    • English
    Essential Computational Modeling in Chemistry presents key contributions selected from the volume in the Handbook of Numerical Analysis: Computational Modeling in Chemistry Vol. 10(2005). Computational Modeling is an active field of scientific computing at the crossroads between Physics, Chemistry, Applied Mathematics and Computer Science. Sophisticated mathematical models are increasingly complex and extensive computer simulations are on the rise. Numerical Analysis and scientific software have emerged as essential steps for validating mathematical models and simulations based on these models. This guide provides a quick reference of computational methods for use in understanding chemical reactions and how to control them. By demonstrating various computational methods in research, scientists can predict such things as molecular properties. The reference offers a number of techniques and the numerical analysis needed to perform rigorously founded computations.

  • An Introduction to Stochastic Modeling

    • 4th Edition
    • Mark Pinsky + 1 more
    • English
    Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Fourth Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems. New to this edition: Realistic applications from a variety of disciplines integrated throughout the text, including more biological applications Plentiful, completely updated problems Completely updated and reorganized end-of-chapter exercise sets, 250 exercises with answers New chapters of stochastic differential equations and Brownian motion and related processes Additional sections on Martingale and Poisson process

  • Essential Bayesian Models

    • 1st Edition
    • C.R. Rao + 1 more
    • English
    This accessible reference includes selected contributions from Bayesian Thinking - Modeling and Computation, Volume 25 in the Handbook of Statistics Series, with a focus on key methodologies and applications for Bayesian models and computation. It describes parametric and nonparametric Bayesian methods for modeling, and how to use modern computational methods to summarize inferences using simulation. The book covers a wide range of topics including objective and subjective Bayesian inferences, with a variety of applications in modeling categorical, survival, spatial, spatiotemporal, Epidemiological, small area and micro array data.

  • Essential Methods for Design Based Sample Surveys

    • 1st Edition
    • Danny Pfeffermann + 1 more
    • English
    Essential Methods for Design Based Sample Surveys presents key method contributions selected from the volume in the Handbook of Statistics: Sample Surveys: Design, Methods and Applications, Vol. 29a (2009). This essential reference provides specific aspects of sample survey design, with references to important contributions and available software. The content is aimed at researchers and practitioners who use statistical methods in design based sample surveys and market research. This book presents the core essential methods of sample selection and data processing. The data processing discussion covers editing and imputation, and methods of disclosure control. This reference contains a large variety of applications in specialized areas such as household and business surveys, marketing research, opinion polls and censuses.

  • Essential Statistical Methods for Medical Statistics

    • 1st Edition
    • J. Philip Miller
    • English
    Essential Statistical Methods for Medical Statistics presents only key contributions which have been selected from the volume in the Handbook of Statistics: Medical Statistics, Volume 27 (2009). While the use of statistics in these fields has a long and rich history, the explosive growth of science in general, and of clinical and epidemiological sciences in particular, has led to the development of new methods and innovative adaptations of standard methods. This volume is appropriately focused for individuals working in these fields. Contributors are internationally renowned experts in their respective areas.

  • Essential Numerical Computer Methods

    • 1st Edition
    • Michael L. Johnson
    • English
    The use of computers and computational methods has become ubiquitous in biological and biomedical research. During the last 2 decades most basic algorithms have not changed, but what has is the huge increase in computer speed and ease of use, along with the corresponding orders of magnitude decrease in cost. A general perception exists that the only applications of computers and computer methods in biological and biomedical research are either basic statistical analysis or the searching of DNA sequence data bases. While these are important applications they only scratch the surface of the current and potential applications of computers and computer methods in biomedical research. The various chapters within this volume include a wide variety of applications that extend far beyond this limited perception. As part of the Reliable Lab Solutions series, Essential Numerical Computer Methods brings together chapters from volumes 210, 240, 321, 383, 384, 454, and 467 of Methods in Enzymology. These chapters provide a general progression from basic numerical methods to more specific biochemical and biomedical applications.

  • Doing Bayesian Data Analysis

    A Tutorial Introduction with R
    • 1st Edition
    • John Kruschke
    • English
    There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis tractable and accessible to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS, is for first year graduate students or advanced undergraduates and provides an accessible approach, as all mathematics is explained intuitively and with concrete examples. It assumes only algebra and ‘rusty’ calculus. Unlike other textbooks, this book begins with the basics, including essential concepts of probability and random sampling. The book gradually climbs all the way to advanced hierarchical modeling methods for realistic data. The text provides complete examples with the R programming language and BUGS software (both freeware), and begins with basic programming examples, working up gradually to complete programs for complex analyses and presentation graphics. These templates can be easily adapted for a large variety of students and their own research needs.The textbook bridges the students from their undergraduate training into modern Bayesian methods.

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