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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.

BooksJournals

    • Advances in Computers

      • 1st Edition
      • Volume 71
      • July 5, 2007
      • Marvin Zelkowitz
      • English
      • Hardback
        9 7 8 0 1 2 3 7 3 7 4 6 5
      • eBook
        9 7 8 0 0 8 0 5 4 5 1 0 3
      Advances in Computers covers new developments in computer technology. Most chapters present an overview of a current subfield within computers, with many citations, and often include new developments in the field by the authors of the individual chapters. Topics include hardware, software, theoretical underpinnings of computing, and novel applications of computers. This current volume includes six chapters on nanotechnology emphasizing its use in biological applications. The book series is a valuable addition to university courses that emphasize the topics under discussion in that particular volume as well as belonging on the bookshelf of industrial practitioners who need to implement many of the technologies that are described.

    • Advances in Computers

      • 1st Edition
      • Volume 70
      • June 7, 2007
      • Marvin Zelkowitz
      • English
      • Hardback
        9 7 8 0 1 2 3 7 3 7 4 7 2
      • eBook
        9 7 8 0 0 8 0 5 2 4 4 1 2
      Advances in Computers covers new developments in computer technology. Most chapters present an overview of a current subfield within computers, with many citations, and often include new developments in the field by the authors of the individual chapters. Topics include hardware, software, theoretical underpinnings of computing, and novel applications of computers. This current volume includes six chapters on hardware development in the educational market, intelligent search strategies, domain specific languages and trustworthiness and risks in computer technology. The book series is a valuable addition to university courses that emphasize the topics under discussion in that particular volume as well as belonging on the bookshelf of industrial practitioners who need to implement many of the technologies that are described.

    • Multiparametric Statistics

      • 1st Edition
      • September 12, 2007
      • Vadim Ivanovich Serdobolskii
      • English
      • Hardback
        9 7 8 0 4 4 4 5 3 0 4 9 3
      • eBook
        9 7 8 0 0 8 0 5 5 5 9 2 8
      This monograph presents mathematical theory of statistical models described by the essentially large number of unknown parameters, comparable with sample size but can also be much larger. In this meaning, the proposed theory can be called "essentially multiparametric". It is developed on the basis of the Kolmogorov asymptotic approach in which sample size increases along with the number of unknown parameters.This theory opens a way for solution of central problems of multivariate statistics, which up until now have not been solved. Traditional statistical methods based on the idea of an infinite sampling often break down in the solution of real problems, and, dependent on data, can be inefficient, unstable and even not applicable. In this situation, practical statisticians are forced to use various heuristic methods in the hope the will find a satisfactory solution.Mathematica... theory developed in this book presents a regular technique for implementing new, more efficient versions of statistical procedures. Near exact solutions are constructed for a number of concrete multi-dimensional problems: estimation of expectation vectors, regression and discriminant analysis, and for the solution to large systems of empiric linear algebraic equations. It is remarkable that these solutions prove to be not only non-degenerating and always stable, but also near exact within a wide class of populations.In the conventional situation of small dimension and large sample size these new solutions far surpass the classical, commonly used consistent ones. It can be expected in the near future, for the most part, traditional multivariate statistical software will be replaced by the always reliable and more efficient versions of statistical procedures implemented by the technology described in this book.This monograph will be of interest to a variety of specialists working with the theory of statistical methods and its applications. Mathematicians would find new classes of urgent problems to be solved in their own regions. Specialists in applied statistics creating statistical packages will be interested in more efficient methods proposed in the book. Advantages of these methods are obvious: the user is liberated from the permanent uncertainty of possible instability and inefficiency and gets algorithms with unimprovable accuracy and guaranteed for a wide class of distributions.A large community of specialists applying statistical methods to real data will find a number of always stable highly accurate versions of algorithms that will help them to better solve their scientific or economic problems. Students and postgraduates will be interested in this book as it will help them get at the foremost frontier of modern statistical science.

    • An Invitation to Biomathematics

      • 1st Edition
      • August 28, 2007
      • Raina Robeva + 6 more
      • English
      • Hardback
        9 7 8 0 1 2 0 8 8 7 7 1 2
      • eBook
        9 7 8 0 0 8 0 5 5 0 9 9 2
      Essential for all biology and biomathematics courses, this textbook provides students with a fresh perspective of quantitative techniques in biology in a field where virtually any advance in the life sciences requires a sophisticated mathematical approach. An Invitation to Biomathematics, expertly written by a team of experienced educators, offers students a solid understanding of solving biological problems with mathematical applications. This text succeeds in enabling students to truly experience advancements made in biology through mathematical models by containing computer-based hands-on laboratory projects with emphasis on model development, model validation, and model refinement. The supplementary work, Laboratory Manual of Biomathematics is available separately ISBN 0123740223, or as a set ISBN: 0123740290)

    • Laboratory Manual of Biomathematics

      • 1st Edition
      • August 28, 2007
      • Raina Robeva + 1 more
      • English
      • Paperback
        9 7 8 0 1 2 3 7 4 0 2 2 9
      • eBook
        9 7 8 0 0 8 0 5 6 5 0 4 0
      Laboratory Manual of Biomathematics is a companion to the textbook An Invitation to Biomathematics. This laboratory manual expertly aids students who wish to gain a deeper understanding of solving biological issues with computer programs. It provides hands-on exploration of model development, model validation, and model refinement, enabling students to truly experience advancements made in biology by mathematical models. Each of the projects offered can be used as individual module in traditional biology or mathematics courses such as calculus, ordinary differential equations, elementary probability, statistics, and genetics. Biological topics include: Ecology, Toxicology, Microbiology, Epidemiology, Genetics, Biostatistics, Physiology, Cell Biology, and Molecular Biology . Mathematical topics include Discrete and continuous dynamical systems, difference equations, differential equations, probability distributions, statistics, data transformation, risk function, statistics, approximate entropy, periodic components, and pulse-detection algorithms. It includes more than 120 exercises derived from ongoing research studies. This text is designed for courses in mathematical biology, undergraduate biology majors, as well as general mathematics. The reader is not expected to have any extensive background in either math or biology.

    • Advances in Computers

      • 1st Edition
      • Volume 68
      • November 22, 2006
      • Chau-wen Tseng + 1 more
      • English
      • Hardback
        9 7 8 0 1 2 0 1 2 1 6 8 7
      • Paperback
        9 7 8 0 1 2 3 9 9 2 7 9 6
      • eBook
        9 7 8 0 0 8 0 4 6 6 3 4 7
      The field of bioinformatics and computational biology arose due to the need to apply techniques from computer science, statistics, informatics, and applied mathematics to solve biological problems. Scientists have been trying to study biology at a molecular level using techniques derived from biochemistry, biophysics, and genetics. Progress has greatly accelerated with the discovery of fast and inexpensive automated DNA sequencing techniques. As the genomes of more and more organisms are sequenced and assembled, scientists are discovering many useful facts by tracing the evolution of organisms by measuring changes in their DNA, rather than through physical characteristics alone. This has led to rapid growth in the related fields of phylogenetics, the study of evolutionary relatedness among various groups of organisms, and comparative genomics, the study of the correspondence between genes and other genomic features in different organisms. Comparing the genomes of organisms has allowed researchers to better understand the features and functions of DNA in individual organisms, as well as provide insights into how organisms evolve over time. The first four chapters of Advances in Computers focus on algorithms for comparing the genomes of different organisms. Possible concrete applications include identifying the basis for genetic diseases and tracking the development and spread of different forms of Avian flu. As researchers begin to better understand the function of DNA, attention has begun shifting towards the actual proteins produced by DNA. The final two chapters explore proteomic techniques for analyzing proteins directly to identify their presence and understand their physical structure.

    • Simulation

      • 4th Edition
      • August 1, 2006
      • Sheldon M. Ross
      • English
      • eBook
        9 7 8 0 0 8 0 5 1 7 2 2 3
      Ross's Simulation, Fourth Edition introduces aspiring and practicing actuaries, engineers, computer scientists and others to the practical aspects of constructing computerized simulation studies to analyze and interpret real phenomena. Readers learn to apply results of these analyses to problems in a wide variety of fields to obtain effective, accurate solutions and make predictions about future outcomes. This text explains how a computer can be used to generate random numbers, and how to use these random numbers to generate the behavior of a stochastic model over time. It presents the statistics needed to analyze simulated data as well as that needed for validating the simulation model.

    • Explorations in Topology

      • 1st Edition
      • November 15, 2006
      • David Gay
      • English
      • Hardback
        9 7 8 0 1 2 3 7 0 8 5 8 8
      • Paperback
        9 7 8 1 4 9 3 3 0 0 8 8 4
      • eBook
        9 7 8 0 0 8 0 4 9 2 6 6 7
      Explorations in Topology gives students a rich experience with low-dimensional topology, enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that would help them make sense of a future, more formal topology course. The innovative story-line style of the text models the problems-solving process, presents the development of concepts in a natural way, and through its informality seduces the reader into engagement with the material. The end-of-chapter Investigations give the reader opportunities to work on a variety of open-ended, non-routine problems, and, through a modified "Moore method", to make conjectures from which theorems emerge. The students themselves emerge from these experiences owning concepts and results. The end-of-chapter Notes provide historical background to the chapter’s ideas, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of projects provides opportunities for continued involvement in "research" beyond the topics of the book.

    • Information-Theoretic Methods for Estimating of Complicated Probability Distributions

      • 1st Edition
      • Volume 207
      • August 15, 2006
      • Zhi Zong
      • English
      • eBook
        9 7 8 0 0 8 0 4 6 3 8 5 8
      Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions.Estima... probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neural networks and quality control. Simple distribution forms such as Gaussian, exponential or Weibull distributions are often employed to represent the distributions of the random variables under consideration, as we are taught in universities. In engineering, physical and social science applications, however, the distributions of many random variables or random vectors are so complicated that they do not fit the simple distribution forms at al.Exact estimation of the probability distribution of a random variable is very important. Take stock market prediction for example. Gaussian distribution is often used to model the fluctuations of stock prices. If such fluctuations are not normally distributed, and we use the normal distribution to represent them, how could we expect our prediction of stock market is correct? Another case well exemplifying the necessity of exact estimation of probability distributions is reliability engineering. Failure of exact estimation of the probability distributions under consideration may lead to disastrous designs.There have been constant efforts to find appropriate methods to determine complicated distributions based on random samples, but this topic has never been systematically discussed in detail in a book or monograph. The present book is intended to fill the gap and documents the latest research in this subject.Determining a complicated distribution is not simply a multiple of the workload we use to determine a simple distribution, but it turns out to be a much harder task. Two important mathematical tools, function approximation and information theory, that are beyond traditional mathematical statistics, are often used. Several methods constructed based on the two mathematical tools for distribution estimation are detailed in this book. These methods have been applied by the author for several years to many cases. They are superior in the following senses:(1) No prior information of the distribution form to be determined is necessary. It can be determined automatically from the sample;(2) The sample size may be large or small;(3) They are particularly suitable for computers. It is the rapid development of computing technology that makes it possible for fast estimation of complicated distributions. The methods provided herein well demonstrate the significant cross influences between information theory and statistics, and showcase the fallacies of traditional statistics that, however, can be overcome by information theory.Key Features:- Density functions automatically determined from samples- Free of assuming density forms- Computation-effectiv... methods suitable for PC

    • Discrete Dynamical Systems, Bifurcations and Chaos in Economics

      • 1st Edition
      • Volume 204
      • January 5, 2006
      • Wei-Bin Zhang
      • English
      • Hardback
        9 7 8 0 4 4 4 5 2 1 9 7 2
      • eBook
        9 7 8 0 0 8 0 4 6 2 4 6 2
      This book is a unique blend of difference equations theory and its exciting applications to economics. It deals with not only theory of linear (and linearized) difference equations, but also nonlinear dynamical systems which have been widely applied to economic analysis in recent years. It studies most important concepts and theorems in difference equations theory in a way that can be understood by anyone who has basic knowledge of calculus and linear algebra. It contains well-known applications and many recent developments in different fields of economics. The book also simulates many models to illustrate paths of economic dynamics.

Related subjects

Mathematics and applied mathematics

Statistics and probability