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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.

  • Handbook of Global Analysis

    • 1st Edition
    • Demeter Krupka + 1 more
    • English
    This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis”, dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry.

  • Epidemiology and Medical Statistics

    • 1st Edition
    • Volume 27
    • English
    This volume, representing a compilation of authoritative reviews on a multitude of uses of statistics in epidemiology and medical statistics written by internationally renowned experts, is addressed to statisticians working in biomedical and epidemiological fields who use statistical and quantitative methods in their work. While the use of statistics in these fields has a long and rich history, explosive growth of science in general and clinical and epidemiological sciences in particular have gone through a see of change, spawning the development of new methods and innovative adaptations of standard methods. Since the literature is highly scattered, the Editors have undertaken this humble exercise to document a representative collection of topics of broad interest to diverse users. The volume spans a cross section of standard topics oriented toward users in the current evolving field, as well as special topics in much need which have more recent origins. This volume was prepared especially keeping the applied statisticians in mind, emphasizing applications-oriente... methods and techniques, including references to appropriate software when relevant.

  • Consciousness Transitions

    Phylogenetic, Ontogenetic and Physiological Aspects
    • 1st Edition
    • Hans Liljenström + 1 more
    • English
    It was not long ago when the consciousness was not considered a problem for science. However, this has now changed and the problem of consciousness is considered the greatest challenge to science. In the last decade, a great number of books and articles have been published in the field, but very few have focused on the how consciousness evolves and develops, and what characterizes the transitions between different conscious states, in animals and humans. This book addresses these questions. Renowned researchers from different fields of science (including neurobiology, evolutionary biology, ethology, cognitive science, computational neuroscience and philosophy) contribute with their results and theories in this book, making it a unique collection of the state-of-the-art of this young field of consciousness studies.

  • Reconfigurable Computing

    The Theory and Practice of FPGA-Based Computation
    • 1st Edition
    • Volume 1
    • Scott Hauck + 1 more
    • English
    Reconfigurable Computing marks a revolutionary and hot topic that bridges the gap between the separate worlds of hardware and software design— the key feature of reconfigurable computing is its groundbreaking ability to perform computations in hardware to increase performance while retaining the flexibility of a software solution. Reconfigurable computers serve as affordable, fast, and accurate tools for developing designs ranging from single chip architectures to multi-chip and embedded systems. Scott Hauck and Andre DeHon have assembled a group of the key experts in the fields of both hardware and software computing to provide an introduction to the entire range of issues relating to reconfigurable computing. FPGAs (field programmable gate arrays) act as the “computing vehicles” to implement this powerful technology. Readers will be guided into adopting a completely new way of handling existing design concerns and be able to make use of the vast opportunities possible with reconfigurable logic in this rapidly evolving field.

  • Multiparametric Statistics

    • 1st Edition
    • Vadim Ivanovich Serdobolskii
    • English
    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.

  • Nine Introductions in Complex Analysis - Revised Edition

    • 1st Edition
    • Volume 208
    • Sanford L. Segal
    • English
    The book addresses many topics not usually in "second course in complex analysis" texts. It also contains multiple proofs of several central results, and it has a minor historical perspective.

  • Computational Theory of Iterative Methods

    • 1st Edition
    • Volume 15
    • Ioannis Argyros
    • English
    The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails. The book contains applications in several areas of applied sciences including mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory.

  • Laboratory Manual of Biomathematics

    • 1st Edition
    • Raina Robeva + 1 more
    • English
    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.

  • An Invitation to Biomathematics

    • 1st Edition
    • Raina Robeva + 6 more
    • English
    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)

  • Modeling and Simulation-Based Data Engineering

    Introducing Pragmatics into Ontologies for Net-Centric Information Exchange
    • 1st Edition
    • Bernard P. Zeigler + 1 more
    • English
    Data Engineering has become a necessary and critical activity for business, engineering, and scientific organizations as the move to service oriented architecture and web services moves into full swing. Notably, the US Department of Defense is mandating that all of its agencies and contractors assume a defining presence on the Net-centric Global Information Grid. This book provides the first practical approach to data engineering and modeling, which supports interoperabililty with consumers of the data in a service- oriented architectures (SOAs). Although XML (eXtensible Modeling Language) is the lingua franca for such interoperability, it is not sufficient on its own. The approach in this book addresses critical objectives such as creating a single representation for multiple applications, designing models capable of supporting dynamic processes, and harmonizing legacy data models for web-based co-existence. The approach is based on the System Entity Structure (SES) which is a well-defined structure, methodology, and practical tool with all of the functionality of UML (Unified Modeling Language) and few of the drawbacks. The SES originated in the formal representation of hierarchical simulation models. So it provides an axiomatic formalism that enables automating the development of XML dtds and schemas, composition and decomposition of large data models, and analysis of commonality among structures. Zeigler and Hammond include a range of features to benefit their readers. Natural language, graphical and XML forms of SES specification are employed to allow mapping of legacy meta-data. Real world examples and case studies provide insight into data engineering and test evaluation in various application domains. Comparative information is provided on concepts of ontologies, modeling and simulation, introductory linguistic background, and support options enable programmers to work with advanced tools in the area. The website of the Arizona Center for Integrative Modeling and Simulation, co-founded by Zeigler in 2001, provides links to downloadable software to accompany the book.

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