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Elsevier

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.

  • Latin Squares and their Applications

    • 2nd Edition
    • A. Donald Keedwell + 1 more
    • English
    Latin Squares and Their Applications, Second edition offers a long-awaited update and reissue of this seminal account of the subject. The revision retains foundational, original material from the frequently-cited 1974 volume but is completely updated throughout. As with the earlier version, the author hopes to take the reader ‘from the beginnings of the subject to the frontiers of research’. By omitting a few topics which are no longer of current interest, the book expands upon active and emerging areas. Also, the present state of knowledge regarding the 73 then-unsolved problems given at the end of the first edition is discussed and commented upon. In addition, a number of new unsolved problems are proposed. Using an engaging narrative style, this book provides thorough coverage of most parts of the subject, one of the oldest of all discrete mathematical structures and still one of the most relevant. However, in consequence of the huge expansion of the subject in the past 40 years, some topics have had to be omitted in order to keep the book of a reasonable length. Latin squares, or sets of mutually orthogonal latin squares (MOLS), encode the incidence structure of finite geometries; they prescribe the order in which to apply the different treatments in designing an experiment in order to permit effective statistical analysis of the results; they produce optimal density error-correcting codes; they encapsulate the structure of finite groups and of more general algebraic objects known as quasigroups. As regards more recreational aspects of the subject, latin squares provide the most effective and efficient designs for many kinds of games tournaments and they are the templates for Sudoku puzzles. Also, they provide a number of ways of constructing magic squares, both simple magic squares and also ones with additional properties.

  • Big Data Analytics

    • 1st Edition
    • Volume 33
    • English
    While the term Big Data is open to varying interpretation, it is quite clear that the Volume, Velocity, and Variety (3Vs) of data have impacted every aspect of computational science and its applications. The volume of data is increasing at a phenomenal rate and a majority of it is unstructured. With big data, the volume is so large that processing it using traditional database and software techniques is difficult, if not impossible. The drivers are the ubiquitous sensors, devices, social networks and the all-pervasive web. Scientists are increasingly looking to derive insights from the massive quantity of data to create new knowledge. In common usage, Big Data has come to refer simply to the use of predictive analytics or other certain advanced methods to extract value from data, without any required magnitude thereon. Challenges include analysis, capture, curation, search, sharing, storage, transfer, visualization, and information privacy. While there are challenges, there are huge opportunities emerging in the fields of Machine Learning, Data Mining, Statistics, Human-Computer Interfaces and Distributed Systems to address ways to analyze and reason with this data. The edited volume focuses on the challenges and opportunities posed by "Big Data" in a variety of domains and how statistical techniques and innovative algorithms can help glean insights and accelerate discovery. Big data has the potential to help companies improve operations and make faster, more intelligent decisions.

  • Essential Statistics, Regression, and Econometrics

    • 2nd Edition
    • Gary Smith
    • English
    Essential Statistics, Regression, and Econometrics, Second Edition, is innovative in its focus on preparing students for regression/econometr... and in its extended emphasis on statistical reasoning, real data, pitfalls in data analysis, and modeling issues. This book is uncommonly approachable and easy to use, with extensive word problems that emphasize intuition and understanding. Too many students mistakenly believe that statistics courses are too abstract, mathematical, and tedious to be useful or interesting. To demonstrate the power, elegance, and even beauty of statistical reasoning, this book provides hundreds of new and updated interesting and relevant examples, and discusses not only the uses but also the abuses of statistics. The examples are drawn from many areas to show that statistical reasoning is not an irrelevant abstraction, but an important part of everyday life.

  • Advances in Independent Component Analysis and Learning Machines

    • 1st Edition
    • Ella Bingham + 3 more
    • English
    In honour of Professor Erkki Oja, one of the pioneers of Independent Component Analysis (ICA), this book reviews key advances in the theory and application of ICA, as well as its influence on signal processing, pattern recognition, machine learning, and data mining. Examples of topics which have developed from the advances of ICA, which are covered in the book are: A unifying probabilistic model for PCA and ICA Optimization methods for matrix decompositions Insights into the FastICA algorithm Unsupervised deep learning Machine vision and image retrieval

  • Introduction to Actuarial and Financial Mathematical Methods

    • 1st Edition
    • Stephen Garrett
    • English
    This self-contained module for independent study covers the subjects most often needed by non-mathematics graduates, such as fundamental calculus, linear algebra, probability, and basic numerical methods. The easily-understandabl... text of Introduction to Actuarial and Mathematical Methods features examples, motivations, and lots of practice from a large number of end-of-chapter questions. For readers with diverse backgrounds entering programs of the Institute and Faculty of Actuaries, the Society of Actuaries, and the CFA Institute, Introduction to Actuarial and Mathematical Methods can provide a consistency of mathematical knowledge from the outset.

  • Algebraic and Discrete Mathematical Methods for Modern Biology

    • 1st Edition
    • Raina Robeva
    • English
    Written by experts in both mathematics and biology, Algebraic and Discrete Mathematical Methods for Modern Biology offers a bridge between math and biology, providing a framework for simulating, analyzing, predicting, and modulating the behavior of complex biological systems. Each chapter begins with a question from modern biology, followed by the description of certain mathematical methods and theory appropriate in the search of answers. Every topic provides a fast-track pathway through the problem by presenting the biological foundation, covering the relevant mathematical theory, and highlighting connections between them. Many of the projects and exercises embedded in each chapter utilize specialized software, providing students with much-needed familiarity and experience with computing applications, critical components of the "modern biology" skill set. This book is appropriate for mathematics courses such as finite mathematics, discrete structures, linear algebra, abstract/modern algebra, graph theory, probability, bioinformatics, statistics, biostatistics, and modeling, as well as for biology courses such as genetics, cell and molecular biology, biochemistry, ecology, and evolution.

  • Mathematical Models for Neglected Tropical Diseases: Essential Tools for Control and Elimination, Part A

    • 1st Edition
    • Volume 87
    • English
    First published in 1963, Advances in Parasitology contains comprehensive and up-to-date reviews in all areas of interest in contemporary parasitology. Advances in Parasitology includes medical studies of parasites of major influence, such as Plasmodium falciparum and trypanosomes. The series also contains reviews of more traditional areas, such as zoology, taxonomy, and life history, which shape current thinking and applications. The 2013 impact factor is 4.36.

  • Advances in Computers

    • 1st Edition
    • Volume 97
    • English
    Since its first volume in 1960, Advances in Computers has presented detailed coverage of innovations in computer hardware, software, theory, design, and applications. It has also provided contributors with a medium in which they can explore their subjects in greater depth and breadth than journal articles usually allow. As a result, many articles have become standard references that continue to be of significant, lasting value in this rapidly expanding field.

  • Bio-Inspired Computation in Telecommunications

    • 1st Edition
    • Xin-She Yang + 2 more
    • English
    Bio-inspired computation, especially those based on swarm intelligence, has become increasingly popular in the last decade. Bio-Inspired Computation in Telecommunications reviews the latest developments in bio-inspired computation from both theory and application as they relate to telecommunications and image processing, providing a complete resource that analyzes and discusses the latest and future trends in research directions. Written by recognized experts, this is a must-have guide for researchers, telecommunication engineers, computer scientists and PhD students.

  • The Linear Algebra Survival Guide

    Illustrated with Mathematica
    • 1st Edition
    • Fred Szabo
    • English
    The Linear Algebra Survival Guide offers a concise introduction to the difficult core topics of linear algebra, guiding you through the powerful graphic displays and visualization of Mathematica that make the most abstract theories seem simple - allowing you to tackle realistic problems using simple mathematical manipulations. This resource is therefore a guide to learning the content of Mathematica in a practical way, enabling you to manipulate potential solutions/outcomes, and learn creatively. No starting knowledge of the Mathematica system is required to use the book. Desktop, laptop, web-based versions of Mathematica are available on all major platforms. Mathematica Online for tablet and smartphone systems are also under development and increases the reach of the guide as a general reference, teaching and learning tool.

  • Semi-Markov Models

    Control of Restorable Systems with Latent Failures
    • 1st Edition
    • Yuriy E Obzherin + 1 more
    • English
    Featuring previously unpublished results, Semi-Markov Models: Control of Restorable Systems with Latent Failures describes valuable methodology which can be used by readers to build mathematical models of a wide class of systems for various applications. In particular, this information can be applied to build models of reliability, queuing systems, and technical control. Beginning with a brief introduction to the area, the book covers semi-Markov models for different control strategies in one-component systems, defining their stationary characteristics of reliability and efficiency, and utilizing the method of asymptotic phase enlargement developed by V.S. Korolyuk and A.F. Turbin. The work then explores semi-Markov models of latent failures control in two-component systems. Building on these results, solutions are provided for the problems of optimal periodicity of control execution. Finally, the book presents a comparative analysis of analytical and imitational modeling of some one- and two-component systems, before discussing practical applications of the results

  • Dataflow Processing

    • 1st Edition
    • Volume 96
    • English
    Since its first volume in 1960, Advances in Computers has presented detailed coverage of innovations in computer hardware, software, theory, design, and applications. It has also provided contributors with a medium in which they can explore their subjects in greater depth and breadth than journal articles usually allow. As a result, many articles have become standard references that continue to be of significant, lasting value in this rapidly expanding field.

  • Nonlinear Differential Equations

    • 1st Edition
    • Volume 2
    • Svatopluk Fucik + 1 more
    • English
    Studies in Applied Mathematics, 2: Nonlinear Differential Equations focuses on modern methods of solutions to boundary value problems in linear partial differential equations. The book first tackles linear and nonlinear equations, free boundary problem, second order equations, higher order equations, boundary conditions, and spaces of continuous functions. The text then examines the weak solution of a boundary value problem and variational and topological methods. Discussions focus on general boundary conditions for second order ordinary differential equations, minimal surfaces, existence theorems, potentials of boundary value problems, second derivative of a functional, convex functionals, Lagrange conditions, differential operators, Sobolev spaces, and boundary value problems. The manuscript examines noncoercive problems and vibrational inequalities. Topics include existence theorems, formulation of the problem, vanishing nonlinearities, jumping nonlinearities with finite jumps, rapid nonlinearities, and periodic problems. The text is highly recommended for mathematicians and engineers interested in nonlinear differential equations.

  • Methods of Contour Integration

    • 1st Edition
    • Volume 3
    • M. L. Rasulov
    • H. A. Lauwerier + 1 more
    • English
    Methods of Contour Integration contains two parts: (1) a systematic exposition of the computational method for solving boundary and mixed problems, and (2) the contour-integral method for investigating general linear mixed problems. The first part includes formulae for expanding arbitrary vector-valued functions in series from integral residues of solutions of boundary-value problems for systems of ordinary differential equations with discontinuous coefficients. These formulae give residue representations of solutions of the corresponding one-dimensional mixed problems for equations with discontinuous coefficients. The book also explains a computational method of separating the variables which is a generalization of the ordinary method of separating variables to the case of nonself-adjoint operators. In part two, the text discusses one-dimensional mixed problems for equations with discontinuous coefficients. Under regular boundary conditions, it proves the existence of solutions for these problems and the representability of the solutions in the form of contour integrals with a complex parameter. The text points out that the contour-integral method is also applicable to parabolic equations and to equations in which the coefficients are functions of time. The book is ideal for mathematicians, students, and professor of calculus and advanced mathematics.

  • A Correlation Study of Methods of Matrix Structural Analysis

    Report to the 14th Meeting, Structures and Materials Panel Advisory Group for Aeronautical Research and Development, NATO, Paris, France, July 6, 1962
    • 1st Edition
    • Volume 69
    • Richard H. Gallagher
    • English
    A Correlation Study of Methods of Matrix Structural Analysis describes the results of a survey and review of airframe matrix structural analysis. The book also explains concepts of force and displacement, as well as the techniques for determining the force-displacement properties of discrete elements employed in analytical idealizations of structures. The text investigates the results of extensive analyses of multiweb low aspect ratio wings, using past evaluative studies and idealizations contained in reports of the AGARD Structures and Materials Panel. The techniques describe in the Panel and other techniques in matrix structural analysis lead to identical formulations of the governing equations. The differences between various references with respect to idealization are independent of the formulation of the governing equations. The solutions to governing equations are precise solutions for the postulated discrete element system. The book also describes a recommended computer program development using whichever is more appropriate between a force approach or displacement approach to matrix structural analysis. The text is valuable for researchers in structural analysis, aeronautics, applied mechanics, and investigators of aircraft engineering.

  • VLSI Electronics

    Microstructure Science
    • 1st Edition
    • Volume 2
    • Norman G. Einspruch
    • English

  • VLSI in Medicine

    • 1st Edition
    • Volume 17
    • Norman G. Einspruch + 1 more
    • English
    VLSI Electronics Microstructure Science, Volume 17: VLSI in Medicine deals with the more important applications of VLSI in medical devices and instruments. This volume is comprised of 11 chapters. It begins with an article about medical electronics. The following three chapters cover diagnostic imaging, focusing on such medical devices as magnetic resonance imaging, neurometric analyzer, and ultrasound. Chapters 5, 6, and 7 present the impact of VLSI in cardiology. The electrocardiograph, implantable cardiac pacemaker, and the use of VLSI in Holter monitoring are detailed in these chapters. The neurostimulator is described in Chapter 8. Chapter 9 discusses both implantable and external drug infusion pumps and describes the use of VLSI in a particular external pump. The last two chapters cover topics that apply to the entire field of medical electronics. Engineers, scientists, medical practitioners and researchers will find the book very useful.

  • Lithography for VLSI

    VLSI Electronics Microstructure Science
    • 1st Edition
    • Volume 16
    • Norman G. Einspruch + 1 more
    • English
    VLSI Electronics Microstructure Science, Volume 16: Lithography for VLSI treats special topics from each branch of lithography, and also contains general discussion of some lithographic methods. This volume contains 8 chapters that discuss the various aspects of lithography. Chapters 1 and 2 are devoted to optical lithography. Chapter 3 covers electron lithography in general, and Chapter 4 discusses electron resist exposure modeling. Chapter 5 presents the fundamentals of ion-beam lithography. Mask/wafer alignment for x-ray proximity printing and for optical lithography is tackled in Chapter 6. Chapters 7 and 8 on metrology deal with the characterization of lithography by measurements of various types. Engineers, scientists, and technical managers in the semiconductor industry, and engineering and applied physics faculty and graduate students will find the text very useful.

  • VLSI Electronics

    Microstructure Science
    • 1st Edition
    • Volume 3
    • Norman G. Einspruch
    • English
    VLSI Electronics: Microstructure Science, Volume 3 evaluates trends for the future of very large scale integration (VLSI) electronics and the scientific base that supports its development. This book discusses the impact of VLSI on computer architectures; VLSI design and design aid requirements; and design, fabrication, and performance of CCD imagers. The approaches, potential, and progress of ultra-high-speed GaAs VLSI; computer modeling of MOSFETs; and numerical physics of micron-length and submicron-length semiconductor devices are also elaborated. This text likewise covers the optical linewidth measurements on photomasks and wafers and effects of materials technology and fabrication tolerances on guided-wave optical communication and signal processing. This volume is recommended for scientists and engineers who wish to become familiar with VLSI electronics, device designers concerned with the fundamental character of and limitations to device performance, systems architects who will be charged with tying VLSI circuits together, and engineers conducting work on the utilization of VLSI circuits in specific areas of application.

  • VLSI Design

    • 1st Edition
    • Volume 14
    • Norman G. Einspruch
    • English
    VLSI Electronics Microstructure Science, Volume 14: VLSI Design presents a comprehensive exposition and assessment of the developments and trends in VLSI (Very Large Scale Integration) electronics. This volume covers topics that range from microscopic aspects of materials behavior and device performance to the comprehension of VLSI in systems applications. Each article is prepared by a recognized authority. The subjects discussed in this book include VLSI processor design methodology; the RISC (Reduced Instruction Set Computer); the VLSI testing program; silicon compilers for VLSI; and specialized silicon compiler and programmable chip for language recognition. Scientists, engineers, researchers, device designers, and systems architects will find the book very useful.

  • Surface and Interface Effects in VLSI

    • 1st Edition
    • Volume 10
    • Norman G. Einspruch + 1 more
    • English
    VLSI Electronics Microstructure Science, Volume 10: Surface and Interface Effects in VLSI provides the advances made in the science of semiconductor surface and interface as they relate to electronics. This volume aims to provide a better understanding and control of surface and interface related properties. The book begins with an introductory chapter on the intimate link between interfaces and devices. The book is then divided into two parts. The first part covers the chemical and geometric structures of prototypical VLSI interfaces. Subjects detailed include, the technologically most important interface, Si-SiO2 and the interplay between interface chemistry and the causes for metal-semiconductor contact behavior, primarily in the III-Vs. The following section deals primarily with the electronic properties of interfaces. Under this section, compound semiconductors, semiconductor-semico... interface, constraints that the microscopic interface places on architectures involving metal-semiconductor (MESFET), "Ohmic" contacts, and the behavior of very small, high-speed devices are discussed extensively. The final chapter shows that the Si - SiO2 interface can play a major role in determining carrier transport when MOSFETS are scaled down to ULSI dimensions. Engineers, designers, and scientists will find the book very useful.

  • Plasma Processing for VLSI

    • 1st Edition
    • Volume 8
    • Norman G. Einspruch + 1 more
    • English
    VLSI Electronics: Microstructure Science, Volume 8: Plasma Processing for VLSI (Very Large Scale Integration) discusses the utilization of plasmas for general semiconductor processing. It also includes expositions on advanced deposition of materials for metallization, lithographic methods that use plasmas as exposure sources and for multiple resist patterning, and device structures made possible by anisotropic etching. This volume is divided into four sections. It begins with the history of plasma processing, a discussion of some of the early developments and trends for VLSI. The second section, Deposition, discusses deposition techniques for VLSI such as sputtering metals for metallization and contacts, plasma-enhanced chemical vapor deposition of metals and suicides, and plasma enhanced chemical vapor deposition of dielectrics. The part on Lithography presents the high-resolution trilayer resist system, pulsed x-ray sources for submicrometer x-ray lithography, and high-intensity deep-UV sources. The last part, Etching, provides methods in etching, like ion-beam etching using reactive gases, low-pressure reactive ion etching, and the uses of inert-gas ion milling. The theory and mechanisms of plasma etching are described and a number of new device structures made possible by anisotropic etching are enumerated as well. Scientists, engineers, researchers, device designers, and systems architects will find the book useful.

  • VLSI Metallization

    • 1st Edition
    • Volume 15
    • Norman G. Einspruch + 2 more
    • English
    VLSI Electronics Microstructure Science, Volume 15: VLSI Metallization discusses the various issues and problems related to VLSI metallization. It details the available solutions and presents emerging trends. This volume is comprised of 10 chapters. The two introductory chapters, Chapter 1 and 2 serve as general references for the electrical and metallurgical properties of thin conducting films. Subsequent chapters review the various aspects of VLSI metallization. The order of presentation has been chosen to follow the common processing sequence. In Chapter 3, some relevant metal deposition techniques are discussed. Chapter 4 presents the methods of VLSI lithography and etching. Conducting films are first deposited at the gate definition step; therefore, the issues related to gate metallization are discussed next in Chapter 5.In Chapter 6, contact metallization is elaborated, and Chapter 7 is devoted to multilevel metallization schemes. Long-time reliability is the subject of Chapter 8, which discusses the issues of contact and interconnect electromigration. GaAs metallization is tackled in Chapter 9. The volume concludes with a general discussion of the functions of interconnect systems in VLSI. Materials scientists, processing and design engineers, and device physicists will find the book very useful.

  • VLSI Electronics

    Microstructure Science
    • 1st Edition
    • Volume 5
    • Norman G. Einspruch
    • English
    VLSI Electronics: Microstructure Science, Volume 5 considers trends for the future of very large scale integration (VLSI) electronics and the scientific base that supports its development. This book discusses the automation for VLSI manufacture, silicon material properties for VLSI circuitry, and high-performance computer packaging and thin-film multichip module. The nanometer-scale fabrication techniques, high-density CCD memories, and solid-state infrared imaging are also elaborated. This text likewise covers the impact of microelectronics upon radar systems and quantum-mechanical limitations on device performance. This volume is a good source for scientists and engineers who wish to become familiar with VLSI electronics, device designers concerned with the fundamental character of and limitations to device performance, systems architects who will be charged with tying VLSI circuits together, and engineers conducting work on the utilization of VLSI circuits in specific areas of application.

  • VLSI Electronics

    Microstructure Science
    • 1st Edition
    • Volume 4
    • Norman G. Einspruch
    • English
    VLSI Electronics: Microstructure Science, Volume 4 reviews trends for the future of very large scale integration (VLSI) electronics and the scientific base that supports its development. This book discusses the silicon-on-insulator for VLSI and VHSIC, X-ray lithography, and transient response of electron transport in GaAs using the Monte Carlo method. The technology and manufacturing of high-density magnetic-bubble memories, metallic superlattices, challenge of education for VLSI, and impact of VLSI on medical signal processing are also elaborated. This text likewise covers the impact of VLSI technology on the design of intelligent measurement instruments and systems. This volume is valuable to scientists and engineers who wish to become familiar with VLSI electronics, device designers concerned with the fundamental character of and limitations to device performance, systems architects who will be charged with tying VLSI circuits together, and engineers conducting work on the utilization of VLSI circuits in specific areas of application.

  • VLSI and Computer Architecture

    • 1st Edition
    • Volume 20
    • Ravi Shankar + 1 more
    • Norman G. Einspruch
    • English
    VLSI Electronics Microstructure Science, Volume 20: VLSI and Computer Architecture reviews the approaches in design principles and techniques and the architecture for computer systems implemented in VLSI. This volume is divided into two parts. The first section is concerned with system design. Chapters under this section focus on the discussion of such topics as the evolution of VLSI; system performance and processor design considerations; and VLSI system design and processing tools. Part II of the book focuses on the architectural possibilities that have become cost effective with the development of VLSI circuits. Topics on architectural requirements and various architectures such as the Reduced Instruction Set, Extended Von Neumann, Language-Oriented, and Microprogrammable architectures are elaborated in detail. Also included are chapters that discuss the evaluation of architecture, multiprocessing configurations, and the future of VLSI. Computer designers, those evaluating computer systems, researchers, and students of computer architecture will find the book very useful.

  • VLSI Electronics Microstructure Science

    • 1st Edition
    • Volume 7
    • Norman G. Einspruch
    • English
    VLSI Electronics: Microstructure Science, Volume 7 presents a comprehensive exposition and assessment of the developments and trends in VLSI (Very Large Scale Integration) electronics. This treatise covers subjects that range from microscopic aspects of materials behavior and device performance to the comprehension of VLSI in systems applications. Each chapter is prepared by a recognized authority. The topics contained in this volume include a basic introduction to the application of superconductivity in high-speed digital systems; the expected impact of VLSI technology on the implementation of AI (artificial intelligence); the limits to improvement of silicon integrated circuits; and the various spontaneous noise sources in VLSI circuits and their effect on circuit operation. Scientists, engineers, researchers, device designers, and systems architects will find the book very useful.

  • Computational Logic

    • 1st Edition
    • Volume 9
    • Dov M. Gabbay + 2 more
    • English
    Handbook of the History of Logic brings to the development of logic the best in modern techniques of historical and interpretative scholarship. Computational logic was born in the twentieth century and evolved in close symbiosis with the advent of the first electronic computers and the growing importance of computer science, informatics and artificial intelligence. With more than ten thousand people working in research and development of logic and logic-related methods, with several dozen international conferences and several times as many workshops addressing the growing richness and diversity of the field, and with the foundational role and importance these methods now assume in mathematics, computer science, artificial intelligence, cognitive science, linguistics, law and many engineering fields where logic-related techniques are used inter alia to state and settle correctness issues, the field has diversified in ways that even the pure logicians working in the early decades of the twentieth century could have hardly anticipated. Logical calculi, which capture an important aspect of human thought, are now amenable to investigation with mathematical rigour and computational support and fertilized the early dreams of mechanised reasoning: “Calculemus”. The Dartmouth Conference in 1956 – generally considered as the birthplace of artificial intelligence – raised explicitly the hopes for the new possibilities that the advent of electronic computing machinery offered: logical statements could now be executed on a machine with all the far-reaching consequences that ultimately led to logic programming, deduction systems for mathematics and engineering, logical design and verification of computer software and hardware, deductive databases and software synthesis as well as logical techniques for analysis in the field of mechanical engineering. This volume covers some of the main subareas of computational logic and its applications.

  • Computational Statistics with R

    • 1st Edition
    • Volume 32
    • English
    R is open source statistical computing software. Since the R core group was formed in 1997, R has been extended by a very large number of packages with extensive documentation along with examples freely available on the internet. It offers a large number of statistical and numerical methods and graphical tools and visualization of extraordinarily high quality. R was recently ranked in 14th place by the Transparent Language Popularity Index and 6th as a scripting language, after PHP, Python, and Perl. The book is designed so that it can be used right away by novices while appealing to experienced users as well. Each article begins with a data example that can be downloaded directly from the R website. Data analysis questions are articulated following the presentation of the data. The necessary R commands are spelled out and executed and the output is presented and discussed. Other examples of data sets with a different flavor and different set of commands but following the theme of the article are presented as well. Each chapter predents a hands-on-experience. R has superb graphical outlays and the book brings out the essentials in this arena. The end user can benefit immensely by applying the graphics to enhance research findings. The core statistical methodologies such as regression, survival analysis, and discrete data are all covered.

  • Doing Bayesian Data Analysis

    A Tutorial with R, JAGS, and Stan
    • 2nd Edition
    • John Kruschke
    • English
    Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, Second Edition provides an accessible approach for conducting Bayesian data analysis, as material is explained clearly with concrete examples. Included are step-by-step instructions on how to carry out Bayesian data analyses in the popular and free software R and WinBugs, as well as new programs in JAGS and Stan. The new programs are designed to be much easier to use than the scripts in the first edition. In particular, there are now compact high-level scripts that make it easy to run the programs on your own data sets. The book is divided into three parts and begins with the basics: models, probability, Bayes’ rule, and the R programming language. The discussion then moves to the fundamentals applied to inferring a binomial probability, before concluding with chapters on the generalized linear model. Topics include metric-predicted variable on one or two groups; metric-predicted variable with one metric predictor; metric-predicted variable with multiple metric predictors; metric-predicted variable with one nominal predictor; and metric-predicted variable with multiple nominal predictors. The exercises found in the text have explicit purposes and guidelines for accomplishment. This book is intended for first-year graduate students or advanced undergraduates in statistics, data analysis, psychology, cognitive science, social sciences, clinical sciences, and consumer sciences in business.

  • An Introduction to Probability and Statistical Inference

    • 2nd Edition
    • George G. Roussas
    • English
    An Introduction to Probability and Statistical Inference, Second Edition, guides you through probability models and statistical methods and helps you to think critically about various concepts. Written by award-winning author George Roussas, this book introduces readers with no prior knowledge in probability or statistics to a thinking process to help them obtain the best solution to a posed question or situation. It provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations. This text contains an enhanced number of exercises and graphical illustrations where appropriate to motivate the reader and demonstrate the applicability of probability and statistical inference in a great variety of human activities. Reorganized material is included in the statistical portion of the book to ensure continuity and enhance understanding. Each section includes relevant proofs where appropriate, followed by exercises with useful clues to their solutions. Furthermore, there are brief answers to even-numbered exercises at the back of the book and detailed solutions to all exercises are available to instructors in an Answers Manual. This text will appeal to advanced undergraduate and graduate students, as well as researchers and practitioners in engineering, business, social sciences or agriculture.

  • Spectral Radius of Graphs

    • 1st Edition
    • Dragan Stevanovic
    • English
    Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the book delves deeper into the properties of the principal eigenvector; a critical subject as many of the results on the spectral radius of graphs rely on the properties of the principal eigenvector for their proofs. A following chapter surveys spectral radius of special graphs, covering multipartite graphs, non-regular graphs, planar graphs, threshold graphs, and others. Finally, the work explores results on the structure of graphs having extreme spectral radius in classes of graphs defined by fixing the value of a particular, integer-valued graph invariant, such as: the diameter, the radius, the domination number, the matching number, the clique number, the independence number, the chromatic number or the sequence of vertex degrees. Throughout, the text includes the valuable addition of proofs to accompany the majority of presented results. This enables the reader to learn tricks of the trade and easily see if some of the techniques apply to a current research problem, without having to spend time on searching for the original articles. The book also contains a handful of open problems on the topic that might provide initiative for the reader's research.

  • Table of Integrals, Series, and Products

    • 8th Edition
    • Daniel Zwillinger
    • English
    The eighth edition of the classic Gradshteyn and Ryzhik is an updated completely revised edition of what is acknowledged universally by mathematical and applied science users as the key reference work concerning the integrals and special functions. The book is valued by users of previous editions of the work both for its comprehensive coverage of integrals and special functions, and also for its accuracy and valuable updates. Since the first edition, published in 1965, the mathematical content of this book has significantly increased due to the addition of new material, though the size of the book has remained almost unchanged. The new 8th edition contains entirely new results and amendments to the auxiliary conditions that accompany integrals and wherever possible most entries contain valuable references to their source.

  • Handbook of Game Theory

    • 1st Edition
    • Volume 4
    • Petyon Young + 1 more
    • English
    The ability to understand and predict behavior in strategic situations, in which an individual’s success in making choices depends on the choices of others, has been the domain of game theory since the 1950s. Developing the theories at the heart of game theory has resulted in 8 Nobel Prizes and insights that researchers in many fields continue to develop. In Volume 4, top scholars synthesize and analyze mainstream scholarship on games and economic behavior, providing an updated account of developments in game theory since the 2002 publication of Volume 3, which only covers work through the mid 1990s.

  • Numerical Linear Algebra with Applications

    Using MATLAB and Octave
    • 1st Edition
    • William Ford
    • English
    Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica.

  • Advances in Computers

    • 1st Edition
    • Volume 95
    • English
    Since its first volume in 1960, Advances in Computers has presented detailed coverage of innovations in computer hardware, software, theory, design, and applications. It has also provided contributors with a medium in which they can explore their subjects in greater depth and breadth than journal articles usually allow. As a result, many articles have become standard references that continue to be of significant, lasting value in this rapidly expanding field.

  • Mathematical Statistics with Applications in R

    • 2nd Edition
    • Kandethody M. Ramachandran + 1 more
    • English
    Mathematical Statistics with Applications in R, Second Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications. The book covers many modern statistical computational and simulation concepts that are not covered in other texts, such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. By combining the discussion on the theory of statistics with a wealth of real-world applications, the book helps students to approach statistical problem solving in a logical manner.This book provides a step-by-step procedure to solve real problems, making the topic more accessible. It includes goodness of fit methods to identify the probability distribution that characterizes the probabilistic behavior or a given set of data. Exercises as well as practical, real-world chapter projects are included, and each chapter has an optional section on using Minitab, SPSS and SAS commands. The text also boasts a wide array of coverage of ANOVA, nonparametric, MCMC, Bayesian and empirical methods; solutions to selected problems; data sets; and an image bank for students.Advanced undergraduate and graduate students taking a one or two semester mathematical statistics course will find this book extremely useful in their studies.

  • Introduction to Probability and Statistics for Engineers and Scientists

    • 5th Edition
    • Sheldon M. Ross
    • English
    Introduction to Probability and Statistics for Engineers and Scientists, Fifth Edition is a proven text reference that provides a superior introduction to applied probability and statistics for engineering or science majors. The book lays emphasis in the manner in which probability yields insight into statistical problems, ultimately resulting in an intuitive understanding of the statistical procedures most often used by practicing engineers and scientists. Real data from actual studies across life science, engineering, computing and business are incorporated in a wide variety of exercises and examples throughout the text. These examples and exercises are combined with updated problem sets and applications to connect probability theory to everyday statistical problems and situations. The book also contains end of chapter review material that highlights key ideas as well as the risks associated with practical application of the material. Furthermore, there are new additions to proofs in the estimation section as well as new coverage of Pareto and lognormal distributions, prediction intervals, use of dummy variables in multiple regression models, and testing equality of multiple population distributions. This text is intended for upper level undergraduate and graduate students taking a course in probability and statistics for science or engineering, and for scientists, engineers, and other professionals seeking a reference of foundational content and application to these fields.

  • The Fundamentals of Mathematical Analysis

    • 1st Edition
    • Volume 72
    • G. M. Fikhtengol'ts
    • I. N. Sneddon
    • English
    The Fundamentals of Mathematical Analysis, Volume 1 is a textbook that provides a systematic and rigorous treatment of the fundamentals of mathematical analysis. Emphasis is placed on the concept of limit which plays a principal role in mathematical analysis. Examples of the application of mathematical analysis to geometry, mechanics, physics, and engineering are given. This volume is comprised of 14 chapters and begins with a discussion on real numbers, their properties and applications, and arithmetical operations over real numbers. The reader is then introduced to the concept of function, important classes of functions, and functions of one variable; the theory of limits and the limit of a function, monotonic functions, and the principle of convergence; and continuous functions of one variable. A systematic account of the differential and integral calculus is then presented, paying particular attention to differentiation of functions of one variable; investigation of the behavior of functions by means of derivatives; functions of several variables; and differentiation of functions of several variables. The remaining chapters focus on the concept of a primitive function (and of an indefinite integral); definite integral; geometric applications of integral and differential calculus. This book is intended for first- and second-year mathematics students.

  • The Fundamentals of Mathematical Analysis

    • 1st Edition
    • G. M. Fikhtengol'ts
    • I. N. Sneddon + 2 more
    • English
    The Fundamentals of Mathematical Analysis, Volume 2 is a continuation of the discussion of the fundamentals of mathematical analysis, specifically on the subject of curvilinear and surface integrals, with emphasis on the difference between the curvilinear and surface ""integrals of first kind"" and ""integrals of second kind."" The discussions in the book start with an introduction to the elementary concepts of series of numbers, infinite sequences and their limits, and the continuity of the sum of a series. The definition of improper integrals of unbounded functions and that of uniform convergence of integrals are explained. Curvilinear integrals of the first and second kinds are analyzed mathematically. The book then notes the application of surface integrals, through a parametric representation of a surface, and the calculation of the mass of a solid. The text also highlights that Green's formula, which connects a double integral over a plane domain with curvilinear integral along the contour of the domain, has an analogue in Ostrogradski's formula. The periodic values and harmonic analysis such as that found in the operation of a steam engine are analyzed. The volume ends with a note of further developments in mathematical analysis, which is a chronological presentation of important milestones in the history of analysis. The book is an ideal reference for mathematicians, students, and professors of calculus and advanced mathematics.

  • Functions of a Complex Variable and Some of Their Applications

    • 1st Edition
    • B. A. Fuchs + 1 more
    • I. N. Sneddon + 1 more
    • English
    Functions of a Complex Variable and Some of Their Applications, Volume 1, discusses the fundamental ideas of the theory of functions of a complex variable. The book is the result of a complete rewriting and revision of a translation of the second (1957) Russian edition. Numerous changes and additions have been made, both in the text and in the solutions of the Exercises. The book begins with a review of arithmetical operations with complex numbers. Separate chapters discuss the fundamentals of complex analysis; the concept of conformal transformations; the most important of the elementary functions; and the complex potential for a plane vector field and the application of the simplest methods of function theory to the analysis of such a field. Subsequent chapters cover the fundamental apparatus of the theory of regular functions, i.e. basic integral theorems and expansions in series; the general concept of an analytic function; applications of the theory of residues; and polygonal domain mapping. This book is intended for undergraduate and postgraduate students of higher technical institutes and for engineers wishing to increase their knowledge of theory.

  • Operational Calculus

    • 2nd Edition
    • Volume 110
    • Thomas K. Boehme
    • I.N. Sneddon
    • English
    Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included. Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-homogeneous equations and applications of operational calculus to partial differential equations. The section section deals with the integral of an operational function and its applications, along with integral transformations. A definition of operators in terms of abstract algebra is then presented. Operators as generalized functions, power series of operators, and Laplace transform are also discussed. Formulas of the operational calculus and tables of functions round out the book. This monograph will be useful to engineers, who regard the operational calculus merely as a tool in their work, and readers who are interested in proofs of theorems and mathematical problems.

  • Advances in Computers

    • 1st Edition
    • Volume 94
    • English
    Since its first volume in 1960, Advances in Computers has presented detailed coverage of innovations in computer hardware, software, theory, design, and applications. It has also provided contributors with a medium in which they can explore their subjects in greater depth and breadth than journal articles usually allow. As a result, many articles have become standard references that continue to be of significant, lasting value in this rapidly expanding field.

  • Convergence Problems of Orthogonal Series

    • 1st Edition
    • Volume 20
    • G. Alexits
    • English
    Convergence Problems of Orthogonal Series deals with the theory of convergence and summation of the general orthogonal series in relation to the general theory and classical expansions. The book reviews orthogonality, orthogonalization, series of orthogonal functions, complete orthogonal systems, and the Riesz-Fisher theorem. The text examines Jacobi polynomials, Haar's orthogonal system, and relations to the theory of probability using Rademacher's and Walsh's orthogonal systems. The book also investigates the convergence behavior of orthogonal series by methods belonging to the general theory of series. The text explains some Tauberian theorems and the classical Abel transform of the partial sums of a series which the investigator can use in the theory of orthogonal series. The book examines the importance of the Lebesgue functions for convergence problems, the generalization of the Walsh series, the order of magnitude of the Lebesgue functions, and the Lebesgue functions of the Cesaro summation. The text also deals with classical convergence problems in which general orthogonal series have limited significance as orthogonal expansions react upon the structural properties of the expanded function. This reaction happens under special assumptions concerning the orthogonal system in whose functions the expansion proceeds. The book can prove beneficial to mathematicians, students, or professor of calculus and advanced mathematics.

  • Variational Methods in Economics

    • 1st Edition
    • Volume 1
    • G. Hadley + 1 more
    • C. J. Bliss
    • English
    Advanced Textbooks in Economics, Volume 1: Variational Methods in Economics focuses on the application of variational methods in economics, including autonomous system, dynamic programming, and phase spaces and diagrams. The manuscript first elaborates on growth models in economics and calculus of variations. Discussions focus on connection with dynamic programming, variable end points-free boundaries, transversality at infinity, sensitivity analysis-end point changes, Weierstrass and Legendre necessary conditions, and phase diagrams and phase spaces. The text then ponders on the constraints of classical theory, including unbounded intervals of integration, free boundary conditions, comparison functions, normality, and the problem of Bolza. The publication explains two-sector models of optimal economic growth, optimal control theory, and connections with the classical theory. Topics include capital good immobile between industries, constrained state variables, linear control problems, conversion of a control problem into a problem of Lagrange, and the conversion of a nonautonomous system into an autonomous system. The book is a valuable source of information for economists and researchers interested in the variational methods in economics.

  • Foundations of Econometrics

    • 1st Edition
    • Volume 7
    • Albert Madansky
    • C. J. Bliss + 1 more
    • English
    Advanced Textbooks in Economics, Volume 7: Foundations of Econometrics focuses on the principles, processes, methodologies, and approaches involved in the study of econometrics. The publication examines matrix theory and multivariate statistical analysis. Discussions focus on the maximum likelihood estimation of multivariate normal distribution parameters, point estimation theory, multivariate normal distribution, multivariate probability distributions, Euclidean spaces and linear transformations, orthogonal transformations and symmetric matrices, and determinants. The manuscript then ponders on linear expected value models and simultaneous equation estimation. Topics include random exogenous variables, maximum likelihood estimation of a single equation, identification of a single equation, linear stochastic difference equations, and errors-in-variables models. The book takes a look at a prolegomenon to econometric model building, tests of hypotheses in econometric models, multivariate statistical analysis, and simultaneous equation estimation. Concerns include maximum likelihood estimation of a single equation, tests of linear hypotheses, testing for independence, and causality in economic models. The publication is a valuable source of data for economists and researchers interested in the foundations of econometrics.

  • Axiomatics of Classical Statistical Mechanics

    • 1st Edition
    • Volume 11
    • Rudolf Kurth
    • I. N. Sneddon + 2 more
    • English
    Axiomatics of Classical Statistical Mechanics provides an understanding of classical statistical mechanics as a deductive system. This book presents the mechanical systems of a finite number of degrees of freedom. Organized into seven chapters, this book begins with an overview of the average behavior of mechanical systems. This text then examines the concept of a mechanical system and explains the equations of motion of the system. Other chapters consider an ensemble of mechanical systems wherein a Hamiltonian function and a truncated canonical probability density corresponds to each system. This book discusses as well the necessary and sufficient conditions that are given for the existence of statistically stationary states and for the approach of mechanical systems towards these states. The final chapter deals with the fundamental laws of thermodynamics. This book is a valuable resource for mathematicians.

  • Integral Equations

    And Their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology
    • 1st Edition
    • Volume 4
    • S. G. Mikhlin
    • I. N. Sneddon + 2 more
    • English
    Integral Equations: And their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology, Second Revised Edition contains an account of the general theory of Fredholm and Hilbert-Schmidt. This edition discusses methods of approximate solution of Fredholm's equation and, in particular, their application to the solution of basic problems in mathematical physics, including certain problems in hydrodynamics and the theory of elasticity. Other topics include the equations of Volterra type, determination of the first eigenvalue by Ritz's method, and systems of singular integral equations. The generalized method of Schwarz, convergence of successive approximations, stability of a rod in compression, and mixed problem of the theory of elasticity are also elaborated. This publication is recommended for mathematicians, students, and researchers concerned with singular integral equations.

  • Investment

    The Study of an Economic Aggregate
    • 1st Edition
    • Volume 13
    • Philip J. Lund
    • C. J. Bliss + 1 more
    • English
    Advanced Textbooks in Economics: Investment: The Study of an Economic Aggregate focuses on the principles, methodologies, and approaches involved in the determination of investments. The book first offers information on the theories of aggregate investment and statistical and questionnaire studies. Discussions focus on statistical studies, tax incentives and disincentives to investment, capital stock adjustment models, acceleration principle, replacement investment, level of aggregation, sources of funds, neoclassical theory of capital accumulation, and tax incentives and disincentives to investment. The text then examines the estimation of lag distributions, including geometrically declining lag distributions, Pascal and rational distributions, variable lag distributions, and the first-in first-out method. The publication ponders on econometric studies, as well as United Kingdom and United States studies, two-stage studies of investment, and guidelines for future research. The text is a dependable source of information for economists and researchers interested in economic aggregates.

  • Theory of Approximation of Functions of a Real Variable

    • 1st Edition
    • Volume 34
    • A. F. Timan
    • I. N. Sneddon + 2 more
    • English
    Theory of Approximation of Functions of a Real Variable discusses a number of fundamental parts of the modern theory of approximation of functions of a real variable. The material is grouped around the problem of the connection between the best approximation of functions to their structural properties. This text is composed of eight chapters that highlight the relationship between the various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Each chapter concludes with a section containing various problems and theorems, which supplement the main text. The first chapters tackle the Weierstrass's theorem, the best approximation by polynomials on a finite segment, and some compact classes of functions and their structural properties. The subsequent chapters describe some properties of algebraic polynomials and transcendental integral functions of exponential type, as well as the direct theorems of the constructive theory of functions. These topics are followed by discussions of differential and constructive characteristics of converse theorems. The final chapters explore other theorems connecting the best approximations functions with their structural properties. These chapters also deal with the linear processes of approximation of functions by polynomials. The book is intended for post-graduate students and for mathematical students taking advanced courses, as well as to workers in the field of the theory of functions.

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