The interaction between computers and mathematics is becoming more and more important at all levels as computers become more sophisticated. This book shows how simple programs can be used to do significant mathematics. The purpose of this book is to give those with some mathematical background a wealth of material with which to appreciate both the power of the microcomputer and its relevance to the study of mathematics. The authors cover topics such as number theory, approximate solutions, differential equations and iterative processes, with each chapter self contained. Many exercises and projects are included giving ready-made material for demonstrating mathematical ideas. Only fundamental knowledge of mathematics is assumed and programming is restricted to "basic BASIC" which will be understood by any microcomputer. The book may be used as a textbook for algorithmic mathematics at several levels, since all the topics covered appear in any undergraduate mathematics course.

Newcomers to R are often intimidated by the command-line interface, the vast number of functions and packages, or the processes of importing data and performing a simple statistical analysis. The R Primer provides a collection of concise examples and solutions to R problems frequently encountered by new users of this statistical software. This new edition adds coverage of R Studio and reproducible research.

This companion to The New Statistical Analysis of Data by Anderson and Finn provides a hands-on guide to data analysis using SPSS. Included with this guide are instructions for obtaining the data sets to be analysed via the World Wide Web. First, the authors provide a brief review of using SPSS, and then, corresponding to the organisation of The New Statistical Analysis of Data, readers participate in analysing many of the data sets discussed in the book. In so doing, students both learn how to conduct reasonably sophisticated statistical analyses using SPSS whilst at the same time gaining an insight into the nature and purpose of statistical investigation.

Maple V Mathematics Programming Guide is the fully updated language and programming reference for Maple V Release 5. It presents a detailed description of Maple V Release 5 - the latest release of the powerful, interactive computer algebra system used worldwide as a tool for problem-solving in mathematics, the sciences, engineering, and education. This manual describes the use of both numeric and symbolic expressions, the data types available, and the programming language statements in Maple. It shows how the system can be extended or customized through user defined routines and gives complete descriptions of the system's user interface and 2D and 3D graphics capabilities.

This upper-division laboratory supplement for courses in abstract algebra consists of several Mathematica packages programmed as a foundation for group and ring theory. Additionally, the "user's guide" illustrates the functionality of the underlying code, while the lab portion of the book reflects the contents of the Mathematica-based electronic notebooks. Students interact with both the printed and electronic versions of the material in the laboratory, and can look up details and reference information in the user's guide. Exercises occur in the stream of the text of the lab, which provides a context within which to answer, and the questions are designed to be either written into the electronic notebook, or on paper. The notebooks are available in both 2.2 and 3.0 versions of Mathematica, and run across all platforms for which Mathematica exits. A very timely and unique addition to the undergraduate abstract algebra curriculum, filling a tremendous void in the literature.

S+SPATIALSTATS is the first comprehensive, object-oriented package for the analysis of spatial data. Providing a whole new set of analysis tools, S+SPATIALSTATS was created specifically for the exploration and modeling of spatially correlated data. It can be used to analyze data arising in areas such as environmental, mining, and petroleum engineering, natural resources, geography, epidemiology, demography, and others where data is sampled spatially. This users manual provides the documentation for the S+SPATIALSTATS module.

COMPSTAT symposia have been held regularly since 1974 when they started in Vienna. This tradition has made COMPSTAT a major forum for the interplay of statistics and computer sciences with contributions from many well known scientists all over the world. The scientific programme of COMPSTAT '96 covers all aspects of this interplay, from user-experiences and evaluation of software through the development and implementation of new statistical ideas. All papers presented belong to one of the three following categories: - Statistical methods (preferable new ones) that require a substantial use of computing; - Computer environments, tools and software useful in statistics; - Applications of computational statistics in areas of substantial interest (environment, health, industry, biometrics, etc.).

A greatly expanded and heavily revised second edition, this popular guide provides instructions and clear examples for running analyses of variance (ANOVA) and several other related statistical tests of significance with SPSS. No other guide offers the program statements required for the more advanced tests in analysis of variance. All of the programs in the book can be run using any version of SPSS, including versions 11 and 11.5. A table at the end of the preface indicates where each type of analysis (e.g., simple comparisons) can be found for each type of design (e.g., mixed two-factor design).
Providing comprehensive coverage of the basic and advanced topics in ANOVA, this is the only book available that provides extensive coverage of SPSS syntax, including the commands and subcommands that tell SPSS what to do, as well as the pull-down menu point-and-click method (PAC). Detailed explanation of the syntax, including what is necessary, desired, and optional helps ensure that users can validate the analysis being performed. The book features the output of each design along with a complete explanation of the related printout.
The new edition was reorganized to provide all analysis related to one design type in the same chapter. It now features expanded coverage of analysis of covariance (ANCOVA) and mixed designs, new chapters on designs with random factors, multivariate designs, syntax used in PAC, and all new examples of output with complete explanations. The new edition is accompanied by a CD-ROM with all of the book's data sets, as well as exercises for each chapter.
This book is ideal for readers familiar with the basic concepts of the ANOVA technique including both practicing researchers and data analysts, as well as advanced students learning analysis of variance.

The book, which contains over two hundred illustrations, is designed for use in school computer labs or with home computers, running the computer algebra system Maple, or its student version. It supports the interactive Maple worksheets, which the authors have developed and which are available free of charge via anonymous ftp (ftp.utirc.utoronto.ca (/pub/ednet/maths/maple)). The book addresses readers who are learning calculus at a pre-university level.

Mathematica combines symbolic and numerical calculations, plots, graphics programming, list calculations and structured documentation into an interactive environment. This book covers the program and shows with practical examples how even more complex problems can be solved with just a few commands.

From the reviews: "A valuable introductory textbook on Mathematica and is very useful to scientists and engineers who use Mathematica in their work." -- ZENTRALBLATT MATH

This book assembles papers which were presented at the biennial sympo sium in Computational Statistics held und er the a uspices of the International Association for Statistical Computing (IASC), a section of ISI, the Interna tional Statistical Institute. This symposium named COMPSTAT '94 was organized by the Statistical Institutes of the University of Vienna and the University of Technology of Vienna, Austria. The series of COMPSTAT Symposia started 1974 in Vienna. Mean while they took place every other year in Berlin (Germany, 1976), Leiden (The Netherlands, 1978), Edinburgh (Great Britain, 1980), Toulouse (France, 1982), Prague (Czechoslovakia, 1984), Rom (Italy, 1986), Copenhagen (Den mark, 1988), Dubrovnik (Yugoslavia, 1990) and Neuchatel (Switzerland, 1992). This year we are celebrating the 20th anniversary in Vienna, Austria. It has obviously been observed a movement from "traditional" computa tional statistics with emphasis on methods which produce results quickly and reliably, to computationally intensive methods like resampling procedures, Bayesian methods, dynamic graphics, to very recent areas like neural net works, accentuation on spatial statistics, huge data sets, analysis strategies, etc. For the organization of the symposium, new guidelines worked out by the IASC in written form were in effect this time. The goal was to refresh somehow the spirit of the start of COMPSTAT '74, keep the tradition of the series and ensure a certain continuity in the sequence of biannual meetings."

The analysis of time series data is an important aspect of data analysis across a wide range of disciplines, including statistics, mathematics, business, engineering, and the natural and social sciences. This package provides both an introduction to time series analysis and an easy-to-use version of a well-known time series computing package called Interactive Time Series Modelling. The programs in the package are intended as a supplement to the text Time Series: Theory and Methods, 2nd edition, also by Peter J. Brockwell and Richard A. Davis. Many researchers and professionals will appreciate this straightforward approach enabling them to run desk-top analyses of their time series data. Amongst the many facilities available are tools for: ARIMA modelling, smoothing, spectral estimation, multivariate autoregressive modelling, transfer-function modelling, forecasting, and long-memory modelling. This version is designed to run under Microsoft Windows 3.1 or later. It comes with two diskettes: one suitable for less powerful machines (IBM PC 286 or later with 540K available RAM and 1.1 MB of hard disk space) and one for more powerful machines (IBM PC 386 or later with 8MB of RAM and 2.6 MB of hard disk space available).

Maple is a computer algebraic system with a fast-growing number of users in universities, schools and other institutions. Werner Burkhardt provides a detailed step-by-step introduction for all first-time users, enabling you to become familiar with the way Maple works, as quickly and easily as possible. Using as examples problems from many different aspects of mathematics, problem solving using Maple is fully described in this easy-to-follow tutorial text. Each chapter is self-contained, so you can easily select areas of your own special interest. There are some 'test yourself' problems at the end of each chapter to check your progress, with solutions provided at the end of the book.

This book is a collection of thirty invited papers, covering the important parts of a rapidly developing area like "computational statistics." All contributions supply information about a specialized topic in a tutorial and comprehensive style. Newest results and developments are discussed. Starting with the foundations of computational statistics, i.e. numerical reliability of software packages or construction principles for pseudorandom number generators, the volume includes design considerations on statistical programming languages and the basic issues of resampling techniques. Also covered are areas like design of experiments, graphical techniques, modelling and testing problems, a review of clustering algorithms, and concise discussions of regression trees or cognitive aspects of authoring systems.

The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).

This second edition is an intensively revised and updated version of the book MATLAB (R) and Design Recipes for Earth Sciences. It aims to introduce students to the typical course followed by a data analysis project in earth sciences. A project usually involves searching relevant literature, reviewing and ranking published books and journal articles, extracting relevant information from the literature in the form of text, data, or graphs, searching and processing the relevant original data using MATLAB, and compiling and presenting the results as posters, abstracts, and oral presentations using graphics design software. The text of this book includes numerous examples on the use of internet resources, on the visualization of data with MATLAB, and on preparing scientific presentations. As with the book MATLAB Recipes for Earth Sciences-4rd Edition (2015), which demonstrates the use of statistical and numerical methods on earth science data, this book uses state-of-the art software packages, including MATLAB and the Adobe Creative Suite, to process and present geoscientific information collected during the course of an earth science project. The book's supplementary electronic material (available online through the publisher's website) includes color versions of all figures, recipes with all the MATLAB commands featured in the book, the example data, exported MATLAB graphics, and screenshots of the most important steps involved in processing the graphics.

This handy reference book detailing the intricacies of R covers version 4.x features, including numerous and significant changes to syntax, strings, reference counting, grid units, and more. Starting with the basic structure of R, the book takes you on a journey through the terminology used in R and the syntax required to make R work. You will find looking up the correct form for an expression quick and easy. Some of the new material includes information on RStudio, S4 syntax, working with character strings, and an example using the Twitter API. With a copy of the R 4 Quick Syntax Reference in hand, you will find that you are able to use the multitude of functions available in R and are even able to write your own functions to explore and analyze data. What You Will Learn Discover the modes and classes of R objects and how to use them Use both packaged and user-created functions in R Import/export data and create new data objects in R Create descriptive functions and manipulate objects in R Take advantage of flow control and conditional statements Work with packages such as base, stats, and graphics Who This Book Is For Those with programming experience, either new to R, or those with at least some exposure to R but who are new to the latest version.

This volume presents the published Proceedings of the joint meeting of GUM92 and the 7th International Workshop on Statistical Modelling, held in Munich, Germany from 13 to 17 July 1992. The meeting aimed to bring together researchers interested in the development and applications of generalized linear modelling in GUM and those interested in statistical modelling in its widest sense. This joint meeting built upon the success of previous workshops and GUM conferences. Previous GUM conferences were held in London and Lancaster, and a joint GUM Conference/4th Modelling Workshop was held in Trento. (The Proceedings of previous GUM conferences/Statistical Modelling Workshops are available as numbers 14 , 32 and 57 of the Springer Verlag series of Lecture Notes in Statistics). Workshops have been organized in Innsbruck, Perugia, Vienna, Toulouse and Utrecht. (Proceedings of the Toulouse Workshop appear as numbers 3 and 4 of volume 13 of the journal Computational Statistics and Data Analysis). Much statistical modelling is carried out using GUM, as is apparent from many of the papers in these Proceedings. Thus the Programme Committee were also keen on encouraging papers which addressed problems which are not only of practical importance but which are also relevant to GUM or other software development. The Programme Committee requested both theoretical and applied papers. Thus there are papers in a wide range of practical areas, such as ecology, breast cancer remission and diabetes mortality, banking and insurance, quality control, social mobility, organizational behaviour.

Design and Analysis of Experiments with R presents a unified treatment of experimental designs and design concepts commonly used in practice. It connects the objectives of research to the type of experimental design required, describes the process of creating the design and collecting the data, shows how to perform the proper analysis of the data, and illustrates the interpretation of results. Drawing on his many years of working in the pharmaceutical, agricultural, industrial chemicals, and machinery industries, the author teaches students how to: Make an appropriate design choice based on the objectives of a research project Create a design and perform an experiment Interpret the results of computer data analysis The book emphasizes the connection among the experimental units, the way treatments are randomized to experimental units, and the proper error term for data analysis. R code is used to create and analyze all the example experiments. The code examples from the text are available for download on the author's website, enabling students to duplicate all the designs and data analysis. Intended for a one-semester or two-quarter course on experimental design, this text covers classical ideas in experimental design as well as the latest research topics. It gives students practical guidance on using R to analyze experimental data.

This book deals with selected problems of machine perception, using various 2D and 3D imaging sensors. It proposes several new original methods, and also provides a detailed state-of-the-art overview of existing techniques for automated, multi-level interpretation of the observed static or dynamic environment. To ensure a sound theoretical basis of the new models, the surveys and algorithmic developments are performed in well-established Bayesian frameworks. Low level scene understanding functions are formulated as various image segmentation problems, where the advantages of probabilistic inference techniques such as Markov Random Fields (MRF) or Mixed Markov Models are considered. For the object level scene analysis, the book mainly relies on the literature of Marked Point Process (MPP) approaches, which consider strong geometric and prior interaction constraints in object population modeling. In particular, key developments are introduced in the spatial hierarchical decomposition of the observed scenarios, and in the temporal extension of complex MRF and MPP models. Apart from utilizing conventional optical sensors, case studies are provided on passive radar (ISAR) and Lidar-based Bayesian environment perception tasks. It is shown, via several experiments, that the proposed contributions embedded into a strict mathematical toolkit can significantly improve the results in real world 2D/3D test images and videos, for applications in video surveillance, smart city monitoring, autonomous driving, remote sensing, and optical industrial inspection.

Presents the main ideas of computer-intensive statistical methods Gives the algorithms for all the methods Uses various plots and illustrations for explaining the main ideas Features the theoretical backgrounds of the main methods. Includes R codes for the methods and examples

Master the tools of MATLAB through hands-on examplesShows How to Solve Math Problems Using MATLAB The mathematical software MATLAB (R) integrates computation, visualization, and programming to produce a powerful tool for a number of different tasks in mathematics. Focusing on the MATLAB toolboxes especially dedicated to science, finance, and engineering, MATLAB (R) with Applications to Engineering, Physics and Finance explains how to perform complex mathematical tasks with relatively simple programs. This versatile book is accessible enough for novices and users with only a fundamental knowledge of MATLAB, yet covers many sophisticated concepts to make it helpful for experienced users as well. The author first introduces the basics of MATLAB, describing simple functions such as differentiation, integration, and plotting. He then addresses advanced topics, including programming, producing executables, publishing results directly from MATLAB programs, and creating graphical user interfaces. The text also presents examples of Simulink (R) that highlight the advantages of using this software package for system modeling and simulation. The applications-dedicated chapters at the end of the book explore the use of MATLAB in digital signal processing, chemical and food engineering, astronomy, optics, financial derivatives, and much more.

CONTRIBUTED BY DR. ANTHONY C. HEARN THE RAND CORPORATION, SANTA MONICA, CALIFORNIA REDUCE is a computer program for algebraic computation that IS III world-wide use by thousands of scientists, engineers, and mathematicians. Although it traces its beginnings to 1963, until recently it has only been available on main-frame computers because of its relatively large resource requirements. In 1980 I predicted (1) that by the mid-1980's it would be possible to obtain personal computers in the $10,000 $20,000 range capable of running REDUCE. I am therefore delighted to see that machines of the power of the IBM PC can now run this system, even though these computers are more modestly priced than my 1980 vision of the personal algebra machine. In addition to the need for the more widespread access that personal computers can now provide, there has been a longstanding need for a textbook to help the beginning user become better acquainted with the system. I am therefore very glad that Dr. Rayna has undertaken to write such a book, just as the era of the REDUCE personal algebra machine is beginning. In order to understand the nature of REDUCE, a little history is in order. In 1963 I met Dr. John McCarthy, the inventor of LISP.

Written for those with little or no experience in using computers for statistical analysis, this book introduces SPSS/PC+, the market leader PC package. A Guide to SPSS/PC+ teaches the use of SPSS/PC+ clearly and simply.

In this monograph some stability properties of linear, time-variant, discrete-time systems are summarized, where some properties are well known, some are little-known facts, and a few may be new. Models for this treatise an the asymp- totical behaviour of solutions of difference equations are the commonly known excellent books of CESARI [3] and CONTI [5]. In the tables of Chapter 1 the definitions and the essen- tial statements an stability of discrete-time systems are summarized, such that Chapter 2 to 5 may be regarded as explaining appendices for these tables. I am grateful to Paul Ludyk, who typed and corrected the manuscript with great skill and patience, and Alois Ludyk, who drew the figures with great artistic skill. Gunter Ludyk Bremen, January 1985 Contents Notations 1 1. Introduction and Summary 4 2. Mathematical Description of Discrete-Time Systems 16 2. 1 State Equations 16 2. 2 Properties of the Transition Matrix 19 2. 3 LAGRANGE-Identity and GREEN's Formula for Difference Equations 20 2. 4 Estimations for the Norm of the Transition Matrix 21 3. Stability of Free Discrete-Time Systems 34 3. 1 LJAPUNOW- and LAGRANGE-Stability 34 3. 2 Short Time Boundedness 40 3. 3 UniformStability 45 3. 4 Asymptotic Stability 63 3. 5 P-stability 70 3. 6 Exponential and Uniform Asymptotic Stability 75 3. 7 Relations between the Stability Glasses 84 4. Stability of Forced Discrete-Time Systems 86 4. 1 Preliminary Results 86 4. 2 Input-State Stability 93 4.