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An Introduction to the Rasch Model with Examples in R (Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences)
by Rudolf Debelak Carolin Strobl Matthew D. ZeigenfuseAn Introduction to the Rasch Model with Examples in R offers a clear, comprehensive introduction to the Rasch model along with practical examples in the free, open-source software R. It is accessible for readers without a background in psychometrics or statistics, while also providing detailed explanations of the relevant mathematical and statistical concepts for readers who want to gain a deeper understanding. Its worked examples in R demonstrate how to apply the methods to real-world examples and how to interpret the resulting output. In addition to motivating and presenting the Rasch model, the book covers different methods for parameter estimation and for assessing fit and differential item functioning (DIF). While focusing on the Rasch model, it also addresses a variety of other dichotomous and polytomous Rasch and item response theory (IRT) models, such as two-parameter logistic (2PL) and Partial Credit models, and extensions, including mixture Rasch models and computerized adaptive testing (CAT). Theory is presented in a self-contained way. All necessary mathematical and statistical background is contained in the chapters and appendices. The book also provides detailed, step-by-step instructions for getting started with R and using the eRm, mirt, TAM and rstan packages for fitting Rasch models.
Introduction to the Representation Theory of Algebras
by Michael BarotThis book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations, explaining the three common setups: representation of quivers, modules over algebras and additive functors over certain categories. The main part is devoted to (i) module categories, presenting the unicity of the decomposition into indecomposable modules, the Auslander-Reiten theory and the technique of knitting; (ii) the use of combinatorial tools such as dimension vectors and integral quadratic forms; and (iii) deeper theorems such as Gabriel's Theorem, the trichotomy and the Theorem of Kac - all accompanied by further examples. Each section includes exercises to facilitate understanding. By keeping the proofs as basic and comprehensible as possible and introducing the three languages at the beginning, this book is suitable for readers from the advanced undergraduate level onwards and enables them to consult related, specific research articles.
Introduction to the Senses
by Terry R.J. BossomaierAn understanding of the senses - vision, hearing, touch, chemical and other non-human senses - is important not only for many fields of biology but also in applied areas such as human computer interaction, robotics and computer games. Using information theory as a unifying framework, this is a wide-ranging survey of sensory systems, covering all known senses. The book draws on three unifying principles to examine senses: the Nyquist sampling theorem; Shannon's information theory; and the creation of different streams of information to subserve different tasks. This framework is used to discuss the fascinating role of sensory adaptation in the context of environment and lifestyle. Providing a fundamental grounding in sensory perception, the book then demonstrates how this knowledge can be applied to the design of human-computer interfaces and virtual environments. It is an ideal resource for both graduate and undergraduate students of biology, engineering (robotics) and computer science.
An Introduction to the Social Geography of India: Concepts, Problems and Prospects
by Asif Ali HemantThis book discusses the significance of social geography, a multidimensional sub-discipline of georgraphy encompassing social health, social security and social ethos. It presents the socio-spatial dynamics of the population in India through an understanding of the various issues related to migration, urbanisation, unemployment, poverty and public health. With a thorough analysis of various social indicators relating to health, education, income and employment, the volume presents a detailed picture of the social geography of India. It discusses in detail, The origin, nature and scope of social geography, its relations with other social sciences and applications The nature and importance of social well-being along with welfare geography and the role of welfare state in ensuring social well-being The population of India and its attributes The status and spatial patterns of various social indicators relating to health, education and income and employment The composite indices which aggregate several social indicators such as the Human Development Index, Multidimensional Poverty Index and Sustainable Developmental Goals Index in the context of India. This comprehensive book will be useful for students, researchers and teachers of social geography, human geography, population geography, demography and sociology. The book can also be used by students preparing for exams like civil services, UPSC, PSC and other competitive exams.
Introduction to the Statistics of Poisson Processes and Applications (Frontiers in Probability and the Statistical Sciences)
by Yury A. KutoyantsThis book covers an extensive class of models involving inhomogeneous Poisson processes and deals with their identification, i.e. the solution of certain estimation or hypothesis testing problems based on the given dataset. These processes are mathematically easy-to-handle and appear in numerous disciplines, including astronomy, biology, ecology, geology, seismology, medicine, physics, statistical mechanics, economics, image processing, forestry, telecommunications, insurance and finance, reliability, queuing theory, wireless networks, and localisation of sources.Beginning with the definitions and properties of some fundamental notions (stochastic integral, likelihood ratio, limit theorems, etc.), the book goes on to analyse a wide class of estimators for regular and singular statistical models. Special attention is paid to problems of change-point type, and in particular cusp-type change-point models, then the focus turns to the asymptotically efficient nonparametric estimation of the mean function, the intensity function, and of some functionals. Traditional hypothesis testing, including some goodness-of-fit tests, is also discussed. The theory is then applied to three classes of problems: misspecification in regularity (MiR),corresponding to situations where the chosen change-point model and that of the real data have different regularity; optical communication with phase and frequency modulation of periodic intensity functions; and localization of a radioactive (Poisson) source on the plane using K detectors.Each chapter concludes with a series of problems, and state-of-the-art references are provided, making the book invaluable to researchers and students working in areas which actively use inhomogeneous Poisson processes.
Introduction to the Taxometric Method: A Practical Guide
by John Ruscio Nick Haslam Ayelet Meron RuscioIntroduction to the Taxometric Method is a user-friendly, practical guide to taxometric research. Drawing from both classic and contemporary research, it provides a comprehensive introduction to the method. With helpful tools and guidance, the book is intended to teach those new to the method, as well as those already familiar with it, tips on how to conduct and evaluate taxometric investigations. The book covers a broad range of analytic techniques, describing their logic and implementation as well as what is known about their performance from systematic study. The book opens with the background material essential to understanding the research problems that the taxometric method addresses. The authors then explain the data requirements of taxometric analysis, the logic of each procedure, factors that can influence results and lead to misinterpretations, suggestions for choosing the best procedures, and methodological safeguards to prevent erroneous conclusions. Illustrative examples of each procedure and consistency test demonstrate how to perform analyses and interpret results using a variety of data sets. A checklist of conceptual and methodological issues that should be addressed in any investigation is included. The downloadable resources provide a variety of programs for performing taxometric analyses along with simulations and analyses of data sets. Introduction to the Taxometric Method is ideal for researchers and students conducting or evaluating taxometric studies in the social and behavioral sciences, especially those in clinical and personality psychology, as well as those in the physical sciences, education, biology, and beyond. The book also serves as a text for courses on this method, or as a supplement in psychological assessment, statistics, or research methods courses. Familiarity with taxometrics is not assumed.
Introduction to the Theory of Abstract Algebras (Dover Books on Mathematics)
by Richard S PierceIntended for beginning graduate-level courses, this text introduces various aspects of the theory of abstract algebra. The book is also suitable as independent reading for interested students at that level as well as a primary source for a one-semester course that an instructor may supplement to expand to a full year. Author Richard S. Pierce, a Professor of Mathematics at Seattle's University of Washington, places considerable emphasis on applications of the theory and focuses particularly on lattice theory.After a preliminary review of set theory, the treatment presents the basic definitions of the theory of abstract algebras. Each of the next four chapters focuses on a major theme of universal algebra: subdirect decompositions, direct decompositions, free algebras, and varieties of algebras. Problems and a Bibliography supplement the text.
An Introduction to the Theory of Canonical Matrices
by H. W. Turnbull A. C. AitkenThorough and self-contained, this penetrating study of the theory of canonical matrices presents a detailed consideration of all the theory's principal features. Topics include elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. The final chapters explore several methods of canonical reduction, including those of unitary and orthogonal transformations. 1952 edition. Index. Appendix. Historical notes. Bibliographies. 275 problems.
Introduction to the Theory of Computation (Third Edition)
by Michael SipserReaders embark on the study of a fascinating and important subject: the theory of computation. It comprises the fundamental mathematical properties of computer hardware, software, and certain applications thereof. This book is intended as an upper-level undergraduate or introductory graduate text in computer science theory. It contains a mathematical treatment of the subject, designed around theorems and proofs.
Introduction to the Theory of Determinants and Matrices
by Edward Tankard BrowneThis text and reference book for mathematics students and for many people working in the social sciences contains in one volume the most important properties of matrices and determinants whose elements are real or complex numbers. The theory is developed from the classical point of view of Bocher, Wedderburn, MacDuffee, and Erobernus.Originally published in 1958.A UNC Press Enduring Edition -- UNC Press Enduring Editions use the latest in digital technology to make available again books from our distinguished backlist that were previously out of print. These editions are published unaltered from the original, and are presented in affordable paperback formats, bringing readers both historical and cultural value.
Introduction to the Theory of Formal Groups
by Jean A. DieudonneThe concept of formal Lie group was derived in a natural way from classical Lie theory by S. Bochner in 1946, for fields of characteristic 0. Its study over fields of characteristic p > 0 began in the early 1950’s, when it was realized, through the work of Chevalley, that the familiar “dictionary” between Lie groups and Lie algebras completely broke down for Lie algebras of algebraic groups over such a field. This volume, starts with the concept of C-group for any category C (with products and final object), but the author’s do not exploit it in its full generality. The book is meant to be introductory to the theory, and therefore the necessary background to its minimum possible level is minimised: no algebraic geometry and very little commutative algebra is required in chapters I to III, and the algebraic geometry used in chapter IV is limited to the Serre- Chevalley type (varieties over an algebraically closed field).
Introduction to the Theory of Games (Dover Books on Mathematics)
by J. C. McKinseyOne of the classic early monographs on game theory, this comprehensive overview illustrates the theory's applications to situations involving conflicts of interest, including economic, social, political, and military contexts. Contents include a survey of rectangular games; a method of approximating the value of a game; games in extensive form and those with infinite strategies; distribution functions; Stieltjes integrals; the fundamental theorem for continuous games; separable games; games with convex payoff functions; applications to statistical inference; and much more. Appropriate for advanced undergraduate and graduate courses; a familiarity with advanced calculus is assumed. 1952 edition. 51 figures. 8 tables.
An Introduction to the Theory of Groups (Dover Books on Mathematics)
by Paul Alexandroff Hazel Perfect G. M. PetersenThis introductory exposition of group theory by an eminent Russian mathematician is particularly suited to undergraduates, developing material of fundamental importance in a clear and rigorous fashion. The treatment is also useful as a review for more advanced students with some background in group theory. Beginning with introductory examples of the group concept, the text advances to considerations of groups of permutations, isomorphism, cyclic subgroups, simple groups of movements, invariant subgroups, and partitioning of groups. An appendix provides elementary concepts from set theory. A wealth of simple examples, primarily geometrical, illustrate the primary concepts. Exercises at the end of each chapter provide additional reinforcement.
An Introduction to the Theory of Linear Spaces (Dover Books on Mathematics)
by Richard A. Silverman Georgi E. ShilovThis introduction to linear algebra and functional analysis offers a clear expository treatment, viewing algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. All abstract ideas receive a high degree of motivation, and numerous examples illustrate many different fields of mathematics. Abundant problems include hints or answers.
Introduction to the Theory of Nonlinear Optimization
by Johannes JahnThis book serves as an introductory text to optimization theory in normed spaces and covers all areas of nonlinear optimization. It presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.
Introduction to the Theory of Optimization in Euclidean Space (Chapman & Hall/CRC Series in Operations Research)
by Samia ChallalIntroduction to the Theory of Optimization in Euclidean Space is intended to provide students with a robust introduction to optimization in Euclidean space, demonstrating the theoretical aspects of the subject whilst also providing clear proofs and applications. Students are taken progressively through the development of the proofs, where they have the occasion to practice tools of differentiation (Chain rule, Taylor formula) for functions of several variables in abstract situations. Throughout this book, students will learn the necessity of referring to important results established in advanced Algebra and Analysis courses. Features Rigorous and practical, offering proofs and applications of theorems Suitable as a textbook for advanced undergraduate students on mathematics or economics courses, or as reference for graduate-level readers Introduces complex principles in a clear, illustrative fashion
An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
by Vern I. Paulsen Mrinal RaghupathiReproducing kernel Hilbert spaces have developed into an important tool in many areas, especially statistics and machine learning, and they play a valuable role in complex analysis, probability, group representation theory, and the theory of integral operators. This unique text offers a unified overview of the topic, providing detailed examples of applications, as well as covering the fundamental underlying theory, including chapters on interpolation and approximation, Cholesky and Schur operations on kernels, and vector-valued spaces. Self-contained and accessibly written, with exercises at the end of each chapter, this unrivalled treatment of the topic serves as an ideal introduction for graduate students across mathematics, computer science, and engineering, as well as a useful reference for researchers working in functional analysis or its applications.
Introduction to the Theory of Sets (Dover Books on Mathematics)
by Joseph Breuer Howard F. FehrSet theory permeates much of contemporary mathematical thought. This text for undergraduates offers a natural introduction, developing the subject through observations of the physical world. Its progressive development leads from concrete finite sets to cardinal numbers, infinite cardinals, and ordinals.Although set theory begins in the intuitive and the concrete, it ascends to a very high degree of abstraction. All that is necessary to its grasp, declares author Joseph Breuer, is patience. Breuer illustrates the grounding of finite sets in arithmetic, permutations, and combinations, which provides the terminology and symbolism for further study. Discussions of general theory lead to a study of ordered sets, concluding with a look at the paradoxes of set theory and the nature of formalism and intuitionalism. Answers to exercises incorporated throughout the text appear at the end, along with an appendix featuring glossaries and other helpful information.
Introduction to the Theory of Statistical Inference (Chapman & Hall/CRC Texts in Statistical Science)
by Hannelore Liero Silvelyn ZwanzigBased on the authors' lecture notes, this text presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Unlike related textbooks, it combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models. Suitable for a second semester undergraduate course on statistical inference, the text offers proofs to support the mathematics and does not require any use of measure theory. It illustrates core concepts using cartoons and provides solutions to all examples and problems.
An Introduction to the Topological Derivative Method (SpringerBriefs in Mathematics)
by Antonio André Novotny Jan SokołowskiThis book presents the topological derivative method through selected examples, using a direct approach based on calculus of variations combined with compound asymptotic analysis. This new concept in shape optimization has applications in many different fields such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena. In particular, the topological derivative is used here in numerical methods of shape optimization, with applications in the context of compliance structural topology optimization and topology design of compliant mechanisms. Some exercises are offered at the end of each chapter, helping the reader to better understand the involved concepts.
Introduction to the Variational Formulation in Mechanics: Fundamentals and Applications
by Edgardo O. Taroco Pablo J. Blanco Raúl A. FeijóoIntroduces readers to the fundamentals and applications of variational formulations in mechanics Nearly 40 years in the making, this book provides students with the foundation material of mechanics using a variational tapestry. It is centered around the variational structure underlying the Method of Virtual Power (MVP). The variational approach to the modeling of physical systems is the preferred approach to address complex mathematical modeling of both continuum and discrete media. This book provides a unified theoretical framework for the construction of a wide range of multiscale models. Introduction to the Variational Formulation in Mechanics: Fundamentals and Applications enables readers to develop, on top of solid mathematical (variational) bases, and following clear and precise systematic steps, several models of physical systems, including problems involving multiple scales. It covers: Vector and Tensor Algebra; Vector and Tensor Analysis; Mechanics of Continua; Hyperelastic Materials; Materials Exhibiting Creep; Materials Exhibiting Plasticity; Bending of Beams; Torsion of Bars; Plates and Shells; Heat Transfer; Incompressible Fluid Flow; Multiscale Modeling; and more. A self-contained reader-friendly approach to the variational formulation in the mechanics Examines development of advanced variational formulations in different areas within the field of mechanics using rather simple arguments and explanations Illustrates application of the variational modeling to address hot topics such as the multiscale modeling of complex material behavior Presentation of the Method of Virtual Power as a systematic tool to construct mathematical models of physical systems gives readers a fundamental asset towards the architecture of even more complex (or open) problems Introduction to the Variational Formulation in Mechanics: Fundamentals and Applications is a ideal book for advanced courses in engineering and mathematics, and an excellent resource for researchers in engineering, computational modeling, and scientific computing.
An Introduction to Thermodynamics and Statistical Physics (UNITEXT for Physics)
by Piero OllaThis textbook offers an advanced undergraduate or initial graduate level introduction to topics such as kinetic theory, equilibrium statistical mechanics and the theory of fluctuations from a modern perspective. The aim is to provide the reader with the necessary tools of probability theory and thermodynamics (especially the thermodynamic potentials) to enable subsequent study at advanced graduate level. At the same time, the book offers a bird's eye view on arguments that are often disregarded in the main curriculum courses. Further features include a focus on the interdisciplinary nature of the subject and in-depth discussion of alternative interpretations of the concept of entropy. While some familiarity with basic concepts of thermodynamics and probability theory is assumed, this does not extend beyond what is commonly obtained in basic undergraduate curriculum courses.
Introduction to Time Series Analysis and Forecasting (WILEY SERIES IN PROB & STATISTICS/see 1345/6,6214/5)
by Murat Kulahci Douglas C. Montgomery Cheryl L. JenningsBring the latest statistical tools to bear on predicting future variables and outcomes A huge range of fields rely on forecasts of how certain variables and causal factors will affect future outcomes, from product sales to inflation rates to demographic changes. Time series analysis is the branch of applied statistics which generates forecasts, and its sophisticated use of time oriented data can vastly impact the quality of crucial predictions. The latest computing and statistical methodologies are constantly being sought to refine these predictions and increase the confidence with which important actors can rely on future outcomes. Time Series Analysis and Forecasting presents a comprehensive overview of the methodologies required to produce these forecasts with the aid of time-oriented data sets. The potential applications for these techniques are nearly limitless, and this foundational volume has now been updated to reflect the most advanced tools. The result, more than ever, is an essential introduction to a core area of statistical analysis. Readers of the third edition of Time Series Analysis and Forecasting will also find: Updates incorporating JMP, SAS, and R software, with new examples throughout Over 300 exercises and 50 programming algorithms that balance theory and practice Supplementary materials in the e-book including solutions to many problems, data sets, and brand-new explanatory videos covering the key concepts and examples from each chapter. Time Series Analysis and Forecasting is ideal for graduate and advanced undergraduate courses in the areas of data science and analytics and forecasting and time series analysis. It is also an outstanding reference for practicing data scientists.
Introduction to Time Series Analysis and Forecasting
by Douglas C. Montgomery Murat Kulahci Cheryl L. JenningsPraise for the First Edition "...[t]he book is great for readers who need to apply the methods and models presented but have little background in mathematics and statistics." -MAA Reviews Thoroughly updated throughout, Introduction to Time Series Analysis and Forecasting, Second Edition presents the underlying theories of time series analysis that are needed to analyze time-oriented data and construct real-world short- to medium-term statistical forecasts. Authored by highly-experienced academics and professionals in engineering statistics, the Second Edition features discussions on both popular and modern time series methodologies as well as an introduction to Bayesian methods in forecasting. Introduction to Time Series Analysis and Forecasting, Second Edition also includes: Over 300 exercises from diverse disciplines including health care, environmental studies, engineering, and finance More than 50 programming algorithms using JMP®, SAS®, and R that illustrate the theory and practicality of forecasting techniques in the context of time-oriented data New material on frequency domain and spatial temporal data analysis Expanded coverage of the variogram and spectrum with applications as well as transfer and intervention model functions A supplementary website featuring PowerPoint® slides, data sets, and select solutions to the problems Introduction to Time Series Analysis and Forecasting, Second Edition is an ideal textbook upper-undergraduate and graduate-levels courses in forecasting and time series. The book is also an excellent reference for practitioners and researchers who need to model and analyze time series data to generate forecasts.
Introduction to Time Series Analysis and Forecasting, 2nd Edition
by Cheryl L. Jennings Murat Kulahci Douglas C. MontgomeryAn accessible introduction to the most current thinking in and practicality of forecasting techniques in the context of time-oriented data.Analyzing time-oriented data and forecasting are among the most important problems that analysts face across many fields, ranging from finance and economics to production operations and the natural sciences. As a result, there is a widespread need for large groups of people in a variety of fields to understand the basic concepts of time series analysis and forecasting. Introduction to Time Series Analysis and Forecasting presents the time series analysis branch of applied statistics as the underlying methodology for developing practical forecasts, and it also bridges the gap between theory and practice by equipping readers with the tools needed to analyze time-oriented data and construct useful, short- to medium-term, statistically based forecasts.Seven easy-to-follow chapters provide intuitive explanations and in-depth coverage of key forecasting topics, including:Regression-based methods, heuristic smoothing methods, and general time series modelsBasic statistical tools used in analyzing time series dataMetrics for evaluating forecast errors and methods for evaluating and tracking forecasting performance over timeCross-section and time series regression data, least squares and maximum likelihood model fitting, model adequacy checking, prediction intervals, and weighted and generalized least squaresExponential smoothing techniques for time series with polynomial components and seasonal dataForecasting and prediction interval construction with a discussion on transfer function models as well as intervention modeling and analysisMultivariate time series problems, ARCH and GARCH models, and combinations of forecastsThe ARIMA model approach with a discussion on how to identify and fit these models for non-seasonal and seasonal time seriesThe intricate role of computer software in successful time series analysis is acknowledged with the use of Minitab, JMP, and SAS software applications, which illustrate how the methods are imple-mented in practice. An extensive FTP site is available for readers to obtain data sets, Microsoft Office PowerPoint slides, and selected answers to problems in the book. Requiring only a basic working knowledge of statistics and complete with exercises at the end of each chapter as well as examples from a wide array of fields, Introduction to Time Series Analysis and Forecasting is an ideal text for forecasting and time series courses at the advanced undergraduate and beginning graduate levels. The book also serves as an indispensable reference for practitioners in business, economics, engineering, statistics, mathematics, and the social, environmental, and life sciences.