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Introductory Statistics with R, (Statistics and Computing Series)
by Peter DalgaardThe statistical methodology covered includes statistical standard distributions, one- and two-sample tests with continuous data, regression analysis, one-and two-way analysis of variance, regression analysis, analysis of tabular data, and sample size calculations. In addition, the last four chapters contain introductions to multiple linear regression analysis, linear models in general, logistic regression, and survival analysis.
Introductory Statistics: A Conceptual Approach Using R
by William B. Ware John M. Ferron Barbara M. MillerThis comprehensive and uniquely organized text is aimed at undergraduate and graduate level statistics courses in education, psychology, and other social sciences. A conceptual approach, built around common issues and problems rather than statistical techniques, allows students to understand the conceptual nature of statistical procedures and to focus more on cases and examples of analysis. Wherever possible, presentations contain explanations of the underlying reasons behind a technique. Importantly, this is one of the first statistics texts in the social sciences using R as the principal statistical package. Key features include the following. Conceptual Focus – The focus throughout is more on conceptual understanding and attainment of statistical literacy and thinking than on learning a set of tools and procedures. Problems and Cases – Chapters and sections open with examples of situations related to the forthcoming issues, and major sections ends with a case study. For example, after the section on describing relationships between variables, there is a worked case that demonstrates the analyses, presents computer output, and leads the student through an interpretation of that output. Continuity of Examples – A master data set containing nearly all of the data used in the book’s examples is introduced at the beginning of the text. This ensures continuity in the examples used across the text. Companion Website – A companion website contains instructions on how to use R, SAS, and SPSS to solve the end-of-chapter exercises and offers additional exercises. Field Tested – The manuscript has been field tested for three years at two leading institutions.
Introductory Statistics: Exploring the World through Data
by Robert Gould Rebecca Wong Colleen RyanFor courses in Introductory Statistics. Data analysis for everyone Data in the real world are dynamic and sometimes messy. This complexity can intimidate students who are new to math and statistics ― but it’s also what makes statistics so interesting! Embracing these characteristics, Introductory Statistics teaches students how to explore and analyze real data to answer real-world problems. Crafted by authors who are active in the classroom and in the statistics education community, the 3rd Edition pairs a clear, conversational writing style with new and frequent opportunities to apply statistical thinking. Its tone and learning aids are designed to equip any student to analyze, interpret, and tell a story about modern data, regardless of the student’s mathematical proficiency.
Introductory Statistics: Lecture Guide And Student Notebook
by KokoskaThis text helps students develop the fundamental lifelong skill of solving problems and interpreting solutions in real-world terms. One of our goals was to make this problem-solving approach accessible and easy to apply in many situations. We certainly want students to appreciate the beauty of statistics and connections to so many other disciplines. However, it is even more important for students to be able to apply problem-solving skills to a wide range of academic and career pursuits, including business, science and technology, and education. Third Edition, presents long-term, universal skills for students taking a one- or two-semester introductory-level statistics course. Examples include guided, explanatory solutions that emphasize problem-solving techniques. Example solutions are presented in a numbered, step-by-step format. The generous collection and variety of exercises provide ample opportunity for practice and review in a variety of contexts. Concepts, examples, and exercises are presented from a practical, realistic perspective. Real and realistic data sets are current and relevant. The text uses mathematically correct notation and symbols and precise definitions to clearly illustrate statistical procedures and proper communication. This text is designed to help students fully understand the steps in basic statistical arguments, emphasizing the importance of assumptions in order to follow valid arguments or identify inaccurate conclusions. Most importantly, students will understand the process of statistical inference. A four-step process (Claim, Experiment, Likelihood, Conclusion) is used throughout the text to present the smaller pieces of introductory statistics upon which the large, essential statistical inference puzzle is built.
Introductory Theory of Topological Vector Spaces (Pure and Applied Mathematics #167)
by Yau-Chuen WongThis text offers an overview of the basic theories and techniques of functional analysis and its applications. It contains topics such as the fixed point theory starting from Ky Fan's KKM covering and quasi-Schwartz operators. It also includes over 200 exercises to reinforce important concepts.
Introductory and Intermediate Algebra
by D. Franklin WrightINTRODUCTORY & INTERMEDIATE ALGEBRA SECOND EDITION
Introductory and Intermediate Algebra for College Students (Fifth Edition)
by Robert F. BlitzerNOTE: This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value-this format costs significantly less than a new textbook. Before purchasing, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson's MyLab & Mastering products. For courses in introductory and intermediate algebra. Gets them engaged. Keeps them engaged. Bob Blitzer's use of realistic applications instantly piques students' curiosity about the presence of mathematical concepts in the world around them. These applications are apparent throughout the entire program-from his relatable examples, friendly writing style, and thought-provoking features in the textbook, to the enhanced digital resources in the MyMathLab course. Blitzer pulls from topics that are relevant to college students, often from pop culture and everyday life, to ensure that students will actually use their learning resources to achieve success. With an expansion of the series to now include a Developmental Math "all-in-one" text (with content spanning prealgebra through intermediate algebra), and with an enhanced media program accompanying this revision, developmental students at all levels will see how math applies to their daily lives and culture. Also available with MyMathLab #65533; MyMathLab is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.
Introduzione al calcolo in più variabili ed equazioni differenziali (UNITEXT #142)
by Carlo MaricondaIl testo riguarda alcuni argomenti tipici di un qualunque corso di Analisi Matematica in più variabili, con cenno di tecniche risolutive di alcune equazioni differenziali:Lo spazio e le curve;Funzioni di più variabili (grafici di base, limiti, continuità);Calcolo differenziale e approssimazioni;Massimi e minimi locali e globali;Integrali curvilinei;Integrali doppi;Integrali tripli;Superficie parametriche;Teoremi della divergenza e di Green - Stokes nel piano e nello spazio;cenni sulle equazioni differenziali ed equazioni differenziali lineari del I ordine e a variabili separabili. Si tratta di note scritte su misura per l'insegnamento di Fondamenti di Analisi e Probabilità (FAMP) per i corsi di laurea in Ingegneria Biomedica, Elettronica e Informatica dell'Università di Padova, nei quali la parte di Analisi Matematica viene svolto in una quarantina di ore. La novità di questo testo, rispetto ad altri con contenuti analoghi, è la struttura in e-book parallela ad un MOOC (Massive Open Online Course) di Analisi matematica: calcolo in più variabili ed equazioni differenziali presente sulla piattaforma Federica WebLearning, la cui fruizione è gratuita. In ogni sezione vi sono dei link che rimandano a dei video brevi, circa una cinquantina, che illustrano e introducono gli argomenti, a dei test di autovalutazione, o ad altre attività del MOOC. Ciò rende il testo adatto a tutti gli studenti di un qualunque corso universitario che affronti contenuti di analisi matematica in più variabili, ed è sicuramente utile anche nei corsi con maggiori contenuti teorici per impadronirsi dei concetti di base.
Introduzione alla termomeccanica dei sistemi continui ed ai sistemi iperbolici (UNITEXT #170)
by Tommaso RuggeriL'obiettivo principale di questo libro è presentare un trattamento unificato della termomeccanica dei continui utilizzando l'approccio assiomatico tipico della meccanica razionale. Mentre molti testi di meccanica dei continui si concentrano su tipi specifici di corpi continui, come i corpi solidi deformabili o i fluidi, questo libro adotta una prospettiva generale. Viene presentata la struttura matematica delle leggi di bilancio e delle equazioni costitutive come un insieme coeso, con particolare attenzione alla moderna teoria delle equazioni costitutive. Si sottolineano principi importanti, come il principio di indifferenza materiale e l'interpretazione contemporanea del principio di entropia. Per garantire la coerenza interna, la prima parte del libro affronta questioni relative all'algebra lineare, con particolare attenzione agli operatori lineari all'interno degli spazi vettoriali a dimensione finita. Successivamente, il libro offre un'esplorazione dettagliata delle deformazioni finite dei continui, seguita da una panoramica sulla cinematica. Vengono caratterizzate le varie forze che possono esistere in un continuo, introdotto il tensore degli sforzi e presentate le leggi di bilancio sia in forma euleriana che lagrangiana. Successivamente viene definita la moderna teoria delle equazioni costitutive, sottolineando il ruolo dei principi generali di indifferenza materiale e di entropia come criteri per la selezione delle classi fisicamente accettabili di equazioni costitutive. Le equazioni di campo risultanti sono specializzate per vari casi, tra cui la termoelasticità, i fluidi euleriani, i fluidi di Fourier-Navier‒Stokes e i conduttori rigidi di calore. Nell'ultima parte del libro vengono discussi i sistemi di equazioni alle derivate parziali nella meccanica dei continui, con particolare attenzione ai sistemi iperbolici. Il metodo delle caratteristiche viene introdotto sia nei casi lineari che non lineari, e si discute la necessità di ampliare la classe delle soluzioni introducendo le soluzioni deboli, con le onde d'urto come caso significativo. Come esempio illustrativo di soluzione debole, viene presentato il problema di Riemann per il modello fluidodinamico del traffico veicolare, in cui le automobili sono inizialmente ferme a un semaforo rosso e poi iniziano a muoversi quando il semaforo diventa verde. Questo libro sarà utile non solo per gli studenti di ingegneria, ma anche per gli studenti di altre discipline scientifiche in cui si studiano aspetti della meccanica dei continui. Fornisce l'opportunità di considerare argomenti tradizionalmente distinti in un contesto più ampio e interconnesso.
Intuition, Trust, and Analytics (Data Analytics Applications)
by Jerzy Gołuchowski Joanna Paliszkiewicz Jay LiebowitzIn order to make informed decisions, there are three important elements: intuition, trust, and analytics. Intuition is based on experiential learning and recent research has shown that those who rely on their “gut feelings” may do better than those who don’t. Analytics, however, are important in a data-driven environment to also inform decision making. The third element, trust, is critical for knowledge sharing to take place. These three elements—intuition, analytics, and trust—make a perfect combination for decision making. This book gathers leading researchers who explore the role of these three elements in the process of decision-making.
Intuitionistic Fuzzy Logics
by Krassimir T. AtanassovThe book offers a comprehensive survey of intuitionistic fuzzy logics. By reporting on both the author's research and others' findings, it provides readers with a complete overview of the field and highlights key issues and open problems, thus suggesting new research directions. Starting with an introduction to the basic elements of intuitionistic fuzzy propositional calculus, it then provides a guide to the use of intuitionistic fuzzy operators and quantifiers, and lastly presents state-of-the-art applications of intuitionistic fuzzy sets. The book is a valuable reference resource for graduate students and researchers alike.
Intuitionistic Proof Versus Classical Truth: The Role Of Brouwer's Creative Subject In Intuitionistic Mathematics (Logic, Epistemology, and the Unity of Science #42)
by Enrico MartinoThis book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers – both new and previously published – it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism.The author explores Brouwer’s idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwer’s work. These figures include Michael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting.This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics.
Intuitive Axiomatic Set Theory (Textbooks in Mathematics)
by José L GarciáSet theory can be rigorously and profitably studied through an intuitive approach, thus independently of formal logic. Nearly every branch of Mathematics depends upon set theory, and thus, knowledge of set theory is of interest to every mathematician. This book is addressed to all mathematicians and tries to convince them that this intuitive approach to axiomatic set theory is not only possible but also valuable.The book has two parts. The first one presents, from the sole intuition of "collection" and "object", the axiomatic ZFC-theory. Then, we present the basics of the theory: the axioms, well-orderings, ordinals and cardinals are the main subjects of this part. In all, one could say that we give some standard interpretation of set theory, but this standard interpretation results in a multiplicity of universes. The second part of the book deals with the independence proofs of the continuum hypothesis (CH) and the axiom of choice (AC), and forcing is introduced as a necessary tool, and again the theory is developed intuitively, without the use of formal logic. The independence results belong to the metatheory, as they refer to things that cannot be proved, but the greater part of the arguments leading to the independence results, including forcing, are purely set-theoretic. The book is self-contained and accessible to beginners in set theory. There are no prerequisites other than some knowledge of elementary mathematics. Full detailed proofs are given for all the results.
Intuitive Concepts in Elementary Topology
by B. H. ArnoldClassroom-tested and much-cited, this concise text offers a valuable and instructive introduction for undergraduates to the basic concepts of topology. It takes an intuitive rather than an axiomatic viewpoint, and can serve as a supplement as well as a primary text.A few selected topics allow students to acquire a feeling for the types of results and the methods of proof in mathematics, including mathematical induction. Subsequent problems deal with networks and maps, provide practice in recognizing topological equivalence of figures, examine a proof of the Jordan curve theorem for the special case of a polygon, and introduce set theory. The concluding chapters examine transformations, connectedness, compactness, and completeness. The text is well illustrated with figures and diagrams.
Invariance Entropy for Deterministic Control Systems
by Christoph KawanThis monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinear stabilization. IEEE Trans. Automat. Control 49 (2004), 1585-1597). The book presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents. While both discrete-time and continuous-time systems are treated, the emphasis lies on systems given by differential equations.
Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem (Studies in Advanced Mathematics #16)
by Peter B. GilkeyThis book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.
Invariance of Modules under Automorphisms of their Envelopes and Covers (London Mathematical Society Lecture Note Series #466)
by Askar Tuganbaev Ashish K. Srivastava Pedro A. Guil AsensioThe theory of invariance of modules under automorphisms of their envelopes and covers has opened up a whole new direction in the study of module theory. It offers a new perspective on generalizations of injective, pure-injective and flat-cotorsion modules beyond relaxing conditions on liftings of homomorphisms. This has set off a flurry of work in the area, with hundreds of papers using the theory appearing in the last decade. This book gives the first unified treatment of the topic. The authors are real experts in the area, having played a major part in the breakthrough of this new theory and its subsequent applications. The first chapter introduces the basics of ring and module theory needed for the following sections, making it self-contained and suitable for graduate students. The authors go on to develop and explain their tools, enabling researchers to employ them, extend and simplify known results in the literature and to solve longstanding problems in module theory, many of which are discussed at the end of the book.
Invariant Integrals in Physics
by Genady P. CherepanovIn this book, all physical laws are derived from a small number of invariant integrals which express the conservation of energy, mass, or momentum. This new approach allows us to unify the laws of theoretical physics, to simplify their derivation, and to discover some novel or more universal laws. Newton's Law of gravity is generalized to take into account cosmic forces of repulsion, Archimedes' principle of buoyancy is modified for account of the surface tension, and Coulomb's Laws for rolling friction and for the interaction of electric charges are substantially repaired and generalized. For postgraduate students, lecturers and researchers.
Invariant Manifold Theory for Hydrodynamic Transition (Dover Books on Mathematics)
by S. S. SritharanInvariant manifold theory serves as a link between dynamical systems theory and turbulence phenomena. This volume consists of research notes by author S. S. Sritharan that develop a theory for the Navier-Stokes equations in bounded and certain unbounded geometries. The main results include spectral theorems and analyticity theorems for semigroups and invariant manifolds."This monograph contains a lot of useful information, including much that cannot be found in the standard texts on the Navier-Stokes equations," observed MathSciNet, adding "the book is well worth the reader's attention." The treatment is suitable for researchers and graduate students in the areas of chaos and turbulence theory, hydrodynamic stability, dynamical systems, partial differential equations, and control theory. Topics include the governing equations and the functional framework, the linearized operator and its spectral properties, the monodromy operator and its properties, the nonlinear hydrodynamic semigroup, invariant cone theorem, and invariant manifold theorem. Two helpful appendixes conclude the text.
Invariant Markov Processes Under Lie Group Actions
by Ming LiaoThe purpose of this monograph is to provide a theory of Markov processes that are invariant under the actions of Lie groups, focusing on ways to represent such processes in the spirit of the classical Lévy-Khinchin representation. It interweaves probability theory, topology, and global analysis on manifolds to present the most recent results in a developing area of stochastic analysis. The author’s discussion is structured with three different levels of generality:— A Markov process in a Lie group G that is invariant under the left (or right) translations— A Markov process xt in a manifold X that is invariant under the transitive action of a Lie group G on X— A Markov process xt invariant under the non-transitive action of a Lie group GA large portion of the text is devoted to the representation of inhomogeneous Lévy processes in Lie groups and homogeneous spaces by a time dependent triple through a martingale property. Preliminary definitions and results in both stochastics and Lie groups are provided in a series of appendices, making the book accessible to those who may be non-specialists in either of these areas.Invariant Markov Processes Under Lie Group Actions will be of interest to researchers in stochastic analysis and probability theory, and will also appeal to experts in Lie groups, differential geometry, and related topics interested in applications of their own subjects.
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences
by George Engelhard Jr.This introductory text describes the principles of invariant measurement, how invariant measurement can be achieved with Rasch models, and how to use invariant measurement to solve measurement problems in the social, behavioral, and health sciences. Rasch models are used throughout but a comparison of Rasch models to other item response theory (IRT) models is also provided. Written with students in mind, the manuscript was class tested to help maximize accessibility. Chapters open with an introduction and close with a summary and discussion. Numerous examples and exercises demonstrate the main issues addressed in each chapter. Key terms are defined when first introduced and in an end-of-text glossary. All of the book’s analyses were conducted with the Facets program. The data sets used in the book, sample syntax files for running the Facets program, Excel files for creating item and person response functions, links to related websites, and other material are available at www.GeorgeEngelhard.com. Highlights include: A strong philosophical and methodological approach to measurement in the human sciences Demonstrations of how measurement problems can be addressed using invariant measurement Practical illustrations of how to create and evaluate scales using invariant measurement A history of measurement based on test-score and scaling traditions Previously unpublished work in analyzing rating data, the detection and measurement of rater errors, and the evaluation of rater accuracy A review of estimation methods, model-data fit, indices used to evaluate the quality of rater-mediated assessments, rater error and bias, and rater accuracy. Intended as a supplementary text for graduate or advanced undergraduate courses on measurement or test theory, item response theory, scaling theory, psychometrics, advanced measurement techniques, research methods, or evaluation research taught in education, psychology, and the social and health sciences, the book also appeals to practitioners and researchers in these fields who develop or use scales and instruments. Only a basic mathematical level is required including a basic course in statistic.
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences
by George Engelhard, Jr. Jue WangThis is the second edition of an introductory text that describes the principles of invariant measurement; how invariant measurement can be achieved using Rasch measurement theory; and how to use invariant measurement to solve a variety of measurement problems in the social, behavioral, and health sciences. Rasch models are used throughout the text, but brief comparisons of Rasch models to other item response theory (IRT) models are also provided.Written with students in mind, this new edition was class-tested to help maximize accessibility. Chapters open with an introduction and close with a discussion and summary. All chapters have been updated from the first edition, and a new chapter on explanatory Rasch models has been added. Features include numerous examples and exercises to demonstrate the main issues addressed in each chapter. Key terms are defined when first introduced and included in a helpful end-of-text glossary.This book also benefits from online materials which include the data sets used in the book, sample syntax files for running the Facets program, Excel files for creating item and person response functions, and links to related websites.This book will act as a supplementary text for graduate or advanced undergraduate courses on measurement or test theory, IRT, scaling theory, psychometrics, advanced measurement techniques, research methods, or evaluation research taught in education, psychology, and other social and health sciences. It will also appeal to practitioners and researchers in these fields who develop or use scales and instruments. Only a basic mathematical level is required, including a basic course in statistics, ensuring it is an accessible resource for students and researchers alike.
Invariant Measures for Stochastic Nonlinear Schrödinger Equations: Numerical Approximations and Symplectic Structures (Lecture Notes in Mathematics #2251)
by Xu Wang Jialin HongThis book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations.This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.
Invariant Probabilities of Transition Functions
by Radu ZaharopolThe structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of the state space, where the invariant ergodic probability measures play a significant role. Other topics covered include: characterizations of the supports of various types of invariant probability measures and the use of these to obtain criteria for unique ergodicity, and the proofs of two mean ergodic theorems for a certain type of transition functions. The book will be of interest to mathematicians working in ergodic theory, dynamical systems, or the theory of Markov processes. Biologists, physicists and economists interested in interacting particle systems and rigorous mathematics will also find this book a valuable resource. Parts of it are suitable for advanced graduate courses. Prerequisites are basic notions and results on functional analysis, general topology, measure theory, the Bochner integral and some of its applications.
Invariant Random Fields on Spaces with a Group Action
by Nicolai Leonenko Anatoliy MalyarenkoThe author describes the current state of the art in the theory of invariant random fields. This theory is based on several different areas of mathematics, including probability theory, differential geometry, harmonic analysis, and special functions. The present volume unifies many results scattered throughout the mathematical, physical, and engineering literature, as well as it introduces new results from this area first proved by the author. The book also presents many practical applications, in particular in such highly interesting areas as approximation theory, cosmology and earthquake engineering. It is intended for researchers and specialists working in the fields of stochastic processes, statistics, functional analysis, astronomy, and engineering.