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Basic Analysis I is designed for students who have completed the usual calculus and ordinary differential equation sequence and a basic course in linear algebra. This is a critical course in the use of abstraction, but is just the first volume in a sequence of courses which prepare students to become practicing scientists. This book is written with the aim of balancing theory and abstraction with clear explanations and arguments, so that students from a variety of disciplines can follow this text and use it profitably for self-study.
Probability, Random Variables, Statistics, and Random Processes by Ali GramiProbability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications is a comprehensive undergraduate-level textbook. With its excellent topical coverage, the focus of this book is on the basic principles and practical applications of the fundamental concepts that are extensively used in various Engineering disciplines as well as in a variety of programs in Life and Social Sciences. The text provides students with the requisite building blocks of knowledge they require to understand and progress in their areas of interest. With a simple, clear-cut style of writing, the intuitive explanations, insightful examples, and practical applications are the hallmarks of this book. The text consists of twelve chapters divided into four parts. Part-I, Probability (Chapters 1 - 3), lays a solid groundwork for probability theory, and introduces applications in counting, gambling, reliability, and security. Part-II, Random Variables (Chapters 4 - 7), discusses in detail multiple random variables, along with a multitude of frequently-encountered probability distributions. Part-III, Statistics (Chapters 8 - 10), highlights estimation and hypothesis testing. Part-IV, Random Processes (Chapters 11 - 12), delves into the characterization and processing of random processes. Other notable features include: Most of the text assumes no knowledge of subject matter past first year calculus and linear algebra With its independent chapter structure and rich choice of topics, a variety of syllabi for different courses at the junior, senior, and graduate levels can be supported A supplemental website includes solutions to about 250 practice problems, lecture slides, and figures and tables from the text Given its engaging tone, grounded approach, methodically-paced flow, thorough coverage, and flexible structure, Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications clearly serves as a must textbook for courses not only in Electrical Engineering, but also in Computer Engineering, Software Engineering, and Computer Science.
How to Free your Inner Mathematician : Notes on Mathematics and Life by Susan D'AgostinoHow to Free Your Inner Mathematician offers readers guidance in managing the fear, freedom, frustration, and joy that often accompany calls to think mathematically. With practical insight and years of award-winning mathematics teaching experience, D'Agostino offers more than 300 hand-drawn sketches alongside accessible descriptions of fractals, symmetry, fuzzy logic, knot theory, Penrose patterns, infinity, the Twin Prime Conjecture, Arrow's Impossibility Theorem, Fermat's Last Theorem, and other intriguing mathematical topics.
Testing Statistical Assumptions in Research by J. P. Verma; Abdel-Salam G. Abdel-SalamComprehensively teaches the basics of testing statistical assumptions in research and the importance in doing so This book facilitates researchers in checking the assumptions of statistical tests used in their research by focusing on the importance of checking assumptions in using statistical methods, showing them how to check assumptions, and explaining what to do if assumptions are not met. Testing Statistical Assumptions in Research discusses the concepts of hypothesis testing and statistical errors in detail, as well as the concepts of power, sample size, and effect size. It introduces SPSS functionality and shows how to segregate data, draw random samples, file split, and create variables automatically. It then goes on to cover different assumptions required in survey studies, and the importance of designing surveys in reporting the efficient findings. The book provides various parametric tests and the related assumptions and shows the procedures for testing these assumptions using SPSS software. To motivate readers to use assumptions, it includes many situations where violation of assumptions affects the findings. Assumptions required for different non-parametric tests such as Chi-square, Mann-Whitney, Kruskal Wallis, and Wilcoxon signed-rank test are also discussed. Finally, it looks at assumptions in non-parametric correlations, such as bi-serial correlation, tetrachoric correlation, and phi coefficient. An excellent reference for graduate students and research scholars of any discipline in testing assumptions of statistical tests before using them in their research study Shows readers the adverse effect of violating the assumptions on findings by means of various illustrations Describes different assumptions associated with different statistical tests commonly used by research scholars Contains examples using SPSS, which helps facilitate readers to understand the procedure involved in testing assumptions Looks at commonly used assumptions in statistical tests, such as z, t and F tests, ANOVA, correlation, and regression analysis Testing Statistical Assumptions in Research is a valuable resource for graduate students of any discipline who write thesis or dissertation for empirical studies in their course works, as well as for data analysts.
Robust Nonlinear Regression : With Applications Using R by Hossein Riazoshams; Habshah Midi; Gebrenegus GhilagaberThe first book to discuss robust aspects of nonlinear regression--with applications using R software Robust Nonlinear Regression: with Applications using R covers a variety of theories and applications of nonlinear robust regression. It discusses both parts of the classic and robust aspects of nonlinear regression and focuses on outlier effects. It develops new methods in robust nonlinear regression and implements a set of objects and functions in S-language under SPLUS and R software. The software covers a wide range of robust nonlinear fitting and inferences, and is designed to provide facilities for computer users to define their own nonlinear models as an object, and fit models using classic and robust methods as well as detect outliers. The implemented objects and functions can be applied by practitioners as well as researchers. The book offers comprehensive coverage of the subject in 9 chapters: Theories of Nonlinear Regression and Inference; Introduction to R; Optimization; Theories of Robust Nonlinear Methods; Robust and Classical Nonlinear Regression with Autocorrelated and Heteroscedastic errors; Outlier Detection; R Packages in Nonlinear Regression; A New R Package in Robust Nonlinear Regression; and Object Sets. The first comprehensive coverage of this field covers a variety of both theoretical and applied topics surrounding robust nonlinear regression Addresses some commonly mishandled aspects of modeling R packages for both classical and robust nonlinear regression are presented in detail in the book and on an accompanying website Robust Nonlinear Regression: with Applications using R is an ideal text for statisticians, biostatisticians, and statistical consultants, as well as advanced level students of statistics.
Statistical Analysis with Missing Data by Roderick J. A. Little; Donald B. RubinAn up-to-date, comprehensive treatment of a classic text on missing data in statistics The topic of missing data has gained considerable attention in recent decades. This new edition by two acknowledged experts on the subject offers an up-to-date account of practical methodology for handling missing data problems. Blending theory and application, authors Roderick Little and Donald Rubin review historical approaches to the subject and describe simple methods for multivariate analysis with missing values. They then provide a coherent theory for analysis of problems based on likelihoods derived from statistical models for the data and the missing data mechanism, and then they apply the theory to a wide range of important missing data problems. Statistical Analysis with Missing Data, Third Edition starts by introducing readers to the subject and approaches toward solving it. It looks at the patterns and mechanisms that create the missing data, as well as a taxonomy of missing data. It then goes on to examine missing data in experiments, before discussing complete-case and available-case analysis, including weighting methods. The new edition expands its coverage to include recent work on topics such as nonresponse in sample surveys, causal inference, diagnostic methods, and sensitivity analysis, among a host of other topics. An updated "classic" written by renowned authorities on the subject Features over 150 exercises (including many new ones) Covers recent work on important methods like multiple imputation, robust alternatives to weighting, and Bayesian methods Revises previous topics based on past student feedback and class experience Contains an updated and expanded bibliography The authors were awarded The Karl Pearson Prize in 2017 by the International Statistical Institute, for a research contribution that has had profound influence on statistical theory, methodology or applications. Their work "has been no less than defining and transforming." (ISI) Statistical Analysis with Missing Data, Third Edition is an ideal textbook for upper undergraduate and/or beginning graduate level students of the subject. It is also an excellent source of information for applied statisticians and practitioners in government and industry.
Number theory : A Very Short Introduction by Robin Wilson (Editor)Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the 'building blocks' of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no-one has ever been able to resolve them.
Pythagoras' Legacy by Marcel DanesiAs the famous Pythagorean statement reads, "Number rules the universe", and its veracity is proven in the many mathematical discoveries that have accelerated the development of science, engineering, and even philosophy. A so called "art of the mind", mathematics has guided and stimulated manyaspects of human innovation down through the centuries.In this book, Marcel Danesi presents a historical overview of the ten greatest achievements in mathematics, and dynamically explores their importance and effects on our daily lives. Considered as a chain of events rather than isolated incidents, Danesi takes us from the beginnings of modern daymathematics with Pythagoras, through the concept of zero, right the way up to modern computational algorithms.Loaded with thought-provoking practical exercises and puzzles, Pythagoras' Legacy allows the reader to apply their knowledge and discover the significance of mathematics in their everyday lives.
Matrix Differential Calculus with Applications in Statistics and Econometrics by Jan Rudolph Magnus and Heinz NeudeckerMatrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioral sciences to econometrics. It is still relevant and used today in a wide range of subjects such as the biosciences and psychology. Matrix Differential Calculus with Applications in Statistics and Econometrics contains all of the essentials of multivariable calculus with an emphasis on the use of differentials. It starts by presenting a concise, yet thorough overview of matrix algebra, then goes on to develop the theory of differentials. The rest of the text combines the theory and application of matrix differential calculus, providing the practitioner and researcher with both a quick review and a detailed reference.
Introduction to Stochastic Differential Equations with Applications to Modelling in Biology and Finance by Carlos A. BraumannThis book offers a comprehensive examination of stochastic differential equations and their applications. The author — a noted expert in the field — includes myriad illustrative examples in modelling dynamical phenomena subject to randomness, mainly in biology, bioeconomics and finance, that clearly demonstrate the usefulness of stochastic differential equations in these and many other areas of science and technology.
The text also features real-life situations with experimental data, thus covering topics such as Monte Carlo simulation and statistical issues of estimation, model choice and prediction. The book includes the basic theory of option pricing and its effective application using real-life examples.
R Graphics Cookbook : Practical Recipes for Visualizing Data by Chang, WinstonWelcome to the R Graphics Cookbook, a practical guide that provides more than 150 recipes to help you generate high-quality graphs quickly, without having to comb through all the details of R’s graphing systems. Each recipe tackles a specific problem with a solution you can apply to your own project, and includes a discussion of how and why the recipe works.
R Cookbook : Proven Recipes for Data Analysis, Statistics, and Graphics by J.D. Long and Paul TeetorThe R language provides everything you need to do statistical work, but its structure can be difficult to master. These task-oriented recipes make you productive with R immediately. Solutions range from basic tasks to input and output, general statistics, graphics, and linear regression. Each recipe addresses a specific problem and includes a discussion that explains the solution and provides insight into how it works. If you're a beginner, R Cookbook will help get you started. If you're an intermediate user, this book will jog your memory and expand your horizons. You'll get the job done faster and learn more about R in the process
Advanced Numerical and Semi-analytical Methods for Differential Equations by Snehashish Chakraverty; Nisha Mahato; Perumandla Karunakar; Tharasi Dilleswar RaoThis student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along.
Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM).
Univariate, Bivariate, and Multivariate Statistics Using R : Quantitative Tools for Data Analysis and Data Science by Daniel J. DenisA practical source for performing essential statistical analyses and data management tasks in R Univariate, Bivariate, and Multivariate Statistics Using R offers a practical and very user-friendly introduction to the use of R software that covers a range of statistical methods featured in data analysis and data science. The author-- a noted expert in quantitative teaching --has written a quick go-to reference for performing essential statistical analyses and data management tasks in R. Requiring only minimal prior knowledge, the book introduces concepts needed for an immediate yet clear understanding of statistical concepts essential to interpreting software output. The author explores univariate, bivariate, and multivariate statistical methods, as well as select nonparametric tests. Altogether a hands-on manual on the applied statistics and essential R computing capabilities needed to write theses, dissertations, as well as research publications. The book is comprehensive in its coverage of univariate through to multivariate procedures, while serving as a friendly and gentle introduction to R software for the newcomer. This important resource: Offers an introductory, concise guide to the computational tools that are useful for making sense out of data using R statistical software Provides a resource for students and professionals in the social, behavioral, and natural sciences Puts the emphasis on the computational tools used in the discovery of empirical patterns Features a variety of popular statistical analyses and data management tasks that can be immediately and quickly applied as needed to research projects Shows how to apply statistical analysis using R to data sets in order to get started quickly performing essential tasks in data analysis and data science Written for students, professionals, and researchers primarily in the social, behavioral, and natural sciences, Univariate, Bivariate, and Multivariate Statistics Using R offers an easy-to-use guide for performing data analysis fast, with an emphasis on drawing conclusions from empirical observations. The book can also serve as a primary or secondary textbook for courses in data analysis or data science, or others in which quantitative methods are featured.
Just Enough R! : An Interactive Approach to Machine Learning and Analytics by Richard J. RoigerJust Enough R! An Interactive Approach to Machine Learning and Analytics presents just enough of the R language, machine learning algorithms, statistical methodology, and analytics for the reader to learn how to find interesting structure in data. The approach might be called "seeing then doing" as it first gives step-by-step explanations using simple, understandable examples of how the various machine learning algorithms work independent of any programming language. This is followed by detailed scripts written in R that apply the algorithms to solve nontrivial problems with real data. The script code is provided, allowing the reader to execute the scripts as they study the explanations given in the text. Features Gets you quickly using R as a problem-solving tool Uses RStudio's integrated development environment Shows how to interface R with SQLite Includes examples using R's Rattle graphical user interface Requires no prior knowledge of R, machine learning, or computer programming Offers over 50 scripts written in R, including several problem-solving templates that, with slight modification, can be used again and again Covers the most popular machine learning techniques, including ensemble-based methods and logistic regression Includes end-of-chapter exercises, many of which can be solved by modifying existing scripts Includes datasets from several areas, including business, health and medicine, and science About the Author Richard J. Roiger is a professor emeritus at Minnesota State University, Mankato, where he taught and performed research in the Computer and Information Science Department for over 30 years.
Applied Unsupervised Learning with R by Alok Malik and Bradford TuckfieldStarting with the basics, Applied Unsupervised Learning with R explains clustering methods, distribution analysis, data encoders, and features of R that enable you to understand your data better and get answers to your most pressing business questions. This book begins with the most important and commonly used method for unsupervised learning - clustering - and explains the three main clustering algorithms - k-means, divisive, and agglomerative. Following this, you'll study market basket analysis, kernel density estimation, principal component analysis, and anomaly detection. You'll be introduced to these methods using code written in R, with further instructions on how to work with, edit, and improve R code.
Graph Algorithms : Practical Examples in Apache Spark and Neo4j by Mark Needham and Amy E. HodlerLearn how graph algorithms can help you leverage relationships within your data to develop intelligent solutions and enhance your machine learning models. With this practical guide,developers and data scientists will discover how graph analytics deliver value, whether they’re used for building dynamic network models or forecasting real-world behavior.
Mark Needham and Amy Hodler from Neo4j explain how graph algorithms describe complex structures and reveal difficult-to-find patterns—from finding vulnerabilities and bottlenecks to detecting communities and improving machine learning predictions. You’ll walk through hands-on examples that show you how to use graph algorithms in Apache Spark and Neo4j, two of the most common choices for graph analytics.
Implementing CDISC Using SAS : An End-to-end Guide by Chris Holland; Jack ShostakFor decades researchers and programmers have used SAS to analyze, summarize, and report clinical trial data. Now Chris Holland and Jack Shostak have updated their popular Implementing CDISC Using SAS, the first comprehensive book on applying clinical research data and metadata to the Clinical Data Interchange Standards Consortium (CDISC) standards. Implementing CDISC Using SAS: An End-to-End Guide, Revised Second Edition, is an all-inclusive guide on how to implement and analyze the Study Data Tabulation Model (SDTM) and the Analysis Data Model (ADaM) data and prepare clinical trial data for regulatory submission. Updated to reflect the 2017 FDA mandate for adherence to CDISC standards, this new edition covers creating and using metadata, developing conversion specifications, implementing and validating SDTM and ADaM data, determining solutions for legacy data conversions, and preparing data for regulatory submission. The book covers products such as Base SAS, SAS Clinical Data Integration, and the SAS Clinical Standards Toolkit, as well as JMP Clinical. Topics included in this edition include an implementation of the Define-XML 2.0 standard, new SDTM domains, validation with Pinnacle 21 software, event narratives in JMP Clinical, STDM and ADAM metadata spreadsheets, and of course new versions of SAS and JMP software. The second edition was revised to add the latest C-Codes from the most recent release as well as update the make_define macro that accompanies this book in order to add the capability to handle C-Codes. The metadata spreadsheets were updated accordingly. Any manager or user of clinical trial data in this day and age is likely to benefit from knowing how to either put data into a CDISC standard or analyzing and finding data once it is in a CDISC format. If you are one such person--a data manager, clinical and/or statistical programmer, biostatistician, or even a clinician--then this book is for you.
An Invitation to Algebraic Numbers and Algebraic Functions by Franz Halter-KochThe author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekind's ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of difference, discriminants, and higher ramification. The theory of function fields is based on the ideal and valuation theory developed before; it presents the Riemann-Roch theorem on the basis of Weil differentials and highlights in detail the connection with classical differentials. The theory of congruence zeta functions and a proof of the Hasse-Weil theorem represent the culminating point of the volume. The volume is accessible with a basic knowledge in algebra and elementary number theory. It empowers the reader to follow the advanced number-theoretic literature, and is a solid basis for the study of the forthcoming volume on the foundations and main results of class field theory. Key features: * A thorough presentation of the theory of Algebraic Numbers and Algebraic Functions on an ideal and valuation-theoretic basis. * Several of the topics both in the number field and in the function field case were not presented before in this context. * Despite presenting many advanced topics, the text is easily readable. Franz Halter-Koch is professor emeritus at the university of Graz. He is the author of "Ideal Systems" (Marcel Dekker,1998), "Quadratic Irrationals" (CRC, 2013), and a co-author of "Non-Unique Factorizations" (CRC 2006).
Multivariate Time Series Analysis and Applications by William W. S. WeiAn essential guide on high dimensional multivariate time series including all the latest topics from one of the leading experts in the field Following the highly successful and much lauded book, Time Series Analysis--Univariate and Multivariate Methods, this new work by William W.S. Wei focuses on high dimensional multivariate time series, and is illustrated with numerous high dimensional empirical time series. Beginning with the fundamentalconcepts and issues of multivariate time series analysis,this book covers many topics that are not found in general multivariate time series books. Some of these are repeated measurements, space-time series modelling, and dimension reduction. The book also looks at vector time series models, multivariate time series regression models, and principle component analysis of multivariate time series. Additionally, it provides readers with information on factor analysis of multivariate time series, multivariate GARCH models, and multivariate spectral analysis of time series. With the development of computers and the internet, we have increased potential for data exploration. In the next few years, dimension will become a more serious problem. Multivariate Time Series Analysis and its Applications provides some initial solutions, which may encourage the development of related software needed for the high dimensional multivariate time series analysis. Written by bestselling author and leading expert in the field Covers topics not yet explored in current multivariate books Features classroom tested material Written specifically for time series courses Multivariate Time Series Analysis and its Applications is designed for an advanced time series analysis course. It is a must-have for anyone studying time series analysis and is also relevant for students in economics, biostatistics, and engineering.
Advanced Time Series Data Analysis : Forecasting Using EViews by I. Gusti Ngurah AgungIntroduces the latest developments in forecasting in advanced quantitative data analysis This book presents advanced univariate multiple regressions, which can directly be used to forecast their dependent variables, evaluate their in-sample forecast values, and compute forecast values beyond the sample period. Various alternative multiple regressions models are presented based on a single time series, bivariate, and triple time-series, which are developed by taking into account specific growth patterns of each dependent variables, starting with the simplest model up to the most advanced model. Graphs of the observed scores and the forecast evaluation of each of the models are offered to show the worst and the best forecast models among each set of the models of a specific independent variable. Advanced Time Series Data Analysis: Forecasting Using EViews provides readers with a number of modern, advanced forecast models not featured in any other book. They include various interaction models, models with alternative trends (including the models with heterogeneous trends), and complete heterogeneous models for monthly time series, quarterly time series, and annually time series. Each of the models can be applied by all quantitative researchers. Presents models that are all classroom tested Contains real-life data samples Contains over 350 equation specifications of various time series models Contains over 200 illustrative examples with special notes and comments Applicable for time series data of all quantitative studies Advanced Time Series Data Analysis: Forecasting Using EViews will appeal to researchers and practitioners in forecasting models, as well as those studying quantitative data analysis. It is suitable for those wishing to obtain a better knowledge and understanding on forecasting, specifically the uncertainty of forecast values.