Mathematics Books

Book SynopsisGeometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and this volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory.Table of Contents CAT(0) cube complexes and groups by M. Sageev Geometric small cancellation by V. Guirardel Lectures on proper CAT(0) spaces and their isometry groups by P.-E. Caprace Lectures on quasi-isometric rigidity by M. Kapovich Geometry of outer space by M. Bestvina Some arithmetic groups that do not act on the circle by D. W. Morris Lectures on lattices and locally symmetric spaces by T. Gelander Lectures on marked length spectrum rigidity by A. Wilkinson Expander graphs, property t and approximate groups by E. Breuillard Cube complexes, subgroups of mapping class groups, and nilpotent genus by M. R. Bridson

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Book SynopsisPresents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic $0$ and positive characteristic are emphasized.Table of Contents A crash course in commutative algebra Affine varieties Projective varieties Regular and rational maps of quasi-projective varieties Products The blow-up of an ideal Finite maps of quasi-projective varieties Dimension of quasi-projective algebraic sets Zariski's main theorem Nonsingularity Sheaves Applications to regular and rational maps Divisors Differential forms and the canonical divisor Schemes The degree of a projective variety Cohomology Curves An introduction to intersection theory Surfaces Ramification and etale maps Bertini's theorem and general fibers of maps Bibliography Index.

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Book SynopsisExam Board: MEILevel: A-levelSubject: MathematicsFirst Teaching: September 2017First Exam: June 2018An OCR endorsed textbookEncourage every student to develop a deeper understanding of mathematical concepts and their applications with textbooks that draw on the well-known MEI (Mathematics in Education and Industry) series, updated and tailored to the 2017 OCR (MEI) specification and developed by subject experts and MEI.- Develop problem-solving, proof and modelling skills with plenty of questions and well-structured exercises that build skills and mathematical techniques.- Build connections between topics, using real-world contexts to help develop mathematical modelling skills, thus providing a fuller and more coherent understanding of mathematical concepts.- Prepare students for assessment with practice questions written by subject experts.- Ensure coverage of the new st

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Book Synopsis Trigonometry: A Complete Introduction is the most comprehensive yet easy-to-use introduction to Trigonometry. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of trigonometry including the theory and equations of tangent, sine and cosine, using trigonometry in three dimensions and for angles for any magnitude, related to triangles. Everything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.

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Book SynopsisLike the best-selling first two editions, A Handbook of Statistical Analyses using R, Third Edition provides an up-to-date guide to data analysis using the R system for statistical computing. The book explains how to conduct a range of statistical analyses, from simple inference to recursive partitioning to cluster analysis.New to the Third Edition Three new chapters on quantile regression, missing values, and Bayesian inference Extra material in the logistic regression chapter that describes a regression model for ordered categorical response variables Additional exercises More detailed explanations of R code New section in each chapter summarizing the results of the analyses Updated version of the HSAUR package (HSAUR3), which includes some slides that can be used in introductory statistics courses Whether you're a data analyst, scientist, or student, this handTrade Review“I truly appreciate how grounded in practicality this book is—and the way its chapters are structured really underlines this. Furthermore, all the datasets are interesting and vary widely in subject matter. If nothing else, this book is an excellent source of examples one might use to illustrate a variety of statistical techniques. … it offers a lot of good places to start if one wants to analyze data. … The book comes hand-in-hand with an R package, HSAUR3, with all the data and the code used in the text. The book is thus fully reproducible. Overall, it provides a great way for a statistician to get started doing a wide variety of things in the R environment. It would be particularly useful, then, for working statisticians looking to change their software. The book cites all the relevant packages one might need, which is quite nice for those attempting to navigate the vast array of packages freely available, and is quite clear in its presentation of the code. Between this and the datasets, it makes for quite a valuable and enjoyable reference.”—The American Statistician, August 2015"… a handy primer for using R to perform standard statistical data analysis. … students, analysts, professors, and scientists: if you are looking to add R to your toolkit for analyzing data statistically, then this book will get you there."—Kendall Giles on his blog, September 2014Praise for the Second Edition:"I find the book by Everitt and Hothorn quite pleasant and bound to fit its purpose. The layout and presentation [are] nice. It should appeal to all readers as it contains a wealth of information about the use of R for statistical analysis. Included seasoned R users: When reading the first chapters, I found myself scribbling small lightbulbs in the margin to point out features of R I was not aware of. In addition, the book is quite handy for a crash introduction to statistics for (well-enough motivated) nonstatisticians."—International Statistical Review (2011), 79"… an extensive selection of real data analyzed with [R] … Viewed as a collection of worked examples, this book has much to recommend it. Each chapter addresses a specific technique. … the examples provide a wide variety of partial analyses and the datasets cover a diversity of fields of study. … This handbook is unusually free of the sort of errors spell checkers do not find."—MAA Reviews, April 2011Table of ContentsAn Introduction to R. Data Analysis Using Graphical Displays. Simple Inference. Conditional Inference. Analysis of Variance. Simple and Multiple Linear Regression. Logistic Regression and Generalized Linear Models. Density Estimation. Recursive Partitioning. Scatterplot Smoothers and Additive Models. Survival Analysis. Quantile Regression. Analyzing Longitudinal Data I. Analyzing Longitudinal Data II. Simultaneous Inference and Multiple Comparisons. Missing Values. Meta-Analysis. Bayesian Inference. Principal Component Analysis. Multidimensional Scaling. Cluster Analysis. Bibliography. Index.

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Book SynopsisIntegral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering. The book is suitable as a textbook for senior undergraduate and first-year graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic development of the underlying theory as well as a modern approach to Fourier, Laplace, Hankel, Mellin, Radon, Gabor, wavelet, and Z transforms and their applications. New to the Third Edition New material on the historical development of classical and modern integral transforms New sections on Fourier transforms of generalized functions, the Poisson summation formula, the Gibbs phenomenon, and the Heisenberg uncertainty principle Revised material on Laplace transforms and double Laplace transforms and their applications New examples of applications in mechanical Table of ContentsIntegral Transforms. Fourier Transforms and Their Applications. Laplace Transforms and Their Basic Properties. Applications of Laplace Transforms. Fractional Calculus and Its Applications. Applications of Integral Transforms to Fractional Differential Equations. Hankel Transforms and Their Applications. Mellin Transforms and Their Applications. Hilbert and Stieltjes Transforms. Finite Fourier Sine and Cosine Transforms. Finite Laplace Transforms. Z Transforms. Finite Hankel Transforms. Legendre Transforms. Jacobi and Gegenbauer Transforms. Laguerre Transforms. Hermite Transforms. The Radon Transform and Its Application. Wavelets and Wavelet Transforms. Appendices.

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Book SynopsisThis book presents a unified and up-to-date introduction to ROC methodologies, covering both diagnosis (classification) and prediction. The emphasis is on the conceptual underpinning of ROC analysis and the practical implementation in diverse scientific fields. A plethora of examples accompany the methodologic discussion using standard statistical software such as R and STATA. The book arrives after two decades of intensive growth in both the methods and the applications of ROC analysis and presents a new synthesis. The authors provide a contemporary, integrated exposition of ROC methodology for both classification and prediction and include material on multiple-class ROC. This book avoids lengthy technical exposition and provides code and datasets in each chapter. ROC Analysis for Classification and Prediction in Practice is intended for researchers and graduate students, but will also be useful for those that use ROC analysis in diverse disciplines such as diagnostic medicineTable of Contents1. Introduction 2. Measures of Diagnostic and Predictive Performance 3. Statistical inference for the ROC curve 4. Comparing ROC curves 5. The ROC surface and k-class classification for k > 2 6. ROC regression 7. Missing data and errors-in-variables in ROC analysis

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Book SynopsisGraph Theory and Its Applications, Third Edition is the latest edition of the international, bestselling textbook for undergraduate courses in graph theory, yet it is expansive enough to be used for graduate courses as well. The textbook takes a comprehensive, accessible approach to graph theory, integrating careful exposition of classical developments with emerging methods, models, and practical needs. The authorsâ unparalleled treatment is an ideal text for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.Features of the Third Edition Expanded coverage on several topics (e.g., applications of graph coloring and tree-decompositions) Provides better coverage of algorithms and algebraic and topological graph theory than any otherTable of ContentsIntroduction to Graph Models Graphs and Digraphs. Common Families of Graphs. Graph Modeling Applications. Walks and Distance. Paths, Cycles, and Trees. Vertex and Edge Attributes. Structure and Representation Graph Isomorphism. Automorphism and Symmetry. Subgraphs. Some Graph Operations. Tests for Non-Isomorphism. Matrix Representation. More Graph Operations. Trees Characterizations and Properties of Trees. Rooted Trees, Ordered Trees, and Binary Trees. Binary-Tree Traversals. Binary-Search Trees. Huffman Trees and Optimal Prefix Codes. Priority Trees. Counting Labeled Trees. Counting Binary Trees. Spanning Trees Tree Growing. Depth-First and Breadth-First Search. Minimum Spanning Trees and Shortest Paths. Applications of Depth-First Search. Cycles, Edge-Cuts, and Spanning Trees. Graphs and Vector Spaces. Matroids and the Greedy Algorithm. Connectivity Vertex and Edge-Connectivity. Constructing Reliable Networks. Max-Min Duality and Menger’s Theorems. Block Decompositions. Optimal Graph Traversals Eulerian Trails and Tours. DeBruijn Sequences and Postman Problems. Hamiltonian Paths and Cycles. Gray Codes and Traveling Salesman Problems. Planarity and Kuratowski’s Theorem Planar Drawings and Some Basic Surfaces. Subdivision and Homeomorphism. Extending Planar Drawings. Kuratowski’s Theorem. Algebraic Tests for Planairty. Planarity Algorithm. Crossing Numbers and Thickness. Graph Colorings Vertex-Colorings. Map-Colorings. Edge-Colorings. Factorization. Special Digraph Models Directed Paths and Mutual Reachability. Digraphs as Models for Relations. Tournaments. Project Scheduling. Finding the Strong Components of a Digraph. Network Flows and Applications Flows and Cuts in Networks. Solving the Maximum-Flow Problem. Flows and Connectivity. Matchings, Transversals, and Vertex Covers. Graph Colorings and Symmetry Automorphisms of Simple Graphs. Equivalence Classes of Colorings. Appendix

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Book SynopsisExpert Guidance on the Math Needed for 3D Game ProgrammingDeveloped from the authors' popular Game Developers Conference (GDC) tutorial, Essential Mathematics for Games and Interactive Applications, Third Edition illustrates the importance of mathematics in 3D programming. It shows you how to properly animate, simulate, and render scenes and discusses the mathematics behind the processes.New to the Third EditionCompletely revised to fix errors and make the content flow better, this third edition reflects the increased use of shader graphics pipelines, such as in DirectX 11, OpenGL ES (GLES), and the OpenGL Core Profile. It also updates the material on real-time graphics with coverage of more realistic materials and lighting.The Foundation for Successful 3D ProgrammingThe book covers the low-level mathematical and geometric representations and algorithms that are the core of any game engine. It also explores all thTrade ReviewPraise for Previous Editions:"It’s the book with all the math you need for games."—Neil Kirby, Researcher, Alcatel-Lucent"Even though I’ve worked with these systems for years, this book showed me new ways of looking at several topics that make them easier to remember and use. For someone new to 3D programming, it is extremely useful—it gives them a solid background in pretty much every area they need to understand."—Peter Lipson, Toys for Bob, Inc.Table of ContentsRepresenting Real Numbers. Vectors and Points. Linear Transformations and Matrices. Affine Transformations. Orientation Representation. Interpolation. Viewing and Projection. Geometry and Programmable Shading. Lighting. Rasterization. Random Numbers. Intersection Testing. Rigid-Body Dynamics.

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Book SynopsisThis book focuses on a development of optimal, flexible, and efficient models and algorithms for cell formation in group technology. Its main aim is to provide a reliable tool that can be used by managers and engineers to design manufacturing cells based on their own preferences and constraints imposed by a particular manufacturing system.Trade Review“The book under review is a very good source … continuing the long term passion of Panos Pardalos and his collaborators in exact solution of difficult problems … . It also adds a very valuable contribution to the body of knowledge of the cell formation problem that can be used in both teaching and research including in bioinformatics.” (Boris Mirkin, Optimization Letters, 2015)Table of Contents1. The problem of cell formation.- 2. ​The p-Median problem.- 3. Application of the PMP to cell formation in group technology.- 4. The minimum multicut problem and an exact model for cell formation.- 5. Multiobjective nature of cell formation.- 6. Pattern-based heuristic for the cell formation problem in group technology.- 7. Branch-and-bound algorithm for bi-criterion cell formation problems.- 8. Summary and conclusions.- A. Solutions to the 35 CF instances from [71].- Index.- References.

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Book SynopsisEmpirical research has now become an essential component of software engineering yet software practitioners and researchers often lack an understanding of how the empirical procedures and practices are applied in the field. Empirical Research in Software Engineering: Concepts, Analysis, and Applications shows how to implement empirical research processes, procedures, and practices in software engineering.Written by a leading researcher in empirical software engineering, the book describes the necessary steps to perform replicated and empirical research. It explains how to plan and design experiments, conduct systematic reviews and case studies, and analyze the results produced by the empirical studies. The book balances empirical research concepts with exercises, examples, and real-life case studies, making it suitable for a course on empirical software engineering. The author discusses the process of developing predictive models, such asTrade Review"In this book, Dr. Malhotra uses her breadth of software engineering experience and expertise to give the reader coverage of many aspects of empirical software engineering. She covers the essential techniques and concepts needed for a researcher to get started on empirical software engineering research, including metrics, experimental design, analysis and statistical techniques, threats to the validity of any research findings, and methods and tools for empirical software engineering research. … The book provides the reader with an introduction and overview of the field and is also backed by references to the literature, allowing the interested reader to follow up on the methods, tools, and concepts described."—From the Foreword by Mark Harman, University College LondonTable of ContentsIntroduction. Systematic Literature Reviews. Software Metrics. Experimental Design. Mining Data from Software Repositories. Data Analysis and Statistical Testing. Model Development and Interpretation. Validity Threats. Reporting Results. Mining Unstructured Data. Demonstrating Empirical Procedures. Tools for Analyzing Data. Appendix. References. Index.

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Book SynopsisMathematical Statistics: Basic Ideas and Selected Topics, Volume II presents important statistical concepts, methods, and tools not covered in the authors' previous volume. This second volume focuses on inference in non- and semiparametric models. It not only reexamines the procedures introduced in the first volume from a more sophisticated point of view but also addresses new problems originating from the analysis of estimation of functions and other complex decision procedures and large-scale data analysis.The book covers asymptotic efficiency in semiparametric models from the Le Cam and Fisherian points of view as well as some finite sample size optimality criteria based on LehmannScheffé theory. It develops the theory of semiparametric maximum likelihood estimation with applications to areas such as survival analysis. It also discusses methods of inference based on sieve models and asymptotic testing theory. The remainder of the book is devoted to Trade Review" . . . the authors have done a superb job of selecting topics comprising most of the essential knowledge needed formodern research. Furthermore, these modern topics are considered with greater depth and sophistication than is usual in a general purpose text. And throughout its pages the book does a good job of linking the mathematical developments to major examples. The choice of topics and examples, along with the depth of coverage are the most attractive features of this volume."~RobertW. Keener, University of MichiganTable of ContentsIntroduction and Examples. Tools for Asymptotic Analysis. Distribution-Free, Unbiased, and Equivariant Procedures. Inference in Semiparametric Models. Monte Carlo Methods. Nonparametric Inference for Functions of One Variable. Prediction and Machine Learning. Appendices. References. Indices.

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Book SynopsisThis book is among the first to present the mathematical models most commonly used to solve optimal execution problems and market making problems in finance. The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making presents a general modeling framework for optimal execution problemsinspired from the Almgren-Chriss approachand then demonstrates the use of that framework across a wide range of areas.The book introduces the classical tools of optimal execution and market making, along with their practical use. It also demonstrates how the tools used in the optimal execution literature can be used to solve classical and new issues where accounting for liquidity is important. In particular, it presents cutting-edge research on the pricing of block trades, the pricing and hedging of options when liquidity matters, and the management of complex share buy-back contracts.What sets this book apart from others is that it focuses onTrade Review"This excellent monograph covers the mathematical theory of market microstructure with particular emphasis in models of optimal execution and market making. Gueant’s book is a superb introduction to these topics for graduate students in mathematical finance or quants who want to work in execution algorithms or market-making strategies."—Jose A. Scheinkman, Charles and Lynn Zhang Professor of Economics, Columbia University, and Theodore Wells '29 Professor of Economics Emeritus, Princeton University"This is a very timely book that cuts across various fields (applied mathematics, operations research, and quantitative finance). Execution costs due to market illiquidity can significantly reduce returns on investment strategies and, for this reason, affect asset prices. It is therefore important to design trading strategies minimizing these costs and to account for their effect on prices. In the last decade, ‘quants’ and researchers in quantitative finance have made considerable progress on these issues, integrating in their models changes in the way financial markets work (e.g., the development of continuous limit order books, market fragmentation, dark pools, the automation of trading, etc.). "Olivier Guéant’s book takes stock of this effort by providing a rigorous and expert presentation of mathematical tools, models, and numerical methods developed in this area. I strongly recommend it for researchers and graduate students interested in how illiquidity costs affect trading strategies and should be accounted for in asset valuation problems."—Thierry Foucault, HEC Foundation Chair Professor of Finance, HEC, Paris"This book is a must-have for quantitative analysts working at algorithmic trading desks. Olivier Guéant could have written a sophisticated book dedicated to cutting-edge research. He rather decided to put his talent at the service of a far more difficult task: deliver a clear view of modern algorithmic trading to strats or quants having decent scientific training. Scientists will find here all the needed keys to control the intraday risk of their trading models, improving their overall efficiency. Covering brokerage algorithms, market making, hedging, and share buyback techniques, this book is the definitive reference for algorithm builders.Moreover, Olivier links algorithmic trading with market microstructure during the first chapter of the book, including interesting thoughts on corporate bonds trading. On the other hand, he provides a nice introduction to mathematical economics in the Appendix. This book is resolutely more than a bunch of equations thrown on blank pages. I consider it an important step forward in the building of the mathematics of market microstructure."—Charles-Albert Lehalle, Senior Research Advisor, Capital Fund ManagementTable of ContentsIntroduction. Optimal Liquidation. Liquidity in Pricing Models. Market Making.

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Book SynopsisIn knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns (generators). Diagram Genus, Generators and Applications presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems.The book begins with an introduction to the origin of knot tables and the background details, including diagrams, surfaces, and invariants. It then derives a new description of generators using Hirasawa's algorithm and extends this description to push the compilation of knot generators one genus further to complete their classification for genus 4. Subsequent chapters cover applications of the genus 4 classification, including the braid index, polynomial invariants, hyperbolic volume, and Vassiliev invariants. The final chapter presents further research related to generators, which helps rTrade Review"Diagram Genus, Generators and Applications contains a systematical study of combinatorial properties of knot diagrams. It focuses on diagrams that represent the canonical genus of a knot, i.e., the minimal genus of all Seifert surfaces for a given knot that are obtained by applying Seifert’s algorithm to diagrams of the knot. The book contains the complete classification of knots up to canonical genus 4. This classification has lots of applications … The book … will certainly become a reference in this area. It is very clearly written and contains enough background material so that it can be used by graduate-level students to learn the subject and do work in this area on their own."—Thomas Fiedler, Institut de Mathématiques, Université Paul Sabatier, Toulouse"This book provides an essential resource for anyone currently doing research or interested in doing research on surfaces in knot complements and their applications. Enough background is included so non-experts can follow the exposition and appreciate the myriad results that ensue."—Professor Colin Adams, Williams College"This monograph is a systematic account of combinatorial knot theory, with a particular focus on spanning surfaces arising from Seifert’s construction. It includes a brief and nicely written introduction to knot theory, concentrating on the background needed for a diagrammatic treatment of knots, including the range of classical and modern knot polynomials.A strong feature of this book, and indeed much of the author’s work elsewhere, is the identification of diagrammatic examples with awkward or unexpected properties, and an analysis of the techniques that can be used effectively on them. This can provide examples that can’t possibly be tackled by certain procedures, and thus directs attention to places where the current repertoire of techniques is lacking.The main topic developed is the notion of diagram genus, or canonical genus, based on Seifert’s algorithm. The related graph theory leads to the selection of a class of alternating knot diagrams, termed generators, and a substantial account of these up to genus 4 is given.This is followed by the discussion of a number of combinatorial results and conjectures. In particular, some nice results for alternating or positive knots are given and their possible extension to the case when k of the knot crossings are switched is explored for small values of k. The earlier calculations are used to extend the knowledge of these results to cover knots with fewer restrictions on their genus or crossing number.There is a good account of the combinatorics for recognizing when a knot diagram actually represents the trivial knot. It is surprisingly easy to draw diagrams of the trivial knot with relatively few crossings that do not have an immediately obvious simplification, and some examples are included in the illustrations.A further section covers the question of finding the braid index for an alternating knot, and the conditions under which the Morton-Franks-Williams bound turn out to be sharp. The concluding section is intended as an appetizer for others and includes a variety of annotated questions and conjectures.The carefully written text is aimed at a graduate-level readership. It gives a comprehensive view of combinatorial questions, both in the monograph itself and in the well-annotated bibliography, and would serve both well as a reference and a source of new ideas.Features A comprehensive account of diagram-centered results in knot theory Focus on Seifert’s construction of oriented-spanning surfaces Analysis of diagrams representing the unknot and their reduction by Reidemeister moves Careful and persuasive writing An excellent reference text and source of ideas" —H.R. Morton, Department of Mathematical Sciences, University of LiverpoolTable of ContentsIntroduction. Preliminaries. The Maximal Number of Generator Crossings and ~-Equivalance Classes. Generators of Genus 4. Unknot Diagrams, Non-Trivial Polynomials, and Achiral Knots. The Signature. Braid Index of Alternating Knots. Minimal String Bennequin Surfaces. The Alexander Polynomial of Alternating Knots. Outlook.

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Book SynopsisIntroduction to Functional Data Analysis provides a concise textbook introduction to the field. It explains how to analyze functional data, both at exploratory and inferential levels. It also provides a systematic and accessible exposition of the methodology and the required mathematical framework.The book can be used as textbook for a semester-long course on FDA for advanced undergraduate or MS statistics majors, as well as for MS and PhD students in other disciplines, including applied mathematics, environmental science, public health, medical research, geophysical sciences and economics. It can also be used for self-study and as a reference for researchers in those fields who wish to acquire solid understanding of FDA methodology and practical guidance for its implementation. Each chapter contains plentiful examples of relevant R code and theoretical and data analytic problems.The material of the book can be roughly divided into four parts of approximaTrade Review"This well-written book provides a great and intuitive introduction to functional data analysis (FDA) which has emerged as an important area in statistics and found tons of scientific applications...This book succeeds at introducing this novel statistical concept and methodology while keeps the level of mathematical and statistical sophistication required to understand at the level of an introductory graduate-level course, which makes for pleasant reading. A nice feature of the book is its strong focus on implementation using R, which makes it a great candidate of textbooks or reference books for (master-level) graduate students and applied researchers...Some unique features of this book as compared to existing ones include (1) its strong focus on implementation using R; (2) chapters on Sparse FDA, generalized functional linear models, functional time series, and spatial functional data; (3) well-designed exercises that can be used as homework problems." ~Xianyang Zhang, Texas A&M University"The main advantage of the book is its emphasis introducing the material through realistic examples and computational tools, while also providing mathematical guidance for the methodologies. Also, important topics like functional time series and spatial functional data are not adequately covered in comparable texts like Ramsay and Silverman, Ramsay and Hooker, Ferraty and Vieu, and Hsing and Eubank. In that respect, the book offers additional and practically relevant material and perspective." ~Debashis Paul, University of California, Davis"The classic tools from the field of functional data analysis are introduced comprehensively and immediately put into a framework of potential application. I would probably advise any reader that is new to functional data analysis to start by reading this book." ~Claudia Klüppelberg, Technische Universität München"Being more advanced and up to date than the Ramsay and Silverman, it complements various topics that are just briefly mentioned or not covered at all by Ramsay and Silverman." ~Laura Sangali, Politecnico di Milano"As a relatively young subfield of statistics, functional data analysis (FDA) has not had a large glut of textbooks pertaining to it. The most famous of the FDA books is the classic text by J. O. Ramsay and B. W. Silverman [Functional data analysis, Springer Ser. Statist., Springer, New York, 1997; second edition, 2005; MR2168993], which introduced many statisticians to the area. Ramsay and Silverman [Applied functional data analysis, Springer Ser. Statist., Springer, New York, 2002; MR1910407] provided a useful collection of FDA case studies, and Ramsay, G. Hooker and S. Graves [Func-tional data analysis with R and MATLAB, Use R, Springer, New York, 2009, doi:10. 1007/978-0-387-98185-7] presented R and MATLAB code for analyzing real functional data sets. [F. Ferraty and P. Vieu, Nonparametric functional data analysis, Springer Ser. Statist., Springer, New York, 2006; MR2229687] and [T. Hsing and R. L. Eubank, Theoretical foundations of functional data analysis, with an introduction to linear opera- tors, Wiley Ser. Probab. Stat., Wiley, Chichester, 2015; MR3379106] are well-respected theoretical presentations of FDA.This book by Kokoszka and Reimherr provides a nice mix of foundational material, accessible theory, and practical examples (including much R code). It is a valuable addition to the FDA literature, and is perhaps an ideal choice of a course textbook for either an undergraduate or graduate course in FDA, whereas several of the other textbooks are more valuable as references for researchers and practitioners than as tutorials for learners. At the end of each chapter is a nice variety of problems that instructors could use for homework assignments.Chapter 1 introduces basic terminology related to FDA, such as the ubiquitous tool of basis expansion and the distinction between dense and sparse functional data. Summary statistics and plots (sample mean and covariance functions, principal components analysis (PCA), functional boxplots) for FDA are briey presented. Chapter 2 continues basic FDA topics with a discussion of derivative information, penalized smoothing, and alignment/registration of curves.The theoretical underpinnings of FDA are presented quickly in Chapter 3, where topics such as square integrable functions, random functions following some distribution, and operator theory are defined briey. A fuller coverage of theoretical concerns is saved for (the optional in a course setting) Chapters 10 and 11. The heart of the book is Chapters 4 through 9, which cover functional linear models in detail, before moving on to specialized FDA topics such as sparse FDA, functionaltime series, and spatial functional data. Scalar-on-function regression, in which the response is a scalar and the predictor is a function, is treated in Chapter 4, and illustrated via the use of the refund package in R. Nonlinear scalar-on-function regression is briey mentioned. Chapter 5 covers both the function-on-scalar regression case and the fully functional regression model in which both response and predictor are functions. Testing and validation of the functional linear model are also shown. Chapter 6 covers functional generalized linear models (GLMs) which have a nonnormal scalar response and a functional predictor. The somewhatnebulous situation with functional-response GLMs is briey covered as well. The next chapter deals with sparse functional data, and presents methods for mean function estimation, covariance function estimation, PCA, and regression in the sparse case when relatively few points are measured for each observed curve. Functional time series occur when the sample functions are observed sequentially over time rather than cross-sectionally. The assumption of independent functional data fails in this case, and Chapter 8 presents a functional autoregressive model for such data that can be used for forecasting. Spatial functional data may commonly be encountered in geostatistics when curves are observed both over time and at various spatial locations. Chapter 9 discusses models for such data and prediction using functional kriging. Chapter 12 discusses treating a functional data set as a sample from some population of functions and performing inference on the population. Of particular interest are the methods presented for formal hypothesis tests and confidence bands about the population mean function.Clustering and classification of functional data are not discussed in detail in thisbook, nor is FDA on manifolds, although references are given to guide readers to recentresearch in these areas."~David Benner HitchcockTable of ContentsFirst steps in the analysis of functional data Basis expansions Sample mean and covariance Principal component functions Analysis of BOA stock returns Diffusion tensor imaging Problems Further topics in exploratory FDA Derivatives Penalized smoothing Curve alignment Further reading Problems Mathematical framework for functional data Square integrable functions Random functions Linear transformations Scalar- on - function regressionExamples Review of standard regression theory Difficulties specific to functional regression Estimation through a basis expansion Estimation with a roughness penalty Regression on functional principal components Implementation in the refund package Nonlinear scalar-on-function regression Problems Functional response models Least squares estimation and application to angular motionPenalized least squares estimation Functional regressors Penalized estimation in the refund package Estimation based on functional principal components Test of no effectVerification of the validity of a functional linear model Extensions and further reading Problems Functional generalized linear models Background Scalar-on-function GLM's Functional response GLM Implementation in the refund package Application to DTI Further reading Problems Sparse FDA Introduction Mean function estimationCovariance function estimation Sparse functional PCA Sparse functional regression Problems Functional time seriesFundamental concepts of time series analysis Functional autoregressive process Forecasting with the Hyndman-Ullah methodForecasting with multivariate predictors Long-run covariance function Testing stationarity of functional time series Generation and estimation of the FAR(1) model using package fda Conditions for the existence of the FAR(1) process Further reading and other topics Problems Spatial functional data and modelsFundamental concepts of spatial statistics Functional spatial fields Functional kriging Mean function estimation Implementation in the R package geofd Other topics and further reading Problems Elements of Hilbert space theoryHilbert space Projections and orthonormal sets Linear operators Basics of spectral theory Tensors ProblemsRandom functions Random elements in metric spaces Expectation and covariance in a Hilbert space Gaussian functions and limit theorems Functional principal components ProblemsInference from a random sampleConsistency of sample mean and covariance functions Estimated functional principal components Asymptotic normality Hypothesis testing about the mean Confidence bands for the mean Application to BOA cumulative returns Proof of Theorem Problems

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Book SynopsisGeneralized Linear Mixed Models: Modern Concepts, Methods, and Applications (2nd edition) presents an updated introduction to linear modeling using the generalized linear mixed model (GLMM) as the overarching conceptual framework. For students new to statistical modeling, this book helps them see the big picture linear modeling as broadly understood and its intimate connection with statistical design and mathematical statistics. For readers experienced in statistical practice, but new to GLMMs, the book provides a comprehensive introduction to GLMM methodology and its underlying theory.Unlike textbooks that focus on classical linear models or generalized linear models or mixed models, this book covers all of the above as members of a unified GLMM family of linear models. In addition to essential theory and methodology, this book features a rich collection of examples using SAS software to illustrate GLMM practice. This second edition is updated to reflect les

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Book SynopsisElementary Probability with Applications, Second Edition shows students how probability has practical uses in many different fields, such as business, politics, and sports. In the book, students learn about probability concepts from real-world examples rather than theory.The text explains how probability models with underlying assumptions are used to model actual situations. It contains examples of probability models as they relate to: Bloc voting Population genetics Doubling strategies in casinos Machine reliability Airline management Cryptology Blood testing Dogs resembling owners Drug detection Jury verdicts Coincidences Number of concert hall aisles 2000 U.S. presidential election Points after deuce in tennis Tests regarding intelligent dogs Music composition Based on the author's course at TheTrade ReviewPraise for the First Edition:"It is desirable that all citizens have an elementary understanding of probability [so] that they better appreciate the uncertainty that surrounds them. Anyone teaching such citizens should consider using this book because, through its applications, it conveys something of the power of probability."—D.V. Lindley, Mathematical Gazette, November 2006"This book was surprisingly refreshing and did a great job using real situations to motivate techniques for calculating discrete probabilities."—Technometrics, August 2006"The problems are graded from fairly straightforward to very challenging and the book is, for this reason at least, a welcome addition to the literature."—MAA Reviews, October 2005"This book would be excellent for a minicourse at a higher level of high school as well as a semester course at the college level."—Larry White, National Council of Teachers of Mathematics (NCTM), October 2005"The chosen approach is practical and entertaining. The book is a useful tool for teachers and anybody interested in basic ideas and applications of classical probability theory."—EMS Newsletter, June 2005Table of ContentsBasic Concepts in Probability. Conditional Probability and the Multiplication Rule. Independence. Combining the Addition and Multiplication Rules. Combining the Addition and Multiplication Rules—Applications. Random Variables, Distributions, and Expected Values. Joint Distributions and Conditional Expectations. Sampling without Replacement. Sampling with Replacement. Sampling with Replacement (Continued). Binomial Tests. Appendix. Short Answers to Selected Exercises. Bibliography. Index.

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Book SynopsisThe newest addition to our Influential Video Game Designers series explores the work of Todd Howard, executive producer at Bethesda Studios, known for how he consistently pushes the boundaries of open-world gaming and player agency. Howard's games create worlds in which players can design their own characters and tell their own stories. While many games tell the story of the game's main character, Todd Howard's worldbuilding approach to game design focuses more on telling the story of the game's world, whether it be the high fantasy environments of the Elder Scrolls series or the post-apocalyptic wasteland of the Fallout series. This focus on sculpting the world allows for remarkable amounts of player freedom and choice in an expansive game environment by creating a landscape rich with open opportunity. Drawing on both academic discussions of narrative, world design, and game design, as well as on officially released interviews, speeches, and presentations given by HowardTrade ReviewIn Todd Howard: Worldbuilding in Tamriel and Beyond, Wendi Sierra illuminates this beloved game developer's mind, his struggles and passions, the history of his career from humble beginnings to towering success, and his visions for the future of games. Choosing to highlight his excellence in worldbuilding, she examines how rich, expansive game worlds like Tamriel keep players coming back again and again, logging hundreds or even thousands of in-game hours trudging up and down snowy mountains, collecting herbs, ore, and flowers, and questing for colorful NPCs—and for the sake of a compelling story in which they are the protagonist. This book is an essential guide to one of the greatest worldbuilders in the history of fantasy, and it belongs on the shelves of game scholars and game lovers alike. * Lauren Woolbright, Assistant Professor of Communication and New Media Studies, Alma College, USA *Table of Contents1: An Unlikely Beginning 2: Little Catastrophes 3: Set Pieces for Player Experience 4: Expanding the Game World 5: Todd Howard: In His Own Words 6: The Future of Open World Gaming Appendix - Chronology of Works Bibliography Index

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Book SynopsisDevelop a deeper understanding of mathematical concepts and their applications with new and updated editions from our bestselling series.- Build connections between topics using real-world contexts that develop mathematical modelling skills, thus providing your students with a fuller and more coherent understanding of mathematical concepts.- Develop fluency in problem-solving, proof and modelling with plenty of questions and well-structured exercises.- Overcome misconceptions and develop mathematical insight with annotated worked examples.- Enhance understanding and map your progress with graduated exercises that support you at every stage of your learning.

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Book SynopsisExam board: EdexcelLevel: A-levelSubject: MathematicsFirst teaching: September 2017First exams: Summer 2018Target success in Edexcel A Level Mathematics with this proven formula for effective, structured revision; key content coverage and plentiful worked examples are combined with exam-style and multiple choice questions to create a revision guide that students can rely on to review, strengthen and test their knowledge.- Help develop the key skills needed for success with skills-focused questions around problem-solving, proof, modelling and the use of ICT (spreadsheets, graphing software and graphing calculators).- Strategically target revision with diagnostic questions to establish which areas need focus. - Get assessment-ready with exam-style questions and advice on common examination pitfalls.- Embed knowledge and identify weaknesses with hundreds of multiple choice 'Test Yourself' questions, all carefully written to elicit misconceptions; full worked solutions online offer detailed, instructive explanations for all choices (whether they are correct or incorrect)- Consolidate revision with summaries for each topic that focus on what to concentrate on in the build-up to exams, with special focus on common pitfalls such as how to show correct workings.-Access answers at the back of the book, with detailed step-by-step worked solutions for ALL questions available for free online.Includes all Year 1 and Year 2 A-level Maths content.

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Book SynopsisExam board: OCRLevel: A-levelSubject: MathematicsFirst teaching: September 2017First exams: Summer 2018Benefit from the expert input of experienced examiners and subject specialists including Heather Davis in this assessment-led Practice Book; tailored to the new 2017 specifications and packed with exam-style questions.- Thoroughly prepare your students for the exam with over 200 exam-style questions that are matched to the new specifications.- Provide structured support and extra practice with questions focused on problem-solving, modelling and technology.- Create opportunities for self-directed learning and assessment with answers at the back of the book, plus full step-by-step worked solutions and mark schemes supplied online.- Enhance learning with extra practice designed to supplement the textbooks and the My Revision Notes series.

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Book SynopsisReinforce learning and deepen understanding of the key concepts covered in the syllabus; an ideal course companion or homework book for use throughout the course.- Develop and strengthen skills and knowledge with a wealth of additional exercises that perfectly supplement the Student's Book- Build confidence with extra practice for each lesson to ensure that a topic is thoroughly understood before moving on- Ensure students know what to expect with hundreds of rigorous practice and exam-style questions.- Keep track of students' work with ready-to-go write-in exercises- Save time with all answers available for free online: www.hoddereducation.co.uk/cambridgeextras.This title has not been through the Cambridge Assessment International Education endorsement process.Available in this series:Five textbooks fully covering the latest Cambridge International AS & A Level Mathematics syllabus (9709) are accompanied by a Workbook, and Student and Whiteboard eTextbooks.Pure Mathematics 1: Student Textbook (ISBN 9781510421721), Student eTextbook (ISBN 9781510420762), Whiteboard eTextbook (ISBN 9781510420779), Workbook (ISBN 9781510421844)Pure Mathematics 2 and 3: Student Textbook (ISBN 9781510421738), Student eTextbook (ISBN 9781510420854), Whiteboard eTextbook (ISBN 9781510420878), Workbook (ISBN 9781510421851)Mechanics: Student Textbook (ISBN 9781510421745), Student eTextbook (ISBN 9781510420953), Whiteboard eTextbook (ISBN 9781510420977), Workbook (ISBN 9781510421837)Probability & Statistics 1: Student Textbook (ISBN 9781510421752), Student eTextbook (ISBN 9781510421066), Whiteboard eTextbook (ISBN 9781510421097), Workbook (ISBN 9781510421875)Probability & Statistics 2: Student Textbook (ISBN 9781510421776), Student eTextbook (ISBN 9781510421158), Whiteboard eTextbook (ISBN 9781510421165), Workbook (9781510421882)

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Book SynopsisThis book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less familiar octonion algebra, concentrating on its remarkable "triality symmetry" after an appropriate study of Moufang loops. The authors also describe the arithmetics of the quaternions and octonions. The book concludes with a new theory of octonion factorization. Topics covered include the geometry of complex numbers, quaternions and 3-dimensional groups, quaternions and 4-dimensional groups, Hurwitz integral quaternions, composition algebras, Moufang loops, octonions and 8-dimensional geometry, integral octonions, and the octonion projective plane.Trade Review"Conway and Smith’s book is a wonderful introduction to the normed division algebras … They develop these number systems from scratch, explore their connections to geometry, and even study number theory in quaternionic and octonionic versions of the integers. … a lucid and elegant introduction. … remarkably self-contained. It assumes no knowledge of number theory, string theory, Lie theory, or lower-case Gothic letters."—John C. Baez, Bulletin of the American Mathematical Society, January 2005"A resonant spike above background noise in one parameter as another parameter is varied is a frequent indicator…"—Geoffrey Dixon, Mathematical Intelligencer, May 2004"Those readers who are fascinated by the links between geometry and groups will find that this book gives them new insights."—Hugh Williams, The Mathematical Gazette, July 2004"This is a beautiful and fascinating book on the geometry and arithmetic of the quaternion algebra and the octonion algebra. … most intriguing to read: it is an excellent exposition of very attractive topics, and it contains several new and significant results."—Theo Grundhöfer, Mathematical Reviews, 2003Table of ContentsPreface, I The Complex Numbers, 1 Introduction, 1.1 The Algebra ℝ of Real Numbers, 1.2 Higher Dimensions, 1.3 The Orthogonal Groups, 1.4 The History of Quaternions and Octonions, 2 Complex Numbers and 2-Dimensional Geometry, 2.1 Rotations and Reflections, 2.2 Finite Subgroups of GO2 and SO2, 2.3 The Gaussian Integers, 2.4 The Kleinian Integers, 2.5 The 2-Dimensional Space Groups, II The Quaternions, 3 Quaternions and 3-Dimensional Groups, 3.1 The Quaternions and 3-Dimensional Rotations, 3.2 Some Spherical Geometry, 3.3 The Enumeration of Rotation Groups, 3.4 Discussion of the Groups, 3.5 The Finite Groups of Quaternions, 3.6 Chiral and Achiral,Diploid and Haploid, 3.7 The Projective or Elliptic Groups, 3.8 The Projective Groups Tell Us All, 3.9 Geometric Description of the Groups, Appendix: v → v̄qv Is a Simple Rotation, 4 Quaternions and 4-Dimensional Groups, 4.1 Introduction, 4.2 Two 2-to-1Maps, 4.3 Naming the Groups, 4.4 Coxeter’s Notations for the Polyhedral Groups, 4.5 Previous Enumerations, 4.6 A Note on Chirality, Appendix: Completeness of the Tables, 5 The Hurwitz Integral Quaternions, 5.1 The Hurwitz Integral Quaternions, 5.2 Primes and Unit, 5.3 Quaternionic Factorization of Ordinary Primes, 5.4 The Metacommutation Problem, 5.5 Factoring the Lipschitz Integers, III The Octonions, 6 The Composition Algebras, 6.1 TheMultiplication Laws, 6.2 The Conjugation Laws, 6.3 The Doubling Laws, 6.4 Completing Hurwitz’s Theorem, 6.5 Other Properties of the Algebras, 6.6 The Maps Lx,Rx,and Bx, 6.7 Coordinates for the Quaternions and Octonions, 6.8 Symmetries of the Octonions: Diassociativity, 6.9 The Algebras over Other Fields, 6.10 The 1-,2-,4-,and 8-Square Identities, 6.11 Higher Square Identities: Pfister Theory, Appendix: What Fixes a Quaternion Subalgebra?, 7 Moufang Loops, 7.1 Inverse Loops, 7.2 Isotopies, 7.3 Monotopies and Their Companions, 7.4 Different Forms of the Moufang Laws, 8 Octonions and 8-Dimensional Geometry, 8.1 Isotopies and SO8, 8.2 Orthogonal Isotopies and the Spin Group, 8.3 Triality, 8.4 Seven Rights Can Make a Left, 8.5 Other Multiplication Theorems, 8.6 Three 7-Dimensional Groups in an 8-Dimensional One, 8.7 On Companions, 9 The Octavian Integers O, 9.1 Defining Integrality, 9.2 Toward the Octavian Integers, 9.3 The E8 Lattice of Korkine,Zolotarev,and Gosset, 9.4 Division with Remainder,and Ideals, 9.5 Factorization in O8, 9.6 The Number of Prime Factorizations, 9.7 “Meta-Problems” for Octavian Factorization, 10 Automorphisms and Subrings of O, 10.1 The 240Octavian Units, 10.2 Two Kinds of Orthogonality, 10.3 The Automorphism Group of O, 10.4 The Octavian Unit Rings, 10.5 Stabilizing the Unit Subrings, Appendix: Proof of Theorem5, 11 Reading O Mod 2, 11.1 Why Read Mod 2?, 11.2 The E8 Lattice,Mod 2, 11.3 What Fixes (λ)?, 11.4 The Remaining Subrings Modulo 2, 12 The Octonion Projective Plane OP2, 12.1 The Exceptional Lie Groups and Freudenthal’s “Magic Square”, 12.2 The Octonion Projective Plane, 12.3 Coordinates for OP2, Bibliography, Index

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Book SynopsisCollected over several years by Peter Winkler, of Bell Labs, dozens of elegant, intriguing challenges are presented in Mathematical Puzzles. The answers are easy to explain, but without this book, devilishly hard to find. Creative reasoning is the key to these puzzles. No involved computation or higher mathematics is necessary, but your ability to construct a mathematical proof will be severly tested--even if you are a professional mathematician. For the truly adventurous, there is even a chapter on unsolved puzzles.Trade Review" Winkler's book will certainly appeal to the mathematician, as well as to students of all ages—high-school, college, and graduate. His philosophy of what constitutes a good puzzle is right on the mark, showing that this Connoisseur's Collection really is of quality and depth. -James Tanton, MAA Online, September 2004 ""I have gained great satisfaction from those [puzzles] I've managed to solve . . . This is a great collection of seriously hard questions."" -The Mathematical Gazette, March 2006 ""As an enthusiastic solver and collector of mathematical puzzles myself, I was absolutely delighted with this book. The sheer density of mathematical ideas and challenges sets it apart from other books of a similar nature while the lucid yet informal style of exposition makes the journey from ignorance to enlightenment enjoyable."" -Norman Do, The Australian Mathematical Society Gazette, July 2004"Table of ContentsPreface, Insight, Numbers, Combinatorics, Probability, Geometry, Geography(!), Games, Algorithms, More Games, Handicaps, Toughies, Unsolved Puzzles, Afterword, Index of Puzzles

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Book SynopsisKeith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces to create this introduction to experimental mathematics. They cover a variety of topics and examples to give the reader a good sense of the current state of play in the rapidly growing new field of experimental mathematics. The writing is clear and the explanations are enhanced by relevant historical facts and stories of mathematicians and their encounters with the field over time.Trade ReviewThe long experience of both authors can be clearly seen in the way they describe a number of problems … they succeeded in exactly the right balance between mathematical depth and accessibility for a wide audience. The result is an easily digestible book full of humor for anyone with an affinity for mathematics …—Dan Roozemond, Nieuw Archief voor WiskundeThe sleuth-like style and lucid writing certainly make this book an enjoyable read. Many explanations are framed by relevant historical context and tales of mathematicians whose use of experimental mathematics helped them gain insights into difficult problems. . . . I thoroughly enjoyed reading this short introduction to experimental mathematics. It will no doubt appeal to a broad mathematical audience, both professional and amateur alike.—Mitch Wheat, Gazette of the Australian Mathematical Society, July 2009It is a pleasant and readable book for any working mathematician who wants to know something more about the use of computers for generating hypotheses on relations among known and less known special numbers.—Newsletter of the European Mathematical Society, June 2009... allows [the reader] to take a look at some interesting problems and solve [them] using [a] computer. The authors are showing how a mathematician can use a computer as a tool. ... The book covers a variety of topics and examples in order to give the reader a good sense of the current state of play in the rapidly growing new field of experimental mathematics. ... The writing is clear and the explanations are enhanced by relevant historical facts and stories of mathematicians and their encounters with the field over time. The book will be of interest to any reader who would like to taste the solving of mathematical problems with a computer. No matter if readers may not have much mathematical knowledge: they can catch the essentials with the book, and have fun exploring some questions.—Valentina Dagiene, Zentralblatt MATH, September 2009... a pleasant and readable book for any working mathematician who wants to know something more about the use of computers for generating hypotheses on relations among known and less known special numbers.—EMS Newsletter, June 2009... a lovely little book which builds a strong case for experimental mathematics. Any practicing mathematician or serious amateur should consider checking out this introduction to a topic that will no doubt transform mathematics.—Antonio Cangiano, Math-Blog.com, July 2010

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Book SynopsisThis engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.Trade Review"With solid theory and references, along with practical advice borne from decades of experience, all presented in an informal and demystifying style, Dunn & Parberry provide an accessible and useful approach to the key mathematical operations needed in 3D computer graphics."—Eric Haines, author of Real-Time Rendering"The book describes the mathematics involved in game development in a very clear and easy to understand way, layered on the practical background of years of game engine programming experience."—Wolfgang Engel, editor of GPU ProTable of ContentsCartesian Coordinate Systems. Vectors. Multiple Coordinate Spaces. Introduction to Matrices. Matrices and Linear Transformations. More on Matrices. Polar Coordinate Systems. Rotation in Three Dimensions. Geometric Primitives. Mathematical Topics from 3D Graphics. Mechanics 1: Linear Kinematics and Calculus. Mechanics 2: Linear and Rotational Dynamics. Curves in 3D. Afterword. Appendices. Bibliography. Index.

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Book SynopsisThis is the fourteenth issue (Vol. 7, No. 2, December 2019) of the Notices of the International Congress of Chinese Mathematicians (or ICCM Notices, for short), the official periodical of the ICCM organization.Published semi-annually, the Notices bring news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education.Readers of the Notices will find research papers on various topics by prominent experts from around the world, interesting and timely articles on current applications and trends, biographical and historical essays, profiles of important institutions of research and learning, and more.

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Book SynopsisData Analysis Using Stata, Third Edition is a comprehensive introduction to both statistical methods and Stata. Beginners will learn the logic of data analysis and interpretation and easily become self-sufficient data analysts. Readers already familiar with Stata will find it an enjoyable resource for picking up new tips and tricks.The book is written as a self-study tutorial and organized around examples. It interactively introduces statistical techniques such as data exploration, description, and regression techniques for continuous and binary dependent variables. Step by step, readers move through the entire process of data analysis and in doing so learn the principles of Stata, data manipulation, graphical representation, and programs to automate repetitive tasks. This third edition includes advanced topics, such as factor-variables notation, average marginal effects, standard errors in complex survey, and multiple imputation in a way, that beginners of both data analysis and Stata can understand.Using data from a longitudinal study of private households, the authors provide examples from the social sciences that are relatable to researchers from all disciplines. The examples emphasize good statistical practice and reproducible research. Readers are encouraged to download the companion package of datasets to replicate the examples as they work through the book. Each chapter ends with exercises to consolidate acquired skills. Table of ContentsThe First Time. Working with Do-Files. The Grammar of Stata. General Comments on the Statistical Commands. Creating and Changing Variables. Creating and Changing Graphs. Describing and Comparing Distributions. Statistical Inference. Introduction to Linear Regression. Regression Models for Categorical Dependent Variables. Reading and Writing Data. Do-Files for Advanced Users and User-Written Programs. Around Stata. References. Indices.

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Book SynopsisOver the past several decades, item response theory (IRT) and item response modeling (IRM) have become increasingly popular in the behavioral, educational, social, business, marketing, clinical, and health sciences. In this book, Raykov and Marcoulides begin with a nontraditional approach to IRT and IRM that is based on their connections to classical test theory, (nonlinear) factor analysis, generalized linear modeling, and logistic regression. Application-oriented discussions follow next. These cover the one-, two-, and three-parameter logistic models, polytomous item response models (with nominal or ordinal items), item and test information functions, instrument construction and development, hybrid models, differential item functioning, and an introduction to multidimensionalIRT and IRM. The pertinent analytic and modeling capabilities of Stata are thoroughly discussed, highlighted, and illustrated on empirical examples from behavioral and social research.Table of ContentsNotation and typography. What is item response theory and item response modeling? Two basic functions for item response theory and item response. Classical test theory, factor analysis, and their connections to item response theory Generalized linear modeling, logistic regression, nonlinear factor analysis, and their links to item response theory and item response modeling. Fundamentals of item response theory and item response modeling. First applications of Stata for item response modeling. Item response theory model fitting and estimation. Information functions and test characteristic curves Instrument construction and development using information functions. Differential item functioning. Polytomous item response models and hybrid models. Introduction to multidimensional item response theory and modeling

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Book SynopsisStata Tips provides concise and insightful notes about commands, features, and tricks that will help you obtain a deeper understanding of Stata.The book comprises the contributions of the Stata community that have appeared in the Stata Journal since 2003. Each tip is a brief article that provides practical advice on using Stata. With tips covering a breadth of topics in statistics, graphics, data management, and programming, both new and experienced Stata users are sure to find tips that will be useful in their research.

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Book SynopsisMaximum Likelihood Estimation with Stata, Fifth Edition is the essential reference and guide for researchers in all disciplines who wish to write maximum likelihood (ML) estimators in Stata. Beyond providing comprehensive coverage of Stata’s commands for writing ML estimators, the book presents an overview of the underpinnings of maximum likelihood and how to think about ML estimation.The fifth edition includes a new second chapter that demonstrates the easy-to-use mlexp command. This command allows you to directly specify a likelihood function and perform estimation without any programming.The core of the book focuses on Stata's ml command. It shows you how to take full advantage of ml’s noteworthy features: Linear constraints Four optimization algorithms (Newton–Raphson, DFP, BFGS, and BHHH) Observed information matrix (OIM) variance estimator Outer product of gradients (OPG) variance estimator Huber/White/sandwich robust variance estimator Cluster–robust variance estimator Complete and automatic support for survey data analysis Direct support of evaluator functions written in Mata When appropriate options are used, many of these features are provided automatically by ml and require no special programming or intervention by the researcher writing the estimator.In later chapters, you will learn how to take advantage of Mata, Stata's matrix programming language. For ease of programming and potential speed improvements, you can write your likelihood-evaluator program in Mata and continue to use ml to control the maximization process. A new chapter in the fifth edition shows how you can use the moptimize() suite of Mata functions if you want to implement your maximum likelihood estimator entirely within Mata.In the final chapter, the authors illustrate the major steps required to get from log-likelihood function to fully operational estimation command. This is done using several different models: logit and probit, linear regression, Weibull regression, the Cox proportional hazards model, random-effects regression, and seemingly unrelated regression. This edition adds a new example of a bivariate Poisson model, a model that is not available otherwise in Stata.The authors provide extensive advice for developing your own estimation commands. With a little care and the help of this book, users will be able to write their own estimation commands---commands that look and behave just like the official estimation commands in Stata.Whether you want to fit a special ML estimator for your own research or wish to write a general-purpose ML estimator for others to use, you need this book.Table of ContentsTheory and practice The likelihood-maximization problem Likelihood theory The maximization problem Estimation with mlexp Syntax Normal linear regression Initial values Restricted parameters Robust standard errors The probit model Specifying derivatives Additional estimation features Wrapping up Introduction to ml The probit mode Normal linear regression Robust standard errors Weighted estimation Other features of method-gf0 evaluators Limitations Overview of ml The terminology of ml Equations in ml Likelihood-evaluator methods Tools for the ml programmer Common ml options Maximizing your own likelihood functions Appendix: More about scalar parameters Method lf The linear-form restrictions Examples The importance of generating temporary variables as doubles Problems you can safely ignore Nonlinear specifications The advantages of lf in terms of execution speed Methods lf0, lf1, and lf2 Comparing these methods Outline of evaluators of methods lf0, lf1, and lf2 Summary of methods lf0, lf1, and lf2 Examples Methods d0, d1, and d2 Comparing these methods Outline of method d0, d1, and d2 evaluators Summary of methods d0, d1, and d2 Panel-data likelihoods Other models that do not meet the linear-form restrictions Debugging likelihood evaluators ml check Using the debug methods ml trace Setting initial values ml search ml plot ml init Interactive maximization The iteration log Pressing the Break key Maximizing difficult likelihood functions Final results Graphing convergence Redisplaying output Writing do-files to maximize likelihoods The structure of a do-file Putting the do-file into production Writing ado-files to maximize likelihoods Writing estimation commands The standard estimation-command outline Outline for estimation commands using ml Using ml in noninteractive mode Advice Writing ado-files for survey data analysis Program properties Writing your own predict command Mata-based likelihood evaluators Introductory examples Evaluator function prototypes Utilities Random-effects linear regression Ado-file considerations Mata’s moptimize() function Introductory examples Restricting the estimation sample Estimation preliminaries Estimation Results Estimation commands Regression redux Other examples The logit model The probit model Normal linear regression The Weibull model The Cox proportional hazards model The random-effects regression model The seemingly unrelated regression model A bivariate Poisson regression model Epilogue Syntax of mlexp Syntax of ml Syntax of moptimize() Likelihood-evaluator checklists Method lf Method d0 Method d1 Method d2 Method lf0 Method lf1 Method lf2 Listing of estimation commands The logit model The probit model The normal model The Weibull model The Cox proportional hazards model The random-effects regression model The seemingly unrelated regression model A bivariate Poisson regression model References

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Book SynopsisDynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks.This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

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Book SynopsisMaterial undergoes the transformation from metal to non-metal or from non-metal to metal when environmental conditions, such as temperature and pressure, or the percentages of constituent components are changed. Such a transition is known as the metal-nonmetal M-NM transition.This book, The Physics of Metal Nonmetal Transitions, explores the mechanisms so far discovered which cause the M-NM transition and presents a systematic discussion of them. All the mechanisms are discussed in terms of energy bands, and the band theory is introduced and explained in chapter 2. Once chapters 1 and 2 have been assimilated, the remaining chapters can be

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