Mathematics Books

Book SynopsisSpherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. This title traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth.Trade ReviewOne of Choice's Outstanding Academic Titles for 2013 Shortlisted for the 2013 BSHM Neumann Book Prize, British Society for the History of Mathematics "Once a mainstay of mathematics, spherical trigonometry no longer appears on school curricula. Here, Glen Van Brummelen reasserts the field's importance, sharing in illuminating detail how it figured in astronomy, cartography and our understanding of Earth's rotation."--Rosalind Metcalfe, Nature "The present book is very well written; it leaves a clear impression that the author intended to endear--not merely present and teach--spherical trigonometry to the reader. Although not a history book, there are separate chapters shedding light on the approaches to the subject in the ancient, medieval, and modern times. There are also chapters on spherical geometry, polyhedra, stereographic projection and the art of navigation. The book is thoroughly illustrated and is a pleasant read. Chapters end with exercises; the appendices contain a long list of available and not so available textbooks and recommendations for further reading organized by individual chapters. The book made a valuable addition to my library. I freely recommend it to math teachers and curious high schoolers."--Alexander Bogomolny, CTK Insights "A no-nonsense introduction to spherical trigonometry."--Book News, Inc. "A beautiful popular book."--ThatsMaths.com "Full of academic, textbook content, the book is a delight to math students. So if you are game for a journey into the world of spherical trigonometry, pick up the book. Van Brummelen gives exercises at the end of the chapters that can be fun."--R. Balashankar, Organiser "Heavenly Mathematicsis a truly enjoyable description of the somewhat forgotten science of spherical trigonometry... As readers discover this discipline, they will also appreciate the beauty inherent in the topic."--Choice "Heavenly Mathematics proves the value of bringing a fascinating piece of mathematical history within the grasp of the general reader."--Florin Diacu, Literary Review of Canada "Van Brummelen has written a wonderful introduction ... that draws on the history of [spherical trigonometry] to illuminate the mathematics itself and at the same time gives readers a real sense of what research in the history of early mathematics is all about."--Metascience "[Heavenly Mathematics] is an excellent survey of spherical trigonometry... Simply an appreciation of a beautiful lost subject, with historical overtones... [D]istinguishable for its appealingly fresh style."--Mathematical Reviews "[Heavenly Mathematics] is a lovely book to read... [A] wonderful introduction for anyone who wishes to learn more about this subject... I am in full agreement with the author that spherical trigonometry ought to be brought to a wider audience, and I believe that this is the book to do it."--Mathematics Today "Engaging, clear and not overly technical; you can safely lend this book to your friends in the history department... [Heavenly Mathematics] is excellent."--Zentralblatt MATH "Heavenly Mathematics will be of interest to mathematically inclined historians of science and also to students of mathematics and engineering. Because spherical trigonometry is relevant in applications of modern science, this elegant book may even contribute to a renaissance of the subject."--Jan P. Hogendijk, Isis "This book could serve as an excellent textbook for any secondary school mathematics classroom at or above the level of geometry and certainly trigonometry; as the basis for a high school honors class; or as a textbook and seminar topic for college students."--Teresa Floyd, Mathematics Teacher "Any reader of this book (and there should be many) will see how present day mathematics may be viewed through the kaleidoscope of its historical origins... Glen Van Brummelen has written a beautifully produced book that includes fascinating biographical detail at every stage of his narrative."--P.N. Ruane, Mathematical Gazette "An engaging read that will appeal to historians of science, mathematicians, trigonometry teachers, and anyone interested in the history of mathematics."--Elizabeth Hamm, Aestimatio Critical Reviews in the History of ScienceTable of ContentsPreface vii 1 Heavenly Mathematics 1 2 Exploring the Sphere 23 3 The Ancient Approach 42 4 The Medieval Approach 59 5 The Modern Approach: Right- Angled Triangles 73 6 The Modern Approach: Oblique Triangles 94 7 Areas, Angles, and Polyhedra 110 8 Stereographic Projection 129 9 Navigating by the Stars 151 Appendix A. Ptolemy's Determination of the Sun's Position 173 Appendix B. Textbooks 179 Appendix C. Further Reading 182 Index 189

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Book SynopsisThis lavishly illustrated book provides a hands-on, step-by-step introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocks--a sort of potato-stamp method--Frank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzliTrade ReviewHonorable Mention for the 2016 PROSE Award in Mathematics, Association of American Publishers "[A] beautifully illustrated guide to fusing mathematical and artistic creativity to generate fascinating and visually appealing designs."--Evelyn Lamb, Scientific American "[A] beautiful book... [Creating Symmetry] is a thoughtful, innovative and interesting piece of work, discussing material that the author is obviously very enthusiastic about; such enthusiasm is, as is often the case, contagious."--Mark Hunacek, MAA Reviews "This is a marvelous book that brings groups, and along the way many other mathematical concepts, to the reader in an unconventional way."--Adhemar Bultheel, European Mathematical Society Bulletin "Mathematics students thus get a visually rich path into group theory that compellingly informs even first steps with ideas usually deemed advanced. Braver art students will find motivation and the means to learn some mathematics they can put right to use."--D. V. Feldman, Choice "[A] delightful showcase of artistic applications of complex wave functions... This attractive book will appeal to and inspire a broad range of practitioners including complex analysts, mathematical artists, and advanced undergraduates."--Heidi Burgiel, College Mathematics JournalTable of ContentsPreface vii 1 Going in Circles 1 2 Complex Numbers and Rotations 5 3 Symmetry of the Mystery Curve 11 4 Mathematical Structures and Symmetry: Groups, Vector Spaces, and More 17 5 Fourier Series: Superpositions of Waves 24 6 Beyond Curves: Plane Functions 34 7 Rosettes as Plane Functions 40 8 Frieze Functions (from Rosettes!) 50 9 Making Waves 60 10 PlaneWave Packets for 3-Fold Symmetry 66 11 Waves, Mirrors, and 3-Fold Symmetry 74 12 Wallpaper Groups and 3-Fold Symmetry 81 13 ForbiddenWallpaper Symmetry: 5-Fold Rotation 88 14 Beyond 3-Fold Symmetry: Lattices, Dual Lattices, andWaves 93 15 Wallpaper with a Square Lattice 97 16 Wallpaper with a Rhombic Lattice 104 17 Wallpaper with a Generic Lattice 109 18 Wallpaper with a Rectangular Lattice 112 19 Color-ReversingWallpaper Functions 120 20 Color-Turning Wallpaper Functions 131 21 The Point Group and Counting the 17 141 22 Local Symmetry in Wallpaper and Rings of Integers 157 23 More about Friezes 168 24 Polyhedral Symmetry (in the Plane?) 172 25 HyperbolicWallpaper 189 26 Morphing Friezes and Mathematical Art 200 27 Epilog 206 A Cell Diagrams for the 17 Wallpaper Groups 209 B Recipes forWallpaper Functions 211 C The 46 Color-ReversingWallpaper Types 215 Bibliography 227 Index 229

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Book SynopsisThis book provides an accessible approach to Bayesian computing and data analysis, with an emphasis on the interpretation of real data sets.Trade Review“A nice guidebook to intermediate and advanced Bayesian models.” (Scientific Computing, 13 January 2015)Table of ContentsPreface xi 1 Bayesian methods and Bayesian estimation 1 1.1 Introduction 1 1.1.1 Summarising existing knowledge: Prior densities for parameters 2 1.1.2 Updating information: Prior, likelihood and posterior densities 3 1.1.3 Predictions and assessment 5 1.1.4 Sampling parameters 6 1.2 MCMC techniques: The Metropolis–Hastings algorithm 7 1.2.1 Gibbs sampling 8 1.2.2 Other MCMC algorithms 9 1.2.3 INLA approximations 10 1.3 Software for MCMC: BUGS, JAGS and R-INLA 11 1.4 Monitoring MCMC chains and assessing convergence 19 1.4.1 Convergence diagnostics 20 1.4.2 Model identifiability 21 1.5 Model assessment 23 1.5.1 Sensitivity to priors 23 1.5.2 Model checks 24 1.5.3 Model choice 25 References 28 2 Hierarchical models for related units 34 2.1 Introduction: Smoothing to the hyper population 34 2.2 Approaches to model assessment: Penalised fit criteria, marginal likelihood and predictive methods 35 2.2.1 Penalised fit criteria 36 2.2.2 Formal model selection using marginal likelihoods 37 2.2.3 Estimating model probabilities or marginal likelihoods in practice 38 2.2.4 Approximating the posterior density 40 2.2.5 Model averaging from MCMC samples 42 2.2.6 Predictive criteria for model checking and selection: Cross-validation 46 2.2.7 Predictive checks and model choice using complete data replicate sampling 50 2.3 Ensemble estimates: Poisson–gamma and Beta-binomial hierarchical models 53 2.3.1 Hierarchical mixtures for poisson and binomial data 54 2.4 Hierarchical smoothing methods for continuous data 61 2.4.1 Priors on hyperparameters 62 2.4.2 Relaxing normality assumptions 63 2.4.3 Multivariate borrowing of strength 65 2.5 Discrete mixtures and dirichlet processes 69 2.5.1 Finite mixture models 69 2.5.2 Dirichlet process priors 72 2.6 General additive and histogram smoothing priors 78 2.6.1 Smoothness priors 79 2.6.2 Histogram smoothing 80 Exercises 83 Notes 86 References 89 3 Regression techniques 97 3.1 Introduction: Bayesian regression 97 3.2 Normal linear regression 98 3.2.1 Linear regression model checking 99 3.3 Simple generalized linear models: Binomial, binary and Poisson regression 102 3.3.1 Binary and binomial regression 102 3.3.2 Poisson regression 105 3.4 Augmented data regression 107 3.5 Predictor subset choice 110 3.5.1 The g-prior approach 114 3.5.2 Hierarchical lasso prior methods 116 3.6 Multinomial, nested and ordinal regression 126 3.6.1 Nested logit specification 128 3.6.2 Ordinal outcomes 130 Exercises 136 Notes 138 References 144 4 More advanced regression techniques 149 4.1 Introduction 149 4.2 Departures from linear model assumptions and robust alternatives 149 4.3 Regression for overdispersed discrete outcomes 154 4.3.1 Excess zeroes 157 4.4 Link selection 160 4.5 Discrete mixture regressions for regression and outlier status 161 4.5.1 Outlier accommodation 163 4.6 Modelling non-linear regression effects 167 4.6.1 Smoothness priors for non-linear regression 167 4.6.2 Spline regression and other basis functions 169 4.6.3 Priors on basis coefficients 171 4.7 Quantile regression 175 Exercises 177 Notes 177 References 179 5 Meta-analysis and multilevel models 183 5.1 Introduction 183 5.2 Meta-analysis: Bayesian evidence synthesis 184 5.2.1 Common forms of meta-analysis 185 5.2.2 Priors for stage 2 variation in meta-analysis 188 5.2.3 Multivariate meta-analysis 193 5.3 Multilevel models: Univariate continuous outcomes 195 5.4 Multilevel discrete responses 201 5.5 Modelling heteroscedasticity 204 5.6 Multilevel data on multivariate indices 206 Exercises 208 Notes 210 References 211 6 Models for time series 215 6.1 Introduction 215 6.2 Autoregressive and moving average models 216 6.2.1 Dependent errors 218 6.2.2 Bayesian priors in ARMA models 218 6.2.3 Further types of time dependence 222 6.3 Discrete outcomes 229 6.3.1 INAR models for counts 231 6.3.2 Evolution in conjugate process parameters 232 6.4 Dynamic linear and general linear models 235 6.4.1 Further forms of dynamic models 238 6.5 Stochastic variances and stochastic volatility 244 6.5.1 ARCH and GARCH models 244 6.5.2 State space stochastic volatility models 245 6.6 Modelling structural shifts 248 6.6.1 Level, trend and variance shifts 249 6.6.2 Latent state models including historic dependence 250 6.6.3 Switching regressions and autoregressions 251 Exercises 258 Notes 261 References 265 7 Analysis of panel data 273 7.1 Introduction 273 7.2 Hierarchical longitudinal models for metric data 274 7.2.1 Autoregressive errors 275 7.2.2 Dynamic linear models 276 7.2.3 Extended time dependence 276 7.3 Normal linear panel models and normal linear growth curves 278 7.3.1 Growth curves 280 7.3.2 Subject level autoregressive parameters 283 7.4 Longitudinal discrete data: Binary, categorical and Poisson panel data 285 7.4.1 Binary panel data 285 7.4.2 Ordinal panel data 288 7.4.3 Panel data for counts 292 7.5 Random effects selection 295 7.6 Missing data in longitudinal studies 297 Exercises 302 Notes 303 References 306 8 Models for spatial outcomes and geographical association 312 8.1 Introduction 312 8.2 Spatial regressions and simultaneous dependence 313 8.2.1 Regression with localised dependence 316 8.2.2 Binary outcomes 317 8.3 Conditional prior models 321 8.3.1 Ecological analysis involving count data 324 8.4 Spatial covariation and interpolation in continuous space 329 8.4.1 Discrete convolution processes 332 8.5 Spatial heterogeneity and spatially varying coefficient priors 337 8.5.1 Spatial expansion and geographically weighted regression 338 8.5.2 Spatially varying coefficients via multivariate priors 339 8.6 Spatio-temporal models 343 8.6.1 Conditional prior representations 345 8.7 Clustering in relation to known centres 348 8.7.1 Areas or cases as data 350 8.7.2 Multiple sources 350 Exercises 352 Notes 354 References 355 9 Latent variable and structural equation models 364 9.1 Introduction 364 9.2 Normal linear structural equation models 365 9.2.1 Cross-sectional normal SEMs 365 9.2.2 Identifiability constraints 367 9.3 Dynamic factor models, panel data factor models and spatial factor models 372 9.3.1 Dynamic factor models 372 9.3.2 Linear SEMs for panel data 374 9.3.3 Spatial factor models 378 9.4 Latent trait and latent class analysis for discrete outcomes 381 9.4.1 Latent trait models 381 9.4.2 Latent class models 382 9.5 Latent trait models for multilevel data 387 9.6 Structural equation models for missing data 389 Exercises 392 Notes 394 References 397 10 Survival and event history models 402 10.1 Introduction 402 10.2 Continuous time functions for survival 403 10.2.1 Parametric hazard models 405 10.2.2 Semi-parametric hazards 408 10.3 Accelerated hazards 411 10.4 Discrete time approximations 413 10.4.1 Discrete time hazards regression 415 10.5 Accounting for frailty in event history and survival models 417 10.6 Further applications of frailty models 421 10.7 Competing risks 423 Exercises 425 References 426 Index 431

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Book SynopsisPresents a novel approach to conducting meta-analysis using structural equation modeling. Structural equation modeling (SEM) and meta-analysis are two powerful statistical methods in the educational, social, behavioral, and medical sciences. They are often treated as two unrelated topics in the literature. This book presents a unified framework on analyzing meta-analytic data within the SEM framework, and illustrates how to conduct meta-analysis using the metaSEM package in the R statistical environment. Meta-Analysis: A Structural Equation Modeling Approach begins by introducing the importance of SEM and meta-analysis in answering research questions. Key ideas in meta-analysis and SEM are briefly reviewed, and various meta-analytic models are then introduced and linked to the SEM framework. Fixed-, random-, and mixed-effects models in univariate and multivariate meta-analyses, three-level meta-analysis, and meta-analytic structural equation modeling, areTrade Review"This book will be a valuable resource for statistical and academic researchers and graduate students carrying out meta-analyses, and will also be useful to researchers and statisticians using SEM in biostatistics. cover, would sit well on the bookshelves of those interested in this increasingly important field of scientific endeavour." (Zentralblatt MATH, 1 June 2015)Table of ContentsPreface xiii Acknowledgments xv List of abbreviations xvii List of figures xix List of tables xxi 1 Introduction 1 1.1 What is meta-analysis? 1 1.2 What is structural equation modeling? 2 1.3 Reasons for writing a book on meta-analysis and structural equation modeling 3 1.4 Outline of the following chapters 6 1.5 Concluding remarks and further readings 8 2 Brief review of structural equation modeling 13 2.1 Introduction 13 2.2 Model specification 14 2.3 Common structural equation models 18 2.4 Estimation methods, test statistics, and goodness-of-fit indices 25 2.5 Extensions on structural equation modeling 38 2.6 Concluding remarks and further readings 42 3 Computing effect sizes for meta-analysis 48 3.1 Introduction 48 3.2 Effect sizes for univariate meta-analysis 50 3.3 Effect sizes for multivariate meta-analysis 57 3.4 General approach to estimating the sampling variances and covariances 60 3.5 Illustrations Using R 68 3.6 Concluding remarks and further readings 78 4 Univariate meta-analysis 81 4.1 Introduction 81 4.2 Fixed-effects model 83 4.3 Random-effects model 87 4.4 Comparisons between the fixed- and the random-effects models 93 4.5 Mixed-effects model 96 4.6 Structural equation modeling approach 100 4.7 Illustrations using R 105 4.8 Concluding remarks and further readings 116 5 Multivariate meta-analysis 121 5.1 Introduction 121 5.2 Fixed-effects model 124 5.3 Random-effects model 127 5.4 Mixed-effects model 134 5.5 Structural equation modeling approach 136 5.6 Extensions: mediation and moderation models on the effect sizes 140 5.7 Illustrations using R 145 5.8 Concluding remarks and further readings 174 6 Three-level meta-analysis 179 6.1 Introduction 179 6.2 Three-level model 183 6.3 Structural equation modeling approach 188 6.4 Relationship between the multivariate and the three-level meta-analyses 195 6.5 Illustrations using R 200 6.6 Concluding remarks and further readings 210 7 Meta-analytic structural equation modeling 214 7.1 Introduction 214 7.2 Conventional approaches 218 7.3 Two-stage structural equation modeling: fixed-effects models 223 7.4 Two-stage structural equation modeling: random-effects models 233 7.5 Related issues 235 7.6 Illustrations using R 244 7.7 Concluding remarks and further readings 273 8 Advanced topics in SEM-based meta-analysis 279 8.1 Restricted (or residual) maximum likelihood estimation 279 8.2 Missing values in the moderators 289 8.3 Illustrations using R 294 8.4 Concluding remarks and further readings 309 9 Conducting meta-analysis with Mplus 313 9.1 Introduction 313 9.2 Univariate meta-analysis 314 9.3 Multivariate meta-analysis 327 9.4 Three-level meta-analysis 346 9.5 Concluding remarks and further readings 353 A A brief introduction to R, OpenMx, and metaSEM packages 356 A.1 R 357 A.2 OpenMx 362 A.3 metaSEM 364 References 368 Index 369

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Book SynopsisProvides a quick, but very readable introduction to stochastic differential equations—that is, to differential equations subject to additive “white noise" and related random disturbances. The exposition is strongly focused upon the interplay between probabilistic intuition and mathematical rigour.Trade Review... [A]n interesting and unusual introduction to stochastic differential equations...topical and appealing to a wide audience. ... This is interesting stuff and, because of Evans' always clear explanations, it is fun too." - MAA ReviewsTable of Contents Preface Introduction A crash course in probability theory Brownian motion and “white noise” Stochastical integrals Stochastic differential equations Applications Appendix Exercises Notes and suggested reading Bibliography Index

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Book SynopsisPraise for the First Edition ...a reference for everyone who is interested in knowing and handling uncertainty. Journal of Applied Statistics The critically acclaimed First Edition of Understanding Uncertainty provided a study of uncertainty addressed to scholars in all fields, showing that uncertainty could be measured by probability, and that probability obeyed three basic rules that enabled uncertainty to be handled sensibly in everyday life. These ideas were extended to embrace the scientific method and to show how decisions, containing an uncertain element, could be rationally made. Featuring new material, the Revised Edition remains the go-to guide for uncertainty and decision making, providing further applications at an accessible level including: A critical study of transitivity, a basic concept in probability A discussion of how the failure of the financial sector to use the proper approachTable of ContentsPreface xi Prologue xiii 1. Uncertainty 1 1.1. Introduction 1 1.2. Examples 2 1.3. Suppression of Uncertainty 7 1.4. The Removal of Uncertainty 8 1.5. The Uses of Uncertainty 9 1.6. The Calculus of Uncertainty 11 1.7. Beliefs 12 1.8. Decision Analysis 13 2. Stylistic Questions 15 2.1. Reason 15 2.2. Unreason 17 Literature 17 Advertising 17 Politics 18 Law 18 Television 18 2.3. Facts 19 2.4. Emotion 19 2.5. Prescriptive and Descriptive Approaches 20 2.6. Simplicity 22 2.7. Mathematics 23 2.8. Writing 25 2.9. Mathematics Tutorial 26 3. Probability 30 3.1. Measurement 30 3.2. Randomness 32 3.3. A Standard for Probability 34 3.4. Probability 35 3.5. Coherence 36 3.6. Belief 37 3.7. Complementary Event 39 3.8. Odds 40 3.9. Knowledge Base 43 3.10. Examples 44 3.11. Retrospect 46 4. Two Events 47 4.1. Two Events 47 4.2. Conditional Probability 49 4.3. Independence 51 4.4. Association 53 4.5. Examples 54 4.6. Supposition and Fact 56 4.7. Seeing and Doing 57 5. The Rules of Probability 59 5.1. Combinations of Events 59 5.2. Addition Rule 61 5.3. Multiplication Rule 62 5.4. The Basic Rules 64 5.5. Examples 66 5.6. Extension of the Conversation 68 5.7. Dutch Books 70 5.8. Scoring Rules 72 5.9. Logic Again 73 5.10. Decision Analysis 74 5.11. The Prisoners’ Dilemma 75 5.12. The Calculus and Reality 76 6. Bayes Rule 79 6.1. Transposed Conditionals 79 6.2. Learning 81 6.3. Bayes Rule 82 6.4. Medical Diagnosis 83 6.5. Odds Form of Bayes Rule 86 6.6. Forensic Evidence 88 6.7. Likelihood Ratio 89 6.8. Cromwell’s Rule 90 6.9. A Tale of Two Urns 92 6.10. Ravens 94 6.11. Diagnosis and Related Matters 97 6.12. Information 98 7. Measuring Uncertainty 101 7.1. Classical Form 101 7.2. Frequency Data 103 7.3. Exchangeability 104 7.4. Bernoulli Series 106 7.5. De Finetti’s Result 107 7.6. Large Numbers 109 7.7. Belief and Frequency 111 7.8. Chance 114 8. Three Events 117 8.1. The Rules of Probability 117 8.2. Simpson’s Paradox 119 8.3. Source of the Paradox 121 8.4. Experimentation 122 8.5. Randomization 123 8.6. Exchangeability 125 8.7. Spurious Association 128 8.8. Independence 130 8.9. Conclusions 132 9. Variation 134 9.1. Variation and Uncertainty 134 9.2. Binomial Distribution 135 9.3. Expectation 137 9.4. Poisson Distribution 139 9.5. Spread 142 9.6. Variability as an Experimental Tool 144 9.7. Probability and Chance 145 9.8. Pictorial Representation 147 9.9. The Normal Distribution 150 9.10. Variation as a Natural Phenomenon 152 9.11. Ellsberg’s Paradox 154 10. Decision Analysis 158 10.1. Beliefs and Actions 158 10.2. Comparison of Consequences 160 10.3. Medical Example 162 10.4. Maximization of Expected Utility 164 10.5. More on Utility 165 10.6. Some Complications 167 10.7. Reason and Emotion 168 10.8. Numeracy 170 10.9. Expected Utility 171 10.10. Decision Trees 172 10.11. The Art and Science of Decision Analysis 175 10.12. Further Complications 177 10.13. Combination of Features 179 10.14. Legal Applications 182 11. Science 186 11.1. Scientific Method 186 11.2. Science and Education 187 11.3. Data Uncertainty 188 11.4. Theories 190 11.5. Uncertainty of a Theory 193 11.6. The Bayesian Development 195 11.7. Modification of Theories 197 11.8. Models 199 11.9. Hypothesis Testing 202 11.10. Significance Tests 204 11.11. Repetition 206 11.12. Summary 208 12. Examples 211 12.1. Introduction 211 12.2. Cards 212 12.3. The Three Doors 213 12.4. The Newcomers to Your Street 215 12.5. The Two Envelopes 217 12.6. Y2K 220 12.7. UFOs 221 12.8. Conglomerability 224 13. Probability Assessment 226 13.1. Nonrepeatable Events 226 13.2. Two Events 227 13.3. Coherence 230 13.4. Probabilistic Reasoning 233 13.5. Trickle Down 234 13.6. Summary 236 Epilogue 238 Subject Index 243 Index of Examples 248 Index of Notations 250

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Book SynopsisTransform your organization''s data into actionable insights with Tableau Tableau is designed specifically to provide fast and easy visual analytics. The intuitive drag-and-drop interface helps you create interactive reports, dashboards, and visualizations, all without any special or advanced training. This all new edition of Tableau Your Data! is your Tableau companion, helping you get the most out of this invaluable business toolset.Tableau Your Data! shows you how to build dynamic, best of breed visualizations using the Tableau Software toolset. This comprehensive guide covers the core feature set for data analytics, and provides clear step-by-step guidance toward best practices and advanced techniques that go way beyond the user manual. You''ll learn how Tableau is different from traditional business information analysis tools, and how to navigate your way around the Tableau 9.0 desktop before delving into functions and calculations, as well as sTable of ContentsIntroduction xxv Part I Desktop 1 1 Creating Visual Analytics with Tableau Desktop 3 The Shortcomings of Traditional Information Analysis 4 The Business Case for Visual Analysis 5 Three Kinds of Data That Exist in Every Entity 5 How Visual Analytics Improves Decision Making 6 Turning Data into Information with Visual Analytics 8 Analysis as a Creative Process 8 Tableau’s Desktop Tools 9 Tableau Desktop Personal Edition 9 Professional Edition 9 Tableau File Types 9 Tableau Reader 11 Tableau Online Help 11 Introducing the Tableau Desktop Workspace 11 New Workspace Design 11 Using the Start Page Controls Effectively 12 The Start Page 12 The Tableau Desktop Workspace 17 Summary 41 2 Connecting to Your Data 43 What You Will Learn in This Chapter 43 How to Connect to Your Data 44 Connecting to Desktop Sources 45 Understanding the Data Source Page 47 What Are Generated Values? 57 Knowing When to Use a Direct Connection or a Data Extract 61 Using Tableau’s File Types Effectively 63 Dealing with Data Shaping and Data Quality 65 The Data Interpreter 68 3 Building Your First Visualization 93 Fast and Easy Analysis via Show Me 93 New Features 94 How Show Me Works 94 The Analytics Pane 103 Sorting Data in Tableau 118 Enhancing View with Filters, Sets, Groups, and Hierarchies 121 How Tableau Uses Date Fields 143 4 Creating Calculations to Enhance Data 155 What Is Aggregation? 156 Dimension versus Attribute 157 What Are Calculated Fields and Table Calculations? 159 How Do Calculated Fields Work? 159 Creating Calculated Fields with the Calculation Editor 160 Performing Ad Hoc Calculations 161 How Do Table Calculations Work? 161 A Word on Calculations and Cubes 162 Using the Calculation Editor to Build Calculated Fields 163 Ad Hoc Calculated Fields 164 Building Formulas Using Table Calculations 166 Adding Flexibility to Calculations with Parameters 177 Why You Should Learn Level of Detail Expressions 183 5 Using Maps to Improve Insight 191 New Map Features 192 Creating a Standard Map View 192 How Tableau Geocodes Your Data 195 Searching for Items in Maps 197 Typical Map Errors and How to Deal with Them 199 Plotting Your Own Locations on a Map 200 Replacing Tableau’s Standard Maps 205 Using Custom Background Images to Plot Spatial Data 211 Notes 219 6 Developing an Ad Hoc Analysis Environment 221 Data Discovery as a Creative Process 221 Preparing Your Team for Success 222 Qualities of a Good Data Analyst 223 Doing Effective Discovery Work 224 What IT Can Do to Help 224 Spreading Discovery to Information Consumers 225 Generating New Data with Forecasts 225 Providing Self-Service Ad Hoc Analysis with Parameters 231 What Are Parameters? 231 How Can Parameters Be Used? 231 Basic Parameter Controls 232 Advanced Parameter Controls 236 Editing Views in Tableau Server 239 7 Tips, Tricks, and Timesavers 243 Saving Time and Improving Formatting 243 Double-Click Fields to Build Faster 243 Reduce Clicks Using the Right Mouse Button Drag 245 Quick Copy Fields with Control-Drag 246 Replace Fields by Dropping the New Field on Top 246 Right-Click to Edit or Format Anything 247 Editing or Removing Titles from Axis Headings 247 Quicken Your Presentation Page Views 248 A Faster Way to Access Field Menu Options 250 Zooming the Formula Dialog Box 250 Drag a Field into the Formula Dialog box 250 Swap Data in Pane and Reference Line Fields 251 Improving Appearance to Convey Meaning More Precisely 251 Changing the Appearance of Dates 251 Formatting Tooltip Content 252 Change the Order of Color Expressed in Charts 252 Exposing a Header in a One-Column Text Table 253 Unpacking a Packaged Workbook File 255 Make a Parameterized Axis Label 255 Using Continuous Quick Filters for Ranges of Values 256 Create Your Own Custom Date Hierarchy 256 Concatenating to Make Custom Fields 258 Using Legends to Build Highlight Actions 258 Formatting Null Value Results 260 When to Use Floating Objects in Dashboards 264 Combined Axis Shading in a Scatter Plot 266 Creating Folders to Hold Fields 268 Customizing Shapes, Colors, Fonts, and Images 269 Customizing Shapes 269 Customizing Colors 271 Customizing Fonts 272 Customizing Images in Dashboards 273 Advanced Chart Types 274 Bar-in-Bar Chart 274 Pareto Charts 275 Sparklines 280 Bullet Graphs 281 8 Bringing It All Together with Dashboards 285 How Dashboards Facilitate Analysis and Understanding 285 How Tableau Improves the Dashboard-Building Process 286 The Wrong Way to Build a Dashboard 287 The Right Way to Build a Dashboard 289 Best Practices for Dashboard Building 290 Size the Dashboard to Fit the Worst-Case Available Space 291 Employ Four-Pane Dashboard Designs 291 Use Actions to Filter Instead of Quick Filters 293 Build Cascading Dashboard Designs to Improve Load Speeds 293 Limit the Use of Color to One Primary Color Scheme 294 Use Small Instructions Near the Work to Make Navigation Obvious 295 Filter Information Presented in Crosstabs to Provide Relevant Details-on-Demand 296 Remove All Non-Data-Ink 298 Avoid One-Size-Fits-All Dashboards 298 Work to Achieve Dashboard Load Times of Less Than Ten Seconds 299 Building Your First Advanced Dashboard 299 Introducing the Dashboard Worksheet 299 Position the Worksheet Objects in the Dashboard Workspace 304 Using Layout Containers to Position Objects 308 Positioning the Select Year Text Table and Legends 311 Inserting and Moving Text Objects 312 Positioning and Fitting the Dashboard Objects 315 Ensure That Each Worksheet Object Fits Its Entire View 316 Create More Descriptive Titles for Each Data Pane 317 Improving the Bullet Graph and Sparkline Charts 318 Improving the Text Tables and Scatter Plot 326 Using Actions to Create Advanced Dashboard Navigation 328 Using the Select Year Text Table to Filter the Main Dashboard 329 Adding a Column Heading to Select Year 331 Adding Dynamic Title Content 332 Auto-Generating Highlight Actions from Legends 333 Understanding the Action Dialog Box 336 Embedding a Live Website in a Dashboard 340 Assemble Dashboard 2 345 Adding Details on Demand with Tooltips 354 Enhancing Tooltips and Titles 356 Adding a Read Me Dashboard 358 Bonus: Adding a Floating Dashboard Object 359 Finishing the Titles in the Main Dashboard 363 Sharing Your Dashboard with Tableau Reader 364 Security Considerations for Publishing via Tableau Reader 365 Using the Tableau Performance Recorder to Improve Load Speed 366 Sharing Dashboards with Tableau Online or Tableau Server 367 9 Designing for Mobile 369 The Physics of Mobile Consumption 370 Security Considerations for Mobile Consumption 370 Offline Access 371 Typical Mobile Usage Patterns 373 Just-In-Time Use 373 Mobile Design Implications 374 Design Best Practices for Mobile Consumption 374 Design Implications Related to Screen Resolution 375 Best Practices for Mobile Design 375 Design for a Specific Orientation 375 Consider the Limits of Finger Navigation 375 Reduce the Number of Worksheets Being Displayed 378 A Tablet Dashboard Example 378 Mobile Authoring and Editing 382 A Note on Project Elastic 383 10 Conveying Your Findings with Stories 385 Turning Analysis into Insight 385 Building a Story 386 The Story Workspace 387 A Story Example 389 Formatting Story Points 390 Sharing Your Story Point Deck 391 Part II Server 393 11 Installing Tableau Server 395 What’s New in Version 9? 396 Reasons to Deploy Tableau Server 397 Data Governance 398 Efficiency 398 Flexibility 399 Licensing Options for Tableau Server and Tableau Online 399 Determining Your Hardware and Software Needs 399 New Feature: Persistent Query Cache 401 Determining What Kind of Server License to Purchase 401 Tableau Server’s Architecture 402 Sizing the Server Hardware 403 A Scale-Up Scenario 404 A Scale-Out Scenario 404 Environmental Factors That Can Affect Performance 405 Network Performance 405 Browser 405 Resource Contention 405 Configuring Tableau Server for the First Time 405 General Setup Menu Tab 406 General: Run as User, User Authentication, and Active Directory 407 General: Gateway Port Number 408 General: Open Port in Windows Firewall 408 General: Include Sample Data and Users 408 Data Connection Tab 409 Alerts and Subscriptions 410 Server Processes 411 Security Options 412 External Secure Sockets Layer 414 SAML—Security Assertion Markup Language 415 Kerberos—A Ticket-Based Security Protocol 416 Managing Ownership Through Hierarchy 417 Workbooks and Views 417 User 418 Project 418 Group 418 Site 418 Permissions 419 Permissions for Web Edit, Save, and Download 420 Providing Data Security with User Filters 421 Applying a User Filter to a Data Source 424 Creating a Hybrid Filter from the Data Source 425 What Is the Data Server? 427 When and How to Deploy Server on Multiple Physical Boxes 428 Deploying Tableau Server in High Availability Environments 429 Three-Node Cluster 429 Four-Node Cluster 430 Leveraging Existing Security with Trusted Authentication 432 Deploying Tableau Server in Multi-national Environments 434 Tableau Server Performance Recorder 436 Show Events Filter 438 Timeline Gantt Chart 439 Events Sorted by Time 439 Query Text 439 Performance-Tuning Tactics 439 Query Execution 439 Geocoding 439 Connecting to the Data Source 440 Layout Computations 440 Generating Extract 440 Blending Data 441 Server Rendering 441 Managing Tableau Server in the Cloud 441 What Does It Mean to Be in the Cloud? 441 Tableau’s Cloud-Based Versions of Server 442 Putting Tableau Server in the Cloud 443 Monitoring Activity on Tableau Server 443 Status Section 445 Analysis Section 445 Log Files Section 445 Rebuilt Search Index Section 446 Editing Server Settings and Monitoring Licensing 446 Server Settings General Page 446 Server Setting License Page 447 Partner Add-On Toolkits 448 12 Managing Tableau Server 449 Managing Published Dashboards in Tableau Server 449 Project 451 Name 452 Tags 452 Views to Share 452 Options 452 Edit 453 Navigating Tableau Server 454 Organizing Reports for Consumption 457 Adding Tags to Workbooks 458 Creating a Favorite 459 Options for Securing Reports 461 The Application Layer 461 Defining Custom Roles 462 A Permission-Setting Example 464 Improve Efficiency with the Data Server 469 Publishing a Data Source 469 Consuming Information in Tableau Server 474 Finding Information 475 Authoring and Editing Reports via Server 480 What Is Required to Author Reports on the Web? 480 Server Design and Usage Considerations Related to Web and Tablet Authoring 481 Differences Between Desktop and Web or Tablet Authoring 482 Saving and Exporting via the Web-Tablet Environment 488 Export 488 Save and Save As 489 Recommendations for Implementing Web/Tablet Authoring 489 Sharing Connections, Data Models, and Data Extracts 490 Offering a Common Data Library 490 Sharing Data Models 490 Embedding Tableau Reports Securely on the Web 491 When to Embed a Dashboard 491 When Your Reports Are a Piece of a Larger SaaS Offering 491 Providing a More Robust Environment 492 How to Embed a Dashboard 492 Further Control Using Passed Parameters 494 Tips and Tricks for Embedding Dashboards 494 Using Trusted Ticket Authentication as an Alternative Single Sign-On Method 495 Using Subscriptions to Deliver Reports via E‑mail 496 Creating Subscription Schedules 496 13 Automating Tableau Server 501 Tableau Server’s APIs 501 What Do Tabcmd and Tabadmin Do? 502 Installing the Command-Line Tools 502 Setting the Windows Path 505 What Kind of Tasks Can Tabcmd Do? 506 Learning to Leverage Tabcmd 507 Manually Entering and Running a Script in Tabcmd 508 Running Tabcmd Scripts via Batch Files 509 The Steps Required to Create Batch Processing Scripts 509 Using Windows Scheduler to Fully Automate Scripts 511 Common Use Cases for Tabcmd 513 Automating Extracts with the Extract API 515 Data Extract API 515 Using the Extract API with Python 517 Data Extract Command-Line Utility 520 REST API 521 Initial Transactions 521 Part III Case Studies 527 14 Ensuring a Successful Tableau Deployment 529 Deploying Tableau—Lessons Learned 529 Effective Use of Consultants 529 Your Team’s Current Knowledge 530 The Data Landscape 530 The Tableau User Group at Cigna 531 Taking Care of Vizness 531 Resourcing 532 Cadence 532 Format 533 Topics 533 Effectiveness and Attendance 534 Tracking Participation 535 Success 535 Part IV Appendixes 537 A Tableau’s Product Ecosystem 539 B S upported Data Source Connections 543 C Keyboard Shortcuts 547 D Recommended Hardware Configurations 551 E Understanding Tableau Functions 555 F Companion Website 657 Glossary 659 Index 673

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Book SynopsisAn accessible guide to the multivariate time series tools used in numerous real-world applications Multivariate Time Series Analysis: With R and Financial Applications is the much anticipated sequel coming from one of the most influential and prominent experts on the topic of time series.Table of ContentsPreface xv Acknowledgements xvii 1 Multivariate Linear Time Series 1 1.1 Introduction, 1 1.2 Some Basic Concepts, 5 1.3 Cross-Covariance and Correlation Matrices, 8 1.4 Sample CCM, 9 1.5 Testing Zero Cross-Correlations, 12 1.6 Forecasting, 16 1.7 Model Representations, 18 1.8 Outline of the Book, 22 1.9 Software, 23 Exercises, 23 2 Stationary Vector Autoregressive Time Series 27 2.1 Introduction, 27 2.2 VAR(1) Models, 28 2.3 VAR(2) Models, 37 2.4 VAR(p) Models, 41 2.5 Estimation, 44 2.6 Order Selection, 61 2.7 Model Checking, 66 2.8 Linear Constraints, 80 2.9 Forecasting, 82 2.10 Impulse Response Functions, 89 2.11 Forecast Error Variance Decomposition, 96 2.12 Proofs, 98 Exercises, 100 3 Vector Autoregressive Moving-Average Time Series 105 3.1 Vector MA Models, 106 3.2 Specifying VMA Order, 112 3.3 Estimation of VMA Models, 113 3.4 Forecasting of VMA Models, 126 3.5 VARMA Models, 127 3.6 Implications of VARMA Models, 139 3.7 Linear Transforms of VARMA Processes, 141 3.8 Temporal Aggregation of VARMA Processes, 144 3.9 Likelihood Function of a VARMA Model, 146 3.10 Innovations Approach to Exact Likelihood Function, 155 3.11 Asymptotic Distribution of Maximum Likelihood Estimates, 160 3.12 Model Checking of Fitted VARMA Models, 163 3.13 Forecasting of VARMA Models, 164 3.14 Tentative Order Identification, 166 3.15 Empirical Analysis of VARMA Models, 176 3.16 Appendix, 192 Exercises, 194 4 Structural Specification of VARMA Models 199 4.1 The Kronecker Index Approach, 200 4.2 The Scalar Component Approach, 212 4.3 Statistics for Order Specification, 220 4.4 Finding Kronecker Indices, 222 4.5 Finding Scalar Component Models, 226 4.6 Estimation, 237 4.7 An Example, 245 4.8 Appendix: Canonical Correlation Analysis, 259 Exercises, 262 5 Unit-Root Nonstationary Processes 265 5.1 Univariate Unit-Root Processes, 266 5.2 Multivariate Unit-Root Processes, 279 5.3 Spurious Regressions, 290 5.4 Multivariate Exponential Smoothing, 291 5.5 Cointegration, 294 5.6 An Error-Correction Form, 297 5.7 Implications of Cointegrating Vectors, 300 5.8 Parameterization of Cointegrating Vectors, 302 5.9 Cointegration Tests, 303 5.10 Estimation of Error-Correction Models, 313 5.11 Applications, 319 5.12 Discussion, 326 5.13 Appendix, 327 Exercises, 328 6 Factor Models and Selected Topics 333 6.1 Seasonal Models, 333 6.2 Principal Component Analysis, 341 6.3 Use of Exogenous Variables, 345 6.4 Missing Values, 357 6.5 Factor Models, 364 6.6 Classification and Clustering Analysis, 386 Exercises, 394 7 Multivariate Volatility Models 399 7.1 Testing Conditional Heteroscedasticity, 401 7.2 Estimation of Multivariate Volatility Models, 407 7.3 Diagnostic Checks of Volatility Models, 409 7.4 Exponentially Weighted Moving Average, 414 7.5 BEKK Models, 417 7.6 Cholesky Decomposition and Volatility Modeling, 420 7.7 Dynamic Conditional Correlation Models, 428 7.8 Orthogonal Transformation, 434 7.9 Copula-Based Models, 443 7.10 Principal Volatility Components, 454 Exercises, 461 Appendix A Review of Mathematics and Statistics 465 A.1 Review of Vectors and Matrices, 465 A.2 Least-Squares Estimation, 477 A.3 Multivariate Normal Distributions, 478 A.4 Multivariate Student-t Distribution, 479 A.5 Wishart and Inverted Wishart Distributions, 480 A.6 Vector and Matrix Differentials, 481 Index 489

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Book SynopsisProviding insight into one of the most fascinating and unique subjects in statistics, this book examines classic problems of probability that have both contributed to the field and have been of historical significance, including Parrondo's Amazing Paradox, Laplace's Rule of Succession, and Jacob Bernoulli and His Golden Theorem.Trade Review“Thus, the book can be highly recommend to every lecturer in this field and every student interested in probability and statistics.” (Zentralblatt Math, 1 September 2013)Table of ContentsPreface ix Acknowledgments xi 1 Cardano and Games of Chance (1564) 1 2 Galileo and a Discovery Concerning Dice (1620) 9 3 The Chevalier de Méré Problem I: The Problem of Dice (1654) 13 4 The Chevalier de Méré Problem II: The Problem of Points (1654) 20 5 Huygens and the Gambler’s Ruin (1657) 39 6 The Pepys–Newton Connection (1693) 49 7 Rencontres with Montmort (1708) 54 8 Jacob Bernoulli and his Golden Theorem (1713) 62 9 De Moivre’s Problem (1730) 81 10 De Moivre, Gauss, and the Normal Curve (1730, 1809) 89 11 Daniel Bernoulli and the St. Petersburg Problem (1738) 108 12 d’Alembert and the “Croix ou Pile” Article (1754) 119 13 d’Alembert and the Gambler’s Fallacy (1761) 124 14 Bayes, Laplace, and Philosophies of Probability (1764, 1774) 129 15 Leibniz’s Error (1768) 156 16 The Buffon Needle Problem (1777) 159 17 Bertrand’s Ballot Problem (1887) 169 18 Bertrand’s Strange Three Boxes (1889) 175 19 Bertrand’s Chords (1889) 179 20 Three Coins and a Puzzle from Galton (1894) 186 21 Lewis Carroll’s Pillow Problem No. 72 (1894) 189 22 Borel and a Different Kind of Normality (1909) 194 23 Borel’s Paradox and Kolmogorov’s Axioms (1909, 1933) 199 24 Of Borel, Monkeys, and the New Creationism (1913) 208 25 Kraitchik’s Neckties and Newcomb’s Problem (1930, 1960) 215 26 Fisher and the Lady Tasting Tea (1935) 224 27 Benford and the Peculiar Behavior of the First Significant Digit (1938) 233 28 Coinciding Birthdays (1939) 240 29 Lévy and the Arc Sine Law (1939) 247 30 Simpson’s Paradox (1951) 253 31 Gamow, Stern, and Elevators (1958) 260 32 Monty-Hall, Cars, and Goats (1975) 264 33 Parrondo’s Perplexing Paradox (1996) 271 Bibliography 277 Photo Credits 296 Index 299

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Book SynopsisThis volume contains 100 papers published between 1841 and 1851 by the prolific Victorian mathematician Arthur Cayley. Approximately half concern geometry, the other half analysis. Cayley went on to become Sadleirian Professor of Pure Mathematics at Cambridge, and president of the British Association for the Advancement of Science.Table of ContentsPreface; Papers 1-100 (1841–1851); Notes and References.

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Book SynopsisArthur Cayley (1821â1895) was a key figure in the creation of modern algebra. He studied mathematics at Cambridge and published three papers while still an undergraduate. He then qualified as a lawyer and published about 250 mathematical papers during his fourteen years at the Bar. In 1863 he became the first Sadleirian Professor of Pure Mathematics at Cambridge, where he continued to publish at a phenomenal rate on nearly every aspect of the subject, his most important work being in matrices, geometry and abstract groups. In 1883 he became president of the British Association for the Advancement of Science. Publication of his Collected Papers - 967 papers in 13 volumes plus an index volume - began in 1889 and was completed after his death. This second volume contains 56 papers published between 1851 and 1860, plus two 1889 papers, and includes six of the Memoirs on Quantics.Table of ContentsPreface; Papers 101-158 (1851–60); Notes and References.

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Book SynopsisAn important factor that affects the duration, complexity and cost of a clinical trial is the endpoint used to study the treatmentâs efficacy. When a true endpoint is difficult to use because of such factors as long follow-up times or prohibitive cost, it is sometimes possible to use a surrogate endpoint that can be measured in a more convenient or cost-effective way. This book focuses on the use of surrogate endpoint evaluation methods in practice, using SAS and R.Trade Review"This is a timely text. The number of published studies using surrogate endpoints has increased dramatically since the early work of the 1980s; however, there is a dearth of available texts or software on this topic. Anyone with an interest in surrogate endpoint evaluation would benefit from this text."~Statistics in Medicine Table of ContentsIntroductory Material. Introduction. Notation and Example Datasets. The History of Surrogate Endpoint Validation. Contemporary Surrogate Endpoint Evaluation Methods. Multiple-Trial Surrogate Endpoint Evaluation Methods. Two Continuous Outcomes. Two Survival Endpoints. Two Categorical Endpoints. A Categorical and a Continuous Endpoint. A Survival and a Continuous Endpoint. A Survival and a Categorical Endpoint. Two Longitudinal Endpoints. A Longitudinal and a Survival Endpoint. Additional Considerations and Further Topics. Software Details. An Alternative Surrogate Endpoint Evaluation Framework: Causal-Inference. Surrogate Endpoint Evaluation Methods in Small Samples. Construction and Evaluation of Genetic Biomarkers in Early Drug Development Experiments. Additional Considerations.

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Book SynopsisDavid J. Eicher's fascinating and spectacular exploration of the cosmos presents a series of remarkable celestial highlights ranging from the exploration of our own solar system to the latest theories on the fate of the cosmos. It features color illustrations including numerous photos, maps and explanatory diagrams.Trade Review'David Eicher has more than three decades' experience of writing about astronomy for a general readership. His experience and enthusiasm shine through in this wide-ranging survey of current 'hot topics'.' Martin Rees, Emeritus Professor of Cosmology and Astrophysics, University of Cambridge'The New Cosmos by David Eicher is a wonderful read! This wonderfully written, accessible, authoritative new book spans the breadth of major topics in early twenty-first-century astronomy, engaging the reader in every chapter. I haven't seen a better book surveying modern astronomy in a decade. I highly recommend this masterpiece as a gift to yourself or anyone interested in space and astronomy.' Alan Stern, Principal Investigator of the New Horizons mission, Southwest Research Institute'If you are looking for a collection of newspaper headlines full of hype about this discovery or that, then The New Cosmos probably isn't for you. On the other hand, if those headlines whet your appetite for something more substantial, then pick up a copy and settle in for a fascinating and enlightening read. The New Cosmos is not simply a survey of astronomy and planetary science - it is more of a travelogue, starting with intriguing questions and then following where each story leads. And there throughout the journey is David J. Eicher's obvious passion and joy for the wonders of the heavens, and for the human quest to make those wonders known.' Jeff Hester, Professor Emeritus, School of Earth and Space Exploration, Arizona State University'In this book, Eicher synthesizes a wealth of relatively new information into an interesting, coherent, up-to-date overview of many of the most important and exciting areas of astronomy … Immersing yourself in the chapters that follow will give you a new sense of wonder at the amazing universe that we inhabit, yet simultaneously awakening both your humility as a cosmic speck of dust and your awe at our present understanding of the cosmos.' Alex Filippenko, University of California, Berkeley, from the Foreword'This is an exceptional book that places our life in a global perspective on the cosmic stage, both in space and in time. It leaves you wondering whether our civilization should reconsider its priorities if it wishes to be regarded as intelligent.' Abraham Loeb, Harvard University'David Eicher provides a much-needed update to Carl Sagan's classic book Cosmos from thirty-five years ago, describing the most fascinating advances in astronomy and planetary science.' Alfred McEwen, Lunar and Planetary Laboratory, University of Arizona, Tucson'The New Cosmos is an enjoyable stroll through our current knowledge of the objects in the cosmic zoo. As a planetary scientist, I welcome the opportunity to learn about fields distant from my own. I know that I can trust their treatment because my own field is expertly and concisely covered. Bravo!' Paul D. Spudis, Lunar and Planetary Institute, Houston'It can be easy to forget just how many different major astrophysical discoveries have taken place in recent years. Eicher takes the reader through a whirlwind tour of the most exciting highlights, from newly discovered planets in our own cosmic backyard, to the dark matter and dark energy that are ubiquitous throughout our universe. The New Cosmos covers all of the 'big questions' that are being nervously and excitedly debated in the hallways of astronomy and physics departments around the world.' Dan Hooper, Fermilab, Illinois'If you want to know what happens when the Sun dies, or wish to understand such puzzles as the true nature of black holes and the long-term fate of the universe, then you should be reading this book. In clear and authoritative prose, David Eicher offers readers a wonderful set of answers to the most consequential questions in astronomy. It's an impressively comprehensive treatment of the biggest subject of all - the cosmos.' Seth Shostak, SETI Institute, CaliforniaTable of ContentsForeword Alex Filippenko; 1. The awakening of astronomy; 2. How the Sun will die; 3. The end of life on Earth; 4. How the moon formed; 5. Where has all the water gone?; 6. Why did Venus turn inside-out?; 7. Is Pluto a planet?; 8. Planets everywhere; 9. The Milky Way as barred spiral; 10. Here comes Milkomeda; 11. The Big Bang's cosmic echo; 12. How large is the universe?; 13. The mystery of dark matter; 14. The bigger mystery of dark energy; 15. Black holes are ubiquitous; 16. What is the universe's fate?; 17. The meaning of life in the cosmos; Glossary; Bibliography; Index.

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Book SynopsisThis undergraduate textbook is a rigorous mathematical introduction to dynamical systems and an accessible guide for students transitioning from calculus to advanced mathematics. It has many student-friendly features, such as graded exercises that range from straightforward to more difficult with hints, and includes concrete applications of real analysis and metric space theory to dynamical problems. Proofs are complete and carefully explained, and there is opportunity to practice manipulating algebraic expressions in an applied context of dynamical problems. After presenting a foundation in one-dimensional dynamical systems, the text introduces students to advanced subjects in the latter chapters, such as topological and symbolic dynamics. It includes two-dimensional dynamics, Sharkovsky''s theorem, and the theory of substitutions, and takes special care in covering Newton''s method. Mathematica code is available online, so that students can see implementation of many of the dynamicalTrade Review'This remarkable book provides a thoroughly field-tested way of teaching analysis while introducing dynamical systems. Combining lightness with rigor, it motivates and applies a wide range of subjects in the theory of metric spaces as it explores a broad variety of topics in dynamics.' Boris Hasselblatt, Tufts University, Massachusetts'This is a most impressive book. The author presents a range of topics which are not usually included in a book at this level (for example Sharkovsky's theorem, fractals, substitutions). The writing is clear and there are exercises of varying difficulty. A fine undergraduate text, which will also be of interest to graduate students and researchers in dynamics.' Joseph Auslander, Professor Emeritus of Mathematics, University of Maryland'This carefully written book introduces the student to a wealth of examples in dynamical systems, including several modern topics such as complex dynamics, topological dynamics and substitutions.' Cesar E. Silva, Williams College, Massachusetts'More rigorous than other undergraduate texts but less daunting than graduate books, this book is perfect for a core course on chaotic dynamic systems for undergraduates in their junior or senior year. Thoughtful, clear, and written with just the right amount of detail, Goodson develops the necessary tools required for an in-depth study of dynamical systems.' Alisa DeStefano, College of the Holy Cross, Massachusetts'… readers familiar with the basics of calculus, linear algebra, topology, and some real analysis will find that the topics are presented in an interesting manner, making this a good treatment of discrete dynamical systems … Summing Up: Recommended. Upper-division undergraduates and above; faculty and professionals.' M. D. Sanford, CHOICE'I think that this attractive textbook would be a welcome addition to the bookshelf of just about anyone with an interest in fractals, chaos, or dynamical systems. It presents most of the basic concepts in these fields at a level appropriate for senior math majors. Additional[ly], it has an extended treatment of substitution dynamical systems - the only undergraduate textbook I'm aware of that does so.' Christopher P. Grant, Mathematical Reviews'This book is a good example of what is possible as an introduction to this broad material of chaos, dynamical systems, fractals, tilings, substitutions, and many other related aspects. To bring all this in one volume and at a moderate mathematical level is an ambitious plan but these notes are the result of many years of teaching experience … The extraordinary combination of abstraction linked to simple yet appealing examples is the secret ingredient that is mastered wonderfully in this text.' Adhemar Bultheel, European Mathematical SocietyTable of Contents1. The orbits of one-dimensional maps; 2. Bifurcations and the logistic family; 3. Sharkovsky's theorem; 4. Dynamics on metric spaces; 5. Countability, sets of measure zero, and the Cantor set; 6. Devaney's definition of chaos; 7. Conjugacy of dynamical systems; 8. Singer's theorem; 9. Conjugacy, fundamental domains, and the tent family; 10. Fractals; 11. Newton's method for real quadratics and cubics; 12. Coppel's theorem and a proof of Sharkovsky's theorem; 13. Real linear transformations, the Hénon Map, and hyperbolic toral automorphisms; 14. Elementary complex dynamics; 15. Examples of substitutions; 16. Fractals arising from substitutions; 17. Compactness in metric spaces and an introduction to topological dynamics; 18. Substitution dynamical systems; 19. Sturmian sequences and irrational rotations; 20. The multiple recurrence theorem of Furstenberg and Weiss; Appendix A: theorems from calculus; Appendix B: the Baire category theorem; Appendix C: the complex numbers; Appendix D: Weyl's equidistribution theorem.

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Book SynopsisNATIONAL BESTSELLER • From the classroom to the courtroom and from financial markets to supermarkets, an intriguing and illuminating look at how randomness, chance, and probability affect our daily lives that will intrigue, awe, and inspire.“Mlodinow writes in a breezy style, interspersing probabilistic mind-benders with portraits of theorists.... The result is a readable crash course in randomness.” —The New York Times Book ReviewWith the born storyteller's command of narrative and imaginative approach, Leonard Mlodinow vividly demonstrates how our lives are profoundly informed by chance and randomness and how everything from wine ratings and corporate success to school grades and political polls are less reliable than we believe.By showing us the true nature of chance and revealing the psychological illusions that cause us to misjudge the world around us, Mlodinow gives us the tools we need to make more

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Trade Review"Mr. Bloch, professor of mathematics at Wheaton College, has woven an elegant, ingenious, scholarly interpretation of Borges's text that contradicts the disingenuous 'unimaginable' of his title."--New York Sun "For the reader of Borges, some of Bloch's observations may offer a useful new way of engaging with the themes of the fiction." -- American Scientist "You need no advanced mathematics to understand 'The Library of Babel' but chances are good that if you like the story, you'll enjoy Professor Bloch's excursions." -- Mathematical Association of America Review "Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature, but also exposes the reader - including those more inclined to the literary world - to many intriguing and entrancing mathematical ideas."--Mathematical ReviewsTable of ContentsPreface ; Introduction ; Combinatorics: Contemplating Variations of the 23 Letter ; Topology and Cosmology: The Universe (Which Others Call the Library) ; Information Theory: Cataloging the Collection ; Geometry and Graph Theory: Ambiguity and Access ; Real Analysis: The Book of Sand ; More Combinatorics: Disorderings into Order ; A Homomorphism: Structure into Meaning ; Critical Points ; Openings ; Acknowledgements ; Appendix IThe Logos of Logarithms ; Appendix IIFlat-Out Disoriented ; Appendix IIIPeeling the 3-Sphere ; Appendix IVA Labyrinth, not a Maze ; Appendix VAn Example of the Ars Combinatoria ; Bibliography

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisProvides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, economics, and the life and social sciences. In this book, the author applies real-world orientation to concepts, problem-solving approach, straight forward and concise writing style, and comprehensive exercise sets.Table of ContentsChapter 1: Functions, Graphs, and Limits1.1Functions1.2The Graph of a Function1.3Lines and Linear Functions1.4Functional Models1.5Limits1.6One-Sided Limits and ContinuityChapter 2: Differentiation: Basic Concepts2.1The Derivative2.2Techniques of Differentiation2.3Product and Quotient Rules; Higher-Order Derivatives2.4The Chain Rule2.5Marginal Analysis and Approximations Using Increments2.6Implicit Differentiation and Related RatesChapter 3: Additional Applications of the Derivative3.1 Increasing and Decreasing Functions; Relative Extrema3.2 Concavity and Points of Inflection3.3 Curve Sketching3.4 Optimization; Elasticity of Demand3.5 Additional Applied OptimizationChapter 4: Exponential and Logarithmic Functions4.1 Exponential Functions; Continuous Compounding4.2 Logarithmic Functions4.3 Differentiation of Exponential and Logarithmic Functions4.4 Additional Applications; Exponential ModelsChapter 5: Integration5.1 Indefinite Integration and Differential Equations5.2 Integration by Substitution5.3 The Definite Integral and the Fundamental Theorem of Calculus5.4 Applying Definite Integration: Distribution of Wealth and Average Value5.5 Additional Applications to Business and Economics5.6 Additional Applications to the Life and Social SciencesChapter 6: Additional Topics in Integration6.1 Integration by Parts; Integral Tables6.2 Numerical Integration6.3 Improper Integrals6.4 Introduction to Continuous ProbabilityChapter 7: Calculus of Several Variables7.1 Functions of Several Variables7.2 Partial Derivatives7.3 Optimizing Functions of Two Variables7.4 The Method of Least-Squares7.5 Constrained Optimization: The Method of Lagrange Multipliers7.6 Double IntegralsAppendix A: Algebra ReviewA.1 A Brief Review of AlgebraA.2 Factoring Polynomials and Solving Systems of EquationsA.3 Evaluating Limits with L’Hopital’s RuleA.4 The Summation Notation

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Book SynopsisPraise for the Second Edition As a comprehensive statistics reference book for quality improvement, it certainly is one of the best books available. Technometrics This new edition continues to provide the most current, proven statistical methods for quality control and quality improvement The use of quantitative methods offers numerous benefits in the fields of industry and business, both through identifying existing trouble spots and alerting management and technical personnel to potential problems. Statistical Methods for Quality Improvement, Third Edition guides readers through a broad range of tools and techniques that make it possible to quickly identify and resolve both current and potential trouble spots within almost any manufacturing or nonmanufacturing process. The book provides detailed coverage of the application of control charts, while also exploring critical topics such as regression, design of experimentsTrade Review"Ryan covers everything you could possibly imagine in a statistical methods book...Those with more advanced statistical experience will get the most from this book, although the reading level is suitable for the average user. This is an excellent reference for any of your quality improvement needs." (Quality Progress, July 2012)Table of ContentsPreface xix Preface to the Second Edition xxi Preface to the First Edition xxiii PART I FUNDAMENTAL QUALITY IMPROVEMENT AND STATISTICAL CONCEPTS 1 Introduction 3 1.1 Quality and Productivity, 4 1.2 Quality Costs (or Does It?), 5 1.3 The Need for Statistical Methods, 5 1.4 Early Use of Statistical Methods for Improving Quality, 6 1.5 Influential Quality Experts, 7 1.6 Summary, 9 2 Basic Tools for Improving Quality 13 2.1 Histogram, 13 2.2 Pareto Charts, 17 2.3 Scatter Plots, 21 2.4 Control Chart, 24 2.5 Check Sheet, 26 2.6 Cause-and-Effect Diagram, 26 2.7 Defect Concentration Diagram, 28 2.8 The Seven Newer Tools, 28 2.9 Software, 30 2.10 Summary, 31 3 Basic Concepts in Statistics and Probability 33 3.1 Probability, 33 3.2 Sample Versus Population, 35 3.3 Location, 36 3.4 Variation, 38 3.5 Discrete Distributions, 41 3.6 Continuous Distributions, 55 3.7 Choice of Statistical Distribution, 69 3.8 Statistical Inference, 69 3.9 Enumerative Studies Versus Analytic Studies, 81 PARTII CONTROL CHARTS AND PROCESS CAPABILITY 4 Control Charts for Measurements With Subgrouping (for One Variable) 89 4.1 Basic Control Chart Principles, 89 4.2 Real-Time Control Charting Versus Analysis of Past Data, 92 4.3 Control Charts: When to Use, Where to Use, How Many to Use, 94 4.4 Benefits from the Use of Control Charts, 94 4.5 Rational Subgroups, 95 4.6 Basic Statistical Aspects of Control Charts, 95 4.7 Illustrative Example, 96 4.8 Illustrative Example with Real Data, 114 4.9 Determining the Point of a Parameter Change, 116 4.10 Acceptance Sampling and Acceptance Control Chart, 117 4.11 Modified Limits, 124 4.12 Difference Control Charts, 124 4.13 Other Charts, 126 4.14 Average Run Length (ARL), 127 4.15 Determining the Subgroup Size, 129 4.16 Out-of-Control Action Plans, 131 4.17 Assumptions for the Charts in This Chapter, 132 4.18 Measurement Error, 140 4.19 Software, 142 4.20 Summary, 143 5 Control Charts for Measurements Without Subgrouping (for One Variable) 157 5.2 Transform the Data or Fit a Distribution?, 170 5.3 Moving Average Chart, 171 5.4 Controlling Variability with Individual Observations, 173 5.5 Summary, 175 6 Control Charts for Attributes 181 6.1 Charts for Nonconforming Units, 182 6.2 Charts for Nonconformities, 202 6.3 Summary, 218 7 Process Capability 225 7.1 Data Acquisition for Capability Indices, 225 7.2 Process Capability Indices, 227 7.3 Estimating the Parameters in Process Capability Indices, 232 7.4 Distributional Assumption for Capability Indices, 235 7.5 Confidence Intervals for Process Capability Indices, 236 7.6 Asymmetric Bilateral Tolerances, 243 7.7 Capability Indices That Are a Function of Percent Nonconforming, 245 7.8 Modified k Index, 250 7.9 Other Approaches, 251 7.10 Process Capability Plots, 251 7.11 Process Capability Indices Versus Process Performance Indices, 252 7.12 Process Capability Indices with Autocorrelated Data, 253 7.13 Software for Process Capability Indices, 253 7.14 Summary, 253 8 Alternatives to Shewhart Charts 261 8.1 Introduction, 261 8.2 Cumulative Sum Procedures: Principles and Historical Development, 263 8.3 CUSUM Procedures for Controlling Process Variability, 283 8.4 Applications of CUSUM Procedures, 286 8.5 Generalized Likelihood Ratio Charts: Competitive Alternative to CUSUM Charts, 286 8.6 CUSUM Procedures for Nonconforming Units, 286 8.7 CUSUM Procedures for Nonconformity Data, 290 8.8 Exponentially Weighted Moving Average Charts, 294 8.9 Software, 301 8.10 Summary, 301 9 Multivariate Control Charts for Measurement and Attribute Data 309 9.1 Hotelling's T2 Distribution, 312 9.2 A T2 Control Chart, 313 9.3 Multivariate Chart Versus Individual X-Charts, 326 9.4 Charts for Detecting Variability and Correlation Shifts, 327 9.5 Charts Constructed Using Individual Observations, 330 9.6 When to Use Each Chart, 335 9.7 Actual Alpha Levels for Multiple Points, 336 9.8 Requisite Assumptions, 336 9.9 Effects of Parameter Estimation on ARLs, 337 9.10 Dimension-Reduction and Variable Selection Techniques, 337 9.11 Multivariate CUSUM Charts, 338 9.12 Multivariate EWMA Charts, 339 9.13 Effect of Measurement Error, 343 9.14 Applications of Multivariate Charts, 344 9.15 Multivariate Process Capability Indices, 344 9.16 Summary, 344 10 Miscellaneous Control Chart Topics 353 10.1 Pre-control, 353 10.2 Short-Run SPC, 356 10.3 Charts for Autocorrelated Data, 359 10.4 Charts for Batch Processes, 364 10.5 Charts for Multiple-Stream Processes, 364 10.6 Nonparametric Control Charts, 365 10.7 Bayesian Control Chart Methods, 366 10.8 Control Charts for Variance Components, 367 10.9 Control Charts for Highly Censored Data, 367 10.10 Neural Networks, 367 10.11 Economic Design of Control Charts, 368 10.12 Charts with Variable Sample Size and/or Variable Sampling Interval, 370 10.13 Users of Control Charts, 371 10.14 Software for Control Charting, 374 PART III BEYOND CONTROL CHARTS: GRAPHICAL AND STATISTICAL METHODS 11 Graphical Methods 387 11.1 Histogram, 388 11.2 Stem-and-Leaf Display, 389 11.3 Dot Diagrams, 390 11.4 Boxplot, 392 11.5 Normal Probability Plot, 396 11.6 Plotting Three Variables, 398 11.7 Displaying More Than Three Variables, 399 11.8 Plots to Aid in Transforming Data, 399 11.9 Summary, 401 12 Linear Regression 407 12.1 Simple Linear Regression, 407 12.2 Worth of the Prediction Equation, 411 12.3 Assumptions, 413 12.4 Checking Assumptions Through Residual Plots, 414 12.5 Confidence Intervals and Hypothesis Test, 415 12.6 Prediction Interval for Y, 416 12.7 Regression Control Chart, 417 12.8 Cause-Selecting Control Charts, 419 12.9 Linear, Nonlinear, and Nonparametric Profiles, 421 12.10 Inverse Regression, 423 12.11 Multiple Linear Regression, 426 12.12 Issues in Multiple Regression, 426 12.13 Software For Regression, 429 12.14 Summary, 429 13 Design of Experiments 435 13.1 A Simple Example of Experimental Design Principles, 435 13.2 Principles of Experimental Design, 437 13.3 Statistical Concepts in Experimental Design, 439 13.4 t-Tests, 441 13.5 Analysis of Variance for One Factor, 445 13.6 Regression Analysis of Data from Designed Experiments, 455 13.7 ANOVA for Two Factors, 460 13.8 The 23 Design, 469 13.9 Assessment of Effects Without a Residual Term, 474 13.10 Residual Plot, 477 13.11 Separate Analyses Using Design Units and Uncoded Units, 479 13.12 Two-Level Designs with More Than Three Factors, 480 13.13 Three-Level Factorial Designs, 482 13.14 Mixed Factorials, 483 13.15 Fractional Factorials, 483 13.16 Other Topics in Experimental Design and Their Applications, 493 13.17 Summary, 500 14 Contributions of Genichi Taguchi and Alternative Approaches 513 14.1 "Taguchi Methods", 513 14.2 Quality Engineering, 514 14.3 Loss Functions, 514 14.4 Distribution Not Centered at the Target, 518 14.5 Loss Functions and Specification Limits, 518 14.6 Asymmetric Loss Functions, 518 14.7 Signal-to-Noise Ratios and Alternatives, 522 14.8 Experimental Designs for Stage One, 524 14.9 Taguchi Methods of Design, 525 14.10 Determining Optimum Conditions, 553 14.11 Summary, 558 15 Evolutionary Operation 565 15.1 EVOP Illustrations, 566 15.2 Three Variables, 576 15.3 Simplex EVOP, 578 15.4 Other EVOP Procedures, 581 15.5 Miscellaneous Uses of EVOP, 581 15.6 Summary, 582 16 Analysis of Means 587 16.1 ANOM for One-Way Classifications, 588 16.2 ANOM for Attribute Data, 591 16.3 ANOM When Standards Are Given, 594 16.4 ANOM for Factorial Designs, 596 16.5 ANOM When at Least One Factor Has More Than Two Levels, 601 16.6 Use of ANOM with Other Designs, 610 16.7 Nonparametric ANOM, 610 16.8 Summary, 611 17 Using Combinations of Quality Improvement Tools 615 17.1 Control Charts and Design of Experiments, 616 17.2 Control Charts and Calibration Experiments, 616 17.3 Six Sigma Programs, 616 17.4 Statistical Process Control and Engineering Process Control, 624 Answers to Selected Exercises 629 Appendix: Statistical Tables 633 Author Index 645 Subject Index 657

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Book SynopsisPraise for the Second Edition "A must-have book for anyone expecting to do research and/or applications in categorical data analysis. " Statistics in Medicine "It is a total delight reading this book.Table of ContentsPreface xiii 1 Introduction: Distributions and Inference for Categorical Data 1 1.1 Categorical Response Data, 1 1.2 Distributions for Categorical Data, 5 1.3 Statistical Inference for Categorical Data, 8 1.4 Statistical Inference for Binomial Parameters, 13 1.5 Statistical Inference for Multinomial Parameters, 17 1.6 Bayesian Inference for Binomial and Multinomial Parameters, 22 Notes, 27 Exercises, 28 2 Describing Contingency Tables 37 2.1 Probability Structure for Contingency Tables, 37 2.2 Comparing Two Proportions, 43 2.3 Conditional Association in Stratified 2 × 2 Tables, 47 2.4 Measuring Association in I × J Tables, 54 Notes, 60 Exercises, 60 3 Inference for Two-Way Contingency Tables 69 3.1 Confidence Intervals for Association Parameters, 69 3.2 Testing Independence in Two-way Contingency Tables, 75 3.3 Following-up Chi-Squared Tests, 80 3.4 Two-Way Tables with Ordered Classifications, 86 3.5 Small-Sample Inference for Contingency Tables, 90 3.6 Bayesian Inference for Two-way Contingency Tables, 96 3.7 Extensions for Multiway Tables and Nontabulated Responses, 100 Notes, 101 Exercises, 103 4 Introduction to Generalized Linear Models 113 4.1 The Generalized Linear Model, 113 4.2 Generalized Linear Models for Binary Data, 117 4.3 Generalized Linear Models for Counts and Rates, 122 4.4 Moments and Likelihood for Generalized Linear Models, 130 4.5 Inference and Model Checking for Generalized Linear Models, 136 4.6 Fitting Generalized Linear Models, 143 4.7 Quasi-Likelihood and Generalized Linear Models, 149 Notes, 152 Exercises, 153 5 Logistic Regression 163 5.1 Interpreting Parameters in Logistic Regression, 163 5.2 Inference for Logistic Regression, 169 5.3 Logistic Models with Categorical Predictors, 175 5.4 Multiple Logistic Regression, 182 5.5 Fitting Logistic Regression Models, 192 Notes, 195 Exercises, 196 6 Building, Checking, and Applying Logistic Regression Models 207 6.1 Strategies in Model Selection, 207 6.2 Logistic Regression Diagnostics, 215 6.3 Summarizing the Predictive Power of a Model, 221 6.4 Mantel–Haenszel and Related Methods for Multiple 2 × 2 Tables, 225 6.5 Detecting and Dealing with Infinite Estimates, 233 6.6 Sample Size and Power Considerations, 237 Notes, 241 Exercises, 243 7 Alternative Modeling of Binary Response Data 251 7.1 Probit and Complementary Log–log Models, 251 7.2 Bayesian Inference for Binary Regression, 257 7.3 Conditional Logistic Regression, 265 7.4 Smoothing: Kernels, Penalized Likelihood, Generalized Additive Models, 270 7.5 Issues in Analyzing High-Dimensional Categorical Data, 278 Notes, 285 Exercises, 287 8 Models for Multinomial Responses 293 8.1 Nominal Responses: Baseline-Category Logit Models, 293 8.2 Ordinal Responses: Cumulative Logit Models, 301 8.3 Ordinal Responses: Alternative Models, 308 8.4 Testing Conditional Independence in I × J × K Tables, 314 8.5 Discrete-Choice Models, 320 8.6 Bayesian Modeling of Multinomial Responses, 323 Notes, 326 Exercises, 329 9 Loglinear Models for Contingency Tables 339 9.1 Loglinear Models for Two-way Tables, 339 9.2 Loglinear Models for Independence and Interaction in Three-way Tables, 342 9.3 Inference for Loglinear Models, 348 9.4 Loglinear Models for Higher Dimensions, 350 9.5 Loglinear—Logistic Model Connection, 353 9.6 Loglinear Model Fitting: Likelihood Equations and Asymptotic Distributions, 356 9.7 Loglinear Model Fitting: Iterative Methods and Their Application, 364 Notes, 368 Exercises, 369 10 Building and Extending Loglinear Models 377 10.1 Conditional Independence Graphs and Collapsibility, 377 10.2 Model Selection and Comparison, 380 10.3 Residuals for Detecting Cell-Specific Lack of Fit, 385 10.4 Modeling Ordinal Associations, 386 10.5 Generalized Loglinear and Association Models, Correlation Models, and Correspondence Analysis, 393 10.6 Empty Cells and Sparseness in Modeling Contingency Tables, 398 10.7 Bayesian Loglinear Modeling, 401 Notes, 404 Exercises, 407 11 Models for Matched Pairs 413 11.1 Comparing Dependent Proportions, 414 11.2 Conditional Logistic Regression for Binary Matched Pairs, 418 11.3 Marginal Models for Square Contingency Tables, 424 11.4 Symmetry, Quasi-Symmetry, and Quasi-Independence, 426 11.5 Measuring Agreement Between Observers, 432 11.6 Bradley–Terry Model for Paired Preferences, 436 11.7 Marginal Models and Quasi-Symmetry Models for Matched Sets, 439 Notes, 443 Exercises, 445 12 Clustered Categorical Data: Marginal and Transitional Models 455 12.1 Marginal Modeling: Maximum Likelihood Approach, 456 12.2 Marginal Modeling: Generalized Estimating Equations (GEEs) Approach, 462 12.3 Quasi-Likelihood and Its GEE Multivariate Extension: Details, 465 12.4 Transitional Models: Markov Chain and Time Series Models, 473 Notes, 478 Exercises, 479 13 Clustered Categorical Data: Random Effects Models 489 13.1 Random Effects Modeling of Clustered Categorical Data, 489 13.2 Binary Responses: Logistic-Normal Model, 494 13.3 Examples of Random Effects Models for Binary Data, 498 13.4 Random Effects Models for Multinomial Data, 511 13.5 Multilevel Modeling, 515 13.6 GLMM Fitting, Inference, and Prediction, 519 13.7 Bayesian Multivariate Categorical Modeling, 523 Notes, 525 Exercises, 527 14 Other Mixture Models for Discrete Data 535 14.1 Latent Class Models, 535 14.2 Nonparametric Random Effects Models, 542 14.3 Beta-Binomial Models, 548 14.4 Negative Binomial Regression, 552 14.5 Poisson Regression with Random Effects, 555 Notes, 557 Exercises, 558 15 Non-Model-Based Classification and Clustering 565 15.1 Classification: Linear Discriminant Analysis, 565 15.2 Classification: Tree-Structured Prediction, 570 15.3 Cluster Analysis for Categorical Data, 576 Notes, 581 Exercises, 582 16 Large- and Small-Sample Theory for Multinomial Models 587 16.1 Delta Method, 587 16.2 Asymptotic Distributions of Estimators of Model Parameters and Cell Probabilities, 592 16.3 Asymptotic Distributions of Residuals and Goodness-of-fit Statistics, 594 16.4 Asymptotic Distributions for Logit/Loglinear Models, 599 16.5 Small-Sample Significance Tests for Contingency Tables, 601 16.6 Small-Sample Confidence Intervals for Categorical Data, 603 16.7 Alternative Estimation Theory for Parametric Models, 610 Notes, 615 Exercises, 616 17 Historical Tour of Categorical Data Analysis 623 17.1 Pearson–Yule Association Controversy, 623 17.2 R. A. Fisher’s Contributions, 625 17.3 Logistic Regression, 627 17.4 Multiway Contingency Tables and Loglinear Models, 629 17.5 Bayesian Methods for Categorical Data, 633 17.6 A Look Forward, and Backward, 634 Appendix A Statistical Software for Categorical Data Analysis 637 Appendix B Chi-Squared Distribution Values 641 References 643 Author Index 689 Example Index 701 Subject Index 705 Appendix C Software Details for Text Examples (text website)

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Book SynopsisStatistical science s first coordinated manual of methods for analyzing ordered categorical data, now fully revised and updated, continues to present applications and case studies in fields as diverse as sociology, public health, ecology, marketing, and pharmacy.Table of ContentsPreface. 1. Introduction. 1.1. Ordinal Categorical Scales. 1.2. Advantages of Using Ordinal Methods. 1.3. Ordinal Modeling Versus Ordinary Regession Analysis. 1.4. Organization of This Book. 2. Ordinal Probabilities, Scores, and Odds Ratios. 2.1. Probabilities and Scores for an Ordered Categorical Scale. 2.2. Ordinal Odds Ratios for Contingency Tables. 2.3. Confidence Intervals for Ordinal Association Measures. 2.4. Conditional Association in Three-Way Tables. 2.5. Category Choice for Ordinal Variables. Chapter Notes. Exercises. 3. Logistic Regression Models Using Cumulative Logits. 3.1. Types of Logits for An Ordinal Response. 3.2. Cumulative Logit Models. 3.3. Proportional Odds Models: Properties and Interpretations. 3.4. Fitting and Inference for Cumulative Logit Models. 3.5. Checking Cumulative Logit Models. 3.6. Cumulative Logit Models Without Proportional Odds. 3.7. Connections with Nonparametric Rank Methods. Chapter Notes. Exercises. 4. Other Ordinal Logistic Regression Models. 4.1. Adjacent-Categories Logit Models. 4.2. Continuation-Ratio Logit Models. 4.3. Stereotype Model: Multiplicative Paired-Category Logits. Chapter Notes. Exercises. 5. Other Ordinal Multinomial Response Models. 5.1. Cumulative Link Models. 5.2. Cumulative Probit Models. 5.3. Cumulative Log-Log Links: Proportional Hazards Modeling. 5.4. Modeling Location and Dispersion Effects. 5.5. Ordinal ROC Curve Estimation. 5.6. Mean Response Models. Chapter Notes. Exercises. 6. Modeling Ordinal Association Structure. 6.1. Ordinary Loglinear Modeling. 6.2. Loglinear Model of Linear-by-Linear Association. 6.3. Row or Column Effects Association Models. 6.4. Association Models for Multiway Tables. 6.5. Multiplicative Association and Correlation Models. 6.6. Modeling Global Odds Ratios and Other Associations. Chapter Notes. Exercises. 7. Non-Model-Based Analysis of Ordinal Association. 7.1. Concordance and Discordance Measures of Association. 7.2. Correlation Measures for Contingency Tables. 7.3. Non-Model-Based Inference for Ordinal Association Measures. 7.4. Comparing Singly Ordered Multinomials. 7.5. Order-Restricted Inference with Inequality Constraints. 7.6. Small-Sample Ordinal Tests of Independence. 7.7. Other Rank-Based Statistical Methods for Ordered Categories. Appendix: Standard Errors for Ordinal Measures. Chapter Notes. Exercises. 8. Matched-Pairs Data with Ordered Categories. 8.1. Comparing Marginal Distributions for Matched Pairs. 8.2. Models Comparing Matched Marginal Distributions. 8.3. Models for The Joint Distribution in A Square Table. 8.4. Comparing Marginal Distributions for Matched Sets. 8.5. Analyzing Rater Agreement on an Ordinal Scale. 8.6. Modeling Ordinal Paired Preferences. Chapter Notes. Exercises. 9. Clustered Ordinal Responses: Marginal Models. 9.1. Marginal Ordinal Modeling with Explanatory Variables. 9.2. Marginal Ordinal Modeling: GEE Methods. 9.3. Transitional Ordinal Modeling, Given the Past. Chapter Notes. Exercises. 10. Clustered Ordinal Responses: Random Effects Models. 10.1. Ordinal Generalized Linear Mixed Models. 10.2. Examples of Ordinal Random Intercept Models. 10.3. Models with Multiple Random Effects. 10.4. Multilevel (Hierarchical) Ordinal Models. 10.5. Comparing Random Effects Models and Marginal Models. Chapter Notes. Exercises. 11. Bayesian Inference for Ordinal Response Data. 11.1. Bayesian Approach to Statistical Inference. 11.2. Estimating Multinomial Parameters. 11.3. Bayesian Ordinal Regression Modeling. 11.4. Bayesian Ordinal Association Modeling. 11.5. Bayesian Ordinal Multivariate Regression Modeling. 11.6. Bayesian Versus Frequentist Approaches to Analyzing Ordinal Data. Chapter Notes. Exercises. Appendix Software for Analyzing Ordinal Categorical Data. Bibliography. Example Index. Subject Index.

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Book SynopsisTrade ReviewPublishers Weekly "Stewart shares his enthusiasm as well as his knowledge in this tour of ground-breaking equations and the research they supported... An entertaining and illuminating collection of curious facts and histories suitable for random dipping-in or reading straight through." Kirkus Reviews "Stewart provides clear, cogent explanations of how the equations work without burdening the reader with cumbersome derivations... He gives a fascinating explanation of how Newton's laws, when extended to three-body problems, are still used by NASA to calculate the best route from Earth to Mars and have laid the basis for chaos theory. Throughout, Stewart's style is felicitous." Discover "Seemingly basic equations have enabled us to predict eclipses, engineer earthquake-proof buildings, and invent the refrigerator. In this lively volume, mathematician Ian Stewart delves into 17 equations that shape our daily existence, including those dreamed up by the likes of Einstein, Newton, and Erwin Schrodinger." Maclean's "Stewart is the finest living math popularizer-a writer who can tackle eye-spraining mathematical topics approachably, and yet dazzle hard-core nerds with new and surprising information. It is hard not to get your money's worth from him, and in a book like this he is at his best because of the very wide ground covered." Library Journal "Stewart's expertise and his well-developed style (enhanced by a nice sense of humor) make for enjoyable reading... [A] worthwhile and entertaining book, accessible to all readers. Recommended for anyone interested in the influence of mathematics on the development of science and on the emergence of our current technology-driven society." Washington Independent Review of Books "Stewart has managed to produce a remarkably readable, informative and entertaining volume on a subject about which few are as well informed as they would like to be." New York Journal of Books "Stewart is a genius in the way he conveys his excitement and sense of wonder... He has that valuable grasp of not only what it takes to make equations interesting, but also to make science cool."Table of ContentsWhy Equations? 1. The squaw on the hippopotamus 2. Shortening the proceedings 3. Ghosts of departed quantities 4. The system of the world 5. Portent of the ideal world 6. Much ado about knotting 7. Patterns of chance 8. Good vibrations 9. Ripples and blips 10. The ascent of humanity 11. Waves in the ether 12. Law and disorder 13. One thing is absolute 14. Quantum weirdness 15. Codes, communications, and computers 16. The imbalance of nature 17. The Midas formula Where Next?

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Book SynopsisAttempts to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. This book is useful for logicians, type theorists, category theorists and (theoretical) computer scientists.Trade Review"The author's achievement in collecting and organizing a very large body of material in coherent form,... this is first and foremost an encyclopaedic work, into which specialists will delve with much pleasure and profit... One very welcome feature of the book is a comprehensive bibliography of nearly 350 items..." --Zentralblatt für Mathematik, vol.905R.A.G. Seely"This book will be the standard reference in its field for some time to come." --The Bulletin of Symbolic Logic, Vol. 6Table of ContentsChapter Headings only. Preface. Contents. Preliminaries. Prospectus. Introduction to fibred category theory. Simple type theory. Equational logic. First order predicate logic. Higher order predicate logic. The effective topos. Internal category theory. Polymorphic type theory. Advanced fibred category theory. First order dependent type theory. Higher order dependent type theory. References. Notation index. Subject index.

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Book SynopsisThis book provides a user-friendly, hands-on introduction to the Nonlinear Mixed Effects Modeling (NONMEM) system, the most powerful tool for pharmacokinetic / pharmacodynamic analysis. Introduces requisite background to using Nonlinear Mixed Effects Modeling (NONMEM), covering data requirements, model building and evaluation, and quality control aspects Provides examples of nonlinear modeling concepts and estimation basics with discussion on the model building process and applications of empirical Bayesian estimates in the drug development environment Includes detailed chapters on data set structure, developing control streams for modeling and simulation, model applications, interpretation of NONMEM output and results, and quality control Has datasets, programming code, and practice exercises with solutions, available on a supplementary websiteTrade Review“This book may make the “User Guide V experience” a story from the good old times for the next generation of pharmacometricians.” (CPT: Pharmacometrics & Systems Pharmacology, 22 December 2014)Table of ContentsPreface xiii CHAPTER 1 The Practice of Pharmacometrics 1 1.1 Introduction 1 1.2 Applications of Sparse Data Analysis 2 1.3 Impact of Pharmacometrics 4 1.4 Clinical Example 5 CHAPTER 2 Population Model Concepts and Terminology 9 2.1 Introduction 9 2.2 Model Elements 10 2.3 Individual Subject Models 11 2.4 Population Models 12 2.4.1 Fixed-Effect Parameters 13 2.4.2 Random-Effect Parameters 14 2.5 Models of Random Between-Subject Variability (L1) 17 2.5.1 Additive Variation 17 2.5.2 Constant Coefficient of Variation 18 2.5.3 Exponential Variation 18 2.5.4 Modeling Sources of Between-Subject Variation 19 2.6 Models of Random Variability in Observations (L2) 19 2.6.1 Additive Variation 20 2.6.2 Constant Coefficient of Variation 21 2.6.3 Additive Plus CCV Model 22 2.6.4 Log-Error Model 24 2.6.5 Relationship Between RV Expressions and Predicted Concentrations 24 2.6.6 Significance of the Magnitude of RV 25 2.7 Estimation Methods 26 2.8 Objective Function 26 2.9 Bayesian Estimation 27 CHAPTER 3 NONMEM Overview and Writing an NM-TRAN Control Stream 28 3.1 Introduction 28 3.2 Components of the NONMEM System 28 3.3 General Rules 30 3.4 Required Control Stream Components 31 3.4.1 $PROBLEM Record 31 3.4.2 The $DATA Record 32 3.4.3 The $INPUT Record 35 3.5 Specifying the Model in NM-TRAN 35 3.5.1 Calling PREDPP Subroutines for Specific PK Models 35 3.5.2 Specifying the Model in the $PK Block 38 3.5.3 Specifying Residual Variability in the $ERROR Block 45 3.5.4 Specifying Models Using the $PRED Block 49 3.6 Specifying Initial Estimates with $THETA, $OMEGA, and $SIGMA 50 3.7 Requesting Estimation and Related Options 56 3.8 Requesting Estimates of the Precision of Parameter Estimates 62 3.9 Controlling the Output 63 CHAPTER 4 Datasets 66 4.1 Introduction 66 4.2 Arrangement of the Dataset 68 4.3 Variables of the Dataset 71 4.3.1 TIME 71 4.3.2 DATE 71 4.3.3 ID 72 4.3.4 DV 74 4.3.5 MDV 74 4.3.6 CMT 74 4.3.7 EVID 75 4.3.8 AMT 76 4.3.9 RATE 77 4.3.10 ADDL 78 4.3.11 II 79 4.3.12 SS 80 4.4 Constructing Datasets with Flexibility to Apply Alternate Models 80 4.5 Examples of Event Records 81 4.5.1 Alternatives for Specifying Time 81 4.5.2 Infusions and Zero-Order Input 81 4.5.3 Using ADDL 82 4.5.4 Steady-State Approach 83 4.5.5 Samples Before and After Achieving Steady State 83 4.5.6 Unscheduled Doses in a Steady-State Regimen 84 4.5.7 Steady-State Dosing with an Irregular Dosing Interval 84 4.5.8 Multiple Routes of Administration 85 4.5.9 Modeling Multiple Dependent Variable Data Types 86 4.5.10 Dataset for $PRED 86 4.6 Beyond Doses and Observations 87 4.6.1 Other Data Items 87 4.6.2 Covariate Changes over Time 88 4.6.3 Inclusion of a Header Row 89 CHAPTER 5 Model Building: Typical Process 90 5.1 Introduction 90 5.2 Analysis Planning 90 5.3 Analysis Dataset Creation 92 5.4 Dataset Quality Control 93 5.5 Exploratory Data Analysis 94 5.5.1 EDA: Population Description 95 5.5.2 EDA: Dose-Related Data 99 5.5.3 EDA: Concentration-Related Data 99 5.5.4 EDA: Considerations with Large Datasets 111 5.5.5 EDA: Summary 115 5.6 Base Model Development 116 5.6.1 Standard Model Diagnostic Plots and Interpretation 116 5.6.2 Estimation of Random Effects 130 5.6.3 Precision of Parameter Estimates (Based on $COV Step) 137 5.7 Covariate Evaluation 138 5.7.1 Covariate Evaluation Methodologies 140 5.7.2 Statistical Basis for Covariate Selection 141 5.7.3 Diagnostic Plots to Illustrate Parameter-Covariate Relationships 143 5.7.4 Typical Functional Forms for Covariate-Parameter Relationships 148 5.7.5 Centering Covariate Effects 156 5.7.6 Forward Selection Process 160 5.7.7 Evaluation of the Full Multivariable Model 167 5.7.8 Backward Elimination Process 169 5.7.9 Other Covariate Evaluation Approaches 171 5.8 Model Refinement 172 CHAPTER 6 Interpreting the NONMEM Output 178 6.1 Introduction 178 6.2 Description of the Output Files 178 6.3 The NONMEM Report File 179 6.3.1 NONMEM-Related Output 179 6.3.2 PREDPP-Related Output 180 6.3.3 Output from Monitoring of the Search 180 6.3.4 Minimum Value of the Objective Function and Final Parameter Estimates 182 6.3.5 Covariance Step Output 186 6.3.6 Additional Output 187 6.4 Error Messages: Interpretation and Resolution 188 6.4.1 NM-TRAN Errors 188 6.4.2 $ESTIMATION Step Failures 189 6.4.3 $COVARIANCE Step Failures 190 6.4.4 PREDPP Errors 191 6.4.5 Other Types of NONMEM Errors 192 6.4.6 FORTRAN Compiler or Other Run-Time Errors 193 6.5 General Suggestions for Diagnosing Problems 193 CHAPTER 7 App lications Using Parameter Estimates from the Individual 198 7.1 Introduction 198 7.2 Bayes Theorem and Individual Parameter Estimates 200 7.3 Obtaining Individual Parameter Estimates 202 7.4 Applications of Individual Parameter Estimates 204 7.4.1 Generating Subject-Specific Exposure Estimates 204 7.4.2 Individual Exposure Estimates for Group Comparisons 210 CHAPTER 8 Introduction to Model Evaluation 212 8.1 Introduction 212 8.2 Internal Validation 212 8.3 External Validation 213 8.4 Predictive Performance Assessment 214 8.5 Objective Function Mapping 217 8.6 Leverage Analysis 220 8.7 Bootstrap Procedures 222 8.8 Visual and Numerical Predictive Check Procedures 223 8.8.1 The VPC Procedure 223 8.8.2 Presentation of VPC Results 225 8.8.3 The Numerical Predictive Check (NPC) Procedure 229 8.9 Posterior Predictive Check Procedures 229 CHAPTER 9 User-Written Models 232 9.1 Introduction 232 9.2 $MODEL 235 9.3 $SUBROUTINES 236 9.3.1 General Linear Models (ADVAN5 and ADVAN7) 236 9.3.2 General Nonlinear Models (ADVAN6, ADVAN8, ADVAN9, and ADVAN13) 238 9.3.3 $DES 238 9.4 A Series of Examples 240 9.4.1 Defined Fractions Absorbed by Zero- and First-Order Processes 240 9.4.2 Sequential Absorption with First-Order Rates, without Defined Fractions 242 9.4.3 Parallel Zero-Order and First-Order Absorption, without Defined Fractions 243 9.4.4 Parallel First-Order Absorption Processes, without Defined Fractions 245 9.4.5 Zero-Order Input into the Depot Compartment 246 9.4.6 Parent and Metabolite Model: Differential Equations 247 CHAPTER 10 PK/PD Models 250 10.1 Introduction 250 10.2 Implementation of PD Models in NONMEM 251 10.3 $PRED 252 10.3.1 Direct-Effect PK/PD Examples: PK Concentrations in the Dataset 253 10.3.2 Direct-Effect PK/PD Example: PK from Computed Concentrations 255 10.4 $PK 256 10.4.1 Specific ADVANs (ADVAN1–ADVAN4 and ADVAN10–ADVAN12) 256 10.4.2 General ADVANs (ADVAN5–ADVAN9 and ADVAN13) 257 10.4.3 PREDPP: Effect Compartment Link Model Example (PD in $ERROR) 257 10.4.4 PREDPP: Indirect Response Model Example: PD in $DES 259 10.5 Odd-Type Data: Analysis of Noncontinuous Data 261 10.6 PD Model Complexity 262 10.7 Communication of Results 263 CHAPTER 11 Simulation Basics 265 11.1 Introduction 265 11.2 The Simulation Plan 265 11.2.1 Simulation Components 266 11.2.2 The Input–Output Model 266 11.2.3 The Covariate Distribution Model 270 11.2.4 The Trial Execution Model 273 11.2.5 Replication of the Study 274 11.2.6 Analysis of the Simulated Data 275 11.2.7 Decision Making Using Simulations 275 11.3 Miscellaneous Other Simulation-Related Considerations 276 11.3.1 The Seed Value 276 11.3.2 Consideration of Parameter Uncertainty 277 11.3.3 Constraining Random Effects or Responses 278 CHAPTER 12 Quality Control 285 12.1 Introduction 285 12.2 QC of the Data Analysis Plan 285 12.3 Analysis Dataset Creation 286 12.3.1 Exploratory Data Analysis and Its Role in Dataset QC 287 12.3.2 QC in Data Collection 287 12.4 QC of Model Development 288 12.4.1 QC of NM-TRAN Control Streams 289 12.4.2 Model Diagnostic Plots and Model Evaluation Steps as QC 290 12.5 Documentation of QC Efforts 290 12.6 Summary 291 References 292 Index 293

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Book SynopsisOur understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them.Table of ContentsChapter 1 1 Chapter 2 9 Chapter 3 15 Chapter 4 32 Chapter 5 44 Chapter 6 67 Chapter 7 75 Chapter 8 88 Chapter 9 105 Chapter 10 139 Chapter 11 158 Chapter 12 175 Chapter 13 190 Chapter 14 197

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Book SynopsisEmphasizes the strategy of experimentation, data analysis, and the interpretation of experimental results. * Features numerous examples using actual engineering and scientific studies. * Presents statistics as an integral component of experimentation from the planning stage to the presentation of the conclusions.Trade Review"With an excellent presentation, this is suitable as a textbook in a graduate level course in design of experiments." (Journal of Statistical Computation and Simulation, April 2005) "...can really provide useful information for the intended audience..." (Zentralblatt Math, Vol. 1029, 2004) “...a practitioner’s guide to statistical methods for designing and analyzing experiments...” (Quarterly of Applied Mathematics, Vol. LXI, No. 3, September 2003) "...a perfect desktop reference..." (Technometrics, Vol. 45, No. 3, August 2003)Table of ContentsPreface. PART I: FUNDAMENTAL STATISTICAL CONCEPTS. Statistics in Engineering and Science. Fundamentals of Statistical Inference. Inferences on Means and Standard Deviations. PART II: DESIGN AND ANALYSIS WITH FACTORIAL STRUCTURE. Statistical Principles in Experimental Design. Factorial Experiments in Completely Randomized Designs. Analysis of Completely Randomized Designs. Fractional Factorial Experiments. Analysis of Fractional Factorial Experiments. PART III: DESIGN AND ANALYSIS WITH RANDOM EFFECTS. Experiments in Randomized Block Designs. Analysis of Designs with Random Factor Levels. Nested Designs. Special Designs for Process Improvement. Analysis of Nested Designs and Designs for Process Improvement. PART IV: DESIGN AND ANALYSIS WITH QUANTITATIVE PREDICTORS AND FACTORS. Linear Regression with One Predicator Variables. Linear Regression with Several Predicator Variables. Linear Regression with Factors and Covariates as Predictors. Designs and Analyses for Fitting Re sponse Surfaces. Model Assessment. Variable Selection Techniques. Appendix: Statistical Tables. Index.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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a huge range and FREE tracked UK delivery on ALL orders.

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Book SynopsisThis concise introduction takes the reader from standard notions to more advanced topics. It introduces the classic results, as well as more recent developments in this vibrant area of mathematical logic. Many worked examples and exercises make the book a useful resource for graduate students as well as researchers.Trade Review'The book is very well written and a pleasure to read.' Tim Netzer, Zentralblatt MATHTable of ContentsPreface; 1. The basics; 2. Elementary extensions and compactness; 3. Quantifier elimination; 4. Countable models; 5. Aleph-1-categorical theories; 6. Morley rank; 7. Simple theories; 8. Stable theories; 9. Prime extensions; 10. The fine structure of 1-categorical theories; A. Set theory; B. Fields; C. Combinatorics; D. Solutions of exercises; Bibliography; Index.

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Book SynopsisSince the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between.Trade Review'… informative and well-written … Not only does this book cover basic material thoroughly, it also presents much of interest to those already familiar with the area of math and music. And the author provides a wealth of citations to the often scattered literature on the subject.' Zentralblatt MATH'… an excellent introduction to the interdisciplinary subject of music and mathematics (which also involves physics, biology, psycho-acoustics, and the history of science and digital technology). The book can easily be used as the text for undergraduate courses.' The Mathematical IntelligencerTable of ContentsPreface; Introduction; Acknowledgements; 1. Waves and harmonics; 2. Fourier theory; 3. A mathematician's guide to the orchestra; 4. Consonance and dissonance; 5. Scales and temperaments: the fivefold way; 6. More scales and temperaments; 7. Digital music; 8. Synthesis; 9. Symmetry in music; Appendix A. Bessel functions; Appendix B. Equal tempered scales; Appendix C. Frequency and MIDI chart; Appendix D. Intervals; Appendix E. Just, equal and meantone scales compared; Appendix F. Music theory; Appendix G. Recordings; Bibliography; Index.

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Book SynopsisCovers the key areas of computer science, including recursive function theory, formal languages, and automata. This book is divided into five parts: Computability, Grammars and Automata, Logic, Complexity, and Unsolvability. It also covers in a variety of different arrangements automata theory, computational logic, and complexity theory.Trade Review"If there is a single book on the theory of computing that should be in every college library collection, this is it. Although written as a text for an advanced undergraduate course in theoretical computer science, the book may serve as an introductory resource, or the foundation for independent study, in many areas of theoretical computing: grammars, automata theory, computability, complexity theory, and unsolvability. The beauty of this book is that the breadth of coverage is complemented with extraordinary depth." --CHOICE "Theoretical computer science is often viewed as a collection of disparate topics, including computability theory, formal language theory, complexity theory, logic, and so on. This well-written book attempts to unify the subject by introducing each of these topics in turn, then showing how they relate to each other... This is an excellent book that succeeds in tying together a number of areas in theoretical computer science." --COMPUTING REVIEWSTable of ContentsPreliminaries. Computability: Programs and Computable Functions. Primitive Recursive Functions. A Universal Program. Calculations on Strings. Turing Machines. Processes and Grammars. Classifying Unsolvable Problems. Grammars and Automata: Regular Languages. Context-Free Languages. Context-Sensitive Languages. Logic: Propositional Calculus. Quantification Theory. Complexity: Abstract Complexity. Polynomial–Time Computability. Semantics: Approximation Orderings. Denotational Semantics of Recursion Equations. Operational Semantics of Recursion Equations. Suggestions for Further Reading. Subject Index.

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Book SynopsisDiscusses algorithmic trading across the various asset classes, provides key insights into ways to develop, test, and build trading algorithms. This title helps readers learn how to evaluate market impact models and assess performance across algorithms, traders, and brokers, and acquire the knowledge to implement electronic trading systems.Trade Review"Kissell... introduces the mathematical models for constructing, calibrating, and testing market impact models that calculate the change in stock price caused by a large trade or order, and presents an advanced portfolio optimization process that incorporates market impact and transaction costs directly into portfolio optimization." --ProtoView.com, March 2014 "This book provides excellent coverage of the challenges faced by portfolio managers and traders in implementing investment ideas and the advanced modeling techniques to address these challenges." --Kumar Venkataraman, Southern Methodist UniversityTable of ContentsI - Introduction 1. Algorithmic Trading 2. Market Microstructure 3. Transaction Cost Analysis (TCA) II – Mathematical Modeling 4.. Market Impact 5. Multi-Asset Class Market Impact 6 Price 7. Algorithmic Trading Risk 8. Algorithmic Decision Making Framework 9. Portfolio Algorithms III – Portfolio Management 10. Portfolio Construction 11. Quant Factors 12. Black Box Models

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Book SynopsisUseful as a text for students and a reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory most useful for its application in modern analysis. Coverage includes sets and classes, measures and outer measures, Haar measure and measure and topology in groups.Trade ReviewP.R. Halmos Measure Theory "As with the first edition, this considerably improved volume will serve the interested student to find his way to active and creative work in the field of Hilbert space theory."—MATHEMATICAL REVIEWSTable of ContentsPreface; 0. Prerequisites; 1. Sets and Classes; 2. Measures and Outer Measures; 3. Extension of Measures; 4. Measurable Functions; 5. Integration; 6. General Set Functions; 7. Product Spaces; 8. Transformations and Functions; 9. Probability; 10. Locally Compact Spaces; 11. Haar Measure; 12. Measure and Topology in Groups; References; Bibliography; List of Frequently Used Symbols; Index.

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Book SynopsisThis book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. The second part is a course given in 1966 to second-year students of l’Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.Trade ReviewFrom the reviews: "Serre’s book gives a fine introduction to representations for various audiences . . . As always with Serre, the exposition is clear and elegant, and the exercises contain a great deal of valuable information that is otherwise hard to find . . . it is highly recommended for specialists and nonspecialists alike." (Bulletin Of The American Mathematical Society)Table of ContentsPart I: Representations and Characters; 1. Generalities on Linear Representation; 2. Character Theory; 3. Subgroups, products, induced representations; 4. Compact Groups; 5. Examples; Bibliography Part I; Part II: Representation in Characteristic Zero; 6. The Group Algebra; 7. Induced Representations- Mackey's Criterion; 8. Examples of Induced Representations; 9. Artin's Theorem; 10. A Theorem of Brauer; 11. Applications of Brauer's Theorem; 12. Rationality Questions; 13. Rationality Questions: Examples; Bibliography Part II; Part III: Introduction to Brauer Theory; 14. The Groups Rk(G), Rk(G) and Pk(G); 15. The cde Triangle; 16. Theorems; 17. Proofs; 18. Modular Characters; 19. Application to Artin Representations; Appendix; Bibliography part III; Index of Notation; Index of Terminology.

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Book SynopsisI Varieties.- II Schemes.- III Cohomology.- IV Curves.- V Surfaces.- Appendix A Intersection Theory.- 1 Intersection Theory.- 2 Properties of the Chow Ring.- 3 Chern Classes.- 4 The Riemann-Roch Theorem.- 5 Complements and Generalizations.- Appendix B Transcendental Methods.- 1 The Associated Complex Analytic Space.- 2 Comparison of the Algebraic and Analytic Categories.- 3 When is a Compact Complex Manifold Algebraic?.- 4 Kähler Manifolds.- 5 The Exponential Sequence.- Appendix C The Weil Conjectures.- 1 The Zeta Function and the Weil Conjectures.- 2 History of Work on the Weil Conjectures.- 3 The /-adic Cohomology.- 4 Cohomological Interpretation of the Weil Conjectures.- Results from Algebra.- Glossary of Notations.Trade ReviewR. Hartshorne Algebraic Geometry "Enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed currently to answer these questions."—MATHEMATICAL REVIEWSTable of ContentsIntroduction. 1: Varieties. 2: Schemes. 3: Cohomology. 4: Curves. 5: Surfaces. Appendix A: Intersection Theory. B: Transcendental Methods. C: The Weil Conjectures. Bibliography. Results from Algebra. Glossary of Notations. Index.

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Book SynopsisA gently guided, profusely illustrated Grand Tour of the world of mathematics.

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Book SynopsisThis text in basic mathematics is ideal for high school or college students. It provides a firm foundation in basic principles of mathematics and thereby acts as a springboard into calculus, linear algebra and other more advanced topics.Table of Contents1: Numbers. 2: Linear Equations. 3: Real Numbers. 4: Quadratic Equations. 5: Distance and Angles. 6: Isometries. 7: Area and Applications. 8: Coordinates and Geometry. 9: Operations on Points. 10: Segments, Rays, and Lines. 11: Trigonometry. 12: Some Analytic Geometry. 13: Functions. 14: Mappings. 15: Complex Numbers. 16: Inductins and Summations. 17: Determinants.

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Book SynopsisAmong the many constants that appear in mathematics, ?, e, and i are the most familiar. Following closely behind is ?,, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonTrade Review"[A] wonderful book... Havil's emphasis on historical context and his conversational style make this a pleasure to read... Gamma is a gold mine of irresistible mathematical nuggets. Anyone with a serious interest in maths will find it richly rewarding."--Ben Longstaff, New Scientist "This book is a joy from start to finish."--Gerry Leversha, Mathematical Gazette "Wonderful... Havil's emphasis on historical context and his conversational style make this a pleasure to read...Gammais a gold mine of irresistible mathematical nuggets. Anyone with a serious interest in math will find it richly rewarding."--New Scientist"A joy from start to finish."--Mathematical Gazette"[Gamma] is not a book about mathematics, but a book of mathematics... [It] is something like a picaresque novel; the hero, Euler's constantg, serves as the unifying motif through a wide range of mathematical adventures."--Notices of the American Mathematical Society "[Gamma] is enjoyable for many reasons. Here are just two. First, the explanations are not only complete, but they have the right amount of generality... Second, the pleasure Havil has in contemplating this material is infectious."--MAA Online "It is only fitting that someone should write a book about gamma, or Euler's constant. Havil takes on this task and does an excellent job."--Choice "Mathematics is presented throughout as something connected to reality... Many readers will find in [Gamma] exactly what they have been missing."--Mohammad Akbar, Plus Magazine, Millennium Mathematics Project, University of Cambridge "This book is written in an informal, engaging, and often amusing style. The author takes pains to make the mathematics clear. He writes about the mathematical geniuses of the past with reverence and awe. It is especially nice that the mathematical topics are discussed within a historical context."--Ward R. Stewart, Mathematics TeacherTable of ContentsForeword xv Acknowledgements xvii Introduction xix Chapter One The Logarithmic Cradle 1 1.1 A Mathematical Nightmare- and an Awakening 1 1.2 The Baron's Wonderful Canon 4 1.3 A Touch of Kepler 11 1.4 A Touch of Euler 13 1.5 Napier's Other Ideas 16 Chapter Two The Harmonic Series 21 2.1 The Principle 21 2.2 Generating Function for Hn 21 2.3 Three Surprising Results 22 Chapter Three Sub-Harmonic Series 27 3.1 A Gentle Start 27 3.2 Harmonic Series of Primes 28 3.3 The Kempner Series 31 3.4 Madelung's Constants 33 Chapter Four Zeta Functions 37 4.1 Where n Is a Positive Integer 37 4.2 Where x Is a Real Number 42 4.3 Two Results to End With 44 Chapter Five Gamma's Birthplace 47 5.1 Advent 47 5.2 Birth 49 Chapter Six The Gamma Function 53 6.1 Exotic Definitions 53 6.2 Yet Reasonable Definitions 56 6.3 Gamma Meets Gamma 57 6.4 Complement and Beauty 58 Chapter Seven Euler's Wonderful Identity 61 7.1 The All-Important Formula 61 7.2 And a Hint of Its Usefulness 62 Chapter Eight A Promise Fulfilled 65 Chapter Nine What Is Gamma Exactly? 69 9.1 Gamma Exists 69 9.2 Gamma Is What Number? 73 9.3 A Surprisingly Good Improvement 75 9.4 The Germ of a Great Idea 78 Chapter Ten Gamma as a Decimal 81 10.1 Bernoulli Numbers 81 10.2 Euler -Maclaurin Summation 85 10.3 Two Examples 86 10.4 The Implications for Gamma 88 Chapter Eleven Gamma as a Fraction 91 11.1 A Mystery 91 11.2 A Challenge 91 11.3 An Answer 93 11.4 Three Results 95 11.5 Irrationals 95 11.6 Pell's Equation Solved 97 11.7 Filling the Gaps 98 11.8 The Harmonic Alternative 98 Chapter Twelve Where Is Gamma? 101 12.1 The Alternating Harmonic Series Revisited 101 12.2 In Analysis 105 12.3 In Number Theory 112 12.4 In Conjecture 116 12.5 In Generalization 116 Chapter Thirteen It's a Harmonic World 119 13.1 Ways of Means 119 13.2 Geometric Harmony 121 13.3 Musical Harmony 123 13.4 Setting Records 125 13.5 Testing to Destruction 126 13.6 Crossing the Desert 127 13.7 Shuffiing Cards 127 13.8 Quicksort 128 13.9 Collecting a Complete Set 130 13.10 A Putnam Prize Question 131 13.11 Maximum Possible Overhang 132 13.12 Worm on a Band 133 13.13 Optimal Choice 134 Chapter Fourteen It's a Logarithmic World 139 14.1 A Measure of Uncertainty 139 14.2 Benford's Law 145 14.3 Continued-Fraction Behaviour 155 Chapter Fifteen Problems with Primes 163 15.1 Some Hard Questions about Primes 163 15.2 A Modest Start 164 15.3 A Sort of Answer 167 15.4 Picture the Problem 169 15.5 The Sieve of Eratosthenes 171 15.6 Heuristics 172 15.7 A Letter 174 15.8 The Harmonic Approximation 179 15.9 Different-and Yet the Same 180 15.10 There are Really Two Questions, Not Three 182 15.11 Enter Chebychev with Some Good Ideas 183 15.12 Enter Riemann, Followed by Proof(s)186 Chapter Sixteen The Riemann Initiative 189 16.1 Counting Primes the Riemann Way 189 16.2 A New Mathematical Tool 191 16.3 Analytic Continuation 191 16.4 Riemann's Extension of the Zeta Function 193 16.5 Zeta's Functional Equation 193 16.6 The Zeros of Zeta 193 16.7 The Evaluation of (x) and p(x)196 16.8 Misleading Evidence 197 16.9 The Von Mangoldt Explicit Formula-and How It Is Used to Prove the Prime Number Theorem 200 16.10 The Riemann Hypothesis 202 16.11 Why Is the Riemann Hypothesis Important? 204 16.12 Real Alternatives 206 16.13 A Back Route to Immortality-Partly Closed 207 16.14 Incentives, Old and New 210 16.15 Progress 213 Appendix A The Greek Alphabet 217 Appendix B Big Oh Notation 219 Appendix C Taylor Expansions 221 C.1 Degree 1 221 C.2 Degree 2 221 C.3 Examples 223 C.4 Convergence 223 Appendix D Complex Function Theory 225 D.1 Complex Differentiation 225 D.2 Weierstrass Function 230 D.3 Complex Logarithms 231 D.4 Complex Integration 232 D.5 A Useful Inequality 235 D.6 The Indefinite Integral 235 D.7 The Seminal Result 237 D.8 An Astonishing Consequence 238 D.9 Taylor Expansions-and an Important Consequence 239 D.10 Laurent Expansions-and Another Important Consequence 242 D.11 The Calculus of Residues 245 D.12 Analytic Continuation 247 Appendix E Application to the Zeta Function 249 E.1 Zeta Analytically Continued 249 E.2 Zeta's Functional Relationship 253 References 255 Name Index 259 Subject Index 263

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Book SynopsisIan Stewart's up-to-the-minute guide to the cosmos moves from the formation of the Earth and its Moon to the planets and asteroids of the solar system and from there out into the galaxy and the universe. He describes the architecture of space and time, dark matter and dark energy, how galaxies form, why stars implode, how everything began, and how it will end. He considers parallel universes, what forms extra-terrestrial life might take, and the likelihood of Earth being hit by an asteroid. Mathematics, Professor Stewart shows, has been the driving force in astronomy and cosmology since the ancient Babylonians. He describes how Kepler's work on planetary orbits led Newton to formulate his theory of gravity, and how two centuries later irregularities in the motion of Mars inspired Einstein's theory of general relativity. In crystal-clear terms he explains the fundamentals of gravity, spacetime, relativity and quantum theory, and shows how they all relate to each other. Eighty years ago the discovery that the universe is expanding led to the Big Bang theory of its origins. This in turn led cosmologists to posit features such as dark matter and dark energy. But does dark matter exist? Could another scientific revolution be on the way to challenge current scientific orthodoxy? These are among the questions Ian Stewart raises in his quest through the realms of astronomy and cosmology.Trade ReviewA fascinating tour, seamlessly spliced and historically contexualised * Nature *Ian Stewart elegantly reviews the uncanny effectiveness of mathematics in explaining the universe... Mr. Stewart beautifully describes how Newton's laws can still produce surprising results. * Wall Street Journal *The book does an excellent job of both explaining and entertaining. The author makes you think about familiar subjects in a new way and is very good at filling in any gaps in your knowledge, while also pointing out those areas that need further research * Sky at Night Magazine *With captivating stories and his signature clarity, Ian Stewart shows us how math makes the world - and the rest of the universe - go round -- Steven Strogatz, Professor of Mathematics, Cornell University, and author of The Joy of XStewart is Britain's most brilliant and prolific populariser of maths. -- Alex BellosStewart is sure to please math lovers, history buffs, and science enthusiasts alike by covering an array of eras, innovators, and disciplines. * Publishers Weekly *Praise for previous books: 'This is not pure maths. It is maths contaminated with wit, wisdom, and wonder. Ian really is unsurpassed as raconteur of the world of numbers. He guides us on a mind-boggling journey from the ultra trivial to the profound. Thoroughly entertaining * New Scientist *Stewart has served up the instructive equivalent of a Michelin-starred tasting menu, or perhaps a smorgasbord of appetisers. And of course, appetisers are designed to give you an appetite for more * Guardian *

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Book SynopsisFully updated for the second edition, this book introduces the growing and dynamic field of particle astrophysics. It provides an overview of high-energy nuclei, photons and neutrinos, including their origins, their propagation in the cosmos, their detection on Earth and their relation to each other. Coverage is expanded to include new content on high energy physics, the propagation of protons and nuclei in cosmic background radiation, neutrino astronomy, high-energy and ultra-high-energy cosmic rays, sources and acceleration mechanisms, and atmospheric muons and neutrinos. Readers are able to master the fundamentals of particle astrophysics within the context of the most recent developments in the field. This book will benefit graduate students and established researchers alike, equipping them with the knowledge and tools needed to design and interpret their own experiments and, ultimately, to address a number of questions concerning the nature and origins of cosmic particles that havTrade Review'With more than 25 years since the first edition, this second edition … has been revised and extended by about 150 pages to account for the progress and important discoveries made in the field since then. These comprise the famous neutrino oscillations, the cutoff in ultrahigh-energy cosmic ray spectra, Tera-electronvolt gamma rays from galactic sources and the unexpected excess of high-energy positrons and astrophysical neutrinos. … The text is well written and presents all material with mathematical rigour and a large number of references to scientific publications … The text is accompanied by numerous black-and-white figures, mainly of spectra. It has an appendix with additional material and a helpful index. … It can be recommended mainly for graduate students and researchers from both theory and experiment who want a thorough introduction to the phenomenology and to the theoretical background of cosmic ray physics at the junction of particle physics and astronomy.' Manuel Vogel, Contemporary PhysicsTable of ContentsPreface to the first edition; Preface to the second edition; 1. Cosmic rays; 2. Cosmic ray data; 3. Particle physics; 4. Hadronic interactions and accelerator data; 5. Cascade equations; 6. Atmospheric muons and neutrinos; 7. Neutrino masses and oscillations; 8. Muons and neutrinos underground; 9. Cosmic rays in the Galaxy; 10. Extragalactic propagation of cosmic rays; 11. Astrophysical - rays and neutrinos; 12. Acceleration; 13. Supernovae in the Milky Way; 14. Astrophysical accelerators and beam dumps; 15. Electromagnetic cascades; 16. Extensive air showers; 17. Very high energy cosmic rays; 18. Neutrino astronomy; A.1. Units, constants and definitions; A.2. References to flux measurements; A.3. Particle flux, density, and interaction cross section; A.4. Fundamentals of scattering theory; A.5. Regge amplitude; A.6. Glauber model of nuclear cross sections; A.7. Earth's atmosphere; A.8. Longitudinal development of air showers; A.9. Secondary positrons and electrons; A.10. Liouville's theorem and cosmic ray propagation; A.11. Cosmology and distances measures; A.12. The Hillas splitting algorithm; References; Index.

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