Mathematics Books

Book SynopsisNow in its second edition, this popular textbook on game theory is unrivalled in the breadth of its coverage, the thoroughness of technical explanations and the number of worked examples included. Covering non-cooperative and cooperative games, this introduction to game theory includes advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. This edition contains new material on stochastic games, rationalizability, and the continuity of the set of equilibrium points with respect to the data of the game. The material is presented clearly and every concept is illustrated with concrete examples from a range of disciplines. With numerous exercises, and the addition of a solution manual for instructors with this edition, the book is an extensive guide to game theory for undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences, and will also serve as useful reTrade ReviewPraise for first edition: 'This is the book for which the world has been waiting for decades: a definitive, comprehensive account of the mathematical theory of games, by three of the world's biggest experts on the subject. Rigorous yet eminently readable, deep yet comprehensible, replete with a large variety of important real-world applications, it will remain the standard reference in game theory for a very long time.' Robert Aumann, Nobel Laureate in Economics, The Hebrew University of JerusalemPraise for first edition: 'Without any sacrifice on the depth or the clarity of the exposition, this book is amazing in its breadth of coverage of the important ideas of game theory. It covers classical game theory, including utility theory, equilibrium refinements and belief hierarchies; classical cooperative game theory, including the core, Shapley value, bargaining set and nucleolus; major applications, including social choice, auctions, matching and mechanism design; and the relevant mathematics of linear programming and fixed point theory. The comprehensive coverage combined with the depth and clarity of exposition makes it an ideal book not only to learn game theory from, but also to have on the shelves of working game theorists.' Ehud Kalai, Kellogg School of Management, Northwestern UniversityPraise for first edition: 'The best and the most comprehensive textbook for advanced courses in game theory.' David Schmeidler, Ohio State University and Tel Aviv UniversityPraise for first edition: 'There are quite a few good textbooks on game theory now, but for rigor and breadth this one stands out.' Eric S. Maskin, Nobel Laureate in Economics, Harvard University, MassachusettsPraise for first edition: 'This textbook provides an exceptionally clear and comprehensive introduction to both cooperative and noncooperative game theory. It deftly combines a rigorous exposition of the key mathematical results with a wealth of illuminating examples drawn from a wide range of subjects. It is a tour de force.' Peyton Young, University of OxfordPraise for first edition: 'This is a wonderful introduction to game theory, written in a way that allows it to serve both as a text for a course and as a reference … The book is written by leading figures in the field [whose] broad view of the field suffuses the material.' Joe Halpern, Cornell University, New YorkTable of Contents1. The game of chess; 2. Utility theory; 3. Extensive-form games; 4. Strategic-form games; 5. Mixed strategies; 6. Behavior strategies and Kuhn's theorem; 7. Equilibrium refinements; 8. Correlated equilibria; 9. Games with incomplete information and common priors; 10. Games with incomplete information: the general model; 11. The universal belief space; 12. Auctions; 13. Repeated games; 14. Repeated games with vector payoffs; 15. Social choice; 16. Bargaining games; 17. Coalitional games with transferable utility; 18. The core; 19. The Shapley value; 20. The bargaining set; 21. The nucleolus; 22. Stable matching; 23. Appendices.

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Book SynopsisStarting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.Trade Review'This long-awaited work focuses on one of the most interesting and important parts of probability theory. Half a century ago, most work on models such as random walks, Ising, percolation and interacting particle systems concentrated on processes defined on the d-dimensional Euclidean lattice. In the intervening years, interest has broadened dramatically to include processes on more general graphs, with trees being a particularly important case. This led to new problems and richer behavior, and as a result, to the development of new techniques. The authors are two of the major developers of this area; their expertise is evident throughout.' Thomas M. Liggett, University of California, Los Angeles'Masterly, beautiful, encyclopaedic, and yet browsable - this great achievement is obligatory reading for anyone working near the conjunction of probability and network theory.' Geoffrey Grimmett, University of Cambridge'For the last ten years, I have not let a doctoral student graduate without reading this [work]. Sadly, the earliest of those students are missing a considerable amount of material that the bound and published edition contains. Not only are the classical topics of random walks, electrical theory, and uniform spanning trees covered in more coherent fashion than in any other source, but this book is also the best place to learn about a number of topics for which the other choices for textual material are limited. These include mass transport, random walk boundaries, and dimension and capacity in the context of Markov processes.' Robin Pemantle, University of Pennsylvania'Lyons and Peres have done an amazing job of motivating their material and of explaining it in a conversational and accessible fashion. Even though the book emphasizes probability on infinite graphs, it is one of my favorite references for probability on finite graphs. If you want to understand random walks, isoperimetry, random trees, or percolation, this is where you should start.' Daniel Spielman, Yale University, Connecticut'This long-awaited book offers a splendid account of several major areas of discrete probability. Both authors have made outstanding contributions to the subject, and the exceptional quality of the book is largely due to their high level of mastery of the field. Although the only prerequisites are basic probability theory and elementary Markov chains, the book succeeds in providing an elegant presentation of the most beautiful and deepest results in the various areas of probability on graphs. The powerful techniques that made these results available, such as the use of isoperimetric inequalities or the mass-transport principle, are also presented in a detailed and self-contained manner. This book will be indispensable to any researcher working in probability on graphs and related topics, and it will also be a must for anybody interested in the recent developments of probability theory.' Jean-François Le Gall, Université Paris-Sud'This is a very timely book about a circle of actively developing subjects in discrete probability. No wonder that it became very popular two decades before publication, while still in development. Not only a comprehensive reference source, but also a good textbook to learn the subject, it will be useful for specialists and newcomers alike.' Stanislav Smirnov, Université of Genève'A glorious labor of love, compiled over more than two decades of work, that brilliantly surveys the deep and expansive relationships between random trees and other areas of mathematics. Rarely does one encounter a text so exquisitely well written or enjoyable to read. One cannot take more than a few steps in modern probability without encountering one of the topics surveyed here. A truly essential resource.' Scott Sheffield, Massachusetts Institute of Technology'There is much to be learned from studying this book. Many of the ideas and tools are useful in a wide variety of different contexts … Geoff Grimmett's quote on the cover calls the book 'Masterly, beautiful, encyclopedic and yet browsable.' I totally agree. Even though it is freely available on the web, you should buy a copy of the book.' Richard Durrett, Mathematical Association of America Reviews (www.maa.org)'This is a monumental book covering a lot of interesting problems in discrete probability, written by two experts in the field … The authors have done a great job of providing full proofs of all main results, hence creating a self-contained reference in this area.' Abbas Mehrabian, Zentralblatt MATH'This long-awaited book, a project that started in 1993, is bound to be the main reference in the fascinating field of probability on trees and weighted graphs. The authors are the leading experts behind the tremendous developments experienced in the subject in recent decades, where the underlying networks evolved from classical lattices to general graphs … This pedagogically written book is a marvelous support for several courses on topics from combinatorics, Markov chains, geometric group theory, etc., as well as on their inspiring relationships. The wealth of exercises (with comments provided at the end of the book) will enable students and researchers to check their understanding of this fascinating mathematics.' Laurent Miclo, MathSciNetTable of Contents1. Some highlights; 2. Random walks and electric networks; 3. Special networks; 4. Uniform spanning trees; 5. Branching processes, second moments, and percolation; 6. Isoperimetric inequalities; 7. Percolation on transitive graphs; 8. The mass-transport technique and percolation; 9. Infinite electrical networks and Dirichlet functions; 10. Uniform spanning forests; 11. Minimal spanning forests; 12. Limit theorems for Galton–Watson processes; 13. Escape rate of random walks and embeddings; 14. Random walks on groups and Poisson boundaries; 15. Hausdorff dimension; 16. Capacity and stochastic processes; 17. Random walks on Galton–Watson trees.

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Book SynopsisTrade Review"One of Choice's Outstanding Academic Titles for 2013""Masterly. . . . Gray encapsulates Poincaré's multiple dimensions; his intellectual biography is both a tour de force and a triumph of readability."---George Szpiro, Nature"Gray shows us the full dazzling sweep of what Poincaré accomplished, including the work on dynamical systems and chaos that only came into its own in recent years. A tour de force, Gray's masterful treatment will long remain an invaluable resource for all who want to understand Poincaré, so embedded within his times and yet so far ahead of them."---Peter Pesic, Science"[A] comprehensive but uncluttered guide to Poincaré's extensive oeuvres."---Madeline Muntersbjorn, Times Higher Education"Full of the mathematical, physical and metaphysical ideas of a man who was not only a dispassionate observer of the world around us, but of our way of understanding it."---Mark Ronan, Standpoint Magazine"[A] comprehensive assessment of Poincare's work and its importance, essential for anyone interested in Poincare's scholarship or the history of mathematics."---Laura Tarwater Scharp, Sacramento Book Review"Comprehensive." * Science News *"A fundamental study of the scientific work of one of the greatest mathematicians and mathematical physicists of the three decades straddling the 19th and 20th centuries. . . . Chapters are organized topically, not chronologically. Each illuminates in depth one or other of Poincaré's works but all are set in context both historical and temathic such that each can serve as an introduction into the many subjects to which Poincaré made a contribution."---Alexander Bogomolny, CTK Insights"Poincare's work is fully alive in science today. This biography is one of the first thorough introductions to his work, it should get the attention of mathematicians, natural scientists and philosophers."---Ferdinand Verhulst, European Legacy"Gray, a mathematics historian and scholar on the life and work of Henry Poincaré, has, with the support of a Leverhulme Research Fellowship, produced this comprehensive and definitive 'scientific biography.' Gray offers abundant rich information on Poincaré's ideas and scientific process, the evolution and maturity of his mathematics including missteps, the dexterity of his reasoning, and the influences that shaped his thought." * Choice *"I recommend [this] book highly."---Robert E. O'Malley, Jr., SIAM Review"Jeremy Gray's book on Poincaré's mathematics, physics, and philosophy is an important contribution to the literature and a huge step towards a full biography of this pioneer ofmodern science."---Reinhard Siegmund-Schultze, Zentralblatt MATH"Gray's book is a comprehensive scientific biography of Poincare. It embraces the broad scope of Poincare's work, from his philosophical speculations to his popular writing, and gives a thorough overview of his extensive mathematical researches."---Peter Lynch, Irish Mathematical Society Bulletin"[T]he author does not simply give platitudes when writing about Poincare's ideas: mathematicians will enjoy reading about his discoveries concerning the three-body problem, the theory of functions, topology, number theory, Lie theory, algebraic geometry, and probability. This scientific biography is the first to comprehensively cover all of Poincare's main contributions to mathematics, philosophy, and physics."---Alan S. McRae, Mathemematical Reviews Clippings"Jeremy Gray has done a marvelous job of exposition and of binding together the many different cognitive, social and biographical strands into the coherent whole of a challenging, but highly rewarding, 'scientific biography'."---Klaus Hentschel, British Journal for the History of Science"A good intellectual biography of an artist should help the reader see how a particular worldview shapes the pursuit of art. Gray's book does that most admirably."---Daniel S. Alexander, H-France Review"Henry Poincaré is likely to remain the standard by which scientific biographies, at least those that concern physicists and mathematicians, are judged for some time."---Christopher Cumo, Canadian Journal of History"I warmly recommend the book to anyone with an interest in the development of modern mathematics. It will surely be the definitive scientific biography of Poincare for the foreseeable future."---John Stillwell, Notices of the AMS"Gray describes Poincaré's scientific epoch in a beautiful way. Due attention is paid to the mathematical and further scientific aspects of his life, and the intellectual complexity of his achievements, both in their range and their depth, are amply discussed. Gray displays a mastery of his material that is rare even among historians of mathematics and science, and his biography is richly rewarding, engrossing, and informative. He deserves our congratulations."---H. W. Broer, Journal of the British Society for the History of Mathematics"Gray succeeds admirably in presenting both the conceptual and the historical context necessary to appreciate Poincaré's contributions. Gray's masterful biography may well serve as a standard example for future endeavors of this kind."---Tilman Sauer, Isis"The obvious virtue of this book is its comprehensiveness. The deeper virtue is to connect Poincaré's views of all the parts of his work and to encourage more of that. Gray gives us Poincaré's view of Science as a whole."---Colin McLarty, Mathematical Intelligencer"The book is an endless source of interesting insights by Poincaré. . . . I would recommend the book for mathematicians, mathematics educators, and philosophers in higher education who want a rich understanding of Poincaré, his work, and his times."---Mary L. Garner, Mathematics Teacher

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Book SynopsisFirst published in 1919, Introduction to Mathematical Philosophy shows Russell drawing on his formidable knowledge of philosophy and mathematics to write a brilliant introduction to the subject. This Routledge Classics edition includes a new Foreword by Michael Potter.Table of ContentsForeword to the Routledge Classics Edition Michael Potter Preface 1. The Series of Natural Numbers 2. Definition of Number 3. Finitude and Mathematical Induction 4. The Definition of Order 5. Kinds of Relations 6. Similarity of Relations 7. Rational, Real, and Complex Numbers 8. Infinite Cardinal Numbers 9. Infinite Series and Ordinals 10. Limits and Continuity 11. Limits and Continuity of Functions 12. Selections and the Multiplicative Axiom 13. The Axiom of Infinity and Logical Types 14. Incompatibility and the Theory of Deduction 15. Propositional Functions 16. Descriptions 17. Classes 18. Mathematics and Logic. Index

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Book SynopsisTrade Review"Visualizing Music provides a rich visual overview of the discipline of music theory while offering practical suggestions for scholars."—Timothy Koozin, Moores School of Music, University of HoustonTable of ContentsPrefaceAcknowledgmentsAccessing Audiovisual MaterialsIntroductionPart 1: Preliminaries1. Leveraging the Power of the Brain2. The Role of Metaphor3. Multivariate Images4. Telling a Story5. Facilitating Comparison6. Information Layers7. Information Integration8. Making Every Part of an Image Count9. Presenting Tabular Data10. Small Multiples11. Using Color12. Additional General Principles13. Case Study: Western NotationPart 2: Musical Spaces14. Pitch Spaces15. Collections, Scales, and Modes16. The Circle of Fifths17. The Tonnetz18. Atonal Spaces19. Symmetrical Pitch Structures20. Tonal Hierarchy, Tendency, Progression21. The Overtone SeriesPart 3: Musical Time22. Basic Durations23. Unmeasured Musical Time24. Musically Measured Musical Time25. Externally Measured Musical Time (Performance Timing)26. ProportionPart 4: Pitch, Texture, Timbre, Form27. Textual Representations of Pitch28. Piano Roll Notation29. Alternate Notational Systems30. Tuning and Temperament31. Microtuning32. Timbre33. Texture34. Voice Leading35. Schematic and Procedural Representations36. Formal Models37. Pitch-Class Set Tables38. Instrument Ranges39. TranslationsPart 5: Music Analysis40. Lutosławksi's Jeux Venitiens41. Annotating Musical Scores42. Thematic Analysis43. Contour Analysis44. Tonal Plans45. Symmetry in Music Analysis46. Rhythmic Analysis47. Formal Analysis48. Hierarchy in Music49. Serialism50. Corpus Studies51. Musical Chronologies, Influences, and Styles52. AnimationPart 6: Visualization in the Professional Realm53. Conference Handouts54. Presentation Slide Shows55. Conference Posters56. Print Publication57. The Essential Visualization ToolboxEpilogueBibliographyIndex

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Book SynopsisMathematical Statistics with Resampling and R This thoroughly updated third edition combines the latest software applications with the benefits of modern resampling techniques Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. The third edition of Mathematical Statistics with Resampling and R combines modern resampling techniques and mathematical statistics. This book is classroom-tested to ensure an accessible presentation, and uses the powerful and flexible computer language R for data analysis. This book introduces permutation tests and bootstrap methods to motivate classical inference methods, as well as to be utilized as useful tools in their own right when classical methods are inaccurate or unavailable. The book strikes a balance between simulation, computing, theory, data, and applications. Throughout the book, new and updated case studies representing a diverse range of subjects, such as flight delays, birth weights of babies, U.S. demographics, views on sociological issues, and problems at Google and Instacart, illustrate the relevance of mathematical statistics to real-world applications. Changes and additions to the third edition include: New and updated case studies that incorporate contemporary subjects like COVID-19Several new sections, including introductory material on causal models and regression methods for causal modeling in practiceModern terminology distinguishing statistical discernibility and practical importanceNew exercises and examples, data sets, and R code, using dplyr and ggplot2A complete instructor's solutions manualA new github site that contains code, data sets, additional topics, and instructor resources Mathematical Statistics with Resampling and R is an ideal textbook for undergraduate and graduate students in mathematical statistics courses, as well as practitioners and researchers looking to expand their toolkit of resampling and classical techniques.Table of ContentsPreface xiii 1 Data and Case Studies 1 1.1 Case Study: Flight Delays 1 1.2 Case Study: BirthWeights of Babies 2 1.3 Case Study: Verizon Repair Times 3 1.4 Case Study: Iowa Recidivism 4 1.5 Sampling 5 1.6 Parameters and Statistics 6 1.7 Case Study: General Social Survey 7 1.8 Sample Surveys 8 1.9 Case Study: Beer and HotWings 9 1.10 Case Study: Black Spruce Seedlings 10 1.11 Studies 11 1.12 Google Interview Question: Mobile Ads Optimization 13 2 Exploratory Data Analysis 21 2.1 Basic Plots 21 2.2 Numeric Summaries 25 2.3 Boxplots 27 2.4 Quantiles and Normal Quantile Plots 29 2.5 Empirical Cumulative Distribution Functions 34 2.6 Scatter Plots 36 2.7 Skewness and Kurtosis 38 3 Introduction to Hypothesis Testing: Permutation Tests 45 3.1 Introduction to Hypothesis Testing 45 3.2 Hypotheses 46 3.3 Permutation Tests 50 3.4 Matched Pairs 66 3.5 Cause and Effect 67 4 Sampling Distributions 77 4.1 Sampling Distributions 77 4.2 Calculating Sampling Distributions 82 4.3 The Central LimitTheorem 85 5 Introduction to Confidence Intervals: The Bootstrap 103 5.1 Introduction to the Bootstrap 103 5.2 The Plug-in Principle 109 5.3 Bootstrap Percentile Intervals 115 5.4 Two Sample Bootstrap 116 5.5 Other Statistics 123 5.6 Bias 126 5.7 Monte Carlo Sampling 130 5.8 Accuracy of Bootstrap Distributions 131 5.9 How Many Bootstrap Samples Are Needed? 136 6 Estimation 147 6.1 Maximum Likelihood Estimation 147 6.2 Method of Moments 158 6.3 Properties of Estimators 160 6.4 Statistical Practice 174 7 More Confidence Intervals 183 7.1 Confidence Intervals for Means 183 7.2 Confidence Intervals Using Pivots 201 7.3 One-Sided Confidence Intervals 209 7.4 Confidence Intervals for Proportions 211 7.5 Bootstrap Confidence Intervals 216 7.6 Confidence Interval Properties 224 7.7 The Delta Method* 226 8 More Hypothesis Testing 245 8.1 Hypothesis Tests for Means and Proportions: One Population 245 8.2 Bootstrap t Tests 250 8.3 Hypothesis Tests for Means and Proportions: Two Populations 252 8.4 Type I and Type II Errors 261 8.5 Interpreting Test Results 276 8.6 Likelihood Ratio Tests 281 8.7 Statistical Practice 289 9 Regression 309 9.1 Covariance 309 9.2 Correlation 313 9.3 Least Squares Regression 316 9.4 The Simple LinearModel 329 9.5 Resampling Correlation and Regression 342 9.6 Logistic Regression 350 10 Categorical Data 367 10.1 Independence in Contingency Tables 367 10.2 Permutation Test of Independence 369 10.3 Chi-Square Test of Independence 371 10.4 Chi-Square Test of Homogeneity 380 10.5 Goodness-of-Fit Tests 382 10.6 Chi-Square and the Likelihood Ratio* 388 11 Bayesian Methods 399 11.1 Bayes Theorem 400 11.2 Binomial Data: Discrete Prior Distributions 400 11.3 Binomial Data: Continuous Prior Distributions 408 11.4 Continuous Data 414 11.5 Sequential Data 417 12 One-Way ANOVA 429 12.1 Comparing Three or More Populations 429 13 Additional Topics 443 13.1 Smoothed Bootstrap 444 13.2 Parametric Bootstrap 449 13.3 Stratified Sampling 452 13.4 Control Variates and Casual Modeling 455 13.5 Computational Issues in Bayesian Analysis 462 13.6 Monte Carlo Integration 464 13.7 Importance Sampling 468 13.8 The EM Algorithm 483 Appendix A Review of Probability 493 A.1 Basic Probability 493 A.2 Mean and Variance 494 A.3 Marginal and Conditional Distributions 496 A.4 The Normal Distribution 497 A.5 The Mean of a Sample of Random Variables 498 A.6 Sums of Normal Random Variables 499 A.7 The Law of Averages 500 A.8 Higher Moments and the Moment Generating Function 501 Appendix B Probability Distributions 505 B.1 The Bernoulli and Binomial Distributions 505 B.2 The Multinomial Distribution 506 B.3 The Geometric Distribution 508 B.4 The Negative Binomial Distribution 509 B.5 The Hypergeometric Distribution 510 B.6 The Poisson Distribution 511 B.7 The Uniform Distribution 513 B.8 The Exponential Distribution 513 B.9 The Gamma Distribution 514 B.10 The Chi-Square Distribution 517 B.11 The Student’s t Distribution 520 B.12 The Beta Distribution 522 B.13 The F Distribution 523 Exercises 525 Appendix C Distributions Quick Reference 527 Problem Solutions 531 Bibliography 545 Index 553

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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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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 SynopsisPresents and organises hundreds of beautiful, surprising and intriguing results about polygons with more than four sides. This panoply consists of eight chapters, one dedicated to polygonal basics, the next ones dedicated to pentagons, hexagons, heptagons, octagons and many-sided polygons.Table of Contents Polygon basics Pentagons Hexagons Heptagons Octagons Many-sided polygons Miscellaneous classes of polygons Polygonal numbers Solutions to the challenges Credits and permissions Index

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Book SynopsisProfessor Stephen A. Cook is a pioneer of the theory of computational complexity. His work on NP-completeness and the P vs. NP problem remains a central focus of this field. Cook won the 1982 Turing Award for "his advancement of our understanding of the complexity of computation in a significant and profound way." This volume includes a selection of seminal papers embodying the work that led to this award, exemplifying Cook's synthesis of ideas and techniques from logic and the theory of computation including NP-completeness, proof complexity, bounded arithmetic, and parallel and space-bounded computation. These papers are accompanied by contributed articles by leading researchers in these areas, which convey to a general reader the importance of Cook's ideas and their enduring impact on the research community. The book also contains biographical material, Cook's Turing Award lecture, and an interview. Together these provide a portrait of Cook as a recognized leader and innovator in mathematics and computer science, as well as a gentle mentor and colleague.

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Book SynopsisRegression Analysis By Example Using R A STRAIGHTFORWARD AND CONCISE DISCUSSION OF THE ESSENTIALS OF REGRESSION ANALYSIS In the newly revised sixth edition of Regression Analysis By Example Using R, distinguished statistician Dr Ali S. Hadi delivers an expanded and thoroughly updated discussion of exploratory data analysis using regression analysis in R. The book provides in-depth treatments of regression diagnostics, transformation, multicollinearity, logistic regression, and robust regression. The author clearly demonstrates effective methods of regression analysis with examples that contain the types of data irregularities commonly encountered in the real world. This newest edition also offers a brand-new, easy to read chapter on the freely available statistical software package R. Readers will also find: Reorganized, expanded, and upgraded exercises at the end of each chapter with an emphasis on data analysisTable of ContentsPreface xiv 1 Introduction 1 1.1 What Is Regression Analysis? 1 1.2 Publicly Available Data Sets 2 1.3 Selected Applications of Regression Analysis 3 1.3.1 Agricultural Sciences 3 1.3.2 Industrial and Labor Relations 4 1.3.3 Government 5 1.3.4 History 5 1.3.5 Environmental Sciences 6 1.3.6 Industrial Production 6 1.3.7 The Space Shuttle Challenger 7 1.3.8 Cost of Health Care 7 1.4 Steps in Regression Analysis 7 1.4.1 Statement of the Problem 9 1.4.2 Selection of Potentially Relevant Variables 9 1.4.3 Data Collection 9 1.4.4 Model Specification 10 1.4.5 Method of Fitting 12 1.4.6 Model Fitting 13 1.4.7 Model Criticism and Selection 14 1.4.8 Objectives of Regression Analysis 15 1.5 Scope and Organization of the Book 16 2 A Brief Introduction to R 19 2.1 What Is R and RStudio? 19 2.2 Installing R and RStudio 20 2.3 Getting Started With R 21 2.3.1 Command Level Prompt 21 2.3.2 Calculations Using R 22 2.3.3 Editing Your R Code 24 2.3.4 Best Practice: Object Names in R 25 2.4 Data Values and Objects in R 25 2.4.1 Types of Data Values in R 25 2.4.2 Types (Structures) of Objects in R 28 2.4.3 Object Attributes 34 2.4.4 Testing (Checking) Object Type 34 2.4.5 Changing Object Type 34 2.5 R Packages (Libraries) 35 2.5.1 Installing R Packages 35 2.5.2 Name Spaces 36 2.5.3 Updating R 37 2.5.4 Datasets in R Packages 37 2.6 Importing (Reading) Data into R Workspace 37 2.6.1 Best Practice: Working Directory 38 2.6.2 Reading ASCII (Text) Files 38 2.6.3 Reading CSV Files 40 2.6.4 Reading Excel Files 40 2.6.5 Reading Files from the Internet 41 2.7 Writing (Exporting) Data to Files 42 2.7.1 Diverting Normal R Output to a File 42 2.7.2 Saving Graphs in Files 42 2.7.3 Exporting Data to Files 43 2.8 Some Arithmetic and Other Operators 43 2.8.1 Vectors 43 2.8.2 Matrix Computations 45 2.9 Programming in R 50 2.9.1 Best Practice: Script Files 50 2.9.2 Some Useful Commands or Functions 50 2.9.3 Conditional Execution 51 2.9.4 Loops 53 2.9.5 Functions and Functionals 54 2.9.6 User Defined Functions 55 2.10 Bibliographic Notes 60 3 Simple Linear Regression 65 3.1 Introduction 65 3.2 Covariance and Correlation Coefficient 65 3.3 Example: Computer Repair Data 69 3.4 The Simple Linear Regression Model 72 3.5 Parameter Estimation 73 3.6 Tests of Hypotheses 77 3.7 Confidence Intervals 82 3.8 Predictions 83 3.9 Measuring the Quality of Fit 84 3.10 Regression Line Through the Origin 88 3.11 Trivial Regression Models 89 3.12 Bibliographic Notes 90 4 Multiple Linear Regression 97 4.1 Introduction 97 4.2 Description of the Data and Model 97 4.3 Example: Supervisor Performance Data 98 4.4 Parameter Estimation 100 4.5 Interpretations of Regression Coefficients 101 4.6 Centering and Scaling 104 4.6.1 Centering and Scaling in Intercept Models 104 4.6.2 Scaling in No-Intercept Models 105 4.7 Properties of the Least Squares Estimators 106 4.8 Multiple Correlation Coefficient 107 4.9 Inference for Individual Regression Coefficients 108 4.10 Tests of Hypotheses in a Linear Model 111 4.10.1 Testing All Regression Coefficients Equal to Zero 4.10.2 Testing a Subset of Regression Coefficients Equal to 113 4.10.3 Testing the Equality of Regression Coefficients 4.10.4 Estimating and Testing of Regression Parameters 118 4.11 Predictions 121 4.12 Summary 122 5 Regression Diagnostics: Detection of Model Violations 131 5.1 Introduction 131 5.2 The Standard Regression Assumptions 132 5.3 Various Types of Residuals 134 5.4 Graphical Methods 136 5.5 Graphs Before Fitting a Model 139 5.5.1 One-Dimensional Graphs 139 5.5.2 Two-Dimensional Graphs 140 5.5.3 Rotating Plots 142 5.5.4 Dynamic Graphs 142 5.6 Graphs After Fitting a Model 143 5.7 Checking Linearity and Normality Assumptions 143 5.8 Leverage, Influence, and Outliers 144 5.8.1 Outliers in the Response Variable 146 5.8.2 Outliers in the Predictors 146 5.8.3 Masking and Swamping Problems 147 5.9 Measures of Influence 148 5.9.1 Cook’s Distance 150 5.9.2 Welsch and Kuh Measure 151 5.9.3 Hadi’s Influence Measure 151 5.10 The Potential-Residual Plot 152 5.11 Regression Diagnostics in R 154 5.12 What to Do with the Outliers? 155 5.13 Role of Variables in a Regression Equation 156 5.11.1 Added-Variable Plot 156 5.11.2 Residual Plus Component Plot 157 5.14 Effects of an Additional Predictor 159 5.15 Robust Regression 161 6 Qualitative Variables as Predictors 167 6.1 Introduction 167 6.2 Salary Survey Data 168 6.3 Interaction Variables 171 6.4 Systems of Regression Equations 175 6.4.1 Models with Different Slopes and Different Intercepts 176 6.4.2 Models with Same Slope and Different Intercepts 183 6.4.3 Models with Same Intercept and Different Slopes 184 6.5 Other Applications of Indicator Variables 185 6.6 Seasonality 186 6.7 Stability of Regression Parameters Over Time 187 7 Transformation of Variables 195 7.1 Introduction 195 7.2 Transformations to Achieve Linearity 197 7.3 Bacteria Deaths Due to X-Ray Radiation 199 7.3.1 Inadequacy of a Linear Model 200 7.3.2 Logarithmic Transformation for Achieving Linearity 201 7.4 Transformations to Stabilize Variance 203 7.5 Detection of Heteroscedastic Errors 208 7.6 Removal of Heteroscedasticity 210 7.7 Weighted Least Squares 211 7.8 Logarithmic Transformation of Data 212 7.9 Power Transformation 213 7.10 Summary 216 8 Weighted Least Squares 223 8.1 Introduction 223 8.2 Heteroscedastic Models 224 8.2.1 Supervisors Data 224 8.2.2 College Expense Data 226 8.3 Two-Stage Estimation 227 8.4 Education Expenditure Data 229 8.5 Fitting a Dose-Response Relationship Curve 237 9 The Problem of Correlated Errors 241 9.1 Introduction: Autocorrelation 241 9.2 Consumer Expenditure and Money Stock 242 9.3 Durbin-Watson Statistic 245 9.4 Removal of Autocorrelation by Transformation 246 9.5 Iterative Estimation with Autocorrelated Errors 249 9.6 Autocorrelation and Missing Variables 250 9.7 Analysis of Housing Starts 251 9.8 Limitations of the Durbin-Watson Statistic 253 9.9 Indicator Variables to Remove Seasonality 255 9.10 Regressing Two Time Series 257 10 Analysis of Collinear Data 261 10.1 Introduction 261 10.2 Effects of Collinearity on Inference 262 10.3 Effects of Collinearity on Forecasting 267 CONTENTS 10.4 Detection of Collinearity 271 10.4.1 Simple Signs of Collinearity 271 10.4.2 Variance Inflation Factors 274 10.4.3 The Condition Indices 276 11 Working With Collinear Data 283 11.1 Introduction 283 11.2 Principal Components 283 11.3 Computations Using Principal Components 287 11.4 Imposing Constraints 289 11.5 Searching for Linear Functions of the β's 292 11.6 Biased Estimation of Regression Coefficients 295 11.7 Principal Components Regression 296 11.8 Reduction of Collinearity in the Estimation Data 298 11.9 Constraints on the Regression Coefficients 300 11.10 Principal Components Regression: A Caution 301 11.11 Ridge Regression 303 11.12 Estimation by the Ridge Method 305 11.13 Ridge Regression: Some Remarks 308 11.14 Summary 311 11.15 Bibliographic Notes 311 12 Variable Selection Procedures 321 12.1 Introduction 321 12.2 Formulation of the Problem 322 12.3 Consequences of Variables Deletion 322 12.4 Uses of Regression Equations 324 12.4.1 Description and Model Building 324 12.4.2 Estimation and Prediction 324 12.4.3 Control 324 12.5 Criteria for Evaluating Equations 325 12.5.1 Residual Mean Square 325 12.5.2 Mallows Cp 326 12.5.3 Information Criteria 327 12.6 Collinearity and Variable Selection 328 12.7 Evaluating All Possible Equations 328 12.8 Variable Selection Procedures 329 12.8.1 Forward Selection Procedure 329 12.8.2 Backward Elimination Procedure 330 12.8.3 Stepwise Method 330 12.9 General Remarks on Variable Selection Methods 331 12.10 A Study of Supervisor Performance 332 12.11 Variable Selection with Collinear Data 336 12.12 The Homicide Data 336 12.13 Variable Selection Using Ridge Regression 339 12.14 Selection of Variables in an Air Pollution Study 339 12.15 A Possible Strategy for Fitting Regression Models 345 12.16 Bibliographic Notes 347 13 Logistic Regression 353 13.1 Introduction 353 13.2 Modeling Qualitative Data 354 13.3 The Logit Model 354 13.4 Example: Estimating Probability of Bankruptcies 356 13.5 Logistic Regression Diagnostics 358 13.6 Determination of Variables to Retain 359 13.7 Judging the Fit of a Logistic Regression 362 13.8 The Multinomial Logit Model 364 13.8.1 Multinomial Logistic Regression 364 13.8.2 Example: Determining Chemical Diabetes 365 13.8.3 Ordinal Logistic Regression 368 13.8.4 Example: Determining Chemical Diabetes Revisited 368 13.9 Classification Problem: Another Approach 370 14 Further Topics 375 14.1 Introduction 375 14.2 Generalized Linear Model 375 14.3 Poisson Regression Model 376 14.4 Introduction of New Drugs 377 14.5 Robust Regression 378 14.6 Fitting a Quadratic Model 379 14.7 Distribution of PCB in U.S. Bays 381 Exercises 384 References 385 Index

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Book SynopsisDesign Techniques for Origami Tessellations is both a collection of origami tessellations and a manual to design them.This book begins by explaining general design methods, the history and definitions of origami tessellations, and the geometric features of flat origami, before moving on to introduce a brand-new design method: the twist-based design method. This method generates base parts that connect twist patterns (that can be folded with a twist) without using a lattice. Therefore, it can generate base parts such as regular pentagons, which cannot be generated with more conventional methods, and can generate new origami tessellations connected to them.Features: No proofs or formulas in the text and minimal jargon. Suitable for readers with a roughly middle school to high school level of mathematical background. Web application implementing the method described in this book is available, allowing the readers to design tTable of Contents0. Origami and Traditional Tessellation Patterns. 0.1. Background of Origami Tessellations. 0.2 Crease Patterns. 0.3 Basic Geometry of Flat-Foldable Crease Patterns. 0.4 Folded State of Crease Patterns. 0.5 Patterns for Twist-Folding. 0.6 Tessellations. 0.7. Tips for Making Beautiful Folds. 1.Folding on Square Grid. 1.1. Square Twist-Patterns. 1.2. Isosceles Right Triangle Twist Pattern. 1.3. Checker Base. 1.4. Changing folded shape. 1.5. Crease patterns as connectable tile. Appendix 1: Pixel Arts Composed of Origami Tessellation. 2. Folding on Equilateral Triangle Grid. 2.1. Equilateral Triangle Twist-Patterns. 2.2. Regular Hexagon Twist-Patterns. 2.3. Right Triangle Twist-Patterns. Column 1: Grid and Twist Pattern. 3. Connecting Triangle Twist Patterns. 3.1. Creating Triangle Twist Patterns. 3.2. Connecting Triangle Twist Patterns. 3.3. Design for Regular Polygon Patterns. Column 02: How to use Triangle Twist Pattern Maker. Appendix 2: Changing Length of Pleat Base. 4.Connecting of Different Base Parts. 4.1. Connectable Side of Boundary. 4.2. Regular Tessellations. 4.3. Tessellation with Equilateral Polygons. 4.4. Combining Crease Patterns Having Different Guide Sides. Appendix 3: Condition that Boundaries are Folded into Similar Shape. 5. Generating Aesthetic Origami Tessellations. 5.1. Origami Tessellations Regarding as Positive-Negative Pattern. 5.2. Parallel Moving Faces by Flat Folding. 5.3. Design for Origami Tessellations Regarding as Positive-Negative Pattern. Appendix 4: Deformation of crease pattern using pleat bases. 6. Folding Bellows. 6.1. Folding Parallel Lines. 6.2. Bent Bellows. 6.3. Periodic Bellows. 6.4. Bending Irregular Bellows. Column 03: Origami Tessellation Design Software “Tess”. 7. Application of Twist Pattern Design Method. 7.1. Reconstructing Guide from Given Origami Tessellation. 7.2. Fractal Origami Tessellations and Guides. 7.3. Guide with Gaps. Column 4: Connecting 3D Origami Arts and Origami Tessellations.

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Book SynopsisMathematik ist eine vielseitige und lebendige Wissenschaft. Von den großen Themen wie Zahlen, Unendlichkeiten, Dimensionen und Wahrscheinlichkeiten spannen die Autoren einen Bogen zu den aktuellen mathematischen Anwendungen in der Logistik, der Finanzwelt, der Kryptographie, der Medizin und anderen Gebieten. Das Buch versammelt verständliche, unterhaltsame Texte ebenso wie anspruchsvollere mathematische Herausforderungen und bietet damit Lesern die Chance, einen ganz individuellen Zugang zu dieser spannenden Wissenschaft zu finden.Table of ContentsI Prolog.- Mathe wird Kult — Beschreibung einer Hoffnung.- Wieviel Mathematik gibt es?.- Die pure Eleganz der Mathematik.- Hilberts Hotel.- Wo Mathematik entsteht: Zehn Orte.- Warum Mathematik?.- Modellierung, Simulation, Optimierung.- II Dauerbrenner.- Die Primzahlen.- Sechs Beweise für die Unendlichkeit der Primzahlen.- Ein Durchbruch für „Jedermann“.- Primzahltests und Primzahlrekorde.- Primzahlen.- Vorwort.- Filmtipp.- Mengen, Funktionen, und die Kontinuumshypothese.- Leonhard Eulers unendliche Summen.- Eine Frage und zwei Antworten.- Der fünfdimensionale Kuchen.- Zur Einführung von Dimensionen.- Topologie.- Dimension (engl.).- Den Zufall kann man nicht überlisten.- Lottotipps - „gleicher als gleich“?.- Filmtipp.- Das Nadelproblem von Buffon.- Buffon: Hat er Stöckchen geworfen oder hat er nicht?.- Frauenfragen oder Mehr ist manchmal weniger.- Drei Paradoxa.- III Harte Nüsse.- Der große Satz von Fermat.- Eine Million Dollar für die Sicherheit Ihrer Kreditkarte?- P = NP?- Die Riemannsche Vermutung.- Der mathematische Olymp.- An Interview with Maryna Viazovska.- IV Heiße Themen.- Eine ungefährliche Explosion und der Handlungsreisende.- Patent auf eine Formel.- Die Rolle der Mathematik auf den Finanzmärkten.- Alles richtig und trotzdem falsch? Anmerkungen zur Finanzkrise und zur Finanzmathematik.- Der RSA-Algorithmus.- Kurze Geschichte des Nash-Gleichgewichts.- Modellierungswerkzeuge.- What Makes Quantum Computing so Hard to Explain?.- Mathematik, Maschine Learning und Artificial Intelligence.- V Mathematik ohne Grenzen.- Invarianten: ... wie ein Fels in der Brandung.- Escher über die Schulter gesehen - eine Einladung.- Zusammenspiel: Mathematik und Architektur.- Von Halbtönen und zwölften Wurzeln.- Die Mehrheit entscheidet. Wirklich?- Maler, Mörder, Mathematiker.- VI Zugaben: Kurioses aus dem Alltag.- Traumjob Mathematik.- Möbiusbänder liegen im Trend.- Mit Mädchen rechnen.- Werbung.- "Penrose-Treppe".- "Parallelen".- "Espiral logaritmica" Schlussbemerkung.

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Book SynopsisSpherical Geometry and Its Applications introduces spherical geometry and its practical applications in a mathematically rigorous form. The text can serve as a course in spherical geometry for mathematics majors. Readers from various academic backgrounds can comprehend various approaches to the subject. The book introduces an axiomatic system for spherical geometry and uses it to prove the main theorems of the subject. It also provides an alternate approach using quaternions. The author illustrates how a traditional axiomatic system for plane geometry can be modified to produce a different geometric world but a geometric world that is no less real than the geometric world of the plane. Features: A well-rounded introduction to spherical geometry Provides several proofs of some theorems to appTable of ContentsReview of three-dimensional geometry Geometry in a plane Geometry in space Plane trigonometry Coordinates and vectors The sphere in space Great circles Distance and angles Area Spherical coordinates Axiomatic spherical geometry Basic axioms Angles Triangles Congruence Inequalities Area Trigonometry Spherical Pythagorean theorem and law of sines Spherical law of cosines and analogue formula Right triangles The four-parts and half angle formulas Dualization Solution of triangles Astronomy The celestial sphere Changing coordinates Rise and set of objects in the sky The measurement of time Rise and set times in standard time Polyhedra Regular solids Crystals Spherical mappings Rotations and reflections Spherical projections Quaternions Review of complex numbers Quaternions: Definitions and basic properties Application to the sphere Triangles Rotations and Reflections Selected solutions to exercises

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Book SynopsisA comprehensive survey of undergraduate mathematics, compressing four years of study into one robust overview.In The Math You Need, Thomas Mack provides a singular, comprehensive survey of undergraduate mathematics, compressing four years of math curricula into one volume. Without sacrificing rigor, this book provides a go-to resource for the essentials that any academic or professional needs. Each chapter is followed by numerous exercises to provide the reader an opportunity to practice what they learned. The Math You Need is distinguished in its use of the Bourbaki style—the gold standard for concision and an approach that mathematicians will find of particular interest. As ambitious as it is compact, this text embraces mathematical abstraction throughout, avoiding ad hoc computations in favor of general results.Covering nine areas—group theory, commutative algebra, linear algebra, topology, real analysis, complex analysis, number theo

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Book SynopsisVedic mathematics has a key to helping both teachers and students alike fall in love with, or at least become really enthusiastic about, number and mathematics in general.

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Book SynopsisA unique and effective way to learn Algebraâupdated with the latest instruction and reviewMust Know High School Algebra provides a fresh approach to learning. As part of our Must Know series, this new edition makes sure what you really need to know is clear up-front. Rather than starting with goals to be met, chapters begin by telling you the most important concepts about the topic at handâand then show you exactly how these concepts help you accomplish your goals.Written by excerpt algebra educators, Must Know High School Algebra, Second Edition provides updated lesson content and useful examples to help clarify each topic. Every chapter closes with reinforcing exercises to get you the practice you need to gain confidence. New features to this edition focus on extra support and helping you avoid common mistakes. In the end, you get everything you need to build your algebra skills quickly and painlessly.Features:Mo

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Book SynopsisVaclav Smil is my favorite author… Numbers Don't Lie takes everything that makes his writing great and boils it down into an easy-to-read format. I unabashedly recommend this book to anyone who loves learning.--Bill Gates, GatesNotesFrom the author of How the World Really Works, an essential guide to understanding how numbers reveal the true state of our world--exploring a wide range of topics including energy, the environment, technology, transportation, and food production.Vaclav Smil's mission is to make facts matter. An environmental scientist, policy analyst, and a hugely prolific author, he is Bill Gates' go-to guy for making sense of our world. In Numbers Don't Lie, Smil answers questions such as: What's worse for the environment--your car or your phone? How much do the world's cows weigh (and what does it matter)? And what makes people happy? From data about our societies and populations, through measures of the

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Book SynopsisTable of ContentsPreface xxv Acknowledgments xxxi Part I – Introduction 1 1 Sequential Decision Problems 3 1.1 The Audience 7 1.2 The Communities of Sequential Decision Problems 8 1.3 Our Universal Modeling Framework 10 1.4 Designing Policies for Sequential Decision Problems 15 1.5 Learning 20 1.6 Themes 21 1.7 Our Modeling Approach 27 1.8 How to Read this Book 27 1.9 Bibliographic Notes 33 Exercises 34 Bibliography 38 2 Canonical Problems and Applications 39 2.1 Canonical Problems 39 2.2 A Universal Modeling Framework for Sequential Decision Problems 64 2.3 Applications 69 2.4 Bibliographic Notes 85 Exercises 90 Bibliography 93 3 Online Learning 101 3.1 Machine Learning for Sequential Decisions 102 3.2 Adaptive Learning Using Exponential Smoothing 110 3.3 Lookup Tables with Frequentist Updating 111 3.4 Lookup Tables with Bayesian Updating 112 3.5 Computing Bias and Variance* 118 3.6 Lookup Tables and Aggregation* 121 3.7 Linear Parametric Models 131 3.8 Recursive Least Squares for Linear Models 136 3.9 Nonlinear Parametric Models 140 3.10 Nonparametric Models* 149 3.11 Nonstationary Learning* 159 3.12 The Curse of Dimensionality 162 3.13 Designing Approximation Architectures in Adaptive Learning 165 3.14 Why Does It Work?** 166 3.15 Bibliographic Notes 174 Exercises 176 Bibliography 180 4 Introduction to Stochastic Search 183 4.1 Illustrations of the Basic Stochastic Optimization Problem 185 4.2 Deterministic Methods 188 4.3 Sampled Models 193 4.4 Adaptive Learning Algorithms 202 4.5 Closing Remarks 210 4.6 Bibliographic Notes 210 Exercises 212 Bibliography 218 Part II – Stochastic Search 221 5 Derivative-Based Stochastic Search 223 5.1 Some Sample Applications 225 5.2 Modeling Uncertainty 228 5.3 Stochastic Gradient Methods 231 5.4 Styles of Gradients 237 5.5 Parameter Optimization for Neural Networks* 242 5.6 Stochastic Gradient Algorithm as a Sequential Decision Problem 247 5.7 Empirical Issues 248 5.8 Transient Problems* 249 5.9 Theoretical Performance* 250 5.10 Why Does it Work? 250 5.11 Bibliographic Notes 263 Exercises 264 Bibliography 270 6 Stepsize Policies 273 6.1 Deterministic Stepsize Policies 276 6.2 Adaptive Stepsize Policies 282 6.3 Optimal Stepsize Policies* 289 6.4 Optimal Step sizes for Approximate Value Iteration* 297 6.5 Convergence 300 6.6 Guidelines for Choosing Stepsize Policies 301 6.7 Why Does it Work* 303 6.8 Bibliographic Notes 306 Exercises 307 Bibliography 314 7 Derivative-Free Stochastic Search 317 7.1 Overview of Derivative-free Stochastic Search 319 7.2 Modeling Derivative-free Stochastic Search 325 7.3 Designing Policies 330 7.4 Policy Function Approximations 333 7.5 Cost Function Approximations 335 7.6 VFA-based Policies 338 7.7 Direct Lookahead Policies 348 7.8 The Knowledge Gradient (Continued)* 362 7.9 Learning in Batches 380 7.10 Simulation Optimization* 382 7.11 Evaluating Policies 385 7.12 Designing Policies 394 7.13 Extensions* 398 7.14 Bibliographic Notes 409 Exercises 412 Bibliography 424 Part III – State-dependent Problems 429 8 State-dependent Problems 431 8.1 Graph Problems 433 8.2 Inventory Problems 439 8.3 Complex Resource Allocation Problems 446 8.4 State-dependent Learning Problems 456 8.5 A Sequence of Problem Classes 460 8.6 Bibliographic Notes 461 Exercises 462 Bibliography 466 9 Modeling Sequential Decision Problems 467 9.1 A Simple Modeling Illustration 471 9.2 Notational Style 476 9.3 Modeling Time 478 9.4 The States of Our System 481 9.5 Modeling Decisions 500 9.6 The Exogenous Information Process 506 9.7 The Transition Function 515 9.8 The Objective Function 518 9.9 Illustration: An Energy Storage Model 523 9.10 Base Models and Lookahead Models 528 9.11 A Classification of Problems* 529 9.12 Policy Evaluation* 532 9.13 Advanced Probabilistic Modeling Concepts** 534 9.14 Looking Forward 540 9.15 Bibliographic Notes 542 Exercises 544 Bibliography 557 10 Uncertainty Modeling 559 10.1 Sources of Uncertainty 560 10.2 A Modeling Case Study: The COVID Pandemic 575 10.3 Stochastic Modeling 575 10.4 Monte Carlo Simulation 581 10.5 Case Study: Modeling Electricity Prices 589 10.6 Sampling vs. Sampled Models 595 10.7 Closing Notes 597 10.8 Bibliographic Notes 597 Exercises 598 Bibliography 601 11 Designing Policies 603 11.1 From Optimization to Machine Learning to Sequential Decision Problems 605 11.2 The Classes of Policies 606 11.3 Policy Function Approximations 610 11.4 Cost Function Approximations 613 11.5 Value Function Approximations 614 11.6 Direct Lookahead Approximations 616 11.7 Hybrid Strategies 620 11.8 Randomized Policies 626 11.9 Illustration: An Energy Storage Model Revisited 627 11.10 Choosing the Policy Class 631 11.11 Policy Evaluation 641 11.12 Parameter Tuning 642 11.13 Bibliographic Notes 646 Exercises 646 Bibliography 651 Part IV – Policy Search 653 12 Policy Function Approximations and Policy Search 655 12.1 Policy Search as a Sequential Decision Problem 657 12.2 Classes of Policy Function Approximations 658 12.3 Problem Characteristics 665 12.4 Flavors of Policy Search 666 12.5 Policy Search with Numerical Derivatives 669 12.6 Derivative-Free Methods for Policy Search 670 12.7 Exact Derivatives for Continuous Sequential Problems* 677 12.8 Exact Derivatives for Discrete Dynamic Programs** 680 12.9 Supervised Learning 686 12.10 Why Does it Work? 687 12.11 Bibliographic Notes 690 Exercises 691 Bibliography 698 13 Cost Function Approximations 701 13.1 General Formulation for Parametric CFA 703 13.2 Objective-Modified CFAs 704 13.3 Constraint-Modified CFAs 714 13.4 Bibliographic Notes 725 Exercises 726 Bibliography 729 Part V – Lookahead Policies 731 14 Exact Dynamic Programming 737 14.1 Discrete Dynamic Programming 738 14.2 The Optimality Equations 740 14.3 Finite Horizon Problems 747 14.4 Continuous Problems with Exact Solutions 750 14.5 Infinite Horizon Problems* 755 14.6 Value Iteration for Infinite Horizon Problems* 757 14.7 Policy Iteration for Infinite Horizon Problems* 762 14.8 Hybrid Value-Policy Iteration* 764 14.9 Average Reward Dynamic Programming* 765 14.10 The Linear Programming Method for Dynamic Programs** 766 14.11 Linear Quadratic Regulation 767 14.12 Why Does it Work?** 770 14.13 Bibliographic Notes 783 Exercises 783 Bibliography 793 15 Backward Approximate Dynamic Programming 795 15.1 Backward Approximate Dynamic Programming for Finite Horizon Problems 797 15.2 Fitted Value Iteration for Infinite Horizon Problems 804 15.3 Value Function Approximation Strategies 805 15.4 Computational Observations 810 15.5 Bibliographic Notes 816 Exercises 816 Bibliography 821 16 Forward ADP I: The Value of a Policy 823 16.1 Sampling the Value of a Policy 824 16.2 Stochastic Approximation Methods 835 16.3 Bellman’s Equation Using a Linear Model* 837 16.4 Analysis of TD(0), LSTD, and LSPE Using a Single State* 842 16.5 Gradient-based Methods for Approximate Value Iteration* 845 16.6 Value Function Approximations Based on Bayesian Learning* 852 16.7 Learning Algorithms and Atepsizes 855 16.8 Bibliographic Notes 860 Exercises 862 Bibliography 864 17 Forward ADP II: Policy Optimization 867 17.1 Overview of Algorithmic Strategies 869 17.2 Approximate Value Iteration and Q-Learning Using Lookup Tables 871 17.3 Styles of Learning 881 17.4 Approximate Value Iteration Using Linear Models 886 17.5 On-policy vs. off-policy learning and the exploration–exploitation problem 888 17.6 Applications 894 17.7 Approximate Policy Iteration 900 17.8 The Actor–Critic Paradigm 907 17.9 Statistical Bias in the Max Operator* 909 17.10 The Linear Programming Method Using Linear Models* 912 17.11 Finite Horizon Approximations for Steady-State Applications 915 17.12 Bibliographic Notes 917 Exercises 918 Bibliography 924 18 Forward ADP III: Convex Resource Allocation Problems 927 18.1 Resource Allocation Problems 930 18.2 Values Versus Marginal Values 937 18.3 Piecewise Linear Approximations for Scalar Functions 938 18.4 Regression Methods 941 18.5 Separable Piecewise Linear Approximations 944 18.6 Benders Decomposition for Nonseparable Approximations** 946 18.7 Linear Approximations for High-Dimensional Applications 956 18.8 Resource Allocation with Exogenous Information State 958 18.9 Closing Notes 959 18.10 Bibliographic Notes 960 Exercises 962 Bibliography 967 19 Direct Lookahead Policies 971 19.1 Optimal Policies Using Lookahead Models 974 19.2 Creating an Approximate Lookahead Model 978 19.3 Modified Objectives in Lookahead Models 985 19.4 Evaluating DLA Policies 992 19.5 Why Use a DLA? 997 19.6 Deterministic Lookaheads 999 19.7 A Tour of Stochastic Lookahead Policies 1005 19.8 Monte Carlo Tree Search for Discrete Decisions 1009 19.9 Two-Stage Stochastic Programming for Vector Decisions* 1018 19.10 Observations on DLA Policies 1024 19.11 Bibliographic Notes 1025 Exercises 1027 Bibliography 1031 Part VI – Multiagent Systems 1033 20 Multiagent Modeling and Learning 1035 20.1 Overview of Multiagent Systems 1036 20.2 A Learning Problem – Flu Mitigation 1044 20.3 The POMDP Perspective* 1059 20.4 The Two-Agent Newsvendor Problem 1062 20.5 Multiple Independent Agents – An HVAC Controller Model 1067 20.6 Cooperative Agents – A Spatially Distributed Blood Management Problem 1070 20.7 Closing Notes 1074 20.8 Why Does it Work? 1074 20.9 Bibliographic Notes 1076 Exercises 1077 Bibliography 1083 Index 1085

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Book SynopsisAn accessible learning resource that develops data analysis skills for natural science students in an efficient style using the R programming language R-ticulate: A Beginner's Guide to Data Analysis for Natural Scientists is a compact, example-based, and user-friendly statistics textbook without unnecessary frills, but instead filled with engaging, relatable examples, practical tips, online exercises, resources, and references to extensions, all on a level that follows contemporary curricula taught in large parts of the world. The content structure is unique in the sense that statistical skills are introduced at the same time as software (programming) skills in R. This is by far the best way of teaching from the authors' experience. Readers of this introductory text will find: Explanations of statistical concepts in simple, easy-to-understand language A variety of approaches to problem solving using both base R and tidyverse

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