Mathematics Books

Book SynopsisCovers stability and stabilization of equilibria for both linear and nonlinear time-invariant systems of ordinary differential equations. Suitable for advanced undergraduates and beginning graduate students in the sciences, engineering, and mathematics, this book takes a modern approach that bridges the gap between linear and nonlinear systems.Trade Review"This book takes a unique modern approach that bridges the gap between linear and nonlinear systems... Clear formulated definitions and theorems, correct proofs and many interesting examples and exercises make this textbook very attractive."--Ferenc Szenkovits, MathematicaTable of ContentsList of Figures xi Preface xiii Chapter 1: Introduction 1 1.1 Open Loop Control 1 1.2 The Feedback Stabilization Problem 2 1.3 Chapter and Appendix Descriptions 5 1.4 Notes and References 11 Chapter 2: Mathematical Background 12 2.1 Analysis Preliminaries 12 2.2 Linear Algebra and Matrix Algebra 12 2.3 Matrix Analysis 17 2.4 Ordinary Differential Equations 30 2.4.1 Phase Plane Examples: Linear and Nonlinear 35 2.5 Exercises 44 2.6 Notes and References 48 Chapter 3: Linear Systems and Stability 49 3.1 The Matrix Exponential 49 3.2 The Primary Decomposition and Solutions of LTI Systems 53 3.3 Jordan Form and Matrix Exponentials 57 3.3.1 Jordan Form of Two-Dimensional Systems 58 3.3.2 Jordan Form of n-Dimensional Systems 61 3.4 The Cayley-Hamilton Theorem 67 3.5 Linear Time Varying Systems 68 3.6 The Stability Definitions 71 3.6.1 Motivations and Stability Definitions 71 3.6.2 Lyapunov Theory for Linear Systems 73 3.7 Exercises 77 3.8 Notes and References 81 Chapter 4: Controllability of Linear Time Invariant Systems 82 4.1 Introduction 82 4.2 Linear Equivalence of Linear Systems 84 4.3 Controllability with Scalar Input 88 4.4 Eigenvalue Placement with Single Input 92 4.5 Controllability with Vector Input 94 4.6 Eigenvalue Placement with Vector Input 96 4.7 The PBH Controllability Test 99 4.8 Linear Time Varying Systems: An Example 103 4.9 Exercises 105 4.10 Notes and References 108 Chapter 5: Observability and Duality 109 5.1 Observability, Duality, and a Normal Form 109 5.2 Lyapunov Equations and Hurwitz Matrices 117 5.3 The PBH Observability Test 118 5.4 Exercises 121 5.5 Notes and References 123 Chapter 6: Stabilizability of LTI Systems 124 6.1 Stabilizing Feedbacks for Controllable Systems 124 6.2 Limitations on Eigenvalue Placement 128 6.3 The PBH Stabilizability Test 133 6.4 Exercises 134 6.5 Notes and References 136 Chapter 7: Detectability and Duality 138 7.1 An Example of an Observer System 138 7.2 Detectability, the PBH Test, and Duality 142 7.3 Observer-Based Dynamic Stabilization 145 7.4 Linear Dynamic Controllers and Stabilizers 147 7.5 LQR and the Algebraic Riccati Equation 152 7.6 Exercises 156 7.7 Notes and References 159 Chapter 8: Stability Theory 161 8.1 Lyapunov Theorems and Linearization 161 8.1.1 Lyapunov Theorems 162 8.1.2 Stabilization from the Jacobian Linearization 171 8.1.3 Brockett's Necessary Condition 172 8.1.4 Examples of Critical Problems 173 8.2 The Invariance Theorem 176 8.3 Basin of Attraction 181 8.4 Converse Lyapunov Theorems 183 8.5 Exercises 183 8.6 Notes and References 187 Chapter 9: Cascade Systems 189 9.1 The Theorem on Total Stability 189 9.1.1 Lyapunov Stability in Cascade Systems 192 9.2 Asymptotic Stability in Cascades 193 9.2.1 Examples of Planar Systems 193 9.2.2 Boundedness of Driven Trajectories 196 9.2.3 Local Asymptotic Stability 199 9.2.4 Boundedness and Global Asymptotic Stability 202 9.3 Cascades by Aggregation 204 9.4 Appendix: The Poincar'e-Bendixson Theorem 207 9.5 Exercises 207 9.6 Notes and References 211 Chapter 10: Center Manifold Theory 212 10.1 Introduction 212 10.1.1 An Example 212 10.1.2 Invariant Manifolds 213 10.1.3 Special Coordinates for Critical Problems 214 10.2 The Main Theorems 215 10.2.1 Definition and Existence of Center Manifolds 215 10.2.2 The Reduced Dynamics 218 10.2.3 Approximation of a Center Manifold 222 10.3 Two Applications 225 10.3.1 Adding an Integrator for Stabilization 226 10.3.2 LAS in Special Cascades: Center Manifold Argument 228 10.4 Exercises 229 10.5 Notes and References 231 Chapter 11: Zero Dynamics 233 11.1 The Relative Degree and Normal Form 233 11.2 The Zero Dynamics Subsystem 244 11.3 Zero Dynamics and Stabilization 248 11.4 Vector Relative Degree of MIMO Systems 251 11.5 Two Applications 254 11.5.1 Designing a Center Manifold 254 11.5.2 Zero Dynamics for Linear SISO Systems 257 11.6 Exercises 263 11.7 Notes and References 267 Chapter 12: Feedback Linearization of Single-Input Nonlinear Systems 268 12.1 Introduction 268 12.2 Input-State Linearization 270 12.2.1 Relative Degree n 271 12.2.2 Feedback Linearization and Relative Degree n 272 12.3 The Geometric Criterion 275 12.4 Linearizing Transformations 282 12.5 Exercises 285 12.6 Notes and References 287 Chapter 13: An Introduction to Damping Control 289 13.1 Stabilization by Damping Control 289 13.2 Contrasts with Linear Systems: Brackets, Controllability, Stabilizability 296 13.3 Exercises 299 13.4 Notes and References 300 Chapter 14: Passivity 302 14.1 Introduction to Passivity 302 14.1.1 Motivation and Examples 302 14.1.2 Definition of Passivity 304 14.2 The KYP Characterization of Passivity 306 14.3 Positive Definite Storage 309 14.4 Passivity and Feedback Stabilization 314 14.5 Feedback Passivity 318 14.5.1 Linear Systems 321 14.5.2 Nonlinear Systems 325 14.6 Exercises 327 14.7 Notes and References 330 Chapter 15: Partially Linear Cascade Systems 331 15.1 LAS from Partial-State Feedback 331 15.2 The Interconnection Term 333 15.3 Stabilization by Feedback Passivation 336 15.4 Integrator Backstepping 349 15.5 Exercises 355 15.6 Notes and References 357 Chapter 16: Input-to-State Stability 359 16.1 Preliminaries and Perspective 359 16.2 Stability Theorems via Comparison Functions 364 16.3 Input-to-State Stability 366 16.4 ISS in Cascade Systems 372 16.5 Exercises 374 16.6 Notes and References 376 Chapter 17: Some Further Reading 378 Appendix A: Notation: A Brief Key 381 Appendix B: Analysis in R and Rn 383 B.1 Completeness and Compactness 386 B.2 Differentiability and Lipschitz Continuity 393 Appendix C: Ordinary Differential Equations 393 C.1 Existence and Uniqueness of Solutions 393 C.2 Extension of Solutions 396 C.3 Continuous Dependence 399 Appendix D: Manifolds and the Preimage Theorem; Distributions and the Frobenius Theorem 403 D.1 Manifolds and the Preimage Theorem 403 D.2 Distributions and the Frobenius Theorem 410 Appendix E: Comparison Functions and a Comparison Lemma 420 E.1 Definitions and Basic Properties 420 E.2 Differential Inequality and Comparison Lemma 424 Appendix F: Hints and Solutions for Selected Exercises 430 Bibliography 443 Index 451

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Book SynopsisCombines ancient mythology and modern mathematics. This book offers helpful hints and complete solutions, and the appendixes include a brief history of the Hercules tale, and a review of mathematics.Trade Review"The figures and diagrams are well chosen, the mathematics is presented attractively, the pace is appropriate. Unobtrusively, the general level of mathematical sophistication tends to rise as the book progresses. This book offers ideas to teachers seeking topics on which to pin some abstract maths, and could encourage students to think imaginatively about their subject, and where it might arise in unexpected circumstances."--John Haigh, London Mathematical Society Newsletter "Though Mythematics is probably best viewed as a recreational mathematics book, the methods used should provide insight into how one applies mathematics to a physical, real-world problem. Students interested in mathematical modeling may certainly find this book of interest."--Choice "Never before has a Greek hero faced such trials armed first and foremost with the weapon of mathematics... This book is ideal for students, providing an entertaining way to practise problem-solving skills and a glimpse of how useful even basic mathematical ideas can be when applied to physical scenarios. The premise of Mythematics is both original and intriguing, but what is most impressive is Huber's inventiveness in translating the twelve labours of Hercules into mathematical conundrums."--Sarah Shepherd, iSquared "The book is unique in its mixture of ancient Greek mythology and applied mathematics... It will certainly be a valuable source of inspiration for math teachers who have to teach these students."--Adhemar Bultheel, European Mathematical SocietyTable of ContentsList of Figures xiii foreword xv Chapter 1: The First Labor: The Nemean Lion 1 1.1 The Tasks 2 1.1.1 Shooting an Arrow 2 1.1.2 Hercules Closes the Cave Mouth 2 1.1.3 Exercise: Zeus Makes a Deal 3 1.2 The Solutions 3 1.2.1 Shooting an Arrow 3 1.2.2 Hercules Closes the Cave Mouth 6 1.2.3 Exercise: Zeus Makes a Deal 10 Chapter 2: The Second Labor: The Lernean Hydra 13 2.1 The Tasks 13 2.1.1 One Head Replaced by Two 14 2.1.2 Cauterizing the Hydra 14 2.2 The Solutions 15 2.2.1 One Head Replaced by Two 15 2.2.2 Cauterizing the Hydra 17 Chapter 3: The Third Labor: The Hind of Ceryneia 20 3.1 The Tasks 20 3.1.1 Optimizing the Hind's Journey 21 3.1.2 Cerynitian Work 21 3.1.3 Exercise: Work with a Variable Force 21 3.2 The Solutions 22 3.2.1 Optimizing the Hind's Journey 22 3.2.2 Cerynitian Work 26 3.2.3 Exercise: Work with a Variable Force 27 Chapter 4: The Fourth Labor: The Erymanthian Boar 29 4.1 The Tasks 30 4.1.1 Exercise: The Centaurs' Wine 30 4.1.2 Chiron's Poison 30 4.1.3 The Capture of the Boar 31 4.2 The Solutions 31 4.2.1 Exercise: The Centaurs' Wine 32 4.2.2 Chiron's Poison 34 4.2.3 The Capture of the Boar 37 4.3 The Erymanthian Sudoku Puzzle 40 Chapter 5: The Fifth Labor: The Augean Stables 41 5.1 The Tasks 42 5.1.1 The Herds of Augeas 42 5.1.2 Exercise: Hydrostatic Pressure on the Stable Walls 43 5.1.3 Cleaning the Stables with Torricelli 43 5.2 The Solutions 43 5.2.1 The Herds of Augeas 43 5.2.2 Exercise: Hydrostatic Pressure on the Stable Walls 45 5.2.3 Cleaning the Stables with Torricelli 48 Chapter 6: The Sixth Labor: The Stymphalian Birds 53 6.1 The Tasks 53 6.1.1 The Spiral of Archimedes 54 6.1.2 Resonating Castanets 54 6.1.3 Exercise: Monte Carlo Shooting Scheme 55 6.2 The Solutions 55 6.2.1 The Spiral of Archimedes 55 6.2.2 Resonating Castanets 59 6.2.3 Exercise: A Monte Carlo Shooting Scheme 64 Chapter 7: The Seventh Labor: The Cretan Bull 69 7.1 The Tasks 69 7.1.1 Exercise: Riding the Bull 70 7.1.2 The Marathon Attacks 70 7.2 The Solutions 70 7.2.1 Exercise: Riding the Bull 70 7.2.2 The Marathon Attacks 73 Chapter 8: The Eighth Labor: The Horses of Diomedes 76 8.1 The Tasks 76 8.1.1 Driving the Mares to the Sea 77 8.1.2 Hercules' Slingshot 77 8.1.3 Exercise: The City of Abdera 78 8.2 The Solutions 78 8.2.1 Driving the Mares to the Sea 78 8.2.2 Hercules' Slingshot 81 8.2.3 Exercise: The City of Abdera 83 8.3 The Diomedes Sudoku Puzzle 87 Chapter 9: The Ninth Labor: The Belt of Hippolyte 89 9.1 The Tasks 90 9.1.1 The Sons of Minos versus Hercules 91 9.1.2 The Amazons and the Spread of a Rumor 91 9.1.3 Exercise: Hercules and the Kraken 92 9.2 The Solutions 92 9.2.1 The Sons of Minos versus Hercules 92 9.2.2 The Amazons and the Spread of a Rumor 98 9.2.3 Exercise: Hercules and the Kraken 101 Chapter 10: The Tenth Labor: Geryon's Cattle 104 10.1 The Tasks 105 10.1.1 The Pillars of Hercules 106 10.1.2 The Golden Goblet 106 10.1.3 Hera Sends the Gadflies 106 10.1.4 Blocking the River Strymon 107 10.2 The Solutions 107 10.2.1 The Pillars of Hercules 107 10.2.2 The Golden Goblet 110 10.2.3 Hera Sends the Gadflies 112 10.2.4 Blocking the River Strymon 114 Chapter 11: The Eleventh Labor: The Apples of the Hesperides 118 11.1 The Tasks 120 11.1.1 Exercise: The Riddles of Nereus 120 11.1.2 Wrestling Antaeus 121 11.1.3 Exercise: Hercules Has the Whole World in His Hands 121 11.2 The Solutions 122 11.2.1 Exercise: The Riddles of Nereus 122 11.2.2 Wrestling Antaeus 125 11.2.3 Exercise: Hercules Has the Whole World in His Hands 131 Chapter 12: The Twelfth Labor: Cerberus 134 12.1 The Tasks 135 12.1.1 The Descent into the Underworld 135 12.1.2 The Fight with Cerberus 135 12.2 The Solutions 136 12.2.1 The Descent into the Underworld 136 12.2.2 The Fight with Cerberus 139 12.3 The Cerberus Sudoku Puzzle 143 Appendix A: The Labors and Subject Areas of Mathematics 147 A.1 Subject Areas by Labors and Tasks 147 A.2 Tasks by Subject Area 149 Appendix B: Hercules before the Labors 151 B.1 Hercules' Background 151 Appendix C: The Authors of the Hercules Myth 154 C.1 The Authors 154 C.2 The Lay of the Labours of Hercules 156 Appendix D:The Laplace Transform 161 D.1 Initial Value Problems and the Laplace Transform 161 D.1.1 Theory 161 D.1.2 An Example 163 Appendix E: Solution to the Sudoku Puzzles 164 Bibliography 167 Index 171

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Book SynopsisTraces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. This book is suitable for mathematicians and historians.Trade ReviewOne of Choice's Outstanding Academic Titles for 2009 "In Plato's Ghost, he has ... present[ed] us with an ambitious and in many respects remarkable synthesis of the modern transformation of mathematics via structural and set-theoretic notions, together not only with its logic and philosophy but also with related developments in artificial languages and psychology... I can certainly recommend Plato's Ghost highly as a rich resource and point of departure for readers who want to learn more about this exciting period in the development of modern mathematics."--Solomon Feferman, American Scientist "This accessible, rigorous volume belongs in every serious library."--J. McCleary, Choice "In a book aimed at the educated public, the author presents an impressive amount of data--both of the kind mathematicians with some awareness of the history of their subject may be aware of, and of an entirely different kind, coming from the outskirts of mathematics, from philosophy, from physics, or from the popularization of mathematics, which will likely be new even to historians of mathematics."--Victor V Pambuccian, Mathematical Reviews "It is ... no small assertion to say that the book under review, Plato's Ghost, is [Gray's] most far-reaching and ambitious work to date... [T]here is a wealth of valuable data here which, if not fully processed and pigeonholed, is at least tagged and cataloged in a helpful way. Plato's Ghost provides an insightful and informative resource for anyone doing mathematics today who has wondered how (and perhaps why) the subject has come to possess the features it has today. The book gives us a lot to think about, which is exactly what a good history should do."--Jeremy Avigad, Mathematical Intelligencer "In this book Jeremy Gray offers us the fruit of more than a decade reading and thinking about modernism in mathematics. He presents it, in very well written form, to a broad audience interested in mathematics, its history and philosophy."--Erhard Scholz, Metascience "What we have here ... is an excellent and detailed survey of how modernism took root in mathematics. Plato's Ghost provides the launching pad for future ruminations on the modernist thesis."--Calvin Jongsma, Perspectives on Science and Christian Faith "I commend Gray for writing an extraordinarily detailed and fascinating history of modernist mathematics, whose philosophical fruits remain ripe for the picking. The sections on geometry shine with clarity and convey the drama of modernism in a compelling and page-turning way. The treatments of less-studied actors are fascinating and promise to be of much use in incorporating their work into ongoing scholarship. The book could be fruitfully used as a supplement to a variety of courses in philosophy, including philosophy of mathematics and logic, history of analytic philosophy, and philosophy of science. It is a monument of scholarship and will reward careful study."--Andrew Arana, Philosophia Mathematica "In the course of this study Gray uncovers many new and unexpected things... Gray's book offers a rich and ... balanced account of how modernist ideas gradually gained inroads within pure mathematics."--David E. Rowe, Bulletin of the American Mathematical SocietyTable of ContentsIntroduction 1 I.1 Opening Remarks 1 I.2 Some Mathematical Concepts 16 CHAPTER 1: Modernism and Mathematics 18 1.1 Modernism in Branches of Mathematics 18 1.2 Changes in Philosophy 24 1.3 The Modernization of Mathematics 32 CHAPTER 2: Before Modernism 39 2.1 Geometry 39 2.2 Analysis 58 2.3 Algebra 75 2.4 Philosophy 78 2.5 British Algebra and Logic 101 2.6 The Consensus in 1880 112 CHAPTER 3: Mathematical Modernism Arrives 113 3.1 Modern Geometry: Piecemeal Abstraction 113 3.2 Modern Analysis 129 3.3 Algebra 148 3.4 Modern Logic and Set Theory 157 3.5 The View from Paris and St. Louis 170 CHAPTER 4: Modernism Avowed 176 4.1 Geometry 176 4.2 Philosophy and Mathematics in Germany 196 4.3 Algebra 213 4.4 Modern Analysis 216 4.5 Modernist Objects 235 4.6 American Philosophers and Logicians 239 4.7 The Paradoxes of Set Theory 247 4.8 Anxiety 266 4.9 Coming to Terms with Kant 277 CHAPTER 5: Faces of Mathematics 305 5.1 Introduction 305 5.2 Mathematics and Physics 306 5.3 Measurement 328 5.4 Popularizing Mathematics around 1900 346 5. Writing the History of Mathematics 365 CHAPTER 6: Mathematics, Language, and Psychology 374 6.1 Languages Natural and Artificial 374 6.2 Mathematical Modernism and Psychology 388 CHAPTER 7: After the War 406 7.1 The Foundations of Mathematics 406 7.2 Mathematics and the Mechanization of Thought 430 7.3 The Rise of Mathematical Platonism 440 7.4 Did Modernism'"Win"? 452 7.5 The Work Is Done 458 Appendix: Four Theorems in Projective Geometry 463 Glossary 467 Bibliography 473 Index 503

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Book SynopsisMeta-analysis is a powerful statistical methodology for synthesizing research evidence across independent studies. This is the first comprehensive handbook of meta-analysis written specifically for ecologists and evolutionary biologists, and it provides an invaluable introduction for beginners as well as an up-to-date guide for experienced meta-anaTrade Review"[T]his is a comprehensive and up-to-date compendium of all relevant aspects for meta-analysis conduction in ecology, evolution, and related topics. Scientists from these areas who already have some knowledge on meta-analysis will find valuable guidance."--Daniela Vetter, Quarterly Review of BiologyTable of ContentsPreface xi SECTION I: Introduction & Planning 1.Place of Meta-analysis among Other Methods of Research Synthesis 3 Julia Koricheva & Jessica Gurevitch 2.The Procedure of Meta-analysis in a Nutshell 14 Isabelle M. Cote & Michael D. Jennions SECTION II : Initiating a Meta-analysis 3.First Steps in Beginning a Meta-analysis 27 Gavin B. Stewart, Isabelle M. Cote, Hannah R. Rothstein, & Peter S. Curtis 4.Gathering Data: Searching Literature & Selection Criteria 37 Isabelle M. Cote, Peter S. Curtis, Hannah R. Rothstein, & Gavin B. Stewart 5.Extraction & Critical Appraisal of Data 52 Peter S. Curtis, Kerrie Mengersen, Marc J. Lajeunesse, Hannah R. Rothstein, & Gavin B. Stewart 6.Effect Sizes: Conventional Choices & Calculations 61 Michael S. Rosenberg, Hannah R. Rothstein, & Jessica Gurevitch 7.Using Other Metrics of Effect Size in Meta-analysis 72 Kerrie Mengersen & Jessica Gurevitch SECTION III : Essential Analytic Models & Methods 8.Statistical Models & Approaches to Inference 89 Kerrie Mengersen, Christopher H. Schmid, Michael D. Jennions, & Jessica Gurevitch 9.Moment & Least-Squares Based Approaches to Meta-analytic Inference 108 Michael S. Rosenberg 10.Maximum Likelihood Approaches to Meta-analysis 125 Kerrie Mengersen & Christopher H. Schmid 11.Bayesian Meta-analysis 145 Christopher H. Schmid & Kerrie Mengersen 12.Software for Statistical Meta-analysis 174 Christopher H. Schmid, Gavin B. Stewart, Hannah R. Rothstein, Marc J. Lajeunesse, & Jessica Gurevitch SECTION IV: Statistical Issues & Problems 13.Recovering Missing or Partial Data from Studies: A Survey of Conversions & Imputations for Meta-analysis 195 Marc J. Lajeunesse 14.Publication & Related Biases 207 Michael D. Jennions, Christopher J. Lortie, Michael S. Rosenberg, & Hannah R. Rothstein 15.Temporal Trends in Effect Sizes: Causes, Detection, & Implications 237 Julia Koricheva, Michael D. Jennions, & Joseph Lau 16.Statistical Models for the Meta-analysis of Nonindependent Data 255 Kerrie Mengersen, Michael D. Jennions, & Christopher H. Schmid 17.Phylogenetic Nonindependence & Meta-analysis 284 Marc J. Lajeunesse, Michael S. Rosenberg, & Michael D. Jennions 18.Meta-analysis of Primary Data 300 Kerrie Mengersen, Jessica Gurevitch, & Christopher H. Schmid 19.Meta-analysis of Results from Multisite Studies 313 Jessica Gurevitch SECTION V: Presentation & Interpretation of Results 20.Quality St&ards for Research Syntheses 323 Hannah R. Rothstein, Christopher J. Lortie, Gavin B. Stewart, Julia Koricheva, & Jessica Gurevitch 21.Graphical Presentation of Results 339 Christopher J. Lortie, Joseph Lau, & Marc J. Lajeunesse 22.Power Statistics for Meta-analysis: Tests for Mean Effects & Homogeneity 348 Marc J. Lajeunesse 23.Role of Meta-analysis in Interpreting the Scientific Literature 364 Michael D. Jennions, Christopher J. Lortie, & Julia Koricheva 24.Using Meta-analysis to Test Ecological & Evolutionary Theory 381 Michael D. Jennions, Christopher J. Lortie, & Julia Koricheva SECTION VI: Contributions of Meta-analysis in Ecology & Evolution 25.History & Progress of Meta-analysis 407 Joseph Lau, Hannah R. Rothstein, & Gavin B. Stewart 26.Contributions of Meta-analysis to Conservation & Management 420 Isabelle M. Cote & Gavin B. Stewart 27.Conclusions: Past, Present, & Future of Meta-analysis in Ecology & Evolution 426 Jessica Gurevitch & Julia Koricheva Glossary 433 Frequently Asked Questions 441 References 447 List of Contributors 487 Subject Index 489

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Book SynopsisPresents the analytic foundations to the theory of the hypoelliptic Laplacian. This book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. It gives the proper functional analytic setting in order to study this operator and develop a pseudodifferential calculus.Table of Contents*Frontmatter, pg. i*Contents, pg. v*Introduction, pg. 1*Chapter 1. Elliptic Riemann-Roch-Grothendieck and flat vector bundles, pg. 11*Chapter 2. The hypoelliptic Laplacian on the cotangent bundle, pg. 25*Chapter 3. Hodge theory, the hypoelliptic Laplacian and its heat kernel, pg. 44*Chapter 4. Hypoelliptic Laplacians and odd Chern forms, pg. 62*Chapter 5. The limit as t --> + and b --> 0 of the superconnection forms, pg. 98*Chapter 6. Hypoelliptic torsion and the hypoelliptic Ray-Singer metrics, pg. 113*Chapter 7. The hypoelliptic torsion forms of a vector bundle, pg. 131*Chapter 8. Hypoelliptic and elliptic torsions: a comparison formula, pg. 162*Chapter 9. A comparison formula for the Ray-Singer metrics, pg. 171*Chapter 10. The harmonic forms for b --> 0 and the formal Hodge theorem, pg. 173*Chapter 11. A proof of equation (8.4.6), pg. 182*Chapter 12. A proof of equation (8.4.8), pg. 190*Chapter 13. A proof of equation (8.4.7), pg. 194*Chapter 14. The integration by parts formula, pg. 214*Chapter 15. The hypoelliptic estimates, pg. 224*Chapter 16. Harmonic oscillator and the J0 function, pg. 247*Chapter 17. The limit of A'2phib,+-H as b --> 0, pg. 264*Bibliography, pg. 353*Subject Index, pg. 359*Index of Notation, pg. 361

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Book SynopsisExplores developments in the theory of planar quasiconformal mappings with a focus on the interactions with partial differential equations and nonlinear analysis. This book presents a modern approach to the classical theory and features applications across a spectrum of mathematics such as dynamical systems and singular integral operators.Trade Review"The nature of the writing is impressive, and any library owning this volume, and other volumes of he series, will be a rich library indeed. This book can work out well as a text for further study at higher graduate level and beyond. For many a mathematician, it works well as a collection of enjoyable chapters; and most importantly, it can comfortably serve well as a reference resource and study material. They will be grateful to the publishers and the authors, for the volume includes a wealth of interesting and useful information on many important topics in the subject... In short, a scintillating volume, full of detailed and thought-provoking contributions. Readers who bring to this book a reasonably strong background of the topics treated in the volume and an open mind will be well rewarded."--Current Engineering PracticeTable of Contents*FrontMatter, pg. i*Contents, pg. vii*Preface, pg. xv*Chapter 1. Introduction, pg. 1*Chapter 2. A Background In Conformal Geometry, pg. 12*Chapter 3. The Foundations Of Quasiconformal Mappings, pg. 48*Chapter 4. Complex Potentials, pg. 92*Chapter 5. The Measurable Riemann Mapping Theorem: The Existence Theory Of Quasiconformal Mappings, pg. 161*Chapter 6. Parameterizing General Linear Elliptic Systems, pg. 195*Chapter 7. The Concept Of Ellipticity, pg. 210*Chapter 8. Solving General Nonlinear First-Order Elliptic Systems, pg. 235*Chapter 9. Nonlinear Riemann Mapping Theorems, pg. 259*Chapter 10. Conformal Deformations And Beltrami Systems, pg. 275*Chapter 11. A Quasilinear Cauchy Problem, pg. 289*Chapter 12. Holomorphic Motions, pg. 293*Chapter 13. Higher Integrability, pg. 316*Chapter 14. Lp-Theory Of Beltrami Operators, pg. 362*Chapter 15. Schauder Estimates For Beltrami Operators, pg. 389*Chapter 16. Applications To Partial Differential Equations, pg. 403*Chapter 17. PDEs Not Of Divergence Type: Pucci'S Conjecture, pg. 472*Chapter 18. Quasiconformal Methods In Impedance Tomography: Calderon's Problem, pg. 490*Chapter 19. Integral Estimates For The Jacobian, pg. 514*Chapter 20. Solving The Beltrami Equation: Degenerate Elliptic Case, pg. 527*Chapter 21. Aspects Of The Calculus Of Variations, pg. 586*Appendix: Elements Of Sobolev Theory And Function Spaces, pg. 624*Basic Notation, pg. 643*Bibliography, pg. 647*Index, pg. 671

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Book SynopsisGives a presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. This book includes numerous results about automorphisms, completions, and residues of these buildings.Table of ContentsPreface vii Chapter 1. Affine Coxeter Diagrams 1 Chapter 2. Root Systems 13 Chapter 3. Root Data with Valuation 25 Chapter 4. Sectors 39 Chapter 5. Faces 45 Chapter 6. Gems 53 Chapter 7. Affine Buildings 59 Chapter 8. The Building at Infinity 67 Chapter 9. Trees with Valuation 77 Chapter 10. Wall Trees 89 Chapter 11. Panel Trees 101 Chapter 12. Tree-Preserving Isomorphisms 107 Chapter 13. The Moufang Property at Infinity 119 Chapter 14. Existence 131 Chapter 15. Partial Valuations 147 Chapter 16. Bruhat-Tits Theory 159 Chapter 17. Completions 167 Chapter 18. Automorphisms and Residues 175 Chapter 19. Quadrangles of Quadratic Form Type 189 Chapter 20. Quadrangles of Indifferent Type 205 Chapter 21. Quadrangles of Type E6, E7 and E8 209 Chapter 22. Quadrangles of Type F4 221 Chapter 23. Quadrangles of Involutory Type 229 Chapter 24. Pseudo-Quadratic Quadrangles 239 Chapter 25. Hexagons 261 Chapter 26. Assorted Conclusions 275 Chapter 27. Summary of the Classification 289 Chapter 28. Locally Finite Bruhat-Tits Buildings 297 Chapter 29. Appendix A 321 Chapter 30. Appendix B 343 Bibliography 361 Index 365

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Book SynopsisWritings by early mathematicians feature language and notations that are quite different from what we're familiar with today. Sourcebooks on the history of mathematics provide some guidance, but what has been lacking is a guide tailored to the needs of readers approaching these writings for the first time. This book intends to fill this gap.Trade ReviewOne of Choice's Outstanding Academic Titles for 2010 "Anyone interested in the history of mathematics should start here, especially those who teach history of mathematics courses. The text is refreshing, relevant, and surprisingly interesting. A great read!"--Choice "[This book] is well written, readable, and straightforward... It should be read by anyone who is using original source material to study the history of mathematics."--David Ebert, Mathematics Teacher "This is an extraordinary book for anyone interested in the history of mathematics. The author notes in the preface that reading historical mathematics can be fascinating, challenging, enriching, and endlessly rewarding. He then proceeds to illustrate how to analyze and get the most out of original source material."--Jim Tattersall, MAA Reviews "What Wardhaugh does exceptionally well is to break the ice for readers interested in the subject. He does this largely by training readers to ask insightful questions when they read a historical text."--Sol Lederman, Wild About Math "How to Read Historical Mathematics is filled with worthwhile advice to historians of mathematics and potential historians of mathematics. Wardhaugh's book should be readily available and kept with your personal reference books. It should also be in your school library."--Donald Cook, Mathematical Review "[A] splendid introduction to what to look for and to think about when reading historical source material in mathematics... This volume provides much food for thought in relatively few pages, yet in a pleasantly relaxed manner."--Leon Harkleroad, Zentralblatt MATH "How to Read Historical Mathematics is more than a useful aid to students being introduced to the field: it is a practical field guide to a whole new way of doing the history of mathematics. I warmly recommend it."--Amir Alexander, British Journal for the History of Science "Although Wardhaugh's examples will likely appeal mainly to those already interested in the history of mathematics, his commentary is broadly applicable to all of history of science and indeed to all students of history generally. There are occasional mentions of technological tools unknown to earlier generations of historians, but for the most part the discussion is generic enough that one expects How to Read Historical Mathematics to remain relevant even in a future where JSTOR and Google Books may no longer have the place they hold now."--David Lindsay Roberts, ISIS "Each item is preceded by a brief sketch of its author and context. The entertainment for the reader rests not only with the mathematical content but also in the evolution of expository style and often inventive presentation."--E. J. Barbeau, Mathematical Reviews Clippings "The book is a small jewel, the book to give to the student who is interested in pursuing history of mathematics. The author is apparently a talented historian."--UMAP JournalTable of ContentsPreface vii Chapter 1: What Does It Say? 1 Chapter 2: How Was It Written? 21 Chapter 3: Paper and Ink 49 Chapter 4: Readers 73 Chapter 5: What to Read, and Why 92 Bibliography 111 Index 115

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Book SynopsisFocusing on evolutionary game theory, this textbook shows students how to apply game theory to model human behavior in ways that reflect the special nature of sociality and individuality. It also includes solutions to the problems presented and information related to agent-based modeling.Trade Review"Gintis has wholeheartedly embraced the evolutionary approach to games... The author is an accomplished economist raised in the classical mold, and his background shows in many aspects of the book ... [He] has important things to say."--Karl Sigmund, Science "Game Theory Evolving is an exceptionally well-written and constructed introduction to the field. And with Gintis' outline of agent-based modeling and his tips for programming, many readers may be motivated to take up his invitation and experiment with a problem in evolutionary dynamics of their own."--Jennifer M. Wilson, Mathematical ReviewsTable of ContentsPreface xv Chapter 1: Probability Theory 1 1.1 Basic Set Theory and Mathematical Notation 1 1.2 Probability Spaces 2 1.3 De Morgan's Laws 3 1.4 Interocitors 3 1.5 The Direct Evaluation of Probabilities 3 1.6 Probability as Frequency 4 1.7 Craps 5 1.8 A Marksman Contest 5 1.9 Sampling 5 1.10 Aces Up 6 1.11 Permutations 6 1.12 Combinations and Sampling 7 1.13 Mechanical Defects 7 1.14 Mass Defection 7 1.15 House Rules 7 1.16 The Addition Rule for Probabilities 8 1.17 A Guessing Game 8 1.18 North Island, South Island 8 1.19 Conditional Probability 9 1.20 Bayes' Rule 9 1.21 Extrasensory Perception 10 1.22 Les Cinq Tiroirs 10 1.23 Drug Testing 10 1.24 Color Blindness 11 1.25 Urns 11 1.26 The Monty Hall Game 11 1.27 The Logic of Murder and Abuse 11 1.28 The Principle of Insufficient Reason 12 1.29 The Greens and the Blacks 12 1.30 The Brain and Kidney Problem 12 1.31 The Value of Eyewitness Testimony 13 1.32 When Weakness Is Strength 13 1.33 The Uniform Distribution 16 1.34 Laplace's Law of Succession 17 1.35 From Uniform to Exponential 17 Chapter 2: Bayesian Decision Theory 18 2.1 The Rational Actor Model 18 2.2 Time Consistency and Exponential Discounting 20 2.3 The Expected Utility Principle 22 2.4 Risk and the Shape of the Utility Function 26 2.5 The Scientific Status of the Rational Actor Model 30 Chapter 3: Game Theory: Basic Concepts 32 3.1 Big John and Little John 32 3.2 The Extensive Form 38 3.3 The Normal Form 41 3.4 Mixed Strategies 42 3.5 Nash Equilibrium 43 3.6 The Fundamental Theorem of Game Theory 44 3.7 Solving for Mixed-Strategy Nash Equilibria 44 3.8 Throwing Fingers 46 3.9 Battle of the Sexes 46 3.10 The Hawk-Dove Game 48 3.11 The Prisoner's Dilemma 50 Chapter 4: Eliminating Dominated Strategies 52 4.1 Dominated Strategies 52 4.2 Backward Induction 54 4.3 Exercises in Eliminating Dominated Strategies 55 4.4 Subgame Perfection 57 4.5 Stackelberg Leadership 59 4.6 The Second-Price Auction 59 4.7 The Mystery of Kidnapping 60 4.8 The Eviction Notice 62 4.9 Hagar's Battles 62 4.10 Military Strategy 63 4.11 The Dr. Strangelove Game 64 4.12 Strategic Voting 64 4.13 Nuisance Suits 65 4.14 An Armaments Game 67 4.15 Football Strategy 67 4.16 Poker with Bluffing 68 4.17 The Little Miss Muffet Game 69 4.18 Cooperation with Overlapping Generations 70 4.19 Dominance-Solvable Games 71 4.20 Agent-based Modeling 72 4.21 Why Play a Nash Equilibrium? 75 4.22 Modeling the Finitely-Repeated Prisoner's Dilemma 77 4.23 Review of Basic Concepts 79 Chapter 5: Pure-Strategy Nash Equilibria 80 5.1 Price Matching as Tacit Collusion 80 5.2 Competition on Main Street 81 5.3 Markets as Disciplining Devices: Allied Widgets 81 5.4 The Tobacco Market 87 5.5 The Klingons and the Snarks 87 5.6 Chess: The Trivial Pastime 88 5.7 No-Draw, High-Low Poker 89 5.8 An Agent-based Model of No-Draw, High-Low Poker 91 5.9 The Truth Game 92 5.10 The Rubinstein Bargaining Model 94 5.11 Bargaining with Heterogeneous Impatience 96 5.12 Bargaining with One Outside Option 97 5.13 Bargaining with Dual Outside Options 98 5.14 Huey, Dewey, and Louie Split a Dollar 102 5.15 Twin Sisters 104 5.16 The Samaritan's Dilemma 104 5.17 The Rotten Kid Theorem 106 5.18 The Shopper and the Fish Merchant 107 5.19 Pure Coordination Games 109 5.20 Pick Any Number 109 5.21 Pure Coordination Games: Experimental Evidence 110 5.22 Introductory Offers 111 5.23 Web Sites (for Spiders) 112 Chapter 6: Mixed-Strategy Nash Equilibria 116 6.1 The Algebra of Mixed Strategies 116 6.2 Lions and Antelope 117 6.3 A Patent Race 118 6.4 Tennis Strategy 119 6.5 Preservation of Ecology Game 119 6.6 Hard Love 120 6.7 Advertising Game 120 6.8 Robin Hood and Little John 122 6.9 The Motorist's Dilemma 122 6.10 Family Politics 123 6.11 Frankie and Johnny 123 6.12 A Card Game 124 6.13 Cheater-Inspector 126 6.14 The Vindication of the Hawk 126 6.15 Characterizing 2 x 2 Normal Form Games I 127 6.16 Big John and Little John Revisited 128 6.17 Dominance Revisited 128 6.18 Competition on Main Street Revisited 128 6.19 Twin Sisters Revisited 129 6.20 Twin Sisters: An Agent-Based Model 129 6.21 One-Card, Two-Round Poker with Bluffing 131 6.22 An Agent-Based Model of Poker with Bluffing 132 6.23 Trust in Networks 133 6.24 El Farol 134 6.25 Decorated Lizards 135 6.26 Sex Ratios as Nash Equilibria 137 6.27 A Mating Game 140 6.28 Coordination Failure 141 6.29 Colonel Blotto Game 141 6.30 Number Guessing Game 142 6.31 Target Selection 142 6.32 A Reconnaissance Game 142 6.33 Attack on Hidden Object 143 6.34 Two-Person, Zero-Sum Games 143 6.35 Mutual Monitoring in a Partnership 145 6.36 Mutual Monitoring in Teams 145 6.37 Altruism(?) in Bird Flocks 146 6.38 The Groucho Marx Game 147 6.39 Games of Perfect Information 151 6.40 Correlated Equilibria 151 6.41 Territoriality as a Correlated Equilibrium 153 6.42 Haggling at the Bazaar 154 6.43 Poker with Bluffing Revisited 156 6.44 Algorithms for Finding Nash Equilibria 157 6.45 Why Play Mixed Strategies? 160 6.46 Reviewing of Basic Concepts 161 Chapter 7: Principal-AgentModels 162 7.1 Gift Exchange 162 7.2 Contract Monitoring 163 7.3 Profit Signaling 164 7.4 Properties of the Employment Relationship 168 7.5 Peasant and Landlord 169 7.6 Bob's Car Insurance 173 7.7 A Generic Principal-Agent Model 174 Chapter 8: Signaling Games 179 8.1 Signaling as a Coevolutionary Process 179 8.2 A Generic Signaling Game 180 8.3 Sex and Piety: The Darwin-Fisher Model 182 8.4 Biological Signals as Handicaps 187 8.5 The ShepherdsWho Never Cry Wolf 189 8.6 My Brother's Keeper 190 8.7 Honest Signaling among Partial Altruists 193 8.8 Educational Signaling 195 8.9 Education as a Screening Device 197 8.10 Capital as a Signaling Device 199 Chapter 9: Repeated Games 201 9.1 Death and Discount Rates in Repeated Games 202 9.2 Big Fish and Little Fish 202 9.3 Alice and Bob Cooperate 204 9.4 The Strategy of an Oil Cartel 205 9.5 Reputational Equilibrium 205 9.6 Tacit Collusion 206 9.7 The One-Stage Deviation Principle 208 9.8 Tit for Tat 209 9.9 I'd Rather Switch Than Fight 210 9.10 The Folk Theorem 213 9.11 The Folk Theorem and the Nature of Signaling 216 9.12 The Folk Theorem Fails in Large Groups 217 9.13 Contingent Renewal Markets Do Not Clear 219 9.14 Short-Side Power in Contingent Renewal Markets 222 9.15 Money Confers Power in Contingent Renewal Markets 223 9.16 The Economy Is Controlled by the Wealthy 223 9.17 Contingent Renewal Labor Markets 224 Chapter 10: Evolutionarily Stable Strategies 229 10.1 Evolutionarily Stable Strategies: Definition 230 10.2 Properties of Evolutionarily Stable Strategies 232 10.3 Characterizing Evolutionarily Stable Strategies 233 10.4 A Symmetric Coordination Game 236 10.5 A Dynamic Battle of the Sexes 236 10.6 Symmetrical Throwing Fingers 237 10.7 Hawks, Doves, and Bourgeois 238 10.8 Trust in Networks II 238 10.9 Cooperative Fishing 238 10.10 Evolutionarily Stable Strategies Are Not Unbeatable 240 10.11 A Nash Equilibrium That Is Not an EES 240 10.12 Rock, Paper, and Scissors Has No ESS 241 10.13 Invasion of the Pure-Strategy Mutants 241 10.14 Multiple Evolutionarily Stable Strategies 242 10.15 Evolutionarily Stable Strategies in Finite Populations 242 10.16 Evolutionarily Stable Strategies in Asymmetric Games 244 Chapter 11: Dynamical Systems 247 11.1 Dynamical Systems: Definition 247 11.2 Population Growth 248 11.3 Population Growth with Limited Carrying Capacity 249 11.4 The Lotka-Volterra Predator-Prey Model 251 11.5 Dynamical Systems Theory 255 11.6 Existence and Uniqueness 256 11.7 The Linearization Theorem 257 11.8 Dynamical Systems in One Dimension 258 11.9 Dynamical Systems in Two Dimensions 260 11.10 Exercises in Two-Dimensional Linear Systems 264 11.11 Lotka-Volterra with Limited Carrying Capacity 266 11.12 Take No Prisoners 266 11.13 The Hartman-Grobman Theorem 267 11.14 Features of Two-Dimensional Dynamical Systems 268 Chapter 12: Evolutionary Dynamics 270 12.1 The Origins of Evolutionary Dynamics 271 12.2 Strategies as Replicators 272 12.3 A Dynamic Hawk-Dove Game 274 12.4 Sexual Reproduction and the Replicator Dynamic 276 12.5 Properties of the Replicator System 278 12.6 The Replicator Dynamic in Two Dimensions 279 12.7 Dominated Strategies and the Replicator Dynamic 280 12.8 Equilibrium and Stability with a Replicator Dynamic 282 12.9 Evolutionary Stability and Asymptotically Stability 284 12.10 Trust in Networks III 284 12.11 Characterizing 2 x 2 Normal Form Games II 285 12.12 Invasion of the Pure-Strategy Nash Mutants II 286 12.13 A Generalization of Rock, Paper, and Scissors 287 12.14 Uta stansburiana in Motion 287 12.15 The Dynamics of Rock, Paper, and Scissors 288 12.16 The Lotka-VolterraModel and Biodiversity 288 12.17 Asymmetric Evolutionary Games 290 12.18 Asymmetric Evolutionary Games II 295 12.19 The Evolution of Trust and Honesty 295 Chapter 13: Markov Economies and Stochastic Dynamical Systems 297 13.1 Markov Chains 297 13.2 The Ergodic Theorem for Markov Chains 305 13.3 The Infinite Random Walk 307 13.4 The Sisyphean Markov Chain 308 13.5 Andrei Andreyevich's Two-Urn Problem 309 13.6 Solving Linear Recursion Equations 310 13.7 Good Vibrations 311 13.8 Adaptive Learning 312 13.9 The Steady State of a Markov Chain 314 13.10 Adaptive Learning II 315 13.11 Adaptive Learning with Errors 316 13.12 Stochastic Stability 317 Chapter 14: Table of Symbols 319 Chapter 15: Answers 321 Sources for Problems 373 References 375

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Book SynopsisOffers a modern and authoritative treatment of the mathematical processes that underlie performance modeling. This book looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers.Trade Review"The book represents a valuable text for courses in statistics and stochastic processes, so it is strongly recommended to libraries."--Hassan S. Bakouch, Journal of Applied StatisticsTable of ContentsPreface and Acknowledgments xv PART I PROBABILITY 1 Chapter 1: Probability 3 1.1 Trials, Sample Spaces, and Events 3 1.2 Probability Axioms and Probability Space 9 1.3 Conditional Probability 12 1.4 Independent Events 15 1.5 Law of Total Probability 18 1.6 Bayes' Rule 20 1.7 Exercises 21 Chapter 2: Combinatorics--The Art of Counting 25 2.1 Permutations 25 2.2 Permutations with Replacements 26 2.3 Permutations without Replacement 27 2.4 Combinations without Replacement 29 2.5 Combinations with Replacements 31 2.6 Bernoulli (Independent) Trials 33 2.7 Exercises 36 Chapter 3: Random Variables and Distribution Functions 40 3.1 Discrete and Continuous Random Variables 40 3.2 The Probability Mass Function for a Discrete Random Variable 43 3.3 The Cumulative Distribution Function 46 3.4 The Probability Density Function for a Continuous Random Variable 51 3.5 Functions of a Random Variable 53 3.6 Conditioned Random Variables 58 3.7 Exercises 60 Chapter 4: Joint and Conditional Distributions 64 4.1 Joint Distributions 64 4.2 Joint Cumulative Distribution Functions 64 4.3 Joint Probability Mass Functions 68 4.4 Joint Probability Density Functions 71 4.5 Conditional Distributions 77 4.6 Convolutions and the Sum of Two Random Variables 80 4.7 Exercises 82 Chapter 5: Expectations and More 87 5.1 Definitions 87 5.2 Expectation of Functions and Joint Random Variables 92 5.3 Probability Generating Functions for Discrete Random Variables 100 5.4 Moment Generating Functions 103 5.5 Maxima and Minima of Independent Random Variables 108 5.6 Exercises 110 Chapter 6: Discrete Distribution Functions 115 6.1 The Discrete Uniform Distribution 115 6.2 The Bernoulli Distribution 116 6.3 The Binomial Distribution 117 6.4 Geometric and Negative Binomial Distributions 120 6.5 The Poisson Distribution 124 6.6 The Hypergeometric Distribution 127 6.7 The Multinomial Distribution 128 6.8 Exercises 130 Chapter 7: Continuous Distribution Functions 134 7.1 The Uniform Distribution 134 7.2 The Exponential Distribution 136 7.3 The Normal or Gaussian Distribution 141 7.4 The Gamma Distribution 145 7.5 Reliability Modeling and the Weibull Distribution 149 7.6 Phase-Type Distributions 155 7.6.1 The Erlang-2 Distribution 155 7.6.2 The Erlang-r Distribution 158 7.6.3 The Hypoexponential Distribution 162 7.6.4 The Hyperexponential Distribution 164 7.6.5 The Coxian Distribution 166 7.6.6 General Phase-Type Distributions 168 7.6.7 Fitting Phase-Type Distributions to Means and Variances 171 7.7 Exercises 176 Chapter 8: Bounds and Limit Theorems 180 8.1 The Markov Inequality 180 8.2 The Chebychev Inequality 181 8.3 The Chernoff Bound 182 8.4 The Laws of Large Numbers 182 8.5 The Central Limit Theorem 184 8.6 Exercises 187 PART II MARKOV CHAINS 191 Chapter 9: Discrete- and Continuous-Time Markov Chains 193 9.1 Stochastic Processes and Markov Chains 193 9.2 Discrete-Time Markov Chains: Definitions 195 9.3 The Chapman-Kolmogorov Equations 202 9.4 Classification of States 206 9.5 Irreducibility 214 9.6 The Potential, Fundamental, and Reachability Matrices 218 9.6.1 Potential and Fundamental Matrices and Mean Time to Absorption 219 9.6.2 The Reachability Matrix and Absorption Probabilities 223 9.7 Random Walk Problems 228 9.8 Probability Distributions 235 9.9 Reversibility 248 9.10 Continuous-Time Markov Chains 253 9.10.1 Transition Probabilities and Transition Rates 254 9.10.2 The Chapman-Kolmogorov Equations 257 9.10.3 The Embedded Markov Chain and State Properties 259 9.10.4 Probability Distributions 262 9.10.5 Reversibility 265 9.11 Semi-Markov Processes 265 9.12 Renewal Processes 267 9.13 Exercises 275 Chapter 10: Numerical Solution of Markov Chains 285 10.1 Introduction 285 10.1.1 Setting the Stage 285 10.1.2 Stochastic Matrices 287 10.1.3 The Effect of Discretization 289 10.2 Direct Methods for Stationary Distributions 290 10.2.1 Iterative versus Direct Solution Methods 290 10.2.2 Gaussian Elimination and LU Factorizations 291 10.3 Basic Iterative Methods for Stationary Distributions 301 10.3.1 The Power Method 301 10.3.2 The Iterative Methods of Jacobi and Gauss-Seidel 305 10.3.3 The Method of Successive Overrelaxation 311 10.3.4 Data Structures for Large Sparse Matrices 313 10.3.5 Initial Approximations, Normalization, and Convergence 316 10.4 Block Iterative Methods 319 10.5 Decomposition and Aggregation Methods 324 10.6 The Matrix Geometric/Analytic Methods for Structured Markov Chains 332 10.6.1 The Quasi-Birth-Death Case 333 10.6.2 Block Lower Hessenberg Markov Chains 340 10.6.3 Block Upper Hessenberg Markov Chains 345 10.7 Transient Distributions 354 10.7.1 Matrix Scaling and Powering Methods for Small State Spaces 357 10.7.2 The Uniformization Method for Large State Spaces 361 10.7.3 Ordinary Differential Equation Solvers 365 10.8 Exercises 375 PART III QUEUEING MODELS 383 Chapter 11: Elementary Queueing Theory 385 11.1 Introduction and Basic Definitions 385 11.1.1 Arrivals and Service 386 11.1.2 Scheduling Disciplines 395 11.1.3 Kendall's Notation 396 11.1.4 Graphical Representations of Queues 397 11.1.5 Performance Measures--Measures of Effectiveness 398 11.1.6 Little's Law 400 11.2 Birth-Death Processes: The M/M/1 Queue 402 11.2.1 Description and Steady-State Solution 402 11.2.2 Performance Measures 406 11.2.3 Transient Behavior 412 11.3 General Birth-Death Processes 413 11.3.1 Derivation of the State Equations 413 11.3.2 Steady-State Solution 415 11.4 Multiserver Systems 419 11.4.1 The M/M/c Queue 419 11.4.2 The M/M/?Queue 425 11.5 Finite-Capacity Systems--The M/M/1/K Queue 425 11.6 Multiserver, Finite-Capacity Systems--The M/M/c/K Queue 432 11.7 Finite-Source Systems--The M/M/c//M Queue 434 11.8 State-Dependent Service 437 11.9 Exercises 438 Chapter 12: Queues with Phase-Type Laws: Neuts' Matrix-Geometric Method 444 12.1 The Erlang-r Service Model--The M/Er/1 Queue 444 12.2 The Erlang-r Arrival Model--The Er/M/1 Queue 450 12.3 The M/H2/1 and H2/M/1 Queues 454 12.4 Automating the Analysis of Single-Server Phase-Type Queues 458 12.5 The H2/E3/1 Queue and General Ph/Ph/1 Queues 460 12.6 Stability Results for Ph/Ph/1 Queues 466 12.7 Performance Measures for Ph/Ph/1 Queues 468 12.8 Matlab code for Ph/Ph/1 Queues 469 12.9 Exercises 471 Chapter 13: The z-Transform Approach to Solving Markovian Queues 475 13.1 The z-Transform 475 13.2 The Inversion Process 478 13.3 Solving Markovian Queues using z-Transforms 484 13.3.1 The z-Transform Procedure 484 13.3.2 The M/M/1 Queue Solved using z-Transforms 484 13.3.3 The M/M/1 Queue with Arrivals in Pairs 486 13.3.4 The M/Er/1 Queue Solved using z-Transforms 488 13.3.5 The Er/M/1 Queue Solved using z-Transforms 496 13.3.6 Bulk Queueing Systems 503 13.4 Exercises 506 Chapter 14: The M/G/1 and G/M/1 Queues 509 14.1 Introduction to the M/G/1 Queue 509 14.2 Solution via an Embedded Markov Chain 510 14.3 Performance Measures for the M/G/1 Queue 515 14.3.1 The Pollaczek-Khintchine Mean Value Formula 515 14.3.2 The Pollaczek-Khintchine Transform Equations 518 14.4 The M/G/1 Residual Time: Remaining Service Time 523 14.5 The M/G/1 Busy Period 526 14.6 Priority Scheduling 531 14.6.1 M/M/1: Priority Queue with Two Customer Classes 531 14.6.2 M/G/1: Nonpreemptive Priority Scheduling 533 14.6.3 M/G/1: Preempt-Resume Priority Scheduling 536 14.6.4 A Conservation Law and SPTF Scheduling 538 14.7 The M/G/1/K Queue 542 14.8 The G/M/1 Queue 546 14.9 The G/M/1/K Queue 551 14.10 Exercises 553 Chapter 15: Queueing Networks 559 15.1 Introduction 559 15.1.1 Basic Definitions 559 15.1.2 The Departure Process--Burke's Theorem 560 15.1.3 Two M/M/1 Queues in Tandem 562 15.2 Open Queueing Networks 563 15.2.1 Feedforward Networks 563 15.2.2 Jackson Networks 563 15.2.3 Performance Measures for Jackson Networks 567 15.3 Closed Queueing Networks 568 15.3.1 Definitions 568 15.3.2 Computation of the Normalization Constant: Buzen's Algorithm 570 15.3.3 Performance Measures 577 15.4 Mean Value Analysis for Closed Queueing Networks 582 15.5 The Flow-Equivalent Server Method 591 15.6 Multiclass Queueing Networks and the BCMP Theorem 594 15.6.1 Product-Form Queueing Networks 595 15.6.2 The BCMP Theorem for Open, Closed, and Mixed Queueing Networks 598 15.7 Java Code 602 15.8 Exercises 607 PART IV SIMULATION 611 Chapter 16: Some Probabilistic and Deterministic Applications of Random Numbers 613 16.1 Simulating Basic Probability Scenarios 613 16.2 Simulating Conditional Probabilities, Means, and Variances 618 16.3 The Computation of Definite Integrals 620 16.4 Exercises 623 Chapter 17: Uniformly Distributed "Random" Numbers 625 17.1 Linear Recurrence Methods 626 17.2 Validating Sequences of Random Numbers 630 17.2.1 The Chi-Square "Goodness-of-Fit" Test 630 17.2.2 The Kolmogorov-Smirnov Test 633 17.2.3 "Run" Tests 634 17.2.4 The "Gap" Test 640 17.2.5 The "Poker" Test 641 17.2.6 Statistical Test Suites 644 17.3 Exercises 644 Chapter 18: Nonuniformly Distributed "Random" Numbers 647 18.1 The Inverse Transformation Method 647 18.1.1 The Continuous Uniform Distribution 649 18.1.2 "Wedge-Shaped" Density Functions 649 18.1.3 "Triangular" Density Functions 650 18.1.4 The Exponential Distribution 652 18.1.5 The Bernoulli Distribution 653 18.1.6 An Arbitrary Discrete Distribution 653 18.2 Discrete Random Variates by Mimicry 654 18.2.1 The Binomial Distribution 654 18.2.2 The Geometric Distribution 655 18.2.3 The Poisson Distribution 656 18.3 The Accept-Reject Method 657 18.3.1 The Lognormal Distribution 660 18.4 The Composition Method 662 18.4.1 The Erlang-r Distribution 662 18.4.2 The Hyperexponential Distribution 663 18.4.3 Partitioning of the Density Function 664 18.5 Normally Distributed Random Numbers 670 18.5.1 Normal Variates via the Central Limit Theorem 670 18.5.2 Normal Variates via Accept-Reject and Exponential Bounding Function 670 18.5.3 Normal Variates via Polar Coordinates 672 18.5.4 Normal Variates via Partitioning of the Density Function 673 18.6 The Ziggurat Method 673 18.7 Exercises 676 Chapter 19: Implementing Discrete-Event Simulations 680 19.1 The Structure of a Simulation Model 680 19.2 Some Common Simulation Examples 682 19.2.1 Simulating the M/M/1 Queue and Some Extensions 682 19.2.2 Simulating Closed Networks of Queues 686 19.2.3 The Machine Repairman Problem 689 19.2.4 Simulating an Inventory Problem 692 19.3 Programming Projects 695 Chapter 20: Simulation Measurements and Accuracy 697 20.1 Sampling 697 20.1.1 Point Estimators 698 20.1.2 Interval Estimators/Confidence Intervals 704 20.2 Simulation and the Independence Criteria 707 20.3 Variance Reduction Methods 711 20.3.1 Antithetic Variables 711 20.3.2 Control Variables 713 20.4 Exercises 716 Appendix A: The Greek Alphabet 719 Appendix B: Elements of Linear Algebra 721 B.1 Vectors and Matrices 721 B.2 Arithmetic on Matrices 721 B.3 Vector and Matrix Norms 723 B.4 Vector Spaces 724 B.5 Determinants 726 B.6 Systems of Linear Equations 728 B.6.1 Gaussian Elimination and LU Decompositions 730 B.7 Eigenvalues and Eigenvectors 734 B.8 Eigenproperties of Decomposable, Nearly Decomposable, and Cyclic Stochastic Matrices 738 B.8.1 Normal Form 738 B.8.2 Eigenvalues of Decomposable Stochastic Matrices 739 B.8.3 Eigenvectors of Decomposable Stochastic Matrices 741 B.8.4 Nearly Decomposable Stochastic Matrices 743 B.8.5 Cyclic Stochastic Matrices 744 Bibliography 745 Index 749

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Book SynopsisExamines how advances in philosophy were led by scientific discoveries - the more humankind understood about the physical world, the more curious we became. Drawing on work by Descartes, Galileo, Hume, Kant, Leibniz, and Newton, this book helps readers understand science through the lens of philosophy.Trade Review"The translation has long been out of print, so this recent publication, with a very fine introduction by Frank Wilczek, is to be highly valued... Weyl's Philosophy of Mathematics and Natural Science should be on every mathematician's or physicist's bookshelf... What a pleasure, what a privilege, to read and contemplate Hermann Weyl's monumental achievements."--Jeremy Butterfield, Physics Today "[W]e remain ever grateful that Hermann Weyl, compromising his conscience to the extent that he did, left behind this unrivaled treasure of insights into the murkiest epistemological depths of mathematics and theoretical physics."--Thomas Ryckman, Metascience

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Book SynopsisOffers an introduction to asset pricing, optimal portfolio selection, risk measurement, and investment evaluation. This title includes research in the area of incomplete markets and unhedgeable risks, and a chapter on finite difference methods. It integrates detailed examples and MATLAB codes.Trade Review"Ales Černy's new edition of Mathematical Techniques in Finance is an excellent master's-level treatment of mathematical methods used in financial asset pricing. By updating the original edition with methods used in recent research, Černy has once again given us an up-to-date first-class textbook treatment of the subject."—Darrell Duffie, Stanford UniversityTable of ContentsPreface to the Second Edition xiii From the Preface to the First Edition xix Chapter 1: The Simplest Model of Financial Markets 1 1.1 One-Period Finite State Model 1 1.2 Securities and Their Payoffs 3 1.3 Securities as Vectors 3 1.4 Operations on Securities 4 1.5 The Matrix as a Collection of Securities 6 1.6 Transposition 6 1.7 Matrix Multiplication and Portfolios 8 1.8 Systems of Equations and Hedging 10 1.9 Linear Independence and Redundant Securities 12 1.10 The Structure of the Marketed Subspace 14 1.11 The Identity Matrix and Arrow-Debreu Securities 16 1.12 Matrix Inverse 17 1.13 Inverse Matrix and Replicating Portfolios 17 1.14 Complete Market Hedging Formula 19 1.15 Summary 20 1.16 Notes 21 1.17 Exercises 22 Chapter 2: Arbitrage and Pricing in the One-Period Model 25 2.1 Hedging with Redundant Securities and Incomplete Market 25 2.2 Finding the Best Approximate Hedge 29 2.3 Minimizing the Expected Squared Replication Error 32 2.4 Numerical Stability of Least Squares 34 2.5 Asset Prices, Returns and Portfolio Units 36 2.6 Arbitrage 38 2.7 No-Arbitrage Pricing 40 2.8 State Prices and the Arbitrage Theorem 41 2.9 State Prices and Asset Returns 44 2.10 Risk-Neutral Probabilities 45 2.11 State Prices and No-Arbitrage Pricing 46 2.12 Asset Pricing Duality 47 2.13 Summary 48 2.14 Notes 49 2.15 Appendix: Least Squares with QR Decomposition 49 2.16 Exercises 52 Chapter 3: Risk and Return in the One-Period Model 55 3.1 Utility Functions 56 3.2 Expected Utility Maximization 59 3.3 The Existence of Optimal Portfolios 61 3.4 Reporting Expected Utility in Terms of Money 62 3.5 Normalized Utility and Investment Potential 63 3.6 Quadratic Utility 67 3.7 The Sharpe Ratio 69 3.8 Arbitrage-Adjusted Sharpe Ratio 71 3.9 The Importance of Arbitrage Adjustment 75 3.10 Portfolio Choice with Near-Arbitrage Opportunities 77 3.11 Summary 79 3.12 Notes 81 3.13 Exercises 82 Chapter 4: Numerical Techniques for Optimal Portfolio Selection in Incomplete Markets 84 4.1 Sensitivity Analysis of Portfolio Decisions with the CRRA Utility 84 4.2 Newton's Algorithm for Optimal Investment with CRRA Utility 88 4.3 Optimal CRRA Investment Using Empirical Return Distribution 90 4.4 HARA Portfolio Optimizer 94 4.5 HARA Portfolio Optimization with Several Risky Assets 96 4.6 Quadratic Utility Maximization with Multiple Assets 99 4.7 Summary 102 4.8 Notes 102 4.9 Exercises 102 Chapter 5: Pricing in Dynamically Complete Markets 104 5.1 Options and Portfolio Insurance 104 5.2 Option Pricing 105 5.3 Dynamic Replicating Trading Strategy 108 5.4 Risk-Neutral Probabilities in a Multi-Period Model 116 5.5 The Law of Iterated Expectations 119 5.6 Summary 121 5.7 Notes 121 5.8 Exercises 121 Chapter 6: Towards Continuous Time 125 6.1 IID Returns, and the Term Structure of Volatility 125 6.2 Towards Brownian Motion 127 6.3 Towards a Poisson Jump Process 136 6.4 Central Limit Theorem and Infinitely Divisible Distributions 142 6.5 Summary 143 6.6 Notes 145 6.7 Exercises 145 Chapter 7: Fast Fourier Transform 147 7.1 Introduction to Complex Numbers and the Fourier Transform 147 7.2 Discrete Fourier Transform (DFT) 152 7.3 Fourier Transforms in Finance 153 7.4 Fast Pricing via the Fast Fourier Transform (FFT) 158 7.5 Further Applications of FFTs in Finance 162 7.6 Notes 166 7.7 Appendix 167 7.8 Exercises 169 Chapter 8: Information Management 170 8.1 Information: Too Much of a Good Thing? 170 8.2 Model-Independent Properties of Conditional Expectation 174 8.3 Summary 178 8.4 Notes 179 8.5 Appendix: Probability Space 179 8.6 Exercises 183 Chapter 9: Martingales and Change of Measure in Finance 187 9.1 Discounted Asset Prices Are Martingales 187 9.2 Dynamic Arbitrage Theorem 192 9.3 Change of Measure 193 9.4 Dynamic Optimal Portfolio Selection in a Complete Market 198 9.5 Summary 206 9.6 Notes 208 9.7 Exercises 208 Chapter 10: Brownian Motion and Ito Formulae 213 10.1 Continuous-Time Brownian Motion 213 10.2 Stochastic Integration and Ito Processes 218 10.3 Important Ito Processes 220 10.4 Function of a Stochastic Process: the Ito Formula 222 10.5 Applications of the Ito Formula 223 10.6 Multivariate Ito Formula 225 10.7 Ito Processes as Martingales 228 10.8 Appendix: Proof of the Ito Formula 229 10.9 Summary 229 10.10 Notes 230 10.11 Exercises 231 Chapter 11: Continuous-Time Finance 233 11.1 Summary of Useful Results 233 11.2 Risk-Neutral Pricing 234 11.3 The Girsanov Theorem 237 11.4 Risk-Neutral Pricing and Absence of Arbitrage 241 11.5 Automatic Generation of PDEs and the Feynman-Kac Formula 246 11.6 Overview of Numerical Methods 250 11.7 Summary 251 11.8 Notes 252 11.9 Appendix: Decomposition of Asset Returns into Uncorrelated Components 252 11.10 Exercises 255 Chapter 12: Finite-Difference Methods 261 12.1 Interpretation of PDEs 261 12.2 The Explicit Method 263 12.3 Instability 264 12.4 Markov Chains and Local Consistency 266 12.5 Improving Convergence by Richardson's Extrapolation 268 12.6 Oscillatory Convergence Due to Grid Positioning 269 12.7 Fully Implicit Scheme 270 12.8 Crank-Nicolson Scheme 273 12.9 Summary 274 12.10 Notes 276 12.11 Appendix: Efficient Gaussian Elimination for Tridiagonal Matrices 276 12.12 Appendix: Richardson's Extrapolation 277 12.13 Exercises 277 Chapter 13: Dynamic Option Hedging and Pricing in Incomplete Markets 280 13.1 The Risk in Option Hedging Strategies 280 13.2 Incomplete Market Option Price Bounds 299 13.3 Towards Continuous Time 304 13.4 Derivation of Optimal Hedging Strategy 309 13.5 Summary 318 13.6 Notes 319 13.7 Appendix: Expected Squared Hedging Error in the Black-Scholes Model 320 13.8 Exercises 322 Appendix A Calculus 326 A.1 Notation 326 A.2 Differentiation 329 A.3 Real Function of Several Real Variables 332 A.4 Power Series Approximations 334 A.5 Optimization 336 A.6 Integration 338 A.7 Exercises 344 Appendix B Probability 348 B.1 Probability Space 348 B.2 Conditional Probability 348 B.3 Marginal and Joint Distribution 351 B.4 Stochastic Independence 352 B.5 Expectation Operator 354 B.6 Properties of Expectation 355 B.7 Mean and Variance 356 B.8 Covariance and Correlation 357 B.9 Continuous Random Variables 360 B.10 Normal Distribution 364 B.11 Quantiles 370 B.12 Relationships among Standard Statistical Distributions 371 B.13 Notes 372 B.14 Exercises 372 References 381 Index 385

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Book SynopsisDevelops a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. This book formulates simple general conditions on the spectral theory of the group and the regularity of the averaging sets, which suffice to guarantee convergence to the ergodic mean.Table of ContentsPreface vii 0.1 Main objectives vii 0.2 Ergodic theory and amenable groups viii 0.3 Ergodic theory and nonamenable groups x Chapter 1. Main results: Semisimple Lie groups case 1 1.1 Admissible sets 1 1.2 Ergodic theorems on semisimple Lie groups 2 1.3 The lattice point-counting problem in admissible domains 4 1.4 Ergodic theorems for lattice subgroups 6 1.5 Scope of the method 8 Chapter 2. Examples and applications 11 2.1 Hyperbolic lattice points problem 11 2.2 Counting integral unimodular matrices 12 2.3 Integral equivalence of general forms 13 2.4 Lattice points in S-algebraic groups 15 2.5 Examples of ergodic theorems for lattice actions 16 Chapter 3. Definitions, preliminaries, and basic tools 19 3.1 Maximal and exponential-maximal inequalities 19 3.2 S-algebraic groups and upper local dimension 21 3.3 Admissible and coarsely admissible sets 21 3.4 Absolute continuity and examples of admissible averages 23 3.5 Balanced and well-balanced families on product groups 26 3.6 Roughly radial and quasi-uniform sets 27 3.7 Spectral gap and strong spectral gap 29 3.8 Finite-dimensional subrepresentations 30 Chapter 4. Main results and an overview of the proofs 33 4.1 Statement of ergodic theorems for S-algebraic groups 33 4.2 Ergodic theorems in the absence of a spectral gap: overview 35 4.3 Ergodic theorems in the presence of a spectral gap: overview 38 4.4 Statement of ergodic theorems for lattice subgroups 40 4.5 Ergodic theorems for lattice subgroups: overview 42 4.6 Volume regularity and volume asymptotics: overview 44 Chapter 5. Proof of ergodic theorems for S-algebraic groups 47 5.1 Iwasawa groups and spectral estimates 47 5.2 Ergodic theorems in the presence of a spectral gap 50 5.3 Ergodic theorems in the absence of a spectral gap, I 56 5.4 Ergodic theorems in the absence of a spectral gap, II 57 5.5 Ergodic theorems in the absence of a spectral gap, III 60 5.6 The invariance principle and stability of admissible averages 67 Chapter 6. Proof of ergodic theorems for lattice subgroups 71 6.1 Induced action 71 6.2 Reduction theorems 74 6.3 Strong maximal inequality 75 6.4 Mean ergodic theorem 78 6.5 Pointwise ergodic theorem 83 6.6 Exponential mean ergodic theorem 84 6.7 Exponential strong maximal inequality 87 6.8 Completion of the proofs 90 6.9 Equidistribution in isometric actions 91 Chapter 7. Volume estimates and volume regularity 93 7.1 Admissibility of standard averages 93 7.2 Convolution arguments 98 7.3 Admissible, well-balanced, and boundary-regular families 101 7.4 Admissible sets on principal homogeneous spaces 105 7.5 Tauberian arguments and Holder continuity 107 Chapter 8. Comments and complements 113 8.1 Lattice point-counting with explicit error term 113 8.2 Exponentially fast convergence versus equidistribution 115 8.3 Remark about balanced sets 116 Bibliography 117 Index 121

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Book SynopsisIntroduces the distributed control of robotic networks. This book presents a set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity. It analyzes various cooperative strategies for tasks such as consensus, rendezvous, connectivity maintenance, deployment, and boundary estimation.Trade Review"This book covers its subject very thoroughly. The framework the authors have established is very elegant and, if it catches on, this book could be the primary reference for this approach. I don't know of any other book that covers this set of topics."—Richard M. Murray, California Institute of Technology"The authors do an excellent job of clearly describing the problems and presenting rigorous, provably correct algorithms with complexity bounds for each problem. The authors also do a fantastic job of providing the mathematical insight necessary for such complex problems."—Ali Jadbabaie, University of Pennsylvania"The order of presentation makes much sense, and the book thoroughly covers what it sets out to cover. The algorithms and results are presented using a clear mathematical and computer science formalism, which allows a uniform presentation. The formalism used and the way of presenting the algorithms may be helpful for structuring the presentation of new algorithms in the future."—Vincent Blondel, Université catholique de LouvainTable of ContentsPreface ix Chapter 1. An introduction to distributed algorithms 1 1.1 Elementary concepts and notation 1 1.2 Matrix theory 6 1.3 Dynamical systems and stability theory 12 1.4 Graph theory 20 1.5 Distributed algorithms on synchronous networks 37 1.6 Linear distributed algorithms 52 1.7 Notes 66 1.8 Proofs 69 1.9 Exercises 85 Chapter 2. Geometric models and optimization 95 2.1 Basic geometric notions 95 2.2 Proximity graphs 104 2.3 Geometric optimization problems and multicenter functions 111 2.4 Notes 124 2.5 Proofs 125 2.6 Exercises 133 Chapter 3. Robotic network models and complexity notions 139 3.1 A model for synchronous robotic networks 139 3.2 Robotic networks with relative sensing 151 3.3 Coordination tasks and complexity notions 158 3.4 Complexity of direction agreement and equidistance 165 3.5 Notes 166 3.6 Proofs 169 3.7 Exercises 176 Chapter 4. Connectivity maintenance and rendezvous 179 4.1 Problem statement 180 4.2 Connectivity maintenance algorithms 182 4.3 Rendezvous algorithms 191 4.4 Simulation results 200 4.5 Notes 201 4.6 Proofs 204 4.7 Exercises 215 Chapter 5. Deployment 219 5.1 Problem statement 220 5.2 Deployment algorithms 222 5.3 Simulation results 233 5.4 Notes 237 5.5 Proofs 239 5.6 Exercises 245 Chapter 6. Boundary estimation and tracking 247 6.1 Event-driven asynchronous robotic networks 248 6.2 Problem statement 252 6.3 Estimate update and cyclic balancing law 256 6.4 Simulation results 266 6.5 Notes 268 6.6 Proofs 270 6.7 Exercises 275 Bibliography 279 Algorithm Index 305 Subject Index 307 Symbol Index 313

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Book SynopsisModular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. This title gives an algorithm for computing coefficients of modular forms of level one in polynomial time.Trade Review"The book is well written and provides sufficient detail and reminders about the big picture. It gives a nice exposition of the material involved and should be accessible to graduate students or researchers with a sufficient background in number theory and algebraic geometry."--Jeremy A. Rouse, Mathematical Reviews ClippingsTable of Contents*FrontMatter, pg. i*Contents, pg. v*Preface, pg. ix*Acknowledgments, pg. x*Author information, pg. xi*Dependencies between the chapters, pg. xii*Chapter 1. Introduction, main results, context, pg. 1*Chapter 2. Modular curves, modular forms, lattices, Galois representations, pg. 29*Chapter 3. First description of the algorithms, pg. 69*Chapter 4. Short introduction to heights and Arakelov theory, pg. 79*Chapter 5. Computing complex zeros of polynomials and power series, pg. 95*Chapter 6. Computations with modular forms and Galois representations, pg. 129*Chapter 7. Polynomials for projective representations of level one forms, pg. 159*Chapter 8. Description of X1(5l), pg. 173*Chapter 9. Applying Arakelov theory, pg. 187*Chapter 10. An upper bound for Green functions on Riemann surfaces, pg. 203*Chapter 11. Bounds for Arakelov invariants of modular curves, pg. 217*Chapter 12. Approximating Vf over the complex numbers, pg. 257*Chapter 13. Computing Vf modulo p, pg. 337*Chapter 14. Computing the residual Galois representations, pg. 371*Chapter 15. Computing coefficients of modular forms, pg. 383*Epilogue, pg. 399*Bibliography, pg. 403*Index, pg. 423

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Book SynopsisFocusing on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). It illustrates through examples Basic gPC methods, and includes polynomial approximation theory and probability theory.Trade Review"[A]s a newbie to this field, by reading this lively written text I was able to gain insight into this really interesting and challenging matter."--Peter Mathe, Mathematical ReviewsTable of ContentsPreface xi Chapter 1: Introduction 1 1.1 Stochastic Modeling and Uncertainty Quantification 1 1.1.1 Burgers' Equation: An Illustrative Example 1 1.1.2 Overview of Techniques 3 1.1.3 Burgers' Equation Revisited 4 1.2 Scope and Audience 5 1.3 A Short Review of the Literature 6 Chapter 2: Basic Concepts of Probability Theory 9 2.1 Random Variables 9 2.2 Probability and Distribution 10 2.2.1 Discrete Distribution 11 2.2.2 Continuous Distribution 12 2.2.3 Expectations and Moments 13 2.2.4 Moment-Generating Function 14 2.2.5 Random Number Generation 15 2.3 Random Vectors 16 2.4 Dependence and Conditional Expectation 18 2.5 Stochastic Processes 20 2.6 Modes of Convergence 22 2.7 Central Limit Theorem 23 Chapter 3: Survey of Orthogonal Polynomials and Approximation Theory 25 3.1 Orthogonal Polynomials 25 3.1.1 Orthogonality Relations 25 3.1.2 Three-Term Recurrence Relation 26 3.1.3 Hypergeometric Series and the Askey Scheme 27 3.1.4 Examples of Orthogonal Polynomials 28 3.2 Fundamental Results of Polynomial Approximation 30 3.3 Polynomial Projection 31 3.3.1 Orthogonal Projection 31 3.3.2 Spectral Convergence 33 3.3.3 Gibbs Phenomenon 35 3.4 Polynomial Interpolation 36 3.4.1 Existence 37 3.4.2 Interpolation Error 38 3.5 Zeros of Orthogonal Polynomials and Quadrature 39 3.6 Discrete Projection 41 Chapter 4: Formulation of Stochastic Systems 44 4.1 Input Parameterization: Random Parameters 44 4.1.1 Gaussian Parameters 45 4.1.2 Non-Gaussian Parameters 46 4.2 Input Parameterization: Random Processes and Dimension Reduction 47 4.2.1 Karhunen-Loeve Expansion 47 4.2.2 Gaussian Processes 50 4.2.3 Non-Gaussian Processes 50 4.3 Formulation of Stochastic Systems 51 4.4 Traditional Numerical Methods 52 4.4.1 Monte Carlo Sampling 53 4.4.2 Moment Equation Approach 54 4.4.3 Perturbation Method 55 Chapter 5: Generalized Polynomial Chaos 57 5.1 Definition in Single Random Variables 57 5.1.1 Strong Approximation 58 5.1.2 Weak Approximation 60 5.2 Definition in Multiple Random Variables 64 5.3 Statistics 67 Chapter 6: Stochastic Galerkin Method 68 6.1 General Procedure 68 6.2 Ordinary Differential Equations 69 6.3 Hyperbolic Equations 71 6.4 Diffusion Equations 74 6.5 Nonlinear Problems 76 Chapter 7: Stochastic Collocation Method 78 7.1 Definition and General Procedure 78 7.2 Interpolation Approach 79 7.2.1 Tensor Product Collocation 81 7.2.2 Sparse Grid Collocation 82 7.3 Discrete Projection: Pseudospectral Approach 83 7.3.1 Structured Nodes: Tensor and Sparse Tensor Constructions 85 7.3.2 Nonstructured Nodes: Cubature 86 7.4 Discussion: Galerkin versus Collocation 87 Chapter 8: Miscellaneous Topics and Applications 89 8.1 Random Domain Problem 89 8.2 Bayesian Inverse Approach for Parameter Estimation 95 8.3 Data Assimilation by the Ensemble Kalman Filter 99 8.3.1 The Kalman Filter and the Ensemble Kalman Filter 100 8.3.2 Error Bound of the EnKF 101 8.3.3 Improved EnKF via gPC Methods 102 Appendix A: Some Important Orthogonal Polynomials in the Askey Scheme 105 A.1 Continuous Polynomials 106 A.2 Discrete Polynomials 108 Appendix B: The Truncated Gaussian Model G(a?, ?ss) 113 References 117 Index 127

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Book SynopsisElectromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. This book introduces the electromagnetics of complex media through a systematic account of their mathematical theory.Trade Review"This monograph is of a very high standard, allowing the reader to learn many facets of the rapidly growing field of complex media and to get up-to-date information on a number of open research problems."--Vilmos Komornik, Mathematical ReviewsTable of ContentsPreface xi PART 1. MODELLING AND MATHEMATICAL PRELIMINARIES 1 Chapter 1. Complex Media 3 Chapter 2. The Maxwell Equations and Constitutive Relations 9 2.1 Introduction 9 2.2 Fundamentals 9 2.3 Constitutive relations 13 2.4 The Maxwell equations in complex media: A variety of problems 23 Chapter 3. Spaces and Operators 38 3.1 Introduction 38 3.2 Function spaces 38 3.3 Standard difierential and trace operators 45 3.4 Function spaces for electromagnetics 48 3.5 Traces 51 3.6 Various decompositions 52 3.7 Compact embeddings 53 3.8 The operators of vector analysis revisited 54 3.9 The Maxwell operator 56 PART 2. TIME-HARMONIC DETERMINISTIC PROBLEMS 59 Chapter 4. Well Posedness 61 4.1 Introduction 61 4.2 Solvability of the interior problem 62 4.3 The eigenvalue problem 68 4.4 Low chirality behaviour 70 4.5 Comments on exterior domain problems 74 4.6 Towards numerics 77 Chapter 5. Scattering Problems: Beltrami Fields and Solvability 83 5.1 Introduction 83 5.2 Elliptic, circular and linear polarisation of waves 84 5.3 Beltrami fields - The Bohren decomposition 86 5.4 Scattering problems: Formulation 88 5.5 An introduction to BIEs 91 5.6 Properties of Beltrami fields 96 5.7 Solvability 99 5.8 Generalised Muller's BIEs 106 5.9 Low chirality approximations 108 5.10 Miscellanea 109 Chapter 6. Scattering Problems: A Variety of Topics 112 6.1 Introduction 112 6.2 Important concepts of scattering theory 113 6.3 Back to chiral media: Scattering relations and the far-field operator 118 6.4 Using dyadics 124 6.5 Herglotz wave functions 129 6.6 Domain derivative 136 6.7 Miscellanea 140 PART 3. TIME-DEPENDENT DETERMINISTIC PROBLEMS 149 Chapter 7. Well Posedness 151 7.1 Introduction 151 7.2 The Maxwell equations in the time domain 151 7.3 Functional framework and assumptions 152 7.4 Solvability 153 7.5 Other possible approaches to solvability 158 7.6 Miscellanea 162 Chapter 8. Controllability 163 8.1 Introduction 163 8.2 Formulation 163 8.3 Controllability of achiral media: The Hilbert Uniqueness method 165 8.4 The forward and backward problems 167 8.5 Controllability: Complex media 174 8.6 Miscellanea 176 Chapter 9. Homogenisation 180 9.1 Introduction 180 9.2 Formulation 181 9.3 A formal two-scale expansion 184 9.4 The optical response region 188 9.5 General bianisotropic media 199 9.6 Miscellanea 207 Chapter 10. Towards a Scattering Theory 212 10.1 Introduction 212 10.2 Formulation 213 10.3 Some basic strategies 214 10.4 On the construction of solutions 217 10.5 Wave operators and their construction 220 10.6 Complex media electromagnetics 225 10.7 Miscellanea 229 Chapter 11. Nonlinear Problems 231 11.1 Introduction 231 11.2 Formulation 231 11.3 Well posedness of the model 232 11.4 Miscellanea 241 PART 4. STOCHASTIC PROBLEMS 245 Chapter 12. Well Posedness 247 12.1 Introduction 247 12.2 Maxwell equations for random media 248 12.3 Functional setting 249 12.4 Well posedness 250 12.5 Other possible approaches to solvability 255 12.6 Miscellanea 261 Chapter 13. Controllability 263 13.1 Introduction 263 13.2 Formulation 263 13.3 Subtleties of stochastic controllability 264 13.4 Approximate controllability I: Random PDEs 266 13.5 Approximate controllability II: BSPDEs 269 13.6 Miscellanea 272 Chapter 14. Homogenisation 275 14.1 Introduction 275 14.2 Ergodic media 276 14.3 Formulation 279 14.4 A formal two-scale expansion 282 14.5 Homogenisation of the Maxwell system 284 14.6 Miscellanea 288 PART 5. APPENDICES 291 Appendix A. Some Facts from Functional Analysis 293 A.1 Duality 293 A.2 Strong, weak and weak-* convergence 295 A.3 Calculus in Banach spaces 297 A.4 Basic elements of spectral theory 300 A.5 Compactness criteria 303 A.6 Compact operators 304 A.7 The Banach-Steinhaus theorem 308 A.8 Semigroups and the Cauchy problem 308 A.9 Some fixed point theorems 312 A.10 The Lax-Milgram lemma 313 A.11 Gronwall's inequality 314 A.12 Nonlinear operators 315 Appendix B. Some Facts from Stochastic Analysis 316 B.1 Probability in Hilbert spaces 316 B.2 Stochastic processes and random fields 318 B.3 Gaussian measures 319 B.4 The Q- and the cylindrical Wiener process 320 B.5 The Ito integral 321 B.6 Ito formula 324 B.7 Stochastic convolution 325 B.8 SDEs in Hilbert spaces 325 B.9 Martingale representation theorem 326 Appendix C. Some Facts from Elliptic Homogenisation Theory 327 C.1 Spaces of periodic functions 327 C.2 Compensated compactness 329 C.3 Homogenisation of elliptic equations 329 C.4 Random elliptic homogenisation theory 332 Appendix D. Some Facts from Dyadic Analysis (by George Dassios) 334 Appendix E. Notation and abbreviations 341 Bibliography 343 Index 377

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Book SynopsisIndividuals and families make key decisions that impact many aspects of financial stability and determine the future of the economy. These decisions involve balancing current sacrifice against future benefits. This book is about modeling this individual or family-based decision making using an optimizing dynamic programming model.Trade Review"Forward-Looking Decision Making provides interesting applications of the dynamic programming approach for analyzing individual decisions that balance current and future welfare. The subjects are timely and the book contains a good selection of topics, united by a common analytical theme."—John Ermisch, University of EssexTable of ContentsForeword vii Preface ix Chapter 1: Basic Analysis of Forward-Looking Decision Making 1 1.1 The Dynamic Program 1 1.2 Approximation 5 1.3 Stationary Case 6 1.4 Markov Representation 7 1.5 Distribution of the Stochastic Driving Force 9 Chapter 2: Research on Properties of Preferences 10 2.1 Research Based on Marshallian and Hicksian Labor Supply Functions 13 2.2 Risk Aversion 15 2.3 Intertemporal Substitution 17 2.4 Frisch Elasticity of Labor Supply 19 2.5 Consumption-Hours Complementarity 20 Chapter 3: Health 23 3.1 The Issues 23 3.2 Basic Facts 25 3.3 Basic Model 26 3.4 The Full Dynamic-Programming Model 31 3.5 The Health Production Function 35 3.6 Preference Parameters 36 3.7 Solving the Model 37 3.8 Concluding Remarks 38 Chapter 4: Insurance 42 4.1 The Model 43 4.2 Calibration 45 4.3 Results 46 Chapter 5: Employment 50 5.1 Insurance 52 5.2 Dynamic Labor-Market Equilibrium 53 5.3 The Employment Function 58 5.4 Econometric Model 59 5.5 Properties of the Data 64 5.6 Results 65 5.7 Concluding Remarks 69 Chapter 6: Idiosyncratic Risk 70 6.1 The Joint Distribution of Lifetime and Exit Value 73 6.2 Economic Payoffs to Entrepreneurs 74 6.3 Entrepreneurs in Aging Companies 82 6.4 Concluding Remarks 85 Chapter 7: Financial Stability with Government-Guaranteed Debt 87 7.1 Introduction 87 7.2 Options 92 7.3 Model 94 7.4 Calibration 100 7.5 Equilibrium 101 7.6 Roles of Key Parameters 113 7.7 Concluding Remarks 115 7.8 Appendix: Value Functions 116 References 119 Index 123

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Book SynopsisIntroduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters. This book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree.Trade Review"The text is easy to read due to ubiquitous remarks, examples and explanations before and after the rigorous mathematical derivations. There are plenty of numerical simulations and figures that illustrate the control designs and compare them to each other. This book is recommended for everybody interested in control systems, system identification for PDEs, or just PDEs in general. From students to researchers, and from engineers to mathematicians everybody can find interesting new results in it."--Andras Balogh, Mathematical ReviewsTable of ContentsPreface ix Chapter 1. Introduction 1 1.1 Parabolic and Hyperbolic PDE Systems 1 1.2 The Roles of PDE Plant Instability, Actuator Location, Uncertainty Structure, Relative Degree, and Functional Parameters 2 1.3 Class of Parabolic PDE Systems 3 1.4 Backstepping 4 1.5 Explicitly Parametrized Controllers 5 1.6 Adaptive Control 5 1.7 Overview of the Literature on Adaptive Control for Parabolic PDEs 6 1.8 Inverse Optimality 7 1.9 Organization of the Book 7 1.10 Notation 9 PART I: NONADAPTIVE CONTROLLERS 11 Chapter 2. State Feedback 13 2.1 Problem Formulation 13 2.2 Backstepping Transformation and PDE for Its Kernel 14 2.3 Converting the PDE into an Integral Equation 17 2.4 Analysis of the Integral Equation by Successive Approximation Series 19 2.5 Stability of the Closed-Loop System 22 2.6 Dirichlet Uncontrolled End 24 2.7 Neumann Actuation 26 2.8 Simulation 27 2.9 Discussion 27 2.10 Notes and References 33 Chapter 3. Closed-Form Controllers 35 3.1 The Reaction-Diffusion Equation 35 3.2 A Family of Plants with Spatially Varying Reactivity 38 3.3 Solid Propellant Rocket Model 40 3.4 Plants with Spatially Varying Diffusivity 42 3.5 The Time-Varying Reaction Equation 45 3.6 More Complex Systems 50 3.7 2D and 3D Systems 52 3.8 Notes and References 54 Chapter 4. Observers 55 4.1 Observer Design for the Anti-Collocated Setup 55 4.2 Plants with Dirichlet Uncontrolled End and Neumann Measurements 58 4.3 Observer Design for the Collocated Setup 59 4.4 Notes and References 61 Chapter 5. Output Feedback 63 5.1 Anti-Collocated Setup 63 5.2 Collocated Setup 65 5.3 Closed-Form Compensators 67 5.4 Frequency Domain Compensator 71 5.5 Notes and References 72 Chapter 6. Control of Complex-Valued PDEs 73 6.1 State-Feedback Design for the Schrodinger Equation 73 6.2 Observer Design for the Schrodinger Equation 76 6.3 Output-Feedback Compensator for the Schrodinger Equation 79 6.4 The Ginzburg-Landau Equation 81 6.5 State Feedback for the Ginzburg-Landau Equation 83 6.6 Observer Design for the Ginzburg-Landau Equation 98 6.7 Output Feedback for the Ginzburg-Landau Equation 101 6.8 Simulations with the Nonlinear Ginzburg-Landau Equation 104 6.9 Notes and References 107 PART II: ADAPTIVE SCHEMES 109 Chapter 7. Systematization of Approaches to Adaptive Boundary Stabilization of PDEs 111 7.1 Categorization of Adaptive Controllers and Identifiers 111 7.2 Benchmark Systems 113 7.3 Controllers 114 7.4 Lyapunov Design 115 7.5 Certainty Equivalence Designs 117 7.6 Trade-offs between the Designs 121 7.7 Stability 122 7.8 Notes and References 124 Chapter 8. Lyapunov-Based Designs 125 8.1 Plant with Unknown Reaction Coefficient 125 8.2 Proof of Theorem 8.1 128 8.3 Well-Posedness of the Closed-Loop System 132 8.4 Parametric Robustness 134 8.5 An Alternative Approach 135 8.6 Other Benchmark Problems 136 8.7 Systems with Unknown Diffusion and Advection Coefficients 142 8.8 Simulation Results 147 8.9 Notes and References 149 Chapter 9. Certainty Equivalence Design with Passive Identifiers 150 9.1 Benchmark Plant 150 9.2 3D Reaction-Advection-Diffusion Plant 154 9.3 Proof of Theorem 9.2 157 9.4 Simulations 163 9.5 Notes and References 164 Chapter 10. Certainty Equivalence Design with Swapping Identifiers 166 10.1 Reaction-Advection-Diffusion Plant 166 10.2 Proof of Theorem 10.1 169 10.3 Simulations 175 10.4 Notes and References 175 Chapter 11. State Feedback for PDEs with Spatially Varying Coefficients 176 11.1 Problem Statement 176 11.2 Nominal Control Design 177 11.3 Robustness to Error in Gain Kernel 179 11.4 Lyapunov Design 185 11.5 Lyapunov Design for Plants with Unknown Advection and Diffusion Parameters 190 11.6 Passivity-Based Design 191 11.7 Simulations 195 11.8 Notes and References 197 Chapter 12. Closed-Form Adaptive Output-Feedback Contollers 198 12.1 Lyapunov Design--Plant with Unknown Parameter in the Domain 199 12.2 Lyapunov Design--Plant with Unknown Parameter in the 205 Boundary Condition 12.3 Swapping Design--Plant with Unknown Parameter in the Domain 210 12.4 Swapping Design--Plant with Unknown Parameter in the Boundary Condition 216 12.5 Simulations 223 12.6 Notes and References 225 Chapter 13. Output Feedback for PDEs with Spatially Varying Coefficients 226 13.1 Reaction-Advection-Diffusion Plant 226 13.2 Transformation to Observer Canonical Form 227 13.3 Nominal Controller 228 13.4 Filters 230 13.5 Frequency Domain Compensator with Frozen Parameters 232 13.6 Update Laws 233 13.7 Stability 235 13.8 Trajectory Tracking 242 13.9 The Ginzburg-Landau Equation 244 13.10 Identifier for the Ginzburg-Landau Equation 246 13.11 Stability of Adaptive Scheme for the Ginzburg-Landau Equation 248 13.12 Simulations 255 13.13 Notes and References 255 Chapter 14. Inverse Optimal Control 261 14.1 Nonadaptive Inverse Optimal Control 262 14.2 Reducing Control Effort through Adaptation 265 14.3 Dirichlet Actuation 267 14.4 Design Example 267 14.5 Comparison with the LQR Approach 268 14.6 Inverse Optimal Adaptive Control 271 14.7 Stability and Inverse Optimality of the Adaptive Scheme 273 14.8 Notes and References 275 Appendix A. Adaptive Backstepping for Nonlinear ODEs--The Basics 277 A.1 Nonadaptive Backstepping--The Known Parameter Case 277 A.2 Tuning Functions Design 279 A.3 Modular Design 289 A.4 Output Feedback Designs 297 A.5 Extensions 303 Appendix B. Poincare and Agmon Inequalities 305 Appendix C. Bessel Functions 307 C.1 Bessel Function Jn 307 C.2 Modified Bessel Function In 307 Appendix D. Barbalat's and Other Lemmas for Proving Adaptive Regulation 310 Appendix E. Basic Parabolic PDEs and Their Exact Solutions 313 E.1 Reaction-Diffusion Equation with Dirichlet Boundary Conditions 313 E.2 Reaction-Diffusion Equation with Neumann Boundary Conditions 315 E.3 Reaction-Diffusion Equation with Mixed Boundary Conditions 315 References 317 Index 327

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Book SynopsisStudies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over Q. The author also uses the method developed by Langlands, Ihara, and Kottwitz, which is to compare the Grothendieck-Lefschetz fixed point formula and the Arthur-Selberg trace formula.Trade Review"This book is a research monograph, yet the author takes care in recalling in detail the relevant notation and previous results instead of just referring to the literature. Also, explicit calculations are given, making the book readable not only for experts but also for interested advanced students."--Eva Viehmann, Mathematical ReviewsTable of ContentsPreface vii Chapter 1: The fixed point formula 1 Chapter 2: The groups 31 Chapter 3: Discrete series 47 Chapter 4: Orbital integrals at p 63 Chapter 5: The geometric side of the stable trace formula 79 Chapter 6: Stabilization of the fixed point formula 85 Chapter 7: Applications 99 Chapter 8: The twisted trace formula 119 Chapter 9: The twisted fundamental lemma 157 Appendix: Comparison of two versions of twisted transfer factors 189 Bibliography 207 Index 215

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Book SynopsisDescribes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. This book provides the mathematical background and explains the theory.Table of ContentsPreface xi PART 1. THEORY 1 Chapter 1. Introduction 3 Chapter 2. Orthogonal Polynomials 8 2.1 Definition of Orthogonal Polynomials 8 2.2 Three-Term Recurrences 10 2.3 Properties of Zeros 14 2.4 Historical Remarks 15 2.5 Examples of Orthogonal Polynomials 15 2.6 Variable-Signed Weight Functions 20 2.7 Matrix Orthogonal Polynomials 21 Chapter 3. Properties of Tridiagonal Matrices 24 3.1 Similarity 24 3.2 Cholesky Factorizations of a Tridiagonal Matrix 25 3.3 Eigenvalues and Eigenvectors 27 3.4 Elements of the Inverse 29 3.5 The QD Algorithm 32 Chapter 4. The Lanczos and Conjugate Gradient Algorithms 39 4.1 The Lanczos Algorithm 39 4.2 The Nonsymmetric Lanczos Algorithm 43 4.3 The Golub-Kahan Bidiagonalization Algorithms 45 4.4 The Block Lanczos Algorithm 47 4.5 The Conjugate Gradient Algorithm 49 Chapter 5. Computation of the Jacobi Matrices 55 5.1 The Stieltjes Procedure 55 5.2 Computing the Coefficients from the Moments 56 5.3 The Modified Chebyshev Algorithm 58 5.4 The Modified Chebyshev Algorithm for Indefinite Weight Functions 61 5.5 Relations between the Lanczos and Chebyshev Semi-Iterative Algorithms 62 5.6 Inverse Eigenvalue Problems 66 5.7 Modifications of Weight Functions 72 Chapter 6. Gauss Quadrature 84 6.1 Quadrature Rules 84 6.2 The Gauss Quadrature Rules 86 6.3 The Anti-Gauss Quadrature Rule 92 6.4 The Gauss-Kronrod Quadrature Rule 95 6.5 The Nonsymmetric Gauss Quadrature Rules 99 6.6 The Block Gauss Quadrature Rules 102 Chapter 7. Bounds for Bilinear Forms uT f(A)v 112 7.1 Introduction 112 7.2 The Case u = v 113 7.3 The Case u <> v 114 7.4 The Block Case 115 7.5 Other Algorithms for u <> v 115 Chapter 8. Extensions to Nonsymmetric Matrices 117 8.1 Rules Based on the Nonsymmetric Lanczos Algorithm 118 8.2 Rules Based on the Arnoldi Algorithm 119 Chapter 9. Solving Secular Equations 122 9.1 Examples of Secular Equations 122 9.2 Secular Equation Solvers 129 9.3 Numerical Experiments 134 PART 2. APPLICATIONS 137 Chapter 10. Examples of Gauss Quadrature Rules 139 10.1 The Golub and Welsch Approach 139 10.2 Comparisons with Tables 140 10.3 Using the Full QR Algorithm 141 10.4 Another Implementation of QR 143 10.5 Using the QL Algorithm 144 10.6 Gauss-Radau Quadrature Rules 144 10.7 Gauss-Lobatto Quadrature Rules 146 10.8 Anti-Gauss Quadrature Rule 148 10.9 Gauss-Kronrod Quadrature Rule 148 10.10 Computation of Integrals 149 10.11 Modification Algorithms 155 10.12 Inverse Eigenvalue Problems 156 Chapter 11. Bounds and Estimates for Elements of Functions of Matrices 162 11.1 Introduction 162 11.2 Analytic Bounds for the Elements of the Inverse 163 11.3 Analytic Bounds for Elements of Other Functions 166 11.4 Computing Bounds for Elements of f(A) 167 11.5 Solving Ax = c and Looking at d T/x 167 11.6 Estimates of tr(A-1) and det(A) 168 11.7 Krylov Subspace Spectral Methods 172 11.8 Numerical Experiments 173 Chapter 12. Estimates of Norms of Errors in the Conjugate Gradient Algorithm 200 12.1 Estimates of Norms of Errors in Solving Linear Systems 200 12.2 Formulas for the A-Norm of the Error 202 12.3 Estimates of the A-Norm of the Error 203 12.4 Other Approaches 209 12.5 Formulas for the l2 Norm of the Error 210 12.6 Estimates of the l2 Norm of the Error 211 12.7 Relation to Finite Element Problems 212 12.8 Numerical Experiments 214 Chapter 13. Least Squares Problems 227 13.1 Introduction to Least Squares 227 13.2 Least Squares Data Fitting 230 13.3 Numerical Experiments 237 13.4 Numerical Experiments for the Backward Error 253 Chapter 14. Total Least Squares 256 14.1 Introduction to Total Least Squares 256 14.2 Scaled Total Least Squares 259 14.3 Total Least Squares Secular Equation Solvers 261 Chapter 15. Discrete Ill-Posed Problems 280 15.1 Introduction to Ill-Posed Problems 280 15.2 Iterative Methods for Ill-Posed Problems 295 15.3 Test Problems 298 15.4 Study of the GCV Function 300 15.5 Optimization of Finding the GCV Minimum 305 15.6 Study of the L-Curve 313 15.7 Comparison of Methods for Computing the Regularization Parameter 325 Bibliography 335 Index 361

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Book SynopsisFeatures simple treatment of uncertain linear programming. This book also presents an analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach.Trade Review"Robust optimization is an active area of research that is likely to find many practical applications in the future. This book is an authoritative reference that will be very useful to researchers working in this area. Furthermore, the book has been structured so that the first part could easily be used as the text for a graduate level course in robust optimization."--Brian Borchers, MAA Reviews "[T]his reference book gives an excellent and stimulating account of the classical and advanced results in the field, and should be consulted by all researchers and practitioners."--Joseph Frederic Bonnans, Zentralblatt MATHTable of ContentsPreface ix PART I. ROBUST LINEAR OPTIMIZATION 1 Chapter 1. Uncertain Linear Optimization Problems and their Robust Counterparts 3 1.1 Data Uncertainty in Linear Optimization 3 1.2 Uncertain Linear Problems and their Robust Counterparts 7 1.3 Tractability of Robust Counterparts 16 1.4 Non-Affne Perturbations 23 1.5 Exercises 25 1.6 Notes and Remarks 25 Chapter 2. Robust Counterpart Approximations of Scalar Chance Constraints 27 2.1 How to Specify an Uncertainty Set 27 2.2 Chance Constraints and their Safe Tractable Approximations 28 2.3 Safe Tractable Approximations of Scalar Chance Constraints: Basic Examples 31 2.4 Extensions 44 2.5 Exercises 60 2.6 Notes and Remarks 64 Chapter 3. Globalized Robust Counterparts of Uncertain LO Problems 67 3.1 Globalized Robust Counterpart | Motivation and Definition 67 3.2 Computational Tractability of GRC 69 3.3 Example: Synthesis of Antenna Arrays 70 3.4 Exercises 79 3.5 Notes and Remarks 79 Chapter 4. More on Safe Tractable Approximations of Scalar Chance Constraints 81 4.1 Robust Counterpart Representation of a Safe Convex Approximation to a Scalar Chance Constraint 81 4.2 Bernstein Approximation of a Chance Constraint 83 4.3 From Bernstein Approximation to Conditional Value at Risk and Back 90 4.4 Majorization 105 4.5 Beyond the Case of Independent Linear Perturbations 109 4.6 Exercises 136 4.7 Notes and Remarks 145 PART II. ROBUST CONIC OPTIMIZATION 147 Chapter 5. Uncertain Conic Optimization: The Concepts 149 5.1 Uncertain Conic Optimization: Preliminaries 149 5.2 Robust Counterpart of Uncertain Conic Problem: Tractability 151 5.3 Safe Tractable Approximations of RCs of Uncertain Conic Inequalities 153 5.4 Exercises 156 5.5 Notes and Remarks 157 Chapter 6. Uncertain Conic Quadratic Problems with Tractable RCs 159 6.1 A Generic Solvable Case: Scenario Uncertainty 159 6.2 Solvable Case I: Simple Interval Uncertainty 160 6.3 Solvable Case II: Unstructured Norm-Bounded Uncertainty 161 6.4 Solvable Case III: Convex Quadratic Inequality with Un-structured Norm-Bounded Uncertainty 165 6.5 Solvable Case IV: CQI with Simple Ellipsoidal Uncertainty 167 6.6 Illustration: Robust Linear Estimation 173 6.7 Exercises 178 6.8 Notes and Remarks 178 Chapter 7. Approximating RCs of Uncertain Conic Quadratic Problems 179 7.1 Structured Norm-Bounded Uncertainty 179 7.2 The Case of \-Ellipsoidal Uncertainty 195 7.3 Exercises 201 7.4 Notes and Remarks 201 Chapter 8. Uncertain Semidefinite Problems with Tractable RCs 203 8.1 Uncertain Semidefinite Problems 203 8.2 Tractability of RCs of Uncertain Semidefinite Problems 204 8.3 Exercises 222 8.4 Notes and Remarks 222 Chapter 9. Approximating RCs of Uncertain Semide-nite Problems 225 9.1 Tight Tractable Approximations of RCs of Uncertain SDPs with Structured Norm-Bounded Uncertainty 225 9.2 Exercises 232 9.3 Notes and Remarks 234 Chapter 10. Approximating Chance Constrained CQIs and LMIs 235 10.1 Chance Constrained LMIs 235 10.2 The Approximation Scheme 240 10.3 Gaussian Majorization 252 10.4 Chance Constrained LMIs: Special Cases 255 10.5 Notes and Remarks 276 Chapter 11. Globalized Robust Counterparts of Uncertain Conic Problems 279 11.1 Globalized Robust Counterparts of Uncertain Conic Problems: De-nition 279 11.2 Safe Tractable Approximations of GRCs 281 11.3 GRC of Uncertain Constraint: Decomposition 282 11.4 Tractability of GRCs 284 11.5 Illustration: Robust Analysis of Nonexpansive Dynamical Systems 292 Chapter 12. Robust Classification and Estimation 301 12.1 Robust Support Vector Machines 301 12.2 Robust Classification and Regression 309 12.3 Affine Uncertainty Models 325 12.4 Random Affine Uncertainty Models 331 12.5 Exercises 336 12.6 Notes and remarks 337 PART III. ROBUST MULTI-STAGE OPTIMIZATION 339 Chapter 13. Robust Markov Decision Processes 341 13.1 Markov Decision Processes 341 13.2 The Robust MDP Problems 345 13.3 The Robust Bellman Recursion on Finite Horizon 347 13.4 Notes and Remarks 352 Chapter 14. Robust Adjustable Multistage Optimization 355 14.1 Adjustable Robust Optimization: Motivation 355 14.2 Adjustable Robust Counterpart 357 14.3 Affinely Adjustable Robust Counterparts 368 14.4 Adjustable Robust Optimization and Synthesis of Linear Controllers 392 14.5 Exercises 408 14.6 Notes and Remarks 411 PART IV. SELECTED APPLICATIONS 415 Chapter 15. Selected Applications 417 15.1 Robust Linear Regression and Manufacturing of TV Tubes 417 15.2 Inventory Management with Flexible Commitment Contracts 421 15.3 Controlling a Multi-Echelon Multi-Period Supply Chain 432 Appendix A. Notation and Prerequisites 447 A.1 Notation 447 A.2 Conic Programming 448 A.3 Efficient Solvability of Convex Programming 460 Appendix B. Some Auxiliary Proofs 469 B.1 Proofs for Chapter 4 469 B.2 S-Lemma 481 B.3 Approximate S-Lemma 483 B.4 Matrix Cube Theorem 489 B.5 Proofs for Chapter 10 506 Appendix C. Solutions to Selected Exercises 511 C.1 Chapter 1 511 C.2 Chapter 2 511 C.3 Chapter 3 513 C.4 Chapter 4 513 C.5 Chapter 5 516 C.6 Chapter 6 519 C.7 Chapter 7 520 C.8 Chapter 8 521 C.9 Chapter 9 523 C.10 Chapter 12 525 C.11 Chapter 14 527 Bibliography 531 Index 539

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Book SynopsisA wealth of research in recent decades has seen the economic approach to human behavior extended over many areas previously considered to belong to sociology, political science, law, and other fields. This book uses soccer to test economic theories and document novel human behavior.Trade Review"[E]njoyably accessible to nonspecialists, especially sports enthusiasts, who will learn a great deal about soccer, economics, and human behavior more generally."--Foreign Affairs "Beautiful Game Theory shows what it is like to think deeply about a sport and to test your ideas with data... [I]t is a book I recommend unconditionally to those economists with even a passing sport."--John Considine, Sportseconomics.orgTable of ContentsIntroduction 1 FIRST HALF 1.Pele Meets John von Neumann in the Penalty Area 9 2.Vernon Smith Meets Messi in the Laboratory 31 3.Lessons for Experimental Design 45 4.Mapping Minimax in the Brain (with Antonio Olivero, Sven Bestmann, Jose Florensa Vila, and Jose Apesteguia) 58 5.Psychological Pressure on the Field and Elsewhere 68 HALFTIME 6.Scoring at Halftime 89 SECOND HALF 7.Favoritism under Social Pressure 107 8.Making the Beautiful Game a Bit Less Beautiful (with Luis Garicano) 124 9.Fear Pitch 151 10.From Argentina without Emotions 164 11.Discrimination: From the Makana Football Association to Europe 174 Acknowledgments 193 References 195 Index 205

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Book SynopsisThe classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, that is it escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems.Trade Review"Highly readable, elegant, and concise... Emil Simiu has succeeded in putting together a highly stimulating book that proposes a promising, unifying approach to various aspects of chaos theory. While encompassing a wide swath of topics, traditionally found only on scattered sources, the book is succinctly written, exhibiting a quality reserved to the best of review works."--Daniel ben-Avraham, Journal of Statistical PhysicsTable of ContentsPreface xi Chapter 1. Introduction 1 PART 1.FUNDAMENTALS 9 Chapter 2. Transitions in Deterministic Systems and the Melnikov Function 11 2.1 Flows and Fixed Points.Integrable Systems.Maps: Fixed and Periodic Points 12 2.2 Homoclinic and Heteroclinic Orbits.Stable and Unstable Manifolds 20 2.3 Stable and Unstable Manifolds in the Three-Dimensional Phase Space 23 2.4 The Melnikov Function 27 2.5 Melnikov Functions for Special Types of Perturbation.Melnikov Scale Factor 29 2.6 Condition for the Intersection of Stable and Unstable Manifolds. Interpretation from a System Energy Viewpoint 36 2.7 Poincare Maps,Phase Space Slices,and Phase Space Flux 38 2.8 Slowly Varying Systems 45 Chapter 3. Chaos in Deterministic Systems and the Melnikov Function 51 3.1 Sensitivity to Initial Conditions and Lyapounov Exponents. Attractors and Basins of Attraction 52 3.2 Cantor Sets.Fractal Dimensions 57 3.3 The Smale Horseshoe Map and the Shift Map 59 3.4 Symbolic Dynamics. Properties of the Space Z2. Sensitivity to Initial Conditions of the Smale Horseshoe Map. Mathematical Definition of Chaos 65 3.5 Smale-Birkhoff Theorem. Melnikov Necessary Condition for Chaos. Transient and Steady-State Chaos 67 3.6 Chaotic Dynamics in Planar Systems with a Slowly Varying Parameter 70 3.7 Chaos in an Experimental System: The Stoker Column 72 Chapter 4. Stochastic Processes 76 4.1 Spectral Density, Autocovariance, Cross-Covariance 76 4.2 Approximate Representations of Stochastic Processes 87 4.3 Spectral Density of the Output of a Linear Filter with Stochastic Input 94 Chapter 5. Chaotic Transitions in Stochastic Dynamical Systems and the Melnikov Process 98 5.1 Behavior of a Fluidelastic Oscillator with Escapes: Experimental and Numerical Results 100 5.2 Systems with Additive and Multiplicative Gaussian Noise: Melnikov Processes and Chaotic Behavior 102 5.3 Phase Space Flux 106 5.4 Condition Guaranteeing Nonoccurrence of Escapes in Systems Excited by Finite-Tailed Stochastic Processes. Example: Dichotomous Noise 109 5.5 Melnikov-Based Lower Bounds for Mean Escape Time and for Probability of Nonoccurrence of Escapes during a Specified Time Interval 112 5.6 Effective Melnikov Frequencies and Mean Escape Time 119 5.7 Slowly Varying Planar Systems 122 5.8 Spectrum of a Stochastically Forced Oscillator: Comparison between Fokker-Planck and Melnikov-Based Approaches 122 PART 2. APPLICATIONS 127 Chapter 6. Vessel Capsizing 129 6.1 Model for Vessel Roll Dynamics in Random Seas 129 6.2 Numerical Example 132 Chapter 7. Open-Loop Control of Escapes in Stochastically Excited Systems 134 7.1 Open-Loop Control Based on the Shape of the Melnikov Scale Factor 134 7.2 Phase Space Flux Approach to Control of Escapes Induced by Stochastic Excitation 140 Chapter 8. Stochastic Resonance 144 8.1 Definition and Underlying Physical Mechanism of Stochastic Resonance. Application of the Melnikov Approach 145 8.2 Dynamical Systems and Melnikov Necessary Condition for Chaos 146 8.3 Signal-to-Noise Ratio Enhancement for a Bistable Deterministic System 147 8.4 Noise Spectrum Effect on Signal-to-Noise Ratio for Classical Stochastic Resonance 148 8.5 System with Harmonic Signal and Noise: Signal-to-Noise Ratio Enhancement through the Addition of a Harmonic Excitation 152 8.6 Nonlinear Transducing Device for Enhancing Signal-to-Noise Ratio 153 8.7 Concluding Remarks 154 Chapter 9. Cutoff Frequency of Experimentally Generated Noise for a First-Order Dynamical System 156 9.1 Introduction 156 9.2 Transformed Equation Excited by White Noise 157 Chapter 10. Snap-Through of Transversely Excited Buckled Column 159 10.1 Equation of Motion 160 10.2 Harmonic Forcing 161 10.3 Stochastic Forcing. Nonresonance Conditions. Melnikov Processes for Gaussian and Dichotomous Noise 163 10.4 Numerical Example 164 Chapter 11. Wind-Induced Along-Shor Currents over a Corrugated Ocean Floor 167 11.1 Offshore Flow Model 168 11.2 Wind Velocity Fluctuations and Wind Stresses 170 11.3 Dynamics of Unperturbed System 172 11.4 Dynamics of Perturbed System 173 11.5 Numerical Example 174 Chapter 12. The Auditory Nerve Fiber as a Chaotic Dynamical System 178 12.1 Experimental Neurophysiological Results 179 12.2 Results of Simulations Based on the Fitzhugh-Nagumo Model. Comparison with Experimental Results 182 12.3 Asymmetric Bistable Model of Auditory Nerve Fiber Response 183 12.4 Numerical Simulations 186 12.5 Concluding Remarks 190 Appendix A1 Derivation of Expression for the Melnikov Function 191 Appendix A2 Construction of Phase Space Slice through Stable and Unstable Manifolds 193 Appendix A3 Topological Conjugacy 199 Appendix A4 Properties of Space Z2 201 Appendix A5 Elements of Probability Theory 203 Appendix A6 Mean Upcrossing Rate for Gaussian Processes 211 Appendix A7 Mean Escape Rate for Systems Excited by White Noise 213 References 215 Index 221

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Book SynopsisReviews and develops Bayesian non-parametric and semi-parametric methods for applications in microeconometrics and quantitative marketing. This book advocates a Bayesian approach in which specific distributional assumptions are replaced with more flexible distributions based on mixtures of normals.Trade Review"As the creator of bayesm (R software for Bayesian inference) and lead author of Bayesian Statistics and Marketing, Rossi has deep knowledge of the book's titular methods."--ChoiceTable of ContentsPreface vii 1 Mixtures of Normals 1 1.1 Finite Mixture of Normals Likelihood Function 6 1.2 Maximum Likelihood Estimation 9 1.3 Bayesian Inference for the Mixture of Normals Model 15 1.4 Priors and the Bayesian Model 16 1.5 Unconstrained Gibbs Sampler 25 1.6 Label-Switching 29 1.7 Examples 34 1.8 Clustering Observations 46 1.9 Marginalized Samplers 49 2 Dirichlet Process Prior and Density Estimation 59 2.1 Dirichlet Processes--A Construction 60 2.2 Finite and Infinite Mixture Models 64 2.3 Stick-Breaking Representation 68 2.4 Polya Urn Representation and Associated Gibbs Sampler 70 2.5 Priors on DP Parameters and Hyper-parameters 72 2.6 Gibbs Sampler for DP Models and Density Estimation 78 2.7 Scaling the Data 80 2.8 Density Estimation Examples 81 3 Non-parametric Regression 90 3.1 Joint vs. Conditional Density Approaches 90 3.2 Implementing the Joint Approach with Mixtures of Normals 93 3.3 Examples of Non-parametric Regression Using Joint Approach 96 3.4 Discrete Dependent Variables 104 3.5 An Example of Expenditure Function Estimation 108 4 Semi-parametric Approaches 115 4.1 Semi-parametric Regression with DP Priors 115 4.2 Semi-parametric IV Models 122 5 Random Coefficient Models 152 5.1 Introduction 152 5.2 Semi-parametric Random Coefficient Logit Models 157 5.3 An Empirical Example of a Semi-parametric Random Coefficient Logit Model 161 6 Conclusions and Directions for Future Research 187 6.1 When Are Non-parametric and Semi-parametric Methods Most Useful? 187 6.2 Semi-parametric or Non-parametric Methods? 189 6.3 Extensions 191 Bibliography 195 Index 201

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Book SynopsisMathematical models and computer simulations of complex social systems have become everyday tools in sociology. This title features a comprehensive, self-contained primer on the mathematical tools and applications that sociologists use to understand social behavior.Trade Review"[T]he volume offers certain important building blocks that can represent a bonus for students willing to learn simulation in the future... Bonacich and Lu's work brillantly introduces much of what ABM students will be requested to know in their subsequent studies."--Giangiacomo Bravo, JASSS "If you are interested in sociology specifically, or in some of the others social sciences (especially political science), then this book is a very good introduction for you... I would certainly recommend it to students and others who have some mathematical maturity and are interested in mathematical sociology, mathematical political science, or mathematical psychology."--JamesM. Cargal, UMAP JournalTable of ContentsList of Figures ix List of Tables xiii Preface xv Chapter 1. Introduction 1 Epidemics 2 Residential Segregation 6 Exercises 11 Chapter 2. Set Theory and Mathematical Truth 12 Boolean Algebra and Overlapping Groups 19 Truth and Falsity in Mathematics 21 Exercises 23 Chapter 3. Probability: Pure and Applied 25 Example: Gambling 28 Two or More Events: Conditional Probabilities 29 Two or More Events: Independence 30 A Counting Rule: Permutations and Combinations 31 The Binomial Distribution 32 Exercises 36 Chapter 4. Relations and Functions 38 Symmetry 41 Reflexivity 43 Transitivity 44 Weak Orders-Power and Hierarchy 45 Equivalence Relations 46 Structural Equivalence 47 Transitive Closure: The Spread of Rumors and Diseases 49 Exercises 51 Chapter 5. Networks and Graphs 53 Exercises 59 Chapter 6. Weak Ties 61 Bridges 61 The Strength of Weak Ties 62 Exercises 66 Chapter 7. Vectors and Matrices 67 Sociometric Matrices 69 Probability Matrices 71 The Matrix, Transposed 72 Exercises 72 Chapter 8. Adding and Multiplying Matrices 74 Multiplication of Matrices 75 Multiplication of Adjacency Matrices 77 Locating Cliques 79 Exercises 82 Chapter 9. Cliques and Other Groups 84 Blocks 86 Exercises 87 Chapter 10. Centrality 89 Degree Centrality 93 Graph Center 93 Closeness Centrality 94 Eigenvector Centrality 95 Betweenness Centrality 96 Centralization 99 Exercises 101 Chapter 11. Small-World Networks 102 Short Network Distances 103 Social Clustering 105 The Small-World Network Model 111 Exercises 116 Chapter 12. Scale-Free Networks 117 Power-Law Distribution 118 Preferential Attachment 121 Network Damage and Scale-Free Networks 129 Disease Spread in Scale-Free Networks 134 Exercises 136 Chapter 13. Balance Theory 137 Classic Balance Theory 137 Structural Balance 145 Exercises 148 The Markov Assumption: History Does Not Matter 156 Transition Matrices and Equilibrium 157 Exercises 158 Chapter 15. Demography 161 Mortality 162 Life Expectancy 167 Fertility 171 Population Projection 173 Exercises 179 Chapter 16. Evolutionary Game Theory 180 Iterated Prisoner's Dilemma 184 Evolutionary Stability 185 Exercises 188 Chapter 17. Power and Cooperative Games 190 The Kernel 195 The Core 199 Exercises 200 Chapter 18. Complexity and Chaos 202 Chaos 202 Complexity 206 Exercises 212 Afterword: "Resistance Is Futile" 213 Bibliography 217 Index 219

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Book SynopsisAn introduction to dynamic programming, presented by the scientist who coined the term and developed the theory in its early stages. It introduces the author's theory and furnishes a new and versatile mathematical tool for the treatment of many complex problems, both within and outside of the discipline.

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Book SynopsisReveals why our faith in scientific certainty is a dangerous illusion, and how only by embracing science's inherent ambiguities and paradoxes can we truly appreciate its beauty and harness its potential. This book challenges our most sacredly held beliefs about science, technology, and progress.Trade Review"Science has been under siege during the last quarter century, first by critics who charge that science itself is a cultural construct and that scientists import their own belief systems into their research. Retired math professor Byers (How Mathematicians Think) argues that much of the problem lies in what he calls the 'science of certainty.' ... Instead, Byers says, scientists need to recognize 'uncertainty, incompleteness, and ambiguity, the ungraspable, the blind spot, or the limits to reason.'"--Publishers Weekly "Is the idea that anything can be determined with absolute certainty an illusion? ... Byers incorporates many brilliant thinkers and seminal scientific breakthroughs into his discussion, offering the cogent, invigorating argument that only by embracing uncertainty can we truly progress."--Kirkus Reviews "Science deals in certainties, right? Wrong, says Montreal-based mathematician William Byers... He contends that this view is wide of the mark and dangerous, influenced by the human need for everything to be 'certain'."--Alison Flood, Wired "I've sometimes remarked that I think our educational system would benefit if we threw Shakespeare in the trash bin, but required all high-schoolers to read Godel and Cantor (well, their interpreters) ... or perhaps now, just substitute Byers! ... [The Blind Spot] should be read and contemplated by every scientist ... and even applied to their own endeavors."--Math-Frolic! "A passionate, informed manifesto that takes aim at our culture's reigning myth of scientific certainty. Byers would like to debunk that myth, and put in its place a science of wonder that freely acknowledges its 'blind spot'--a metaphor for all that remains inherently and irreducibly unknowable, ambiguous, and mysterious... The Blind Spot is an important book for our time, part of a necessary and pressing debate about how to think, and live, within limits both certain and otherwise."--Alex Good, Quill & Quire "[The Blind Spot] is an enjoyable read and makes several interesting points."--Choice "Byers' breadth of learning is impressive, appealing to chaos theory, quantum mechanics, philosophy and beyond in making his case."--Paul Taylor, Mathematics Today "Byers skillfully evokes questions about science and causes readers to reflect on the implications of the blind spots in mathematics and sciences by drawing on notable works across multiple academic fields. I highly recommend this book for anyone in higher education with an appreciation for the philosophy of mathematics and the sciences."--Ruthmae Sears, Mathematics TeacherTable of ContentsPreface: The Revelation of Uncertainty vii Chapter 1: The Blind Spot 1 Chapter 2: The Blind Spot Revealed 17 Chapter 3: Certainty or Wonder? 38 Chapter 4: A World in Crisis! 59 Chapter 5: Ambiguity 69 Chapter 6: Self-Reference: The Human Element in Science 91 Chapter 7: The Mystery of Number 106 Chapter 8: Science as the Ambiguous Search for Unity 124 Chapter 9: The Still Point 156 Chapter 10: Conclusion: Living in a World of Uncertainty 179 Acknowledgments 187 Notes 189 References 197 Index 203

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Book SynopsisEmphasizing the theory behind the computation, this book provides a self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software. It presents the mathematical foundations of numerical analysis. It introduces many advanced concepts in modern analysis.Trade Review"[Numerical Analysis] is a solid narrative of mathematical aspects of numerical analysis with an 'inquiry-based' learning method... There are more than 350 frequently challenging exercises that will interest both beginning students and readers with strong mathematical backgrounds."--Choice "A student who picks up this book and works through it systematically will learn a lot of interesting and important mathematics."--David S. Watkins, SIAM Review "Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks."--World Book IndustryTable of ContentsPreface xi Chapter 1. Numerical Algorithms 1 1.1 Finding roots 2 1.2 Analyzing Heron's algorithm 5 1.3 Where to start 6 1.4 An unstable algorithm 8 1.5 General roots: effects of floating-point 9 1.6 Exercises 11 1.7 Solutions 13 Chapter 2. Nonlinear Equations 15 2.1 Fixed-point iteration 16 2.2 Particular methods 20 2.3 Complex roots 25 2.4 Error propagation 26 2.5 More reading 27 2.6 Exercises 27 2.7 Solutions 30 Chapter 3. Linear Systems 35 3.1 Gaussian elimination 36 3.2 Factorization 38 3.3 Triangular matrices 42 3.4 Pivoting 44 3.5 More reading 47 3.6 Exercises 47 3.7 Solutions 50 Chapter 4. Direct Solvers 51 4.1 Direct factorization 51 4.2 Caution about factorization 56 4.3 Banded matrices 58 4.4 More reading 60 4.5 Exercises 60 4.6 Solutions 63 Chapter 5. Vector Spaces 65 5.1 Normed vector spaces 66 5.2 Proving the triangle inequality 69 5.3 Relations between norms 71 5.4 Inner-product spaces 72 5.5 More reading 76 5.6 Exercises 77 5.7 Solutions 79 Chapter 6. Operators 81 6.1 Operators 82 6.2 Schur decomposition 84 6.3 Convergent matrices 89 6.4 Powers of matrices 89 6.5 Exercises 92 6.6 Solutions 95 Chapter 7. Nonlinear Systems 97 7.1 Functional iteration for systems 98 7.2 Newton's method 103 7.3 Limiting behavior of Newton's method 108 7.4 Mixing solvers 110 7.5 More reading 111 7.6 Exercises 111 7.7 Solutions 114 Chapter 8. Iterative Methods 115 8.1 Stationary iterative methods 116 8.2 General splittings 117 8.3 Necessary conditions for convergence 123 8.4 More reading 128 8.5 Exercises 128 8.6 Solutions 131 Chapter 9. Conjugate Gradients 133 9.1 Minimization methods 133 9.2 Conjugate Gradient iteration 137 9.3 Optimal approximation of CG 141 9.4 Comparing iterative solvers 147 9.5 More reading 147 9.6 Exercises 148 9.7 Solutions 149 Chapter 10. Polynomial Interpolation 151 10.1 Local approximation: Taylor's theorem 151 10.2 Distributed approximation: interpolation 152 10.3 Norms in infinite-dimensional spaces 157 10.4 More reading 160 10.5 Exercises 160 10.6 Solutions 163 Chapter 11. Chebyshev and Hermite Interpolation 167 11.1 Error term ! 167 11.2 Chebyshev basis functions 170 11.3 Lebesgue function 171 11.4 Generalized interpolation 173 11.5 More reading 177 11.6 Exercises 178 11.7 Solutions 180 Chapter 12. Approximation Theory 183 12.1 Best approximation by polynomials 183 12.2 Weierstrass and Bernstein 187 12.3 Least squares 191 12.4 Piecewise polynomial approximation 193 12.5 Adaptive approximation 195 12.6 More reading 196 12.7 Exercises 196 12.8 Solutions 199 Chapter 13. Numerical Quadrature 203 13.1 Interpolatory quadrature 203 13.2 Peano kernel theorem 209 13.3 Gregorie-Euler-Maclaurin formulas 212 13.4 Other quadrature rules 219 13.5 More reading 221 13.6 Exercises 221 13.7 Solutions 224 Chapter 14. Eigenvalue Problems 225 14.1 Eigenvalue examples 225 14.2 Gershgorin's theorem 227 14.3 Solving separately 232 14.4 How not to eigen 233 14.5 Reduction to Hessenberg form 234 14.6 More reading 237 14.7 Exercises 238 14.8 Solutions 240 Chapter 15. Eigenvalue Algorithms 241 15.1 Power method 241 15.2 Inverse iteration 250 15.3 Singular value decomposition 252 15.4 Comparing factorizations 253 15.5 More reading 254 15.6 Exercises 254 15.7 Solutions 256 Chapter 16. Ordinary Differential Equations 257 16.1 Basic theory of ODEs 257 16.2 Existence and uniqueness of solutions 258 16.3 Basic discretization methods 262 16.4 Convergence of discretization methods 266 16.5 More reading 269 16.6 Exercises 269 16.7 Solutions 271 Chapter 17. Higher-order ODE Discretization Methods 275 17.1 Higher-order discretization 276 17.2 Convergence conditions 281 17.3 Backward differentiation formulas 287 17.4 More reading 288 17.5 Exercises 289 17.6 Solutions 291 Chapter 18. Floating Point 293 18.1 Floating-point arithmetic 293 18.2 Errors in solving systems 301 18.3 More reading 305 18.4 Exercises 305 18.5 Solutions 308 Chapter 19. Notation 309 Bibliography 311 Index 323

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Book SynopsisExplains why fantasy in the Harry Potter and Dresden Files novels cannot adhere strictly to scientific laws, and when magic might make scientific sense in the muggle world. This title discusses exoplanets and how the search for alien life has shifted from radio communications to space-based telescopes.Trade ReviewCo-Winner of the 2015 AIP Science Writing Award for Books, American Institute of Physics One of Physics World's Top Ten Books of the Year for 2014 One of The Guardian's Best Popular Physical Science Books of 2014, chosen by GrrlScientist "Whether as a text for a course or as a vehicle for self-study, this book makes for interesting, educational and thought-provoking reading."--Mark Hunacek, MAA Reviews "Adler does a grand job of showing just how powerful even basic maths and physics can be. If you're a budding back-of-the-envelope boffin not afraid of a bit of algebra, you'll love this book."--Robert Matthews, BBC Focus Magazine "I can't work out whether I love or hate this book. I love it because its analysis of the physics behind numerous accounts of magic and space exploration in fantasy and science fiction writing is fascinating. I hate it because it reveals why I will never be able to realise my dream of saying 'Beam me up, Scotty' before being teleported; or so Charles Adler has convinced me... The physics is well explained and Adler offers entertaining examples."--Noel-Ann Bradshaw, Times Higher Education "Wizards, Aliens, and Starships is a great book by itself or as a starting point for exploring the physics of space exploration as well as the classics in science fiction."--Robert Schaefer, New York Journal of Books "For those who want to learn the hard facts about the realities of space travel or the chances for alien life, and as an engaging supplemental text for physics and astronomy courses, Wizards, Aliens, and Starships would be an admirable choice."--Sidney Perkowitz, Scientists' Bookshelf "[A] rewarding and thought-provoking read."--Paul Sutherland, BBC Sky at Night "[T]his book offers a lot, not only to SF authors but to any of you who want to see the real science in operation because this supplies most of the answers you need. Make sure your copy gets a serious read and well-thumbed."--G.F. Willmetts, SFCrowsnest "This book will speak to anyone wanting to know about the correct--and incorrect--science of science fiction and fantasy."--Lunar and Planetary Information Bulletin "[T]his is an interesting, well-written book, and Adler has put a lot of work into it. It should be invaluable for anyone wanting to write really accurate science fiction."--Popular Science "There is much ... in this book to interest readers interested in astronomy and astronautics and I think it will be likely to appeal to physics students."--John Harney, Magonia "Charles L. Adler, professor in the physics department at St. Mary's College in Maryland, is one of us--he's a lifelong fan of SF, and he knows what he's talking about. And Wizards, Aliens, and Starships is a great book for Analog readers, as well as anyone who wants to write hard SF. I mean, it's got honest-to-goodness equations--and the book is dedicated to Poul Anderson... Wizards, Aliens, and Starships is a love letter to science fiction."--Don Sakers, Analog Science Fiction and Fact "Hugely entertaining and scientifically sound."--Paul Gilster, Centauri Dreams "What a fun book!"--Keith Cooper, Astronomy Now "Wizards, Aliens, and Starships manages to thread the needles of both scientific literacy and accuracy when it comes to the properties he's exploring. Whether it's conservation of mass in shapeshifting, lighting candles at Hogwarts, or building a planet, Adler keeps the science accessible and the fanboys and girls happy."--Glenn Dallas, San Francisco Book Review "Wizards, Aliens, and Starships [is] a book that combines my love for science and my love for science fiction... I did quite like this book and would recommend it for any academic library that collects popular science or science fiction. Large public libraries would also find this book to be useful as would many high school libraries. It would also make a great gift to any young person (or not so young!) who loves science fiction and has a bit of scientific background."--John Dupuis, Confessions of a Science Librarian "[T]his is a towering achievement... [I]t is certainly one of the coolest textbooks one will find anywhere... Any fan of science fiction or fantasy who wants to understand what is real and what is imaginary will almost certainly enjoy this book, and can look forward to learning what may be possible, both in great fiction and in the real universe."--Jonathan T. Malay, Quest "This is a good, interesting, well-written, and often humorous work. Adler obviously loves all types of science fiction--books, short stories, films, TV--and enjoys thinking through their scientific aspects... Overall, the book provides a thorough treatment of science fiction and an introduction to much of physics and astronomy."--Choice "[T]his is an exciting book... I would not hesitate to recommend it to anyone who is interested in understanding the relationship between physics and science fiction. Instructors of introductory physics courses, especially, will find it a valuable supplement to dry physics textbooks, and its use may even boost students' evaluations of the course. I will certainly use it in my classes."--Costas Efthimiou, Physics World "Wizards, Aliens, and Starships: Physics and Math in Fantasy and Science Fiction is a fascinating book. As I started to read it, what immediately caught my attention was the passion and excitement that author Charles Adler instills in the text. I couldn't put it down."--Edward Belbruno, Physics Today "One pleasure to be had from the book is learning how to work out why some fantastic idea is ridiculous (but another one just might succeed) from a couple of physical principles and a few lines of algebra. Another pleasure is being infected by Adler's enthusiasm for epic science fiction."--Peter Macgregor, Mathematical GazetteTable of Contents1 PLAYING THE GAME 1 1.1 The Purpose of the Book 1 1.2 The Assumptions I Make 3 1.3 Organization 4 1.4 The Mathematics and Physics You Need 5 1.5 Energy and Power 6 I POTTER PHYSICS 11 2HARRY POTTER AND THE GREAT CONSERVATION LAWS 13 2.1 The Taxonomy of Fantasy 13 2.2 Transfiguration and the Conservation of Mass 14 2.3 Disapparition and the Conservation of Momentum 16 2.4 Reparo and the Second Law of Thermodynamics 21 3WHY HOGWARTS IS SO DARK 27 3.1 Magic versus Technology 27 3.2 Illumination 28 4FANTASTIC BEASTS AND HOW TO DISPROVE THEM 38 4.1 Hic sunt Dracones 38 4.2 How to Build a Giant 39 4.3 Kleiber's Law, Part 1: Mermaids 45 4.4 Kleiber's Law, Part 2: Owls, Dragons, Hippogriffs, and Other Flying Beasts 49 II SPACE TRAVEL 57 5WHY COMPUTERS GET BETTER AND CARS CAN'T (MUCH) 59 5.1 The Future of Transportation 59 5.2 The Reality of Space Travel 61 5.3 The Energetics of Computation 63 5.4 The Energetics of the Regular and the Flying Car 64 5.5 Suborbital Flights 68 6VACATIONS IN SPACE 71 6.1 The Future in Science Fiction: Cheap, Easy Space Travel? 71 6.2 Orbital Mechanics 74 6.3 Halfway to Anywhere: The Energetics of Spaceflight 74 6.4 Financing Space Travel 82 7SPACE COLONIES 86 7.1 Habitats in Space 86 7.2 O'Neill Colonies 87 7.3 Matters of Gravity 89 7.4 Artificial "Gravity" on a Space Station 93 7.5 The Lagrange Points 103 7.6 Off-Earth Ecology and Energy Issues 106 7.7 The Sticker Price 112 8THE SPACE ELEVATOR 115 8.1 Ascending into Orbit 115 8.2 The Physics of Geosynchronous Orbits 116 8.3 What Is a Space Elevator, and Why WouldWeWant One? 118 8.4 Why Buildings Stand Up--or Fall Down 119 8.5 Stresses and Strains: Carbon Nanotubes 122 8.6 Energy, "Climbers," Lasers, and Propulsion 123 8.7 How Likely Is It? 125 8.8 The Unapproximated Elevator 127 9MANNED INTERPLANETARY TRAVEL 130 9.1 It's Not an Ocean Voyage or a Plane Ride 130 9.2 Kepler's Three Laws 131 9.3 The Hohmann Transfer Orbit 134 9.4 Delta v and All That 136 9.5 Getting Back 137 9.6 Gravitational Slingshots and Chaotic Orbits 138 9.7 Costs 142 10ADVANCED PROPULSION SYSTEMS 145 10.1 Getting There Quickly 145 10.2 Why Chemical Propulsion Won'tWork 146 10.3 The Most Famous Formula in Physics 147 10.4 Advanced Propulsion Ideas 148 10.5 Old "Bang-Bang": The Orion Drive 153 10.6 Prospects for Interplanetary Travel 155 11SPECULATIVE PROPULSION SYSTEMS 157 11.1 More Speculative Propulsion Systems 157 11.2 Mass Ratios for Matter-Antimatter Propulsion Systems 168 11.3 Radiation Problems 173 12INTERSTELLAR TRAVEL AND RELATIVITY 176 12.1 Time Enough for Anything 176 12.2 Was Einstein Right? 178 12.3 Some Subtleties 182 12.4 Constant Acceleration in Relativity 184 13FASTER-THAN-LIGHT TRAVEL AND TIME TRAVEL 188 13.1 The Realistic Answer 188 13.2 The Unrealistic Answer 188 13.3 Why FTL Means Time Travel 190 13.4 The General Theory 193 13.5 Gravitational Time Dilation and Black Holes 195 13.6 Wormholes and Exotic Matter 198 13.7 The Grandfather Paradox and Other Oddities 205 III WORLDS AND ALIENS 215 14DESIGNING A HABITABLE PLANET 217 14.1 Adler's Mantra 218 14.2 Type of Star 221 14.3 Planetary Distance from Its Star 226 14.4 The Greenhouse Effect 229 14.5 Orbital Eccentricity 232 14.6 Planetary Size and Atmospheric Retention 233 14.7 The Anna Karenina Principle and Habitable Planets 237 14.8 Imponderables 239 15THE SCIENTIFIC SEARCH FOR SPOCK 242 15.1 Exoplanets and Exoplants 242 15.2 Doppler Technique 246 15.3 Transits and the Kepler Mission 249 15.4 The Spectral Signatures of Life 250 15.5 Alien Photosynthesis 251 16THE MATHEMATICS OF TALKING WITH ALIENS 255 16.1 Three Views of Alien Intelligences 255 16.2 Motivation for Alien Contact 259 16.3 Drake-Equation Models and the Mathematics of Alien Contact 267 IV YEAR GOOGOL 273 17THE SHORT-TERM SURVIVAL OF HUMANITY 275 17.1 This Is the Way the WorldWill End 275 17.2 The Short-Term: Man-Made Catastrophes 275 18WORLD-BUILDING 292 18.1 Terraforming 292 18.2 Characteristics of Mars 294 18.3 Temperature and the Martian Atmosphere 295 18.4 Atmospheric Oxygen 299 18.5 Economics 301 19DYSON SPHERES AND RINGWORLDS 303 19.1 Dyson's Sphere 303 19.2 The Dyson Net 305 19.3 Niven's Ringworld 311 19.4 The Ringworld, GPS, and Ehrenfest's Paradox 318 19.5 The Ringworld Is Unstable! 320 19.6 Getting There from Here--and Do We Need To? 324 20ADVANCED CIVILIZATIONS AND THE KARDASHEV SCALE 326 20.1 The Kardashev Scale 326 20.2 Our Type 0.7 Civilization 327 20.3 Type I Civilizations 329 20.4 Moving Upward 331 20.5 Type II Civilizations 332 20.6 Type III Civilizations 334 21A GOOGOL YEARS 336 21.1 The Future of the Future 336 21.2 The "Short Term": Up to 500 Million Years or so 336 21.3 The "Medium Term": Up to about 1013 Years 338 21.4 The "Long Term": Up to a Googol Years 341 21.5 Black Hole-Powered Civilizations 344 21.6 Protons Decay--or Do They? 346 21.7 A Googol Years--All the Black Holes Evaporate 346 21.8 Our Last Bow 349 Acknowledgments 351 Appendix: Newton's Three Laws of Motion 353 Bibliography 359 Index 371

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Book SynopsisOffers an introduction to steady flight and performance for fixed-wing aircraft from a twenty-first-century flight systems perspective. This title covers various aspect of flight performance, including maximum and minimum air speed, maximum climb rate, minimum turn radius, flight ceiling, maximum range, and maximum endurance.Trade Review"Steady Aircraft Flight and Performance is very well written, and it contains many useful figures and illustrations. The level of presentation is readily accessible to its intended audience—undergraduate students in aerospace engineering—and the numerous examples and problems help solidify the concepts presented in the book. MATLAB code is included for many problems, facilitating the transition from concepts to computation."—Robert F. Stengel, Princeton University"This book is right on the mark. McClamroch's theoretical developments are, as usual, very rigorous and detailed."—Eric Feron, Georgia Institute of TechnologyTable of ContentsLIST OF ILLUSTRATIONS xi LIST OF MATLAB M-FILES xv PREFACE AND ACKNOWLEDGMENTS xix Chapter 1: Aircraft Components and Subsystems 1 1.1 Aircraft Subsystems for Conventional Fixed-Wing Aircraft 1 1.2 Aerodynamic Control Surfaces 2 1.3 Aircraft Propulsion Systems 3 1.4 Aircraft Structural Systems 4 1.5 Air Data and Flight Instrumentation 5 1.6 Guidance, Navigation, and Control 5 1.7 Flight Control Computers 6 1.8 Communication Systems 6 1.9 Aircraft Pilots 6 1.10 Autonomous Aircraft 7 1.11 Interconnection and Integration of Flight Systems 7 Chapter 2: Fluid Mechanics and Aerodynamics 9 2.1 Fundamental Properties of Air 9 2.2 Standard Atmosphere Model 10 2.3 Aerodynamics Fundamentals 15 2.4 Aerodynamics of Flow over a Wing 18 2.5 Wing Geometry 19 2.6 Problems 21 Chapter 3: Aircraft Translational Kinematics, Attitude, Aerodynamic Forces and Moments 24 3.1 Cartesian Frames 25 3.2 Aircraft Translational Kinematics 26 3.3 Aircraft Attitude and the Translational Kinematics 29 3.4 Translational Kinematics for Flight in a Fixed Vertical Plane 30 3.5 Translational Kinematics for Flight in a Fixed Horizontal Plane 32 3.6 Small Angle Approximations 34 3.7 Coordinated Flight 34 3.8 Clarification of Bank Angles 35 3.9 Aerodynamic Forces 35 3.10 Aerodynamic Moments 39 3.11 Problems 41 Chapter 4: Propulsion Systems 47 4.1 Steady Thrust and Power Relations 47 4.2 Jet Engines 47 4.3 Propeller Driven by Internal Combustion Engine 50 4.4 Turboprop Engines 53 4.5 Throttle as a Pilot Input 53 4.6 Problems 53 Chapter 5: Prelude to Steady Flight Analysis 56 5.1 Aircraft Forces and Moments 57 5.2 Steady Flight Equations 58 5.3 Steady Longitudinal Flight 60 5.4 Steady Level Turning Flight 60 5.5 Flight Constraints 60 5.6 Aircraft Case Studies 61 5.7 Characteristics of an Executive Jet Aircraft 62 5.8 Characteristics of a Single Engine Propeller-Driven General Aviation Aircraft 63 5.9 Characteristics of an Uninhabited Aerial Vehicle (UAV) 64 5.10 Problems 66 Chapter 6: Aircraft Steady Gliding Longitudinal Flight 69 6.1 Steady Gliding Longitudinal Flight 69 6.2 Steady Gliding Longitudinal Flight Analysis 71 6.3 Minimum Glide Angle 74 6.4 Minimum Descent Rate 74 6.5 Maximum Glide Angle 75 6.6 Maximum Descent Rate 75 6.7 Steady Gliding Longitudinal Flight Envelopes 76 6.8 Steady Gliding Longitudinal Flight: Executive Jet Aircraft 76 6.9 Steady Gliding Longitudinal Flight: General Aviation Aircraft 81 6.10 Conclusions 85 6.11 Problems 86 Chapter 7: Aircraft Cruise in Steady Level Longitudinal Flight 90 7.1 Steady Level Longitudinal Flight 90 7.2 Steady Level Longitudinal Flight Analysis 94 7.3 Jet Aircraft Steady Level Longitudinal Flight Performance 99 7.4 General Aviation Aircraft Steady Level Longitudinal Flight Performance 100 7.5 Steady Level Longitudinal Flight: Executive Jet Aircraft 102 7.6 Steady Level Longitudinal Flight Envelopes: Executive Jet Aircraft 106 7.7 Steady Level Longitudinal Flight: General Aviation Aircraft 109 7.8 Steady Level Longitudinal Flight Envelopes: General Aviation Aircraft 113 7.9 Conclusions 116 7.10 Problems 116 Chapter 8: Aircraft Steady Longitudinal Flight 121 8.1 Steady Longitudinal Flight 121 8.2 Steady Longitudinal Flight Analysis 125 8.3 Jet Aircraft Steady Longitudinal Flight Performance 130 8.4 General Aviation Aircraft Steady Longitudinal Flight Performance 133 8.5 Steady Climbing Longitudinal Flight: Executive Jet Aircraft 136 8.6 Steady Descending Longitudinal Flight: Executive Jet Aircraft 143 8.7 Steady Longitudinal Flight Envelopes: Executive Jet Aircraft 149 8.8 Steady Climbing Longitudinal Flight: General Aviation Aircraft 150 8.9 Steady Descending Longitudinal Flight: General Aviation Aircraft 157 8.10 Steady longitudinal Flight Envelopes: General Aviation Aircraft 162 8.11 Conclusions 164 8.12 Problems 165 Chapter 9: Aircraft Steady Level Turning Flight 171 9.1 Turns by Side-Slipping 171 9.2 Steady Level Banked Turning Flight 171 9.3 Steady Level Banked Turning Flight Analysis 175 9.4 Jet Aircraft Steady Level Turning Flight Performance 180 9.5 General Aviation Aircraft Steady Level Turning Flight Performance 183 9.6 Steady Level Turning Flight: Executive Jet Aircraft 186 9.7 Steady Level Turning Flight Envelopes: Executive Jet Aircraft 195 9.8 Steady Level Turning Flight: General Aviation Aircraft 196 9.9 Steady Level Turning Flight Envelopes: General Aviation Aircraft 207 9.10 Conclusions 209 9.11 Problems 209 Chapter 10: Aircraft Steady Turning Flight 214 10.1 Steady Banked Turns 214 10.2 Steady Banked Turning Flight Analysis 218 10.3 Jet Aircraft Steady Turning Flight Performance 225 10.4 General Aviation Aircraft Steady Turning Flight Performance 229 10.5 Steady Climbing and Turning Flight: Executive Jet Aircraft 233 10.6 Steady Descending and Turning Flight: Executive Jet Aircraft 244 10.7 Steady Turning Flight Envelopes: Executive Jet Aircraft 253 10.8 Steady Climbing and Turning Flight: General Aviation Aircraft 255 10.9 Steady Descending and Turning Flight: General Aviation Aircraft 266 10.10 Steady Turning Flight Envelopes: General Aviation Aircraft 276 10.11 Conclusions 278 10.12 Problems 279 Chapter 11: Aircraft Range and Endurance in Steady Flight 285 11.1 Fuel Consumption 285 11.2 Steady Flight Background 286 11.3 Range and Endurance of a Jet Aircraft in Steady Level Longitudinal Flight 286 11.4 Range and Endurance of a General Aviation Aircraft in Steady Level Longitudinal Flight 291 11.5 Range and Endurance of a Jet Aircraft in a Steady Level Turn 297 11.6 Range and Endurance of a General Aviation Aircraft in a Steady Level Turn 298 11.7 Range and Endurance of a Jet Aircraft in a Steady Turn 299 11.8 Range and Endurance of a General Aviation Aircraft in a Steady Turn 300 11.9 Maximum Range and Maximum Endurance: Executive Jet Aircraft 301 11.10 Maximum Range and Maximum Endurance: General Aviation Aircraft 307 11.11 Conclusions 313 11.12 Problems 313 Chapter 12: Aircraft Maneuvers and Flight Planning 319 12.1 Static Flight Stability 319 12.2 Flight Maneuvers 321 12.3 Pilot Inputs That Achieve a Desired Flight Condition 324 12.4 Flight Plans Defined by a Sequence of Waypoints 325 12.5 A Flight Planning Problem: Executive Jet Aircraft 327 12.6 A Flight Planning Problem: General Aviation Aircraft 331 12.7 Conclusions 336 12.8 Problems 336 Chapter 13: From Steady Flight to Flight Dynamics 344 13.1 Flight Dynamics Assumptions 345 13.2 Differential Equations for the Translational Flight Dynamics 346 13.3 Including Engine Characteristics and Fuel Consumption 349 13.4 Differential Equations for Longitudinal Translational Flight Dynamics 351 13.5 Differential Equations for Takeoff and Landing 353 13.6 Steady Flight and the Translational Flight Dynamics 355 13.7 Dynamic Flight Stability 356 13.8 Computing Dynamic Flight Performance Measures and Flight Envelopes 357 13.9 Flight Simulations: Executive Jet Aircraft 359 13.10 Flight Simulations: General Aviation Aircraft 365 13.11 Conclusions 372 13.12 Problems 372 Appendix A The Standard Atmosphere Model 379 Appendix B End-of-Chapter Problems 382 B.1 Executive Jet Aircraft 382 B.2 Single Engine Propeller-Driven General Aviation Aircraft 383 B.3 Uninhabited Aerial Vehicle (UAV) 383 REFERENCES 385 INDEX 387

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Book SynopsisProvides a variety of state-space-based numerical algorithms for the synthesis of feedback algorithms for linear systems with input saturation. This title addresses and solves the anti-windup problem, presenting the objectives and terminology of the problem and the mathematical tools behind anti-windup algorithms.Trade Review"This book goes a long way toward providing comprehensive coverage of systematic procedures for anti-windup synthesis, emphasizing algorithmic issues and modern design techniques. A valuable resource for researchers and practitioners, it should interest a broad audience in control engineering, as well as in other disciplines, such as mechanical and chemical engineering."—Prodromos Daoutidis, University of MinnesotaTable of Contents*FrontMatter, pg. i*Contents, pg. v*Preface, pg. ix*Arlgorithms Summary, pg. xi*Chapter One. The Windup Phenomenon and Anti-windup Illustrated, pg. 3*Chapter Two. Anti-windup: Definitions, Objectives, and Architectures, pg. 23*Chapter Three. Analysis and Synthesis of Feedback Systems: Quadratic Functions and LMIs, pg. 48*Chapter Four. Static Linear Anti-windup Augmentation, pg. 77*Chapter Five. Dynamic Linear Anti-windup Augmentation, pg. 109*Chapter Six. The MRAW Framework, pg. 157*Chapter Seven. Linear MRAW Synthesis, pg. 174*Chapter Eight. Nonlinear MRAVV Synthesis, pg. 200*Chapter Nine. The MRAVV Structure Applied to Other Problems, pg. 226*Chapter Ten. Anti-windup for Euler-Lagrange Plants, pg. 245*Chapter Eleven. Annotated Bibliography, pg. 269*Index, pg. 285

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Book SynopsisSpin glasses are disordered magnetic systems that have led to the development of mathematical tools with an array of real-world applications, from airline scheduling to neural networks. This book offers an introduction to the subject, explaining what spin glasses are, and how they are opening up new ways of thinking about complexity.Trade Review"The challenge that Stein and Newman faced in creating this book ... was to write for a broad range of readers and still offer interesting depth. As they state in the preface, they are aiming for a reading level that is between Scientific American and research journals. This reviewer believes they have succeeded... Stein and Newman write well and keep the mathematics to a minimum."--Choice "[A] surprisingly broad field of view is visible through the lens of the classical, equilibrium using spin glass and the authors are able to use it to explore many fascinating topics. Stein and Newman have written an excellent introduction to the field of spin glasses and the many ramifications of spin glass theory outside of condensed matter physics and statistical mechanics. Experts and novices alike will find this book interesting and useful."--Jonathan Machta, Journal of Statistical Physics "Spin Glasses and Complexity is not a journalistic book that merely reports on the subject. Based on profound mathematical insights, here distilled into an incisive presentation, it represents the fruit of the lifelong commitments two experts have made to spin-glass theory within and beyond physics... Spin Glasses and Complexity is unique in successfully bringing this thrilling theme to a broader scientific audience."--Stefan Boettcher, Physics Today "[T]he work is well presented and the reader will surely find it both inspiring and interesting."--Marco Castrillon Lopez, European Mathematical Society "Well presented and the reader will surely find it both inspiring and interesting."--Marco Castrillon Lopez, European Mathematical SocietyTable of ContentsPreface xi Introduction: Why Spin Glasses? 1 *1. Order, Symmetry, and the Organization of Matter 15 *1.1 The Symmetry of Physical Laws 17 *1.2 The Hamiltonian 23 *1.3 Broken Symmetry 26 *1.4 The Order Parameter 31 *1.5 Phases of Matter 35 *1.6 Phase Transitions 39 *1.7 Summary: The Unity of Condensed Matter Physics 41 2. Glasses and Quenchied Disorder 43 *2.1 Equilibrium and Non Equilibrium 43 * 2.2 The Glass Transition 45 *2.3 Localization 49 3. Magnetic Systems 51 *3.1 Spin 51 *3.2 Magnetism in Solids 53 *3.3 The Paramagnetic Phase 55 *3.4 Magnetization 55 *3.5 The Ferromagnetic Phase and Magnetic Susceptibility 57 *3.6 The Antiferromagnetic Phase 59 *3.7 Broken Symmetry and the Heisenberg Hamiltonian 59 4. Spin Glasses: General Features 63 *4.1 Dilute Magnetic Alloys and the Kondo Effect 64 *4.2 A New State of Matter? 65 *4.3 Nonequilibrium and Dynamical Behavior 71 *4.4 Mechanisms Underlying Spin Glass Behavior 74 *4.5 The Edwards-Anderson Hamiltonian 78 *4.6 Frustration 81 *4.7 Dimensionality and Phase Transitions 83 *4.8 Broken Symmetry and the Edwards-Anderson Order Parameter 85 *4.9 Energy Landscapes and Metastability 86 5. The Infinite-Range Spin Glass 90 *5.1 Mean Field Theory 90 *5.2 The Sherrington-Kirkpatrick Hamiltonian 92 *5.3 A Problem Arises 93 *5.4 The Remedy 95 *5.5 Thermodynamic States 97 *5.6 The Meaning of Replica Symmetry Breaking 98 *5.7 The Big Picture 109 6. Applications to Other Fields 112 *6.1 Computational Time Complexity and Combinatorial Optimization 113 *6.2 Neural Networks and Neural Computation 129 *6.3 Protein Folding and Conformational Dynamics 144 *6.4 Short Takes 168 7. Short-Range Spin Glasses: Some Basic Questions 175 *7.1 Ground States 177 *7.2 Pure States 188 *7.3 Scenarios for the Spin Glass Phase of the EA Model 193 *7.4 The Replica Symmetry Breaking and Droplet/Scaling Scenarios 194 *7.5 The Parisi Overlap Distribution 197 *7.6 Self-Averaging and Non-Self-Averaging 199 *7.7 Ruling Out the Standard RSB Scenario 201 *7.8 Chaotic Size Dependence and Metastates 203 *7.9 A New RSB Scenario 206 *7.10 Two More (Relatively) New Scenarios 211 *7.11 Why Should the SK Model Behave Differently from the EA Model? 214 *7.12 Summary: Where Do We Stand? 216 8. Are Spin Glasses Complex Systems? 218 *8.1 Three Foundational Papers 219 *8.2 Spin Glasses as a Bridge to Somewhere 227 *8.3 Modern Viewpoints on Complexity 228 *8.4 Spin Glasses: Old, New, and Quasi-Complexity 233 Notes 239 Glossary 265 Bibliography 285 Index 309

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Book SynopsisBenford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from electricity bills and street addresses to stock prices, population numbers, mortality rates, and the lengths of rivers. Here, Steven Miller brings together maTrade Review"This book will prove to be both a valuable reference and a first source to turn to for whoever is interested in the mathematical genesis and empirical usefulness of Benford's law."--Walter Kramer, Statistical PapersTable of Contents*Frontmatter, pg. i*Contents, pg. vii*Foreword, pg. xiii*Preface, pg. xvii*Notation, pg. xxiii*Chapter One. A Quick Introduction to Benford's Law, pg. 3*Chapter Two. A Short Introduction to the Mathematical Theory of Benford's Law, pg. 23*Chapter Three. Fourier Analysis and Benford's Law, pg. 68*Chapter Four. Benford's Law Geometry, pg. 109*Chapter Five. Explicit Error Bounds via Total Variation, pg. 119*Chapter Six. Levy Processes and Benford's Law, pg. 135*Chapter Seven. Benford's Law as a Bridge between Statistics and Accounting, pg. 177*Chapter Eight. Detecting Fraud and Errors Using Benford's Law, pg. 191*Chapter Nine. Can Vote Counts' Digits and Benford's Law Diagnose Elections?, pg. 212*Chapter Ten. Complementing Benford's Law for Small N: A Local Bootstrap, pg. 223*Chapter Eleven. Measuring the Quality of European Statistics, pg. 235*Chapter Twelve. Benford's Law and Fraud in Economic Research, pg. 244*Chapter Thirteen. Testing for Strategic Manipulation of Economic and Financial Data, pg. 257*Chapter Fourteen. Psychology and Benford's Law, pg. 267*Chapter Fifteen. Managing Risk in Numbers Games, pg. 276*Chapter Sixteen. Benford's Law in the Natural Sciences, pg. 290*Chapter Seventeen. Generalizing Benford's Law, pg. 304*Chapter Eighteen. PV Modeling of Medical Imaging Systems, pg. 319*Chapter Nineteen. Application of Benford's Law to Images, pg. 338*Chapter Twenty. Exercises, pg. 373*Bibliography, pg. 402*Index, pg. 433

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Book SynopsisAn anthology that gathers together nearly one hundred selections from the past 500 years of popular math writing. Ranging from the late fifteenth to the late twentieth century, and drawing from books, newspapers, magazines, and websites, it includes recreational, classroom, and work mathematics; mathematical histories and biographies; and, more.Trade Review"One of the pleasures of this book is reading the texts in the language of the day... The collection as a whole provides the general reader with a history of mathematics, biographical and otherwise, through popular writing. Because the writing was aimed at general readers of its time, it is usually accessible to the average mathematical reader of our time. The book would be an excellent reference for teachers of mathematics and for those researching the history of the dissemination of mathematical ideas."--Carol Dorf, American Scientist "[F]or the enthusiast for the history of popular maths writing this is a must-have book."--Brian Clegg, Popular Science "In A Wealth of Numbers, we have the end product of what must have been a lot of challenging research... This book works well for random browsing as well as for sustained reading; purely recreational essays and puzzle problems are well-mixed with more serious topics such as an article explaining Cantor's diagonalization proof and 'Cubic equations for the practical man.' There's something in here for everyone, and it's a great contribution to the mathematics literature to have it all in one place."--Mark Bollman, MAA Reviews "Wardhaugh provides an exciting addition to mathematics anthologies... The physical format is very reader-friendly, with especially good line spacing and margins. The book is valuable for all libraries supporting undergraduate and graduate study, as well as many public libraries. Faculty should consider this as a source of comprehensible readings for aspiring mathematics majors. Individuals interested in math history will want a copy for their personal libraries."--Choice "The Wardhaugh book is a welcome addition to anthologies that have preceded it... Although written for the general reader who is interested in mathematics, the collection is apropos for those who are more mathematically oriented as well... [T]his well-thought-out, eclectic collection will provide hours of enjoyable reading."--Jim Tattersall, CSHPM "Fascinating to browse, a delight to read, and informative... Get this book! It is as much fun to read as it is to share with others, especially students who can gain from doses of past mathematical realities."--Jerry Johnson, Mathematics Teacher "This book permits the reader to pick it up whenever he or she has a few minutes (or longer) to spare, and find a section to fit the available free time and mood. It will provide the reader, novice and expert alike, many hours of learning filled with surprise, pleasure, amazement, and sometimes laughter."--Godfried Toussaint, Zentralblatt MATH "A Wealth of Numbers explores the often overlooked history of popular mathematics in an easy to read and captivating manner. I recommend the book, not only as an excellent research text in this area of mathematics, but as an interesting and entertaining read."--Steve Humble, Mathematics Today MagazineTable of Contents*FrontMatter, pg. i*Contents, pg. v*Preface, pg. xiii*1. "Sports and Pastimes, Done by Number": Mathematical Tricks, Mathematical Games, pg. 1*2. "Much Necessary for All States of Men": From Arithmetic to Algebra, pg. 32*3. "A Goodly Struggle": Problems, Puzzles, and Challenges, pg. 62*4. "Drawyng, Measuring and Proporcion": Geometry and Trigonometry, pg. 84*5. Maps, Monsters, and Riddles: The Worlds of Mathematical Popularization, pg. 108*6. "To Ease and Expedite the Work": Mathematical Instruments and How to Use Them, pg. 152*7. "How Fine a Mind": Mathematicians Past, pg. 176*8. "By Plain and Practical Rules": Mathematics at Work, pg. 216*9. "The Speedier Expedition of Their Learning": Thoughts on Teaching and Learning Mathematics, pg. 245*10. "So Fundamentally Useful a Science": Reflections on Mathematics and Its Place in the World, pg. 290*11. The Mathematicians Who Never Were: Fiction and Humor, pg. 326*Index, pg. 367

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Book SynopsisMath - the application of reasonable logic to reasonable assumptions - usually produces reasonable results. But sometimes math generates astonishing paradoxes - conclusions that seem completely unreasonable or just plain impossible but that are nevertheless demonstrably true. This book is a collection of paradoxes from different areas of math.Trade Review"Nonplussed! is a collection of lovely paradoxes: facts that are provable logically but are nevertheless seriously counterintuitive...It is an exciting book. It should be in every...college library. It would even be the right gift for mathematicians and anyone who uses mathematics--economists, business analysts and many others--and indeed for anyone who would claim to be educated."--Peter M. Neumann, Times Higher Education Supplement "This is a splendid collection of articles, inspired by Martin Gardner's writings. Old conundrums are given new twists and applications, newer perplexing ideas are described with panache. The forthcoming companion book has a high standard to maintain."--John Haigh, London Mathematical Society Newsletter "It is therefore recommended that Julian Havil's headmaster award him further sabbatical leave for the purpose of producing a sequel to this welcome addition to the mathematical literature."--Peter Ruane, MAA Review "A review of a book as good as this must either repeat the positive adjectives other reviewers have used, or require a very large thesaurus. Since I find myself in complete agreement with all of the following words from other reviews, I will repeat them immediately: marvelous, crystal-clear, great, amazing, stimulating, delightful, fascinating, strong, surprising, classic, interesting, eclectic, insightful, magnificent. That one book could encourage such gushing praise seems as unlikely as one book being able to cram in a great variety and depth of mathematical problems, colourful historical anecdotes, significant nods to ethno-mathematics, difficult but well-explained proofs, clear and engaging prose and beautiful diagrams. Yet Havil's book succeeds on all accounts...The brilliant writing, the wonderful problems, the weaving together of past and future, games and discovery, and world number cultures will have you returning to this ageless book time and again."--Phil Wilson, Plus Magazine "This fascinating expedition by Havil through some engaging and often surprising mathematical and statistical oddities is more demanding than the usual 'popular math book' it is billed...All topics are covered by an always carefully crafted mathematical exposition, not leaving out necessary preliminaries and providing rigorous proofs."--J. Mayer, Choice "Even many high school students without a calculus background will benefit from the problems contained in the book... The book contains a little algebra, some geometry, and a great deal of probability. It could serve as recreational reading for teachers as well as for student use in a probability course or courses following algebra 2. Mathematics clubs and teams would also find Nonplussed! useful."--Paul Kelley, Mathematics Teacher "This is a fun book containing many diverse problems that I had not seen before but it also stimulates some genuinely interesting mathematical thought. Above all, this book highlights the 'frailty of the intuition we routinely use to guide us through our everyday lives' and that, in my mind, is no bad thing."--Nathan Green, Mathematics Today "I recommend the book to everyone interested in entertaining mathematics."--Christina Birkenhake, Mathematical Intelligencer "This book discusses such problems in a generally accessible way, but it does not shy away from using rigorous mathematical arguments to explain them... Some of these topics are quite familiar, but even so I found the discussions clear and often learned some new and quite surprising tidbits."--Stan Wagon, Mathematical Reviews "Those that spend their working lives avoiding mathematics by approaching their problems in all sorts of different ways will benefit from looking at this text, even if it involves following through but one single problem and its mathematical solution."--C.J.H. Mann, Kybernetes "The book is perfect for independent or group study for students in advanced high school mathematics classes or university-level undergraduate mathematics classes. Selected chapters are suitable for discussion during professional development sessions aimed at engaging mathematics teachers in rigorous mathematics investigations and discussions."--Anne Papakonstantinou, Mathematics Teacher "This lovely book will attract the attention of readers who are interested in recreational mathematics like mathematical puzzles and paradoxes."--Yuri V. Rogovchenko, Zentralblatt MATH "Havil has an excellent mix of an interesting history of each topic and clear and lucid solutions to the problems... Havil's strength is the historical background he gives to each topic and his style of writing which is so easy to read... An interesting and challenging book well worth reading."--John Sykes, Mathematics in SchoolTable of ContentsPreface xi Acknowledgements xiii Introduction 1 Chapter 1: Three Tennis Paradoxes 4 Chapter 2: The Uphill Roller 16 Chapter 3: The Birthday Paradox 25 Chapter 4: The Spin of a Table 37 Chapter 5: Derangements 46 Chapter 6: Conway's Chequerboard Army 62 Chapter 7: The Toss of a Needle 68 Chapter 8: Torricelli's Trumpet 82 Chapter 9: Nontransitive Effects 92 Chapter 10: A Pursuit Problem 105 Chapter 11: Parrondo's Games 115 Chapter 12: Hyperdimensions 127 Chapter 13: Friday the 13th 151 Chapter 14: Fractran 162 The Motifs 180 Appendix A: The Inclusion-Exclusion Principle 187 Appendix B: The Binomial Inversion Formula 189 Appendix C: Surface Area and Arc Length 193 Index 195

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Book SynopsisA collection of informal interviews and memoirs of sixteen prominent members of the mathematical community of the twentieth century, many still active.Trade ReviewWinner of the 2012 Book Merit Award in the Professional, Reference category, New York Book Show "What do a Beatles expert, a professional magician and a Los Angeles dentist have in common? If they're Joseph Gallian, Arthur Benjamin and Leon Bankoff, it's mathematics. The words of these and other researchers, mentors and teachers in the maths community feature in this compilation by educator Donald Albers and mathematician Gerald Alexanderson. There is much to relish in these accounts--not least geometer Thomas Banchoff's friendship with Salvador Dali, who explored the nexus of atomic science, maths and art late in life."--Nature "Albers and Alexanderson pick up where they left off from their earlier books, Mathematical People and More Mathematical People, with profiles of 16 unique individuals involved in all areas of mathematics teaching and research... A handy way to learn about contemporary mathematic ideas and interrelated areas of research, the book seems more like a dinner party filled with intriguing personalities than a textbook... Strongly recommended for readers interested in mathematics and anyone wanting to understand the creative process."--Elizabeth Brown, Library Journal (starred review) "A beautifully illustrated collection of interviews and biographical etudes of 16 mathematicians of different backgrounds, varied professional interests, diverse level of achievement--all incredibly interesting as human beings... [A]n awfully good and entertaining read."--Alexander Bogomolny, CTK Insights "This book is an assortment of interviews and memoirs of 16 contemporary mathematicians with a variety of backgrounds. The volume includes some unique, never-published photographs of the mathematicians--at work and/or with their families--that add a nice personal touch. As this reviewer read about these individuals, she found herself wanting to know more about them, and even considering inviting one to be a guest speaker at a math club meeting... [Fascinating Mathematical People] would be a useful supplementary resource for an undergraduate history of mathematics class; it would also be a valuable work for students to browse on their own."--J.A. Bakal, Choice "[T]his is a book to discontinuous reading: one picks it at leisure, takes a look at the contents and chooses what to read. No order is required, nor any systematic dedication, but in the end one sure will read it all."--Jesus M. Ruiz, European Mathematical Society Newsletter "Interesting personal sketches of mathematicians at work and at home... For students considering a career in mathematics, this book can be an enlightening read. For readers who are already mathematicians, it gives insight into some mathematical history of the twentieth century."--Dorothy Janice Radin, Mathematics Teacher "It is packed with anecdotes and suitable for the general reader or historian. A range of themes are introduced in the preface raising the potential for a more specialized biographical insight. An enjoyable read and learning experience."--Wallace A Ferguson, Mathematics TodayTable of ContentsForeword by Philip J. Davis vii Preface ix Acknowledgments xiii Sources xv One: Lars V. Ahlfors 1 Two: Tom Apostol 17 Three: Harold M. Bacon 43 Four: Tom Banchoff 52 Five: Leon Bankoff 79 Six: Alice Beckenbach 96 Seven: Arthur Benjamin 107 Eight: Dame Mary L. Cartwright 129 Nine: Joe Gallian 146 Ten: Richard K. Guy 165 Eleven: Fern Hunt 193 Twelve: Dusa McDuff 215 Thirteen: Donald G. Saari 240 Fourteen: Atle Selberg 254 Fifteen: Jean Taylor 274 Sixteen: Philippe Tondeur 294 Biographical Notes 319 Glossary 321 Index 325

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Book SynopsisTrade Review"A tour de force of the mathematical description of waves. . . . I sincerely wish I had encountered such a book early in my teaching career. The material presented in it would have provided a very useful enhancement to a number of courses I have taught to undergraduate physics majors over the years."---James A. Lock, American Journal of Physics

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Book SynopsisAn anthology featuring the year's finest writing on mathematics from around the world. It helps readers discover why Freeman Dyson thinks some mathematicians are birds while others are frogs; why Keith Devlin believes there's more to mathematics than proof; and what Samuel Arbesman can tell us about the epidemiology of the undead in zombie flicks.Trade Review"[Pitici] has put together a mathematics anthology gleaned from articles published in 2009 in a range of popular and scholarly sources. The collection is quite international in scope... This collection is more than just a set of reprints; the assembly from diverse and, in some cases, not easily accessible publications and the arrangement add value to this work."--Library Journal "Imagine for a moment that you had a friend who was a voracious reader of Math journals and periodicals. And, imagine that this friend had a knack for finding articles that were of interest to mathematicians and non-mathematicians alike by well-known writers and by new talent. Would you be interested in reading a few dozen of these articles? Mircea Pitici, editor of The Best Writing on Mathematics 2010 is such a friend, even if you've never met him... A nice set of stimulating articles that appeal to a wide audience."--Sol Lederman, Wild About Math! "As a mathematician engrossed in my own area ... I've been delighted to have this book in my house. One inevitably will not agree with every choice of work for inclusion, but it would be a dull book if it simply presented us with what we like. What is important is that it is varied and balanced, and contains the odd surprise."--Charles Eaton, LMS Newsletter "Mircea Pitici has succeeded in putting together a wonderful and varied bouquet of texts related to mathematics... I highly recommend this book to everyone with an interest in mathematics, whether they are professional mathematician, graduate or undergraduate students, teachers, or enthusiastic amateurs."--Stephen Buckley, Irish Math Society Bulletin "I would highly recommend this book as a good read to anyone with an interest in mathematics. Whether a professional mathematician, university or sixth form student, teacher, or recreational mathematician, there will be something there for you."--Steve Humble, Mathematics Today "I recommend this book to Gazette readers as enjoyable bedside reading."--Phill Schultz, Australian Math Society Gazette "[The Best Writing on Mathematics 2014] contributors are a fascinating and diverse bunch... [The] series should be lauded for Mercia Pitici's role as editor in not just selecting these essays but also their order and flow."-- Robert Schaefer, New York Journal of BooksTable of ContentsForeword by William P. Thurston xi Introduction by Mircea Pitici xv Mathematics Alive The Role of the Untrue in Mathematics by Chandler Davis 3 Desperately Seeking Mathematical Proof by Melvyn B. Nathanson 13 An Enduring Error by Branko Grunbaum 18 What Is Experimental Mathematics? By Keith Devlin 32 What Is Information-Based Complexity? By Henryk Woz'niakowski 37 What Is Financial Mathematics? By Tim Johnson 43 If Mathematics Is a Language, How Do You Swear in It? By David Wagner 47 Mathematicians and the Practice of Mathematics Birds and Frogs by Freeman Dyson 57 Mathematics Is Not a Game But ... by Robert Thomas 79 Massively Collaborative Mathematics by Timothy Gowers and Michael Nielsen 89 Bridging the Two Cultures: Paul Valery by Philip J. Davis 94 A Hidden Praise of Mathematics by Alicia Dickenstein 99 Mathematics and Its Applications Mathematics and the Internet: A Source of Enormous Confusion and Great Potential by Walter Willinger, David L. Alderson, and John C. Doyle 109 The Higher Arithmetic: How to Count to a Zillion without Falling Off the End of the Number Line by Brian Hayes 134 Knowing When to Stop: How to Gamble If You Must--The Mathematics of Optimal Stopping by Theodore P. Hill 145 Homology: An Idea Whose Time Has Come by Barry A. Cipra 158 Mathematics Education Adolescent Learning and Secondary Mathematics by Anne Watson 163 Accommodations of Learning Disabilities in Mathematics Courses by Kathleen Ambruso Acker, Mary W. Gray, and Behzad Jalali 175 Audience,Style and Criticism by David Pimm and Nathalie Sinclair 194 Aesthetics as a Liberating Force in Mathematics Education? By Nathalie Sinclair 206 Mathematics Textbooks and Their Potential Role in Supporting Misconceptions by Ann Kajander and Miroslav Lovric 236 Exploring Curvature with Paper Models by Howard T. Iseri 247 Intuitive vs Analytical Thinking: Four Perspectives by Uri Leron and Orit Hazzan 260 History and Philosophy of Mathematics Why Did Lagrange "Prove" the Parallel Postulate? By Judith V. Grabiner 283 Kronecker's Algorithmic Mathematics by Harold M. Edwards 303 Indiscrete Variations on Gian-Carlo Rota's Themes by Carlo Cellucci 311 Circle Packing: A Personal Reminiscence by Philip L. Bowers 330 Applying Inconsistent Mathematics by Mark Colyvan 346 Why Do We Believe Theorems? By Andrzej Pelc 358 Mathematics in the Media Mathematicians Solve 45-Year-Old Kervaire Invariant Puzzle by Erica Klarreich 373 Darwin: The Reluctant Mathematician by Julie Rehmeyer 377 Loves Me, Loves Me Not (Do the Math) by Steven Strogatz 380 The Mysterious Equilibrium of Zombies and Other Things Mathematicians See at the Movies by Samuel Arbesman 383 Strength in Numbers: On Mathematics and Musical Rhythm by Vijay Iyer 387 Math-hattan by Nick Paumgarten 391 Contributors 395 Acknowledgments 403 Credits 405

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Book SynopsisRecalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier - "Don't disturb my circles" - words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction.Trade Review"Editors Doxiadis and Mazur have compiled a collection of 15 essays that look at the many possible roles narrative can play in mathematics, which is usually considered far removed from storytelling... Circles Disturbed will be of special value to collections in history of mathematics, philosophy of mathematics, and mathematical pedagogy."--Choice "Circles Disturbed presents a cohesive narrative whose strength lies in helping each side to understand the other. It should encourage scientists to grasp the logic behind storytelling and literary critics to sense the allure of mathematics."--Mel Bayley, British Society for the History of Mathematics Bulletin "Well thought and well written and with a careful balance between erudition and down-to-earthness all through it, Circles Disturbed is a highly recommended reading for mathematicians and students of mathematics, as well as for anyone who wishes to better understand what it is to do mathematics and why they are done the way they are done."--Capi Corrales Rodriganez, European Mathematical Society "Circles Disturbed will spark interest in younger readers in the commonalities among these three disciplines as well as engage other readers. Further, readers with greater background in one or more topics can see the intra- and the intersections rather naturally and inquisitively. The diverse perspectives represented by the various authors are quite refreshing."--Farshid Safi, Mathematics TeacherTable of ContentsIntroduction vii Chapter 1: From Voyagers to Martyrs: Toward a Storied History of Mathematics 1 By AMIR ALEXANDER Chapter 2 Structure of Crystal, Bucket of Dust 52 By PETER GALISON Chapter 3: Deductive Narrative and the Epistemological Function of Belief in Mathematics: On Bombelli and Imaginary Numbers 79 By FEDERICA LANAVE Chapater 4: Hilbert on Theology and Its Discontents: The Origin Myth of Modern Mathematics 105 By COLIN MCLARTY Chapter 5: Do Androids Prove Theorems in Their Sleep? 130 By MICHAEL HARRIS Chapter 6: Visions, Dreams, and Mathematics 183 By BARRY MAZUR Chapter 7: Vividness in Mathematics and Narrative 211 By TIMOTHY GOWERS Chapter 8: Mathematics and Narrative: Why Are Stories and Proofs Interesting? 232 By BERNARD TEISSIER Chapter 9: Narrative and the Rationality of Mathematical Practice 244 By DAVID CORFIELD Chapter 10: A Streetcar Named (among Other Things) Proof: From Storytelling to Geometry, via Poetry and Rhetoric 281 By APOSTOLOS DOXIADIS Chapter 11: Mathematics and Narrative: An Aristotelian Perspective 389 By G .E .R . LLOYD Chapter 12: Adventures of the Diagonal: Non-Euclidean Mathematics and Narrative 407 By ARADY PLOTNITSKY Chapter 13: Formal Models in Narrative Analysis 447 By DAVID HERMAN Chapter 14: Mathematics and Narrative: A Narratological Perspective 481 By URI MARGOL N Chapter 15: Tales of Contingency, Contingencies of Telling: Toward an Algorithm of Narrative Subjectivity 508 By JAN CHRISTOPH MEISTER Contributors 541 Index 545

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Book SynopsisWhat is algebra? For some, it is an abstract language of x's and y's. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. This title considers how these two seemingly different types of algebra evolved and how they relate.Trade Review"An excellent book; its accurate historical and pedagogical purpose offers an accessible read for historians and mathematicians."--Raffaele Pisano, Metascience "Well written and engaging with a wealth of useful material and a substantial bibliography for further reading, this book is a valuable resource for anyone with a serious interest in the history of algebra. With Taming the Unknown, Victor Katz and Karen Parshall have created a comprehensive synthesis of recent research on the subject, accessible to mathematicians, historians of mathematics and anyone involved in the teaching of algebra."--Adrian Rice, BSHM Bulletin "The authors have ... pitched their writing perfectly for their intended audience. The broad outline of the story is expressed in clear prose, combined with a judicious use of that other 'native tongue' of the college mathematics graduate, symbolic algebra... There is an extensive bibliography presenting the more detailed historical research that has been carried out... You could base a really nice third-year course on this book."--John Hannah, AestimatioTable of ContentsAcknowledgments xi 1 Prelude: What Is Algebra? 1 Why This Book? 3 Setting and Examining the Historical Parameters 4 The Task at Hand 10 2 Egypt and Mesopotamia 12 Proportions in Egypt 12 Geometrical Algebra in Mesopotamia 17 3 The Ancient Greek World 33 Geometrical Algebra in Euclid's Elements and Data 34 Geometrical Algebra in Apollonius's Conics 48 Archimedes and the Solution of a Cubic Equation 53 4 Later Alexandrian Developments 58 Diophantine Preliminaries 60 A Sampling from the Arithmetica: The First Three Greek Books 63 A Sampling from the Arithmetica: The Arabic Books 68 A Sampling from the Arithmetica: The Remaining Greek Books 73 The Reception and Transmission of the Arithmetica 77 5 Algebraic Thought in Ancient and Medieval China 81 Proportions and Linear Equations 82 Polynomial Equations 90 Indeterminate Analysis 98 The Chinese Remainder Problem 100 6 Algebraic Thought in Medieval India 105 Proportions and Linear Equations 107 Quadratic Equations 109 Indeterminate Equations 118 Linear Congruences and the Pulverizer 119 The Pell Equation 122 Sums of Series 126 7 Algebraic Thought in Medieval Islam 132 Quadratic Equations 137 Indeterminate Equations 153 The Algebra of Polynomials 158 The Solution of Cubic Equations 165 8 Transmission, Transplantation, and Diffusion in the Latin West 174 The Transplantation of Algebraic Thought in the Thirteenth Century 178 The Diffusion of Algebraic Thought on the Italian Peninsula and Its Environs from the Thirteenth Through the Fifteenth Centuries 190 The Diffusion of Algebraic Thought and the Development of Algebraic Notation outside of Italy 204 9 The Growth of Algebraic Thought in Sixteenth-Century Europe 214 Solutions of General Cubics and Quartics 215 Toward Algebra as a General Problem-Solving Technique 227 10 From Analytic Geometry to the Fundamental Theorem of Algebra 247 Thomas Harriot and the Structure of Equations 248 Pierre de Fermat and the Introduction to Plane and Solid Loci 253 Albert Girard and the Fundamental Theorem of Algebra 258 Rene Descartes and The Geometry 261 Johann Hudde and Jan de Witt, Two Commentators on The Geometry 271 Isaac Newton and the Arithmetica universalis 275 Colin Maclaurin's Treatise of Algebra 280 Leonhard Euler and the Fundamental Theorem of Algebra 283 11 Finding the Roots of Algebraic Equations 289 The Eighteenth-Century Quest to Solve Higher-Order Equations Algebraically 290 The Theory of Permutations 300 Determining Solvable Equations 303 The Work of Galois and Its Reception 310 The Many Roots of Group Theory 317 The Abstract Notion of a Group 328 12 Understanding Polynomial Equations in n Unknowns 335 Solving Systems of Linear Equations in n Unknowns 336 Linearly Transforming Homogeneous Polynomials in n Unknowns: Three Contexts 345 The Evolution of a Theory of Matrices and Linear Transformations 356 The Evolution of a Theory of Invariants 366 13 Understanding the Properties of "Numbers" 381 New Kinds of "Complex" Numbers 382 New Arithmetics for New "Complex" Numbers 388 What Is Algebra?: The British Debate 399 An "Algebra" of Vectors 408 A Theory of Algebras, Plural 415 14 The Emergence of Modern Algebra 427 Realizing New Algebraic Structures Axiomatically 430 The Structural Approach to Algebra 438 References 449 Index 477

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Book SynopsisProvides key concepts and technologies underlying the dynamics, control, and guidance of fixed-wing unmanned aircraft, and enables students with an introductory-level background in controls or robotics to enter this important area. This title explores the essential underlying physics and sensors of unmanned air vehicles problems.Trade Review"It is very nicely written with a presentation style that engineers in industry will appreciate. Most of the mathematics involved is very straightforward and the results are presented in a very clear manner. This is a text that should be very useful to those working on unmanned aerial vehicles and may even be of interest to those working on unmanned land or marine vehicles."--Applied Control Technology ConsortiumTable of ContentsPreface xi Chapter 1 Introduction 1 1.1 System Architecture 1 1.2 Design Models 4 1.3 Design Project 6 Chapter 2 Coordinate Frames 8 2.1 RotationMatrices 9 2.2 MAV Coordinate Frames 12 2.3 Airspeed,Wind Speed, and Ground Speed 18 2.4 TheWind Triangle 20 2.5 Differentiation of a Vector 24 2.6 Chapter Summary 25 2.7 Design Project 27 Chapter 3 Kinematics and Dynamics 28 3.1 State Variables 28 3.2 Kinematics 30 3.3 Rigid-body Dynamics 31 3.4 Chapter Summary 37 3.5 Design Project 38 Chapter 4 Forces and Moments 39 4.1 Gravitational Forces 39 4.2 Aerodynamic Forces andMoments 40 4.3 Propulsion Forces andMoments 52 4.4 Atmospheric Disturbances 54 4.5 Chapter Summary 57 4.6 Design Project 58 Chapter 5 Linear Design Models 60 5.1 Summary of Nonlinear Equations of Motion 60 5.2 Coordinated Turn 64 5.3 Trim Conditions 65 5.4 Transfer Function Models 68 5.5 Linear State-space Models 77 5.6 Reduced-order Modes 87 5.7 Chapter Summary 91 5.8 Design Project 92 Chapter 6 Autopilot Design Using Successive Loop Closure 95 6.1 Successive Loop Closure 95 6.2 Saturation Constraints and Performance 97 6.3 Lateral-directional Autopilot 99 6.4 Longitudinal Autopilot 105 6.5 Digital Implementation of PID Loops 114 6.6 Chapter Summary 117 6.7 Design Project 118 Chapter 7 Sensors for MAVs 120 7.1 Accelerometers 120 7.2 Rate Gyros 124 7.3 Pressure Sensors 126 7.4 Digital Compasses 131 7.5 Global Positioning System 134 7.6 Chapter Summary 141 7.7 Design Project 141 Chapter 8 State Estimation 143 8.1 Benchmark Maneuver 143 8.2 Low-pass Filters 144 8.3 State Estimation by Inverting the Sensor Model 145 8.4 Dynamic-observer Theory 149 8.5 Derivation of the Continuous-discrete Kalman Filter 151 8.6 Attitude Estimation 156 8.7 GPS Smoothing 158 8.8 Chapter Summary 161 8.9 Design Project 162 Chapter 9 Design Models for Guidance 164 9.1 AutopilotModel 164 9.2 Kinematic Model of Controlled Flight 165 9.3 Kinematic Guidance Models 168 9.4 Dynamic Guidance Model 170 9.5 Chapter Summary 172 9.6 Design Project 173 Chapter 10 Straight-line and Orbit Following 174 10.1 Straight-line Path Following 175 10.2 Orbit Following 181 10.3 Chapter Summary 183 10.4 Design Project 185 Chapter 11 Path Manager 187 11.1 Transitions BetweenWaypoints 187 11.2 Dubins Paths 194 11.3 Chapter Summary 202 11.4 Design Project 204 Chapter 12 Path Planning 206 12.1 Point-to-Point Algorithms 207 12.2 Coverage Algorithms 220 12.3 Chapter Summary 223 12.4 Design Project 224 Chapter 13 Vision-guided Navigation 226 13.1 Gimbal and Camera Frames and Projective Geometry 226 13.2 Gimbal Pointing 229 13.3 Geolocation 231 13.4 Estimating Target Motion in the Image Plane 234 13.5 Time to Collision 238 13.6 Precision Landing 240 13.7 Chapter Summary 244 13.8 Design Project 245 APPENDIX A: Nomenclature and Notation 247 APPENDIX B: Quaternions 254 B.1 Quaternion Rotations 254 B.2 Aircraft Kinematic and Dynamic Equations 255 B.3 Conversion Between Euler Angles and Quaternions 259 APPENDIX C: Animations in Simulink 260 C.1 Handle Graphics inMatlab 260 C.2 Animation Example: Inverted Pendulum 261 C.3 Animation Example: Spacecraft Using Lines 263 C.4 Animation Example: Spacecraft Using Vertices and Faces 268 APPENDIX D: Modeling in Simulink Using S-Functions 270 D.1 Example: Second-order Differential Equation 270 APPENDIX E: Airframe Parameters 275 E.1 Zagi Flying Wing 275 E.2 Aerosonde UAV 276 APPENDIX F: Trim and Linearization in Simulink 277 F.1 Using the Simulink trim Command 277 F.2 Numerical Computation of Trim 278 F.3 Using the Simulink linmod Command to Generate a State-space Model 282 F.4 Numerical Computation of State-space Model 284 APPENDIX G: Essentials from Probability Theory 286 APPENDIX H: Sensor Parameters 288 H.1 Rate Gyros 288 H.2 Accelerometers 288 H.3 Pressure Sensors 289 H.4 Digital Compass/Magnetometer 289 H.5 GPS 290 Bibliography 291 Index 299

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Book SynopsisTrade Review"I recommend the book to everyone who is studying and fascinated by statistics."---Singalakha Menziwa, Mathemafrica"Steven J. Miller’s The Probability Lifesaver presents, as its subtitle claims, 'all the tools you need to understand chance' in a clear, straightforward manner. . . . For the students that have a good understanding of Calculus, the combination of the probability discussions along with the calculus behind these topics is very beneficial." * MAA Reviews *"The breadth of the book’s coverage and its clear, informal tone in addressing highly formal problems remind one of a friendly professor offering unlimited office hours, and the book will be a highly accessible supplement for students working through another, more conventional text. . . . [This is] a volume that deserves to be widely known in educational circles and will likely find its way to the shelves of practicing statisticians who wish to probe below the surface of fundamental theorems that they have learned by rote."---H. Van Dyke Parunak, Computing Reviews

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Book SynopsisWhenever Forty-second Street in New York is temporarily closed, traffic doesn't gridlock but flows more smoothly - why is that? Or consider that cities that build new roads can experience dramatic increases in traffic congestion - how is this possible? This title includes some of these counterintuitive mathematical occurrences.Trade Review"Havil once again explores a variety of mathematical results and problems that at first appear to be self-contradictory, or stated in such a way that no solution could exist. In each case, he then either sketches a proof of why the result is not contradictory, or explains the solution to the seemingly unsolvable problem ... Like a magician revealing secrets, Havil maintains this sense through most chapters, dropping the punch line at just the right moment."--J.T. Noonan, Choice "This sequel to the author's book Nonplussed! supplies another set of brain-stretching problems and ideas. Its subtitle is 'Surprising Solutions to Counterintuitive Conundrums'; the surprise often consisting of the fact that it is possible to obtain a solution at all! ... This is another excellent book by Havil, following in the Martin Gardner tradition."--Alan Stevens, Mathematics Today "Julian Havil has quietly joined the ranks of the very best writers of popular mathematics. His two volume set Impossible? and Nonplussed! Mathematical Proof of Implausible Ideas not only belong in every library, but in the hands of every young person interested in mathematics and especially in the hands of their teachers."--John J. Watkins, Mathematical Intelligencer "Impossible? is an immensely thought-provoking book. Even if you skim or skip the more complex abstract math, you may have a hard time letting these puzzles go, so strongly do they flout common sense. You'll just have to do your best to put them our of your mind when you need to get some sleep, but if the situation ever arises, be sure to take Monty up on his offer."--Ray Bert, Civil Engineering "I would highly recommend this book as a reference for the mathematician who likes recreational mathematics, or as a good read for the recreational enthusiast with a penchant for more rigor."--Blair Madore, MAA ReviewsTable of ContentsAcknowledgments xi Introduction 1 Chapter 1: It's Common Knowledge 3 Chapter 2: Simpson's Paradox 11 Chapter 3: The Impossible Problem 21 Chapter 4: Braess's Paradox 31 Chapter 5: The Power of Complex Numbers 39 Chapter 6: Bucking the Odds 50 Chapter 7: Cantor's Paradise 68 Chapter 8: Gamow-Stern Elevators 82 Chapter 9: The Toss of a Coin 88 Chapter 10: Wild-Card Poker 103 Chapter 11: Two Series 113 Chapter 12: Two Card Tricks 131 Chapter 13: The Spin of a Needle 146 Chapter 14: The Best Choice 165 Chapter 15: The Power of Powers 176 Chapter 16: Benford's Law 190 Chapter 17: Goodstein Sequences 201 Chapter 18: The Banach-Tarski Paradox 210 The Motifs 217 Appendix 221 Index 233

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