Mathematics Books

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Book SynopsisAll the Math Your 4th Grader Needs to SucceedThis book will help your elementary school student develop the math skills needed to succeed in the classroom and on standardized tests. The user-friendly, full-color pages are filled to the brim with engaging activities for maximum educational value. The book includes easy-to-follow instructions, helpful examples, and tons of practice problems to help students master each concept, sharpen their problem-solving skills, and build confidence.Features include:â A guide that outlines national standards for Grade 4â Concise lessons combined with lot of practice that promote better scoresâin class and on achievement testsâ A pretest to help identify areas where students need more workâ End-of-chapter tests to measure studentsâ progressâ A helpful glossary of key terms used in the bookâ More than 1,000 math problems with answersTopics covered:â Adding and

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Book SynopsisAll the Math Your 5th Grader Needs to SucceedThis book will help your elementary school student develop the math skills needed to succeed in the classroom and on standardized tests. The user-friendly, full-color pages are filled to the brim with engaging activities for maximum educational value. The book includes easy-to-follow instructions, helpful examples, and tons of practice problems to help students master each concept, sharpen their problem-solving skills, and build confidence.Features include:â A guide that outlines national standards for Grade 5â Concise lessons combined with lot of practice that promote better scoresâin class and on achievement testsâ A pretest to help identify areas where students need more workâ End-of-chapter tests  to measure studentsâ progressâ A helpful glossary of key terms used in the bookâ More than 1,000 math problems with answersTopics covered:â Opera

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Book SynopsisTrade Review"Excellent. . . . [A]n exceptionally well-informed, very readable and clear introduction to the subject. If you are looking for an entry point into the extensive philosophical literature on the nature of mathematics, look no further."---A. C. Paseau, Mathematical Gazette"Linnebo's slender volume is an admirable addition to the many existing books on the philosophy of mathematics. It is clear, concise, and well written. . . . All in all, this is an excellent introduction to the philosophy of mathematics and should be seriously considered by any individual interested in the subject." * Choice *"This is a thought-provoking book, and is a useful addition to the textbook literature on this subject." * MAA Reviews *"This book provides a nice lay of the land for anyone interested in contemporary philosophy of mathematics."---Gregory Lavers, Philosophia Mathematica"[This book] is very, very good. Superbly clear, concise, well organised, it gives not only a very accessible introduction but also takes the reader all the way to the cutting edge of what philosophers are doing in the philosophy of mathematics. Above all, Linnebo writes as a fully engaged philosopher and makes his preferred choice of philosophical position clear. But this is no mere polemic: I felt he clearly and forcefully presents the strengths and weaknesses of all the philosophical positions he discusses."---Henri Laurie, Mathemafrica"[A] very readable and . . . superb introduction to the philosophy of mathematics."---Jason Wakefield, Avello Publishing JournalTable of ContentsAcknowledgments vii Introduction 1 1 Mathematics as a Philosophical Challenge 4 2 Frege's Logicism 21 3 Formalism and Deductivism 38 4 Hilbert's Program 56 5 Intuitionism 73 6 Empiricism about Mathematics 88 7 Nominalism 101 8 Mathematical Intuition 116 9 Abstraction Reconsidered 126 10 The Iterative Conception of Sets 139 11 Structuralism 154 12 The Quest for New Axioms 170 Concluding Remarks 183 Bibliography 189 Index 199

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Book SynopsisTeacher Materials include: Presentation Books include a Guide section containing information for presenting exercises, correcting mistakes, and administering the pre-skill and placement tests. There is also a Presentation section that contains detailed lessons plans. Answer Key Booklets quickly and easily compare students' work with the actual calculations and word problem results.

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Book SynopsisThis substantially revised edition of Wittgenstein's Remarks on the Foundations of Mathematics contains one section, an essay of fifty pages, not previously published, as well as considerable additions to others sections.Table of ContentsPreface to The Revised Edition Part I Circa 1937-1938 Part II 1938 Part III 1939-40 Part IV 1942-1944 Part V 1942-1944 Part VI ca. 1943/1944 Part VII 1941 and 1944 Index

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Book SynopsisTrade Review"A volume that should be on every scientist's reading list."—Barbara Kiser, Nature"A terrific book."—Mathematics Magazine"Fun and entertaining to read."—MAA Reviews"To anyone with an interest in probability or statistics, this is a book you must read. . . . [It] is far-ranging and can be read at many levels, from the novice to the expert. It is also thoroughly engaging."—David M. Bressoud, UMAP Journal"A very enriching journey. Your vision will be broadened."—Adhemar Bultheel, European Mathematical Society"A great book for anyone who wants to understand some of the central tenets of probability, how they were discovered, and how they can be tamed in our day-to-day lives."—ZME Science

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Book SynopsisThis hands-on introduction to numerical geodynamic modelling provides a solid grounding in the necessary mathematical theory and techniques, including continuum mechanics and partial differential equations, before introducing key numerical modelling methods and applications. Fully updated, this second edition includes four completely new chapters covering the most recent advances in modelling inertial processes, seismic cycles and fluid-solid interactions, and the development of adaptive mesh refinement algorithms. Many well-documented, state-of-the-art visco-elasto-plastic 2D models are presented, which allow robust modelling of key geodynamic processes. Requiring only minimal prerequisite mathematical training, and featuring over sixty practical exercises and ninety MATLAB examples, this user-friendly resource encourages experimentation with geodynamic models. It is an ideal introduction for advanced courses and can be used as a self-study aid for graduates seeking to master geodynamic modelling for their own research projects.Trade Review'A great introduction to computational geodynamics with vivid examples, hands-on exercises and step-by-step derivations of formulas. Even better than the first edition.' Sascha Brune, Das Helmholtz-Zentrum Potsdam – Deutsches GeoForschungsZentrum'This book is so much more than an introduction to geodynamic modelling. Taras Gerya opens the world of geodynamic experiments by taking the reader through a carefully designed set of hands-on programming exercises that will convince you that modelling is not terribly complicated, but a process to logically follow through. Go ahead and get started!' Susanne Buiter, Geological Survey of Norway'This comprehensive textbook challenges all solid Earth scientists to give geodynamic modelling a try in a hands-on, empowering style. The new edition covers even more ground, including cutting-edge topics. A great achievement, and the community will be the better for it.' Thorsten Becker, University of Texas, AustinPraise for the first edition: '… the book provides excellent value for those wanting an introduction to the field. Anyone who works carefully through this book and completes all the exercises should be well prepared for further work in geodynamic modelling.' GeoscientistPraise for the first edition: 'The book is written in a light and engaging style such that it deserves a place on the recommended reading list of any undergraduate or Masters course that includes geodynamics. Additionally, it will be a valuable resource for any geoscientist who wants to include geodynamic modelling within their research activities.' Geological MagazineTable of Contents1. The continuity equation; 2. Density and gravity; 3. Numerical solutions of partial differential equations; 4. Stress and strain; 5. The momentum equation; 6. Viscous rheology of rocks; 7. Numerical solutions of the momentum and continuity equations; 8. The advection equation and marker-in-cell method; 9. The heat conservation equation; 10. Numerical solution of the heat conservation equation; 11. 2D thermomechanical code structure; 12. Elasticity and plasticity; 13. 2D implementation of visco-elasto-plasticity; 14. 2D thermomechanical modelling of inertial processes; 15. Seismo-thermomechanical modelling; 16. Hydro-thermomechanical modelling; 17. Adaptive mesh refinement; 18. The multigrid method; 19. Programming of 3D problems; 20. Numerical benchmarks; 21. Design of 2D numerical geodynamic models; Epilogue: outlook; Appendix: MATLAB® program examples; References; Index.

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Book SynopsisAubrey Clayton traces the history of the flaw that underlies modern statistics, beginning with the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Ranging across math, philosophy, and culture, Bernoulli’s Fallacy explains why something has gone wrong with how we use data—and how to fix it.Trade ReviewAn entertaining mix of history and science. -- Andrew Gelman, Columbia UniversityI like it! Anything that gets people thinking about the uses and abuses of statistics is important and Clayton's book does just this. Fifty years ago E. T. Jaynes opened my eyes to the importance of Bayesian ideas in the real world and this readable account brings these ideas up to date. -- Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford UniversityThis story of the 'statistics wars' is gripping, and Clayton is an excellent writer. He argues that scientists have been doing statistics all wrong, a case that should have profound ramifications for medicine, biology, psychology, the social sciences, and other empirical disciplines. Few books accessible to a broad audience lay out the Bayesian case so clearly. -- Eric-Jan Wagenmakers, coauthor of Bayesian Cognitive Modeling: A Practical CourseAs well-written as it is fascinating, and for my money is the best single-volume work describing and contributing to the debates in modern statistics on the shelves today. It can be profitably read by those with no background in the field, but will surely contain new ideas for experts as well. Having read the book, I myself will never think about statistics the same way. -- Dominic Klyve * American Mathematical Monthly *A timely story, well-told. It makes a compelling case for a shake-up in the world of statistics that may just be strident enough to spark change. * MAA Reviews *The author writes with style and humor and tries to make the read minimally pedantic. * Non-Stop Reader *The book is highly accessible. . . . Even readers who ultimately disagree with the author's position will still benefit from reading this text. * Choice *Bernoulli’s Fallacy will be of use to readers of any mathematical background who wish to understand not only the math but also the motivations behind the rising Bayesian wave. It is a vivid, nontechnical look at the bees in the contemporary statistician’s bonnet. * H-Sci-Med_Tech *Table of ContentsPrefaceAcknowledgmentsIntroduction1. What Is Probability?2. The Titular Fallacy3. Adolphe Quetelet’s Bell Curve Bridge4. The Frequentist Jihad5. The Quote-Unquote Logic of Orthodox Statistics6. The Replication Crisis/Opportunity7. The Way OutNotesBibliographyIndex

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Book SynopsisEssays on Game Theory is a unique collection of seven of John Nash's essays which highlight his pioneering contribution to game theory in economics. Featuring a comprehensive introduction by Ken Binmore which explains and summarizes John Nash's achievements in the field of non-cooperative and cooperative game theory, this book will be an indispensable reference for scholars and will be welcomed by those with an interest in game theory and its applications to the social sciences.Trade Review'This short volume is very welcome . . . Most importantly, on pages 32-33, the volume reprints as an appendix to the journal article based on Nash's Princeton doctoral dissertation on non-cooperative games a section of the thesis on "motivation and interpretation" that was omitted from the article. An editorial note remarks mildly that "The missing section is of considerable interest". This section, not available in any other published source, makes the present volume indispensable for research libraries . . . Nash's Essays on Game Theory, dating from his years as a Princeton graduate student . . . has a lasting impact on economics and related fields unmatched by any series of articles written in such a brief time . . . To economists, his name will always bring to mind his game theory papers of the early 1950s. It is good to have these conveniently reprinted in this volume.'Table of ContentsContents: Introduction (K. Binmore) 1. The Bargaining Problem 2. Equilibrium Points in N-Person Games 3. A Simple Three-Person Poker Game 4. Non-cooperative Games 5. Two Person Cooperative Games 6. A Comparison of Treatments of a Duopoly Situation 7. Some Experimental n-Person Games Index

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Book SynopsisCompletely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance.Trade Review“As supplementary reading for a second course or as s comprehensive (!) resource for the general theory of processes aimed at Ph. D. students and scholars, this second edition will stay a valuable resource.” (René L. Schilling, Mathematical Reviews, October, 2016)“This is a fundamental book in modern stochastic calculus and its applications: rich contents, well structured material, comprehensive coverage of all significant results given with complete proofs and well illustrated by examples, carefully written text. Hence, there are more than enough reasons to strongly recommend the book to a wide audience. Among them, there are good and motivated graduate university students. … Also, the book is an excellent reference book.” (Jordan M. Stoyanov, zbMATH 1338.60001, 2016)Table of ContentsPart I: Measure Theoretic Probability.- Measure Integral.- Probabilities and Expectation.- Part II: Stochastic Processes.- Filtrations, Stopping Times and Stochastic Processes.- Martingales in Discrete Time.- Martingales in Continuous Time.- The Classification of Stopping Times.- The Progressive, Optional and Predicable -Algebras.- Part III: Stochastic Integration.- Processes of Finite Variation.- The Doob-Meyer Decomposition.- The Structure of Square Integrable Martingales.- Quadratic Variation and Semimartingales.- The Stochastic Integral.- Random Measures.- Part IV: Stochastic Differential Equations.- Ito's Differential Rule.- The Exponential Formula and Girsanov's Theorem.- Lipschitz Stochastic Differential Equations.- Markov Properties of SDEs.- Weak Solutions of SDEs.- Backward Stochastic Differential Equations.- Part V: Applications.- Control of a Single Jump.- Optimal Control of Drifts and Jump Rates.- Filtering. Part VI: Appendices.

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Book Synopsis1, 1, 2, 3, 5, 8, 13, 21, 34. . . Look carefully. Do you see the pattern? Each number above is the sum of the two numbers before it. Though most of us are unfamiliar with it, this numerical series, called the Fibonacci sequence, is part of a code that can be found everywhere in nature. Count the petals on a flower or the peas in a peapod. The numbers are all part of the Fibonacci sequence. In Wild Fibonacci, readers will discover this mysterious code in a special shape called an equiangular spiral. Why so special? It mysteriously appears in the natural world: a sundial shell curves to fit the spiral. So does a parrot''s beak. . . a hawk''s talon. . . a ram''s horn. . . even our own human teeth! Joy Hulme provides a clear and accessible introduction to the Fibonacci sequence and its presence in the animal world.

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Book SynopsisFor centuries, the sorites paradox has spurred philosophers to think and argue about the problem of vagueness. This volume offers a guide to the paradox which is both an accessible survey and an expositionof the state of the art, with a chapter-by-chapter presentation of all of the main solutions to the paradox and of all its main areas of influence. Each chapter offers a gentle introduction to its topic, gradually building up to a final discussion of some open problems. Students will find a comprehensive guide to the fundamentals of the paradox, together withlucid explanations of the challenges it continues to raise. Researchers will find exciting new ideas and debates on the paradox.Trade Review'In this comprehensive and systematic collection, Oms (Univ. of Barcelona, Spain) and Zardini (Univ. of Lisbon, Portugal) provide nine excellent papers that characterize, and provide possible solutions for, the paradox's vagueness and another five papers that assess the influence of the sorites paradox's influence in philosophy, linguistics, and psychology … Released in the 'Classic Philosophical Arguments' series, this is the most outstanding treatment of the topic presently available.' L. C. Archie, ChoiceTable of ContentsList of contributors; Acknowledgements; Prelude; An introduction to the sorites paradox Sergi Oms and Elia Zardini; Part I. Solutions to the Sorites Paradox: 1. Epistemicism and the sorites paradox Ofra Magidor; 2. Supervaluationism, subvaluationism and the sorites paradox Pablo Cobreros and Luca Tranchini; 3. Contextualism and the sorites paradox Inga Bones and Diana Raffman; 4. Incoherentism and the sorites paradox Matti Eklund; 5. Intuitionism and the sorites paradox Crispin Wright; 6. Rejection of excluded middle and the sorites paradox Scott Soames; 7. Dialetheism and the sorites paradox Graham Priest; 8. Degree theory and the sorites paradox Francesco Paoli; 9. Non-transitivism and the sorites paradox Elia Zardini; Part II. The Influence of the Sorites Paradox: 10. The sorites paradox in philosophy of logic Sergi Oms; 11. The sorites paradox in metaphysics Irem Kurtsal; 12. The sorites paradox in practical philosophy Hrafn Asgeirsson; 13. The sorites paradox in linguistics Chris Kennedy; 14. The sorites paradox in psychology Paul Égré, David Ripley and Steven Verheyen; Coda: 15. The pre-analytic history of the sorites paradox Ricardo Santos; References; Index.

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Book SynopsisMake the most of R's extensive toolset R Projects For Dummies offers a unique learn-by-doing approach. You will increase the depth and breadth of your R skillset by completing a wide variety of projects. By using R's graphics, interactive, and machine learning tools, you'll learn to apply R's extensive capabilities in an array of scenarios. The depth of the project experience is unmatched by any other content online or in print. And you just might increase your statistics knowledge along the way, too! R is a free tool, and it's the basis of a huge amount of work in data science. It's taking the place of costly statistical software that sometimes takes a long time to learn. One reason is that you can use just a few R commands to create sophisticated analyses. Another is that easy-to-learn R graphics enable you make the results of those analyses available to a wide audience. This book will help you sharpen your skills by applying them in the context of projects with R, including dashbTable of ContentsIntroduction 1 About This Book 2 Part 1: The Tools of the Trade 2 Part 2: Interacting with a User 2 Part 3: Machine Learning 2 Part 4: Large(ish) Data Sets 2 Part 5: Maps and Images 2 Part 6: The Part of Tens 3 What You Can Safely Skip 3 Foolish Assumptions 3 Icons Used in This Book 3 Beyond the Book 4 Where to Go from Here 4 Part 1: the Tools of the Trade 5 Chapter 1: R: What It Does and How It Does It 7 Getting R 7 Getting RStudio 8 A Session with R 11 The working directory 11 Getting started 12 R Functions 15 User-Defined Functions 16 Comments 18 R Structures 18 Vectors 18 Numerical vectors 19 Matrices 21 Lists 24 Data frames 25 Of for Loops and if Statements 28 Chapter 2: Working with Packages 31 Installing Packages 31 Examining Data 33 Heads and tails 33 Missing data 33 Subsets 34 R Formulas 35 More Packages 36 Exploring the tidyverse 37 Chapter 3: Getting Graphic 43 Touching Base 43 Histograms 44 Density plots 45 Bar plots 47 Grouping the bars 49 Quick Suggested Project 51 Pie graphs 53 Scatterplots 53 Scatterplot matrix 55 Box plots 56 Graduating to ggplot2 57 How it works 58 Histograms 59 Bar plots 61 Grouped bar plots 62 Grouping yet again 64 Scatterplots 67 The plot thickens 68 Scatterplot matrix 72 Box plots 73 Part 2: Interacting with a User 77 Chapter 4: Working with a Browser 79 Getting Your Shine On 79 Creating Your First shiny Project 80 The user interface 83 The server 84 Final steps 85 Getting reactive 86 Working with ggplot 89 Changing the server 90 A few more changes 92 Getting reactive with ggplot 94 Another shiny Project 96 The base R version 97 The ggplot version 104 Suggested Project 106 Chapter 5: Dashboards — How Dashing! 107 The shinydashboard Package 107 Exploring Dashboard Layouts 108 Getting started with the user interface 109 Building the user interface: Boxes, boxes, boxes 110 Lining up in columns 117 A nice trick: Keeping tabs 121 Suggested project: Add statistics 125 Suggested project: Place valueBoxes in tabPanels 126 Working with the Sidebar 126 The user interface 128 The server 131 Suggested project: Relocate the slider 133 Interacting with Graphics 135 Clicks, double-clicks, and brushes — oh, my! 135 Why bother with all this? 138 Suggested project: Experiment with airquality 141 Part 3: Machine Learning 143 Chapter 6: Tools and Data for Machine Learning Projects 145 The UCI (University of California-Irvine) ML Repository 146 Downloading a UCI dataset 146 Cleaning up the data 148 Exploring the data 150 Exploring relationships in the data 152 Introducing the Rattle package 157 Using Rattle with iris 159 Getting and (further) exploring the data 159 Finding clusters in the data 162 Chapter 7: Decisions, Decisions, Decisions 167 Decision Tree Components 167 Roots and leaves 168 Tree construction 168 Decision Trees in R 169 Growing the tree in R 169 Drawing the tree in R 171 Decision Trees in Rattle 173 Creating the tree 174 Drawing the tree 175 Evaluating the tree 176 Project: A More Complex Decision Tree 177 The data: Car evaluation 177 Data exploration 179 Building and drawing the tree 180 Evaluating the tree 181 Quick suggested project: Understanding the complexity parameter 181 Suggested Project: Titanic 182 Chapter 8: Into the Forest, Randomly 185 Growing a Random Forest 185 Random Forests in R 187 Building the forest 187 Evaluating the forest 189 A closer look 190 Plotting error 191 Plotting importance 193 Project: Identifying Glass 194 The data 194 Getting the data into Rattle 195 Exploring the data 196 Growing the random forest 198 Visualizing the results 198 Suggested Project: Identifying Mushrooms 200 Chapter 9: Support Your Local Vector 201 Some Data to Work With 201 Using a subset 202 Defining a boundary 202 Understanding support vectors 203 Separability: It’s Usually Nonlinear 205 Support Vector Machines in R 207 Working with e1071 207 Working with kernlab 212 Project: House Parties 214 Reading in the data 216 Exploring the data 217 Creating the SVM 218 Evaluating the SVM 220 Suggested Project: Titanic Again 220 Chapter 10: K-Means Clustering 221 How It Works 221 K-Means Clustering in R 223 Setting up and analyzing the data 223 Understanding the output 224 Visualizing the clusters 225 Finding the optimum number of clusters 226 Quick suggested project: Adding the sepals 229 Project: Glass Clusters 231 The data 231 Starting Rattle and exploring the data 232 Preparing to cluster 233 Doing the clustering 234 Going beyond Rattle 234 Suggested Project: A Few Quick Ones 235 Visualizing data points and clusters 235 The optimum number of clusters 236 Adding variables 236 Chapter 11: Neural Networks 237 Networks in the Nervous System 237 Artificial Neural Networks 238 Overview 238 Input layer and hidden layer 239 Output layer 240 How it all works 240 Neural Networks in R 241 Building a neural network for the iris data frame 241 Plotting the network 243 Evaluating the network 244 Quick suggested project: Those sepals 245 Project: Banknotes 245 The data 245 Taking a quick look ahead 246 Setting up Rattle 247 Evaluating the network 249 Going beyond Rattle: Visualizing the network 249 Suggested Projects: Rattling Around 251 Part 4: Large(ish) Data Sets 253 Chapter 12: Exploring Marketing 255 Project: Analyzing Retail Data 255 The data 256 RFM in R 257 Enter Machine Learning 265 K-means clustering 265 Working with Rattle 267 Digging into the clusters 268 The clusters and the classes 270 Quick suggested project 271 Suggested Project: Another Data Set 272 Chapter 13: From the City That Never Sleeps 275 Examining the Data Set 275 Warming Up 276 Glimpsing and viewing 276 Piping, filtering, and grouping 277 Visualizing 279 Joining 280 Quick Suggested Project: Airline names 283 Project: Departure Delays 283 Adding a variable: weekday 283 Quick Suggested Project: Analyze weekday differences 284 Delay, weekday, and airport 285 Delay and flight duration 287 Suggested Project: Delay and Weather 289 Part 5: Maps and Images 291 Chapter 14: All Over the Map 293 Project: The Airports of Wisconsin 293 Dispensing with the preliminaries 293 Getting the state geographic data 294 Getting the airport geographic data 295 Plotting the airports on the state map 298 Quick Suggested Project: Another source of airport geographic info 299 Suggested Project 1: Map Your State 299 Suggested Project 2: Map the Country 299 Plotting the state capitals 301 Plotting the airports 302 Chapter 15: Fun with Pictures 305 Polishing a Picture: It’s magick! 305 Reading the image 306 Rotating, flipping, and flopping 307 Annotating 308 Combining transformations 309 Quick suggested project: Three F’s 309 Combining images 310 Animating 311 Making your own morphs 312 Project: Two Legends in Search of a Legend 313 Getting Stan and Ollie 313 Combining the boys with the background 314 Explaining image_apply() 314 Getting back to the animation 316 Suggested Project: Combine an Animation with a Plot 316 Part 6: the Part of Tens 319 Chapter 16: More Than Ten Packages for Your R Projects 321 Machine Learning 321 Databases 322 Maps 322 Image Processing 324 Text Analysis 324 Chapter 17: More than Ten Useful Resources 327 Interacting with Users 327 Machine Learning 328 Databases 328 Maps and Images 329 Index 331

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Book SynopsisThis volume presents topics in probability theory covered during a first-year graduate course given at the Courant Institute of Mathematical Sciences, USA. The necessary background material in measure theory is developed, including all the standard topics.Table of ContentsMeasure theory; Weak convergence; Independent sums; Dependent random variables; Martingales; Stationary stochastic processes; Dynamic programming and filtering; Bibliography; Index

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Book SynopsisLeonhard Euler's polyhedron formula describes the structure of many objects - from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. This title tells the story of this indispensable mathematical idea.Trade ReviewWinner of the 2010 Euler Book Prize, Mathematical Association of America One of Choice's Outstanding Academic Titles for 2009 "The author has achieved a remarkable feat, introducing a naive reader to a rich history without compromising the insights and without leaving out a delicious detail. Furthermore, he describes the development of topology from a suggestion by Gottfried Leibniz to its algebraic formulation by Emmy Noether, relating all to Euler's formula. This book will be valuable to every library with patrons looking for an awe-inspiring experience."--Choice "This is an excellent book about a great man and a timeless formula."--Charles Ashbacher, Journal of Recreational Mathematics "I liked Richeson's style of writing. He is enthusiastic and humorous. It was a pleasure reading this book, and I recommend it to everyone who is not afraid of mathematical arguments and has ever wondered what this field of 'rubbersheet geometry' is about. You will not be disappointed."--Jeanine Daems, Mathematical Intelligencer "The book is a pleasure to read for professional mathematicians, students of mathematicians or anyone with a general interest in mathematics."--European Mathematical Society Newsletter "I found much more to like than to criticize in Euler's Gem. At its best, the book succeeds at showing the reader a lot of attractive mathematics with a well-chosen level of technical detail. I recommend it both to professional mathematicians and to their seatmates."--Jeremy L. Martin, Notices of the AMS "I highly recommend this book for teachers interested in geometry or topology, particularly for university faculty. The examples, proofs, and historical anecdotes are interesting, informative, and useful for encouraging classroom discussions. Advanced students will also glimpse the broad horizons of mathematics by reading (and working through) the book."--Dustin L. Jones, Mathematics Teacher "The book should interest non-mathematicians as well as mathematicians. It is written in a lively way, mathematical properties are explained well and several biographical details are included."--Krzysztof Ciesielski, Mathematical ReviewsTable of ContentsPreface ix Introduction 1 Chapter 1: Leonhard Euler and His Three "Great" Friends 10 Chapter 2: What Is a Polyhedron? 27 Chapter 3: The Five Perfect Bodies 31 Chapter 4: The Pythagorean Brotherhood and Plato's Atomic Theory 36 Chapter 5: Euclid and His Elements 44 Chapter 6: Kepler's Polyhedral Universe 51 Chapter 7: Euler's Gem 63 Chapter 8: Platonic Solids, Golf Balls, Fullerenes, and Geodesic Domes 75 Chapter 9: Scooped by Descartes? 81 Chapter 10: Legendre Gets It Right 87 Chapter 11: A Stroll through Konigsberg 100 Chapter 12: Cauchy's Flattened Polyhedra 112 Chapter 13: Planar Graphs, Geoboards, and Brussels Sprouts 119 Chapter 14: It's a Colorful World 130 Chapter 15: New Problems and New Proofs 145 Chapter 16: Rubber Sheets, Hollow Doughnuts, and Crazy Bottles 156 Chapter 17: Are They the Same, or Are They Different? 173 Chapter 18: A Knotty Problem 186 Chapter 19: Combing the Hair on a Coconut 202 Chapter 20: When Topology Controls Geometry 219 Chapter 21: The Topology of Curvy Surfaces 231 Chapter 22: Navigating in n Dimensions 241 Chapter 23: Henri Poincare and the Ascendance of Topology 253 Epilogue The Million-Dollar Question 265 Acknowledgements 271 Appendix A Build Your Own Polyhedra and Surfaces 273 Appendix B Recommended Readings 283 Notes 287 References 295 Illustration Credits 309 Index 311

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Book SynopsisTrade ReviewWinner of the 2016 PROSE Award in Mathematics, Association of American Publishers One of Choice's Outstanding Academic Titles for the Year Winner of the 2016 PROSE Award in Mathematics, Association of American Publishers One of Choice's Outstanding Academic Titles for 2015 "Mathematics without Apologies is a kaleidoscope of philosophical, sociological, historical and literary perspectives on what mathematicians do, and why."--Amir Alexander, Nature "A wry and insightful look at what being a pure mathematician is all about, as seen from the inside."--Steven Strogatz, Physics Today "If you are interested at all in what mathematics really is and what the best mathematicians really do (and you're up for an intellectual challenge), I highly recommend that you get a copy and set some time aside for delving into this unusual book... Harris manages to move back and forth between the deepest ideas about mathematics at the frontiers of the subject, insightful takes on the sociology of mathematical research, and a variety of topics pursued in a sometimes gonzo version of post-modern academic style. You will surely sometimes be baffled, but definitely will come away knowing about many things you'd never heard of before, and with a lot of new ideas to think about."--Peter Woit, Not Even Wrong "Harris is the kind of mathematician one hopes to meet at an intimate dinner party. By sharing his professional and personal relationship to mathematics, [he] links art, philosophy, music, and literature to academic culture and research problems."--Library Journal "Extraordinary, extravagant... Harris is a polyglot, deeply learned. Threading through his remarkable book, unifying it, is Hardy's lament regarding whether a pure mathematician can make a claim that the vocation has a philosophically 'useful' purpose. Harris's reply is multivalent, persuasive, and profound. A book to be read and then read again."--Choice "The erudition displayed by Harris in this book is amazing... The satisfaction it gives is more than rewarding."--A. Bultheel, Adhemar Bultheel Blog "This book is a rich tapestry interweaving various aspects of culture and tradition--social, economic, religious, aesthetic--in an attempt to explicate the three basic philosophical questions underlying mathematics as a human endeavor: the What, Why and How of it."--Swami Vidyanathananda, Prabuddha Bharata "Michael Harris is more than a mathematician; he is a Parisian intellectual."--Brendan Larvor, London Mathematical Society Newsletter "Even apprentice number theorists can understand and enjoy this well-written book. Harris's theories are coherent and rational, and he provides lay readers clarity into what contemporary mathematicians really do."--Bernadette Trainer, Mathematics TeacherTable of ContentsPreface ix Acknowledgments xix Part 1 Chapter 1. Introduction: The Veil 3 Chapter 2. How I Acquired Charisma 7 Chapter alpha. How to Explain Number Theory at a Dinner Party 41 (First Session: Primes) 43 Chapter 3. Not Merely Good, True, and Beautiful 54 Chapter 4. Megaloprepeia 80 Chapter ss. How to Explain Number Theory at a Dinner Party 109 (Second Session: Equations) 109 Bonus Chapter 5. An Automorphic Reading of Thomas Pynchon's Against the Day (Interrupted by Elliptical Reflections on Mason & Dixon) 128 Part II 139 Chapter 6. Further Investigations of the Mind-Body Problem 141 Chapter ss.5. How to Explain Number Theory at a Dinner Party 175 (Impromptu Minisession: Transcendental Numbers) 175 Chapter 7. The Habit of Clinging to an Ultimate Ground 181 Chapter 8. The Science of Tricks 222 Part III 257 Chapter gamma. How to Explain Number Theory at a Dinner Party 259 (Third Session: Congruences) 259 Chapter 9. A Mathematical Dream and Its Interpretation 265 Chapter 10. No Apologies 279 Chapter delta. How to Explain Number Theory at a Dinner Party 311 (Fourth Session: Order and Randomness) 311 Afterword: The Veil of Maya 321 Notes 327 Bibliography 397 Index of Mathematicians 423 Subject Index 427

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Book SynopsisRandom matrix theory, both as an application and as a theory, has evolved rapidly over the years. This title chronicles these developments, emphasizing log-gases as a physical picture. It covers topics such as beta ensembles and Jack polynomials. It develops the application and theory of Gaussian and circular ensembles of random matrix theory.Trade Review"Log-Gases and Random Matrices is an excellent book. It is bound to become an instant classic and the standard reference to a large body of contemporary random matrix theory. It is a well-written tour through a vast landscape. The contemporary literature is extensively referenced and incorporated in the text, and the material is presented from several perspectives. Forrester has achieved the pedagogical equivalent of Dyson's 'Threefold Way' by writing an advanced monograph appealing equally to physicists, mathematicians, and statisticians."--Steven Joel Miller and Eduardo Duenez, Mathematical ReviewsTable of Contents*FrontMatter, pg. i*Preface, pg. v*Contents, pg. xi*Chapter One. Gaussian Matrix Ensembles, pg. 1*Chapter Two. Circular Ensembles, pg. 53*Chapter Three. Laguerre And Jacobi Ensembles, pg. 85*Chapter Four. The Selberg Integral, pg. 133*Chapter Five. Correlation functions at ss = 2, pg. 186*Chapter Six. Correlation Functions At ss= 1 And 4, pg. 236*Chapter Seven. Scaled limits at ss = 1, 2 and 4, pg. 283*Chapter Eight. Eigenvalue probabilities - Painleve systems approach, pg. 328*Chapter Nine. Eigenvalue probabilities- Fredholm determinant approach, pg. 380*Chapter Ten. Lattice paths and growth models, pg. 440*Chapter Eleven. The Calogero-Sutherland model, pg. 505*Chapter Twelve. Jack polynomials, pg. 543*Chapter Thirteen. Correlations for general ss, pg. 592*Chapter Fourteen. Fluctuation formulas and universal behavior of correlations, pg. 658*Chapter Fifteen. The two-dimensional one-component plasma, pg. 701*Bibliography, pg. 765*Index, pg. 785

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Book SynopsisTrade Review"Offers a clear and beautiful progression from addition to modern number theory."--Math-Blog "The authors did a remarkable job in making some aspects of modern number theory very accessible to readers with only a minimal knowledge of mathematics, say a student who had a first calculus course. However, also mathematicians who do not have number theory as their main focus will enjoy this book."--Adhemar Bultheel, European Mathematical Society "Ash and Gross do a masterful job of leading students from finite sums to modular forms and to the forefront of modern number theory... This is an excellent piece of mathematical writing."--Choice "[A]n accessible and fun introduction to modular forms... [Summing It Up] is engaging and conversational, without losing accuracy or essential rigor."--Dominic Lanphier, American Mathematical MonthlyTable of Contents*Frontmatter, pg. i*CONTENTS, pg. vii*PREFACE, pg. xi*ACKNOWLEDGMENTS, pg. xv*INTRODUCTION: WHAT THIS BOOK IS ABOUT, pg. 1*CHAPTER 1. PROEM, pg. 11*CHAPTER 2. SUMS OF TWO SQUARES, pg. 22*CHAPTER 3. SUMS OF THREE AND FOUR SQUARES, pg. 32*CHAPTER 4. SUMS OF HIGHER POWERS: WARING'S PROBLEM, pg. 37*CHAPTER 5. SIMPLE SUMS, pg. 42*CHAPTER 6. SUMS OF POWERS, USING LOTS OF ALGEBRA, pg. 50*CHAPTER 7. INFINITE SERIES, pg. 73*CHAPTER 8. CAST OF CHARACTERS, pg. 96*CHAPTER 9. ZETA AND BERNOULLI, pg. 103*CHAPTER 10. COUNT THE WAYS, pg. 110*CHAPTER 11. THE UPPER HALF-PLANE, pg. 127*CHAPTER 12. MODULAR FORMS, pg. 147*CHAPTER 13. HOW MANY MODULAR FORMS ARE THERE?, pg. 160*CHAPTER 14. CONGRUENCE GROUPS, pg. 179*CHAPTER 15. PARTITIONS AND SUMS OF SQUARES REVISITED, pg. 186*CHAPTER 16. MORE THEORY OF MODULAR FORMS, pg. 201*CHAPTER 17. MORE THINGS TO DO WITH MODULAR FORMS: APPLICATIONS, pg. 213*BIBLIOGRAPHY, pg. 225*INDEX, pg. 227

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Book SynopsisExcellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.

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Book SynopsisChallenging the common gene-centric approach to organisms, this book articulates a relativistic theory of biology. It is grounded in up-to-date biological research and rigorous application of mathematics to biology; however, it is presented in a non-technical manner for the general reader, and requires no familiarity with complex biology, mathematics or philosophy.Trade Review'Among its many merits, this remarkable book deserves to become a classic text in the philosophy of science. Almost alone among philosophers of science, Noble is a practising scientist; and unusually among practising scientists, he is an accomplished philosopher. His book brings out, with unparalleled clarity, how the scientific endeavour involves not only empirical inquiry but also conceptual structure. Noble shows how, on the negative side, popular presentations of sound biological results may be vitiated by bad metaphysics, and how, on the positive side, science and philosophy may extend the boundaries of knowledge by a unified epistemology. He ends, however, with a salutary warning that there may well be a limit to the human capacity to know the answers to ultimate questions.' Sir Anthony Kenny, University of Oxford'I think this a marvellous book. Denis Noble emphasises that genes, organs and systems dance to the tune of the organism and its social and physical environment. He sets the relativity of biology in a remarkable scientific sweep, ranging from cosmology to human belief systems. He reminds me of another great biologist, C. H. Waddington, to whom Noble pays handsome tribute. Writing with clarity and charm, Noble attempts to break down silos of knowledge inhabited by scientists who fail to come out and engage with others. … Broadening minds in an era of intense specialisation is more important than ever. Noble deserves to be successful in his desire to do just that and I hope that he will be.' Sir Patrick Bateson, University of Cambridge'In my view Dance to The Tune of Life is a 'must read'. In it Denis Noble lucidly deconstructs how and why reductionism came to prominence in biology and led to the current state of molecular Humpty-Dumptyism. His central idea that there is no privileged level of causation is the first conceptual step to putting Humpty Dumpty back together again.' Michael J. Joyner, Mayo Clinic, Minnesota'Denis Noble is renowned for his mission to reintegrate the physiological sciences with mainstream biology, including evolutionary theory. His new book combines clear exposition of basic principles with many valuable examples. He gives the reader, general or expert, a completely new view of life.' Yung E. Earm, Seoul National University, South Korea'Dance to the Tune of Life is one of the most fascinating and impressive books I have ever read. Denis Noble, a world-renowned physiologist and systems biologist, has revolutionized our traditional notion of the nature of life. The title Dance to the Tune of Life mirrors the essence of the argument of the book. The life emerges from numerous biological processes at different scales and levels. Such actors and actresses, stage properties, and stage are not separately present they act together in harmony, dancing to a tune with a music performed by an orchestra, an organism. By describing his research experiences and achievements on the cardiac rhythm evolutionary biology, medicine, and philosophy, Denis has not only provided us with very modern knowledge of the biological reactions and their network but also described to us the nature of life. I believe that this book impacts everyone involved in biomedicine.' Yoshihisa Kurachi, Osaka University, Japan'Having demolished the 'Selfish Gene' fiction, Noble in this marvelous book moves both science and philosophy from an antiquated 'either/or' static model to an 'and' model. 'Dance' shows elegantly and brilliantly that from the miracle of the ancient symbiosis of mitochondrial bacterial remnants in human cells, through the rock-solid interrelationship between genes and the feedback from the environment in all senses - from the core phenomenon of functional epigenetics, to the universe itself and our place in it - that we are, at heart, inter-beings, co-arising.' Samuel Shem, New York University'Denis Noble is a pioneer in understanding human physiology through quantitative studies linking behaviour across multiple scales of biological organization - from proteins to cells, tissues, organs and organ systems. These studies have led him to characterize biological function in terms of a Principle of Biological Relativity: there is no privileged level of causation in biology, because living organisms are multilevel open stochastic systems in which the behaviour at any level depends on higher and lower levels, and so cannot be fully understood in isolation. This engaging book defends this view in depth, and thereby also provides strong support for an extended synthesis of evolutionary theory that goes beyond the Modern Synthesis of Neo-Darwinism. It is highly recommended as a thoughtful study of the kind of complexity real living organisms display.' George Ellis FRS, University of Cape Town, South Africa'In this elegantly written and personal book world-renowned physiologist and systems biologist Denis Noble effectively argues for a fundamental revision of the theory of evolution. Against the reductionist, gene-centered approach of Neo-Darwinism, which has dominated biology for more than a century, Noble passionately pleas for a more integrated approach. Massively supported by recent postgenomic and epigenetic empirical research, Dance to the Tune of Life deepens and synthesizes ideas Noble earlier developed in The Music of Life. Biology beyond the Genome (2006) and subsequent writings. Just like Newtonian physics underwent a major transformation in the beginning of the 20th century due to Einstein's general theory of relativity, the life sciences are facing a no less fundamental transformation. Noble's book is a must read for anyone who wants to understand this transformation.' Jos de Mul, Erasmus University Rotterdam, Netherlands'… enlightening … The illustrations are both vibrant and clarifying, giving this title a sparkle that compels you to imagine how each concept fits into the larger scheme. I commend this author for relishing the subtle reminders of what makes this inquiry important. It's a best read.' D. Wayne Dworsky, San Francisco Book Review (www.sanfranciscobookreview.com)'… a very informative read … Noble's Dance to the Tune of Life is an illuminating account of why philosophy is necessary in doing science.' Sepehr Ehsani, Metascience'The narrative is remarkable … Dance to the Tune of Life is a marvellous text reflecting on the complexity of biology.' Anna Holderbaum, The BiologistTable of ContentsPreface; Acknowledgments; 1. The universe and the principle of relativity; 2. Biological scales and levels; 3. Biological networks; 4. Nature and origin of cells; 5. Blind chance and natural selection; 6. Biological relativity; 7. Dancing nucleotides: natural genetic engineering; 8. Epigenetics and a relativistic theory of evolution; 9. The relativity of epistemology: the meaning of it all; 10. Postscript; Glossary; Index.

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Book SynopsisContemporary Abstract Algebra, Tenth EditionFor more than three decades, this classic text has been widely appreciated by instructors and students alike. The book offers an enjoyable read and conveys and develops enthusiasm for the beauty of the topics presented. It is comprehensive, lively, and engaging.The author presents the concepts and methodologies of contemporary abstract algebra as used by working mathematicians, computer scientists, physicists, and chemists. Students will learn how to do computations and to write proofs. A unique feature of the book are exercises that build the skill of generalizing, a skill that students should develop but rarely do. Applications are included to illustrate the utility of the abstract concepts.Examples and exercises are the heart of the book. Examples elucidate the definitions, theorems, and proof techniques; exercises facilitate understanding, provide insight, and develop the ability to do proofs. The Trade Review"It has now been 35 years since Gallian's classic textbook Contemporary Abstract Algebra was first published. The book is deservedly popular with instructors of abstract algebra courses. It is written at an appropriate level for junior and senior undergraduates, has lucid coverage of all of the standard topics and several nonstandard ones (Frieze Groups and Crystallographic Groups, Coding Theory, Greek Geometric Construction Problems, etc), is example-driven, and contains thousands of exercises at various levels of difficulty. Moreover, every chapter begins with an interesting quote or two (by as diverse a group of people as Einstein, Miguel de Cervantes, Ralph Waldo Emerson, Bob Dylan, etc) and most conclude with a mini- biography of a mathematician whose work relates to the chapter's content. This is an interesting book that is a pleasure to read. According to the Preface, changes made for the tenth edition include: 1. Approximately 200 new exercises2. Many new examples3. New quotes4. A freshening of the discussion portions"- Benjamin Linowitz, Oberlin College, Published in MAATable of Contents1 Introduction to Groups 2 Groups 3 Finite Groups; Subgroups 4 Cyclic Groups 5 Permutation Groups 6 Ismorphisms 7 Cosets and Lagrange's Theorem 8 External Direct Products 9 Normal Subgroups and Factor Groups 10 Group Homomorphisms 11 Fundamental Theorem of Finite Abelian Groups 12 Introduction to Rings 13 Integral Domains 14 Ideals and Factor Rings 15 Ring Homomorphisms 16 Polynomial Rings 17 Factorization of Polynomials 18 Divisibilty in Integral Domains 19 Extension Fields 20 Algebraic Extensions 21 Finite Fields 22 Geometric Constructions 23 Sylow Theorems 24 Finite Simple Groups 25 Generators and Relations 26 Symmetry Groups 27 Symmetry and Counting 28 Cayley Digraphs of Groups 29 Introduction to Algebraic Coding Theory 30 An Introduction to Galois Theory 31 Cyclotomic Extensions

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Book SynopsisCalculus. For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun, accessible, and surrounds us everywhere we go. This book shows us how to see the math in our coffee, on the highway, and even in the night sky.Trade ReviewOne of American Association for the Advancement of Science's Books for General Audiences and Young Adults 2014 "For every befuddled math student who's ever sat in class and thought, 'When am I ever going to use this?' Fernandez, assistant professor of mathematics at Wellesley College, gleefully reveals the truth: the world really does run on math... Whether describing how biology uses math to design more efficient organs and body structures or the best way to figure out when to overhaul a subway car, Fernandez keeps the tone light, as entertaining as it is informative. The book will speak most strongly to readers with some experience in trigonometry and basic calculus, but it's also accessible to those willing to put in a little extra effort. Either way, Fernandez's witty, delightful approach makes for a winning introduction to the wonderland of math behind the scenes of everyday life."--Publishers Weekly (starred review) "The author earnestly and excitedly seeks to make the principles of calculus near and natural, without the intimidation of a five-pound textbook dense with equations... Fernandez invites the reader along on this work day and telegraphs an enthusiasm for seeing calculus, with hints of differential equations, presented to him. This excitement will communicate itself to the math enthusiast becoming acquainted with calculus through the author's style, which is both lively and confident."--Tom Schulte, MAA Reviews "Written in a bright conversational tone, this book wonderfully integrates calculus into everyday life."--Devorah Bennu, GrrlScientist, The Guardian "Professor Fernandez is a delightfully quirky writer and his book Everyday Calculus is lighthearted and compelling, connecting mathematics to daily life... Everyday Calculus will not only be found to be understandable by non-mathematicians but will also be found to be quite entertaining. Indeed, not everyone considers the calculus going on inside Tandoori ovens, and they should."--Robert Schaefer, New York Journal of Books "Written in a bright conversational tone, this book wonderfully integrates calculus into everyday life."--GrrrlScientist "[T]he book is perfect for a reader who really wants to know what mathematics are governing our lives and who wants to learn and understand or polish up his rusty knowledge of these mathematics."--A. Bultheel, European Mathematical Society "Everyday Calculus is a triumph in the pursuit of the lofty goal of comprehending the world. Fernandez has touched upon a sensitive nerve, not just because mathematics makes most people cringe, but because the subject has allowed the passage of great things from some of the greatest minds ever to wander within the twentieth century. Oscar Fernandez is as bold as Alfred S. Posementier in his quest to deliver mathematical thinking as nature's gift to the thinking person."--D. Wayne Dworsky, San Francisco Book Review "Fernandez is especially effective when linking together seemingly disparate activities for which the underlying mathematical basis is identical. As the subtitle of the book suggests, the thrust is more one of 'discovering the hidden math all around us' rather than showing 'how mathematics is used,' which provides an honest and very pleasurable journey."--Choice "The book offers in clear and concise fashion much of the material found in a traditional calculus textbook, but presents it beginning with a real world observation and then developing the mathematics needed to understand the observation."--AAAS "The author's style is witty, conversational and comfortable... A very captivating read."--Andrew Jones, Mathematics TodayTable of ContentsPreface ix Calculus Topics Discussed by Chapter xi CHAPTER 1 Wake Up and Smell the Functions 1 What's Trig Got to Do with Your Morning? 2 How a Rational Function Defeated Thomas Edison, and Why Induction Powers the World 5 The Logarithms Hidden in the Air 10 The Frequency of Trig Functions 14 Galileo's Parabolic Thinking 17 CHAPTER 2 Breakfast at Newton's 21 Introducing Calculus, the CNBC Way 21 Coffee Has Its Limits 25 A Multivitamin a Day Keeps the Doctor Away 30 Derivatives Are about Change 34 CHAPTER 3 Driven by Derivatives 35 Why Do We Survive Rainy Days? 36 Politics in Derivatives, or Derivatives in Politics? 39 What the Unemployment Rate Teaches Us about the Curvature of Graphs 41 America's Ballooning Population 44 Feeling Derivatives 46 The Calculus of Time Travel 47 CHAPTER 4 Connected by Calculus 51 E-Mails, Texts, Tweets, Ah! 51 The Calculus of Colds 53 What Does Sustainability Have to Do with Catching a Cold? 56 What Does Your Retirement Income Have to Do with Traffic? 58 The Calculus of the Sweet Tooth 61 CHAPTER 5 Take a Derivative and You'll Feel Better 65 I "Heart" Differentials 65 How Life (and Nature) Uses Calculus 67 The Costly Downside of Calculus 73 The Optimal Drive Back Home 75 Catching Speeders Efficiently with Calculus 77 CHAPTER 6 Adding Things Up, the Calculus Way 81 The Little Engine That Could ... Integrate 82 The Fundamental Theorem of Calculus 90 Using Integrals to Estimate Wait Times 93 CHAPTER 7 Derivatives Integrals: The Dream Team 97 Integration at Work-Tandoori Chicken 98 Finding the Best Seat in the House 101 Keeping the T Running with Calculus 104 Look Up to Look Back in Time 108 The Ultimate Fate of the Universe 109 The Age of the Universe 113 Epilogue 116 Appendix A Functions and Graphs 119 Appendices 1-7 125 Notes 147 Index 149

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Book SynopsisElliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjectureTrade Review"The authors present their discussion in an informal, sometimes playful manner and with detail that will appeal to an audience with a basic understanding of calculus. This book will captivate math enthusiasts as well as readers curious about an intriguing and still unanswered question."--Margaret Dominy, Library Journal "Minimal prerequisites and its clear writing make this book (which even has a few exercises) a great choice for a seminar for mathematics majors, who at some point should have such an excursion to one of the frontiers of mathematics."--Mathematics Magazine "The authors of Elliptic Tales do a superb job in demonstrating the approach that mathematicians take when they confront unsolved problems involving elliptic curves."--Sungkon Chang, Times Higher Education "One cannot help being impressed, in reading the book and pursuing a few of the references, by the magnitude of the enterprise it chronicles."--James Case, SIAM News "Ash and Gross thoroughly explain the statement and significance of the linchpin Birch and Swinnerton-Dyer conjection... [A]sh and Gross deliver ample and current intellectual and technical substance."--Choice "I would envision this book as an excellent text for an undergraduate 'capstone' course in mathematics; the book lends itself to independent reading, but topics may be explored in much greater depth and rigor in the classroom. Additionally, the book indeed brings together ideas from calculus, complex variables and algebra, showing how a single mathematical research question may require an integrated understanding of the various branches of mathematics. Thus, it encourages students to reinforce their understanding of these various fields, while simultaneously introducing them to an open question in mathematics and a vibrant field of study."--Lisa A. Berger, Mathematical Reviews Clippings "The book is very pleasantly written, and in my opinion, the authors have done an admirable job in giving an idea to non-experts what the Birch-Swinnerton Dyer conjecture is about."--Jan-Hendrik Evertse, Zentralblatt MATH "The book's most important contributions ... are the sense of discovery, invention, and insight into the habits of mind used by mathematicians on this journey. I would recommend this book to anyone who wants to be challenged mathematically or who wants to experience mathematics as creative and exciting."--Jacqueline Coomes, Mathematics Teacher "[T]his book is a wonderful introduction to what is arguably one of the most important mathematical problems of our time and for that reason alone it deserves to be widely read. Another reason to recommend this book is the opportunity to share in the readily apparent joy the authors have for their subject and the beauty they see in it, not least because ... joy and beauty are the most important reasons for doing mathematics, irrespective of its dollar value."--Rob Ashmore, Mathematics Today "This book has many nice aspects. Ash and Gross give a truly stimulating introduction to elliptic curves and the BSD conjecture for undergraduate students. The main achievement is to make a relative easy exposition of these so technical topics."--Jonathan Sanchez-Hernandez, Mathematical SocietyTable of ContentsPreface xiii Acknowledgments xix Prologue 1 PART I. DEGREE Chapter 1. Degree of a Curve 13 1.Greek Mathematics 13 2.Degree 14 3.Parametric Equations 20 4.Our Two Definitions of Degree Clash 23 Chapter 2. Algebraic Closures 26 1.Square Roots of Minus One 26 2.Complex Arithmetic 28 3.Rings and Fields 30 4.Complex Numbers and Solving Equations 32 5.Congruences 34 6.Arithmetic Modulo a Prime 38 7.Algebraic Closure 38 Chapter 3. The Projective Plane 42 1.Points at Infinity 42 2.Projective Coordinates on a Line 46 3.Projective Coordinates on a Plane 50 4.Algebraic Curves and Points at Infinity 54 5.Homogenization of Projective Curves 56 6.Coordinate Patches 61 Chapter 4. Multiplicities and Degree 67 1.Curves as Varieties 67 2.Multiplicities 69 3.Intersection Multiplicities 72 4.Calculus for Dummies 76 Chapter 5. B'ezout's Theorem 82 1.A Sketch of the Proof 82 2.An Illuminating Example 88 PART II. ELLIPTIC CURVES AND ALGEBRA Chapter 6. Transition to Elliptic Curves 95 Chapter 7. Abelian Groups 100 1.How Big Is Infinity? 100 2.What Is an Abelian Group? 101 3.Generations 103 4.Torsion 106 5.Pulling Rank 108 Appendix: An Interesting Example of Rank and Torsion 110 Chapter 8. Nonsingular Cubic Equations 116 1.The Group Law 116 2.Transformations 119 3.The Discriminant 121 4.Algebraic Details of the Group Law 122 5.Numerical Examples 125 6.Topology 127 7.Other Important Facts about Elliptic Curves 131 5.Two Numerical Examples 133 Chapter 9. Singular Cubics 135 1.The Singular Point and the Group Law 135 2.The Coordinates of the Singular Point 136 3.Additive Reduction 137 4.Split Multiplicative Reduction 139 5.Nonsplit Multiplicative Reduction 141 6.Counting Points 145 7.Conclusion 146 Appendix A: Changing the Coordinates of the Singular Point 146 Appendix B: Additive Reduction in Detail 147 Appendix C: Split Multiplicative Reduction in Detail 149 Appendix D: Nonsplit Multiplicative Reduction in Detail 150 Chapter 10. Elliptic Curves over Q 152 1.The Basic Structure of the Group 152 2.Torsion Points 153 3.Points of Infinite Order 155 4.Examples 156 PART III. ELLIPTIC CURVES AND ANALYSIS Chapter 11. Building Functions 161 1.Generating Functions 161 2.Dirichlet Series 167 3.The Riemann Zeta-Function 169 4.Functional Equations 171 5.Euler Products 174 6.Build Your Own Zeta-Function 176 Chapter 12. Analytic Continuation 181 1.A Difference that Makes a Difference 181 2.Taylor Made 185 3.Analytic Functions 187 4.Analytic Continuation 192 5.Zeroes, Poles, and the Leading Coefficient 196 Chapter 13. L-functions 199 1.A Fertile Idea 199 2.The Hasse-Weil Zeta-Function 200 3.The L-Function of a Curve 205 4.The L-Function of an Elliptic Curve 207 5.Other L-Functions 212 Chapter 14. Surprising Properties of L-functions 215 1.Compare and Contrast 215 2.Analytic Continuation 220 3.Functional Equation 221 Chapter 15. The Conjecture of Birch and Swinnerton-Dyer 225 1.How Big Is Big? 225 2.Influences of the Rank on the Np's 228 3.How Small Is Zero? 232 4.The BSD Conjecture 236 5.Computational Evidence for BSD 238 6.The Congruent Number Problem 240 Epilogue 245 Retrospect 245 Where DoWe Go from Here? 247 Bibliography 249 Index 251

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Book SynopsisHigher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. This title presents the foundations of this theory.Trade Review"This book is a remarkable achievement, and the reviewer thinks it marks the beginning of a major change in algebraic topology."--Mark Hovey, Mathematical ReviewsTable of ContentsPreface vii Chapter 1. An Overview of Higher Category Theory 1 1.1 Foundations for Higher Category Theory 1 1.2 The Language of Higher Category Theory 26 Chapter 2. Fibrations of Simplicial Sets 53 2.1 Left Fibrations 55 2.2 Simplicial Categories and 1-Categories 72 2.3 Inner Fibrations 95 2.4 Cartesian Fibrations 114 Chapter 3. The 1-Category of 1-Categories 145 3.1 Marked Simplicial Sets 147 3.2 Straightening and Unstraightening 169 3.3 Applications 204 Chapter 4. Limits and Colimits 223 4.1 Co_nality 223 4.2 Techniques for Computing Colimits 240 4.3 Kan Extensions 261 4.4 Examples of Colimits 292 Chapter 5. Presentable and Accessible 1-Categories 311 5.1 1-Categories of Presheaves 312 5.2 Adjoint Functors 331 5.3 1-Categories of Inductive Limits 377 5.4 Accessible 1-Categories 414 5.5 Presentable 1-Categories 455 Chapter 6. 1-Topoi 526 6.1 1-Topoi: De_nitions and Characterizations 527 6.2 Constructions of 1-Topoi 569 6.3 The 1-Category of 1-Topoi 593 6.4 n-Topoi 632 6.5 Homotopy Theory in an 1-Topos 651 Chapter 7. Higher Topos Theory in Topology 682 7.1 Paracompact Spaces 683 7.2 Dimension Theory 711 7.3 The Proper Base Change Theorem 742 Appendix. Appendix 781 A.1 Category Theory 781 A.2 Model Categories 803 A.3 Simplicial Categories 844 Bibliography 909 General Index 915 Index of Notation 923

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Book SynopsisStep-by-step instructions enable chemical engineers to master key software programs and solve complex problems Today, both students and professionals in chemical engineering must solve increasingly complex problems dealing with refineries, fuel cells, microreactors, and pharmaceutical plants, to name a few. With this book as their guide, readers learn to solve these problems using their computers and Excel, MATLAB, Aspen Plus, and COMSOL Multiphysics. Moreover, they learn how to check their solutions and validate their results to make sure they have solved the problems correctly. Now in its Second Edition, Introduction to Chemical Engineering Computing is based on the author's firsthand teaching experience. As a result, the emphasis is on problem solving. Simple introductions help readers become conversant with each program and then tackle a broad range of problems in chemical engineering, including: Equations of state Chemical reactTable of ContentsPreface xv 1 Introduction 1 Organization, 2 Algebraic Equations, 3 Process Simulation, 3 Differential Equations, 3 Appendices, 4 2 Equations of State 7 Equations of State—Mathematical Formulation, 8 Solving Equations of State Using Excel (Single Equation in One Unknown), 12 Solution Using “Goal Seek”, 12 Solution Using “Solver”, 13 Example of a Chemical Engineering Problem Solved Using “Goal Seek”, 13 Solving Equations of State Using MATLAB (Single Equation in One Unknown), 15 Example of a Chemical Engineering Problem Solved Using MATLAB, 16 Another Example of a Chemical Engineering Problem Solved Using MATLAB, 18 Equations of State With Aspen Plus, 20 Example Using Aspen Plus, 20 Specific Volume of a Mixture, 21 Chapter Summary, 26 Problems, 26 Numerical Problems, 28 3 Vapor–Liquid Equilibria 29 Flash and Phase Separation, 30 Isothermal Flash—Development of Equations, 30 Example Using Excel, 32 Thermodynamic Parameters, 33 Example Using MATLAB, 34 Example Using Aspen Plus, 35 Nonideal Liquids—Test of Thermodynamic Model, 39 NIST Thermo Data Engine in Aspen Plus, 41 Chapter Summary, 44 Problems, 44 Numerical Problems, 48 4 Chemical Reaction Equilibria 49 Chemical Equilibrium Expression, 50 Example of Hydrogen for Fuel Cells, 51 Solution Using Excel, 52 Solution Using MATLAB, 53 Chemical Reaction Equilibria with Two or More Equations, 56 Multiple Equations, Few Unknowns Using MATLAB, 56 Chemical Reaction Equilibria Using Aspen Plus, 59 Chapter Summary, 59 Problems, 60 Numerical Problems, 63 5 Mass Balances with Recycle Streams 65 Mathematical Formulation, 66 Example Without Recycle, 68 Example with Recycle; Comparison of Sequential and Simultaneous Solution Methods, 70 Example of Process Simulation Using Excel for Simple Mass Balances, 72 Example of Process Simulation Using Aspen Plus for Simple Mass Balances, 73 Example of Process Simulation with Excel Including Chemical Reaction Equilibria, 74 Did the Iterations Converge?, 75 Extensions, 76 Chapter Summary, 76 Class Exercises, 76 Class Discussion (After Viewing Problem 5.10 on the Book Website), 76 Problems, 77 6 Thermodynamics and Simulation of Mass Transfer Equipment 85 Thermodynamics, 86 Guidelines for Choosing, 89 Properties Environment | Home | Methods Selection Assistant, 89 Thermodynamic Models, 90 Example: Multicomponent Distillation with Shortcut Methods, 91 Multicomponent Distillation with Rigorous Plate-to-Plate Methods, 95 Example: Packed Bed Absorption, 97 Example: Gas Plant Product Separation, 100 Example: Water Gas Shift Equilibrium Reactor with Sensitivity Block and Design Specification Block, 102 Chapter Summary, 106 Class Exercise, 106 Problems (using Aspen Plus), 106 7 Process Simulation 109 Model Library, 110 Example: Ammonia Process, 110 Development of the Model, 112 Solution of the Model, 115 Examination of Results, 115 Testing the Thermodynamic Model, 118 Utility Costs, 118 Greenhouse Gas Emissions, 120 Convergence Hints, 120 Optimization, 122 Integrated Gasification Combined Cycle, 125 Cellulose to Ethanol, 126 Chapter Summary, 128 Class Exercise, 128 Problems, 128 Problems Involving Corn Stover and Ethanol, 131 8 Chemical Reactors 137 Mathematical Formulation of Reactor Problems, 138 Example: Plug Flow Reactor and Batch Reactor, 138 Example: Continuous Stirred Tank Reactor, 140 Using MATLAB to Solve Ordinary Differential Equations, 140 Simple Example, 140 Use of the “Global” Command, 142 Passing Parameters, 143 Example: Isothermal Plug Flow Reactor, 144 Example: Nonisothermal Plug Flow Reactor, 146 Using Comsol Multiphysics to Solve Ordinary Differential Equations, 148 Simple Example, 148 Example: Isothermal Plug Flow Reactor, 150 Example: Nonisothermal Plug Flow Reactor, 151 Reactor Problems with Mole Changes and Variable Density, 153 Chemical Reactors with Mass Transfer Limitations, 155 Plug Flow Chemical Reactors in Aspen Plus, 158 Continuous Stirred Tank Reactors, 161 Solution Using Excel, 162 Solution Using MATLAB, 163 CSTR with Multiple Solutions, 163 Transient Continuous Stirred Tank Reactors, 164 Chapter Summary, 168 Problems, 169 Numerical Problems (See Appendix E), 174 9 Transport Processes in One Dimension 175 Applications in Chemical Engineering—Mathematical Formulations, 176 Heat Transfer, 176 Diffusion and Reaction, 177 Fluid Flow, 178 Unsteady Heat Transfer, 180 Introduction to Comsol Multiphysics, 180 Example: Heat Transfer in a Slab, 181 Solution Using Comsol Multiphysics, 181 Solution Using MATLAB, 184 Example: Reaction and Diffusion, 185 Parametric Solution, 186 Example: Flow of a Newtonian Fluid in a Pipe, 188 Example: Flow of a Non-Newtonian Fluid in a Pipe, 190 Example: Transient Heat Transfer, 193 Solution Using Comsol Multiphysics, 193 Solution Using MATLAB, 195 Example: Linear Adsorption, 196 Example: Chromatography, 199 Pressure Swing Adsorption, 203 Chapter Summary, 204 Problems, 204 Chemical Reaction, 204 Chemical Reaction and Heat Transfer, 205 Mass Transfer, 207 Heat Transfer, 207 Electrical Fields, 207 Fluid Flow, 208 Numerical Problems (See Appendix E), 213 10 Fluid Flow in Two and Three Dimensions 215 Mathematical Foundation of Fluid Flow, 217 Navier–Stokes Equation, 217 Non-Newtonian Fluid, 218 Nondimensionalization, 219 Option One: Slow Flows, 219 Option Two: High-Speed Flows, 220 Example: Entry Flow in a Pipe, 221 Example: Entry Flow of a Non-Newtonian Fluid, 226 Example: Flow in Microfluidic Devices, 227 Example: Turbulent Flow in a Pipe, 230 Example: Start-Up Flow in a Pipe, 233 Example: Flow Through an Orifice, 235 Example: Flow in a Serpentine Mixer, 239 Microfluidics, 240 Mechanical Energy Balance for Laminar Flow, 243 Pressure Drop for Contractions and Expansions, 245 Generation of Two-Dimensional Inlet Velocity Profiles for Three-Dimensional Simulations, 246 Chapter Summary, 249 Problems, 249 11 Heat and Mass Transfer in Two and Three Dimensions 259 Convective Diffusion Equation, 260 Nondimensional Equations, 261 Example: Heat Transfer in Two Dimensions, 262 Example: Heat Conduction with a Hole, 264 Example: Convective Diffusion in Microfluidic Devices, 265 Example: Concentration-Dependent Viscosity, 268 Example: Viscous Dissipation, 269 Example: Chemical Reaction, 270 Example: Wall Reactions, 272 Example: Mixing in a Serpentine Mixer, 272 Microfluidics, 274 Characterization of Mixing, 276 Average Concentration along an Optical Path, 276 Peclet Number, 276 Example: Convection and Diffusion in a Three-Dimensional T-Sensor, 278 Chapter Summary, 280 Problems, 280 Steady, Two-Dimensional Problems, 280 Heat Transfer with Flow, 283 Reaction with Known Flow, 284 Reaction with No Flow, 285 Solve for Concentration and Flow, 286 Numerical Problems, 289 Appendix A HintsWhen Using Excel® 291 Introduction, 291 Calculation, 292 Plotting, 293 Import and Export, 294 Presentation, 294 Appendix B HintsWhen Using MATLAB® 297 General Features, 298 Screen Format, 298 Stop/Closing the Program, 299 m-files and Scripts, 299 Workspaces and Transfer of Information, 300 “Global” Command, 300 Display Tools, 301 Classes of Data, 301 Programming Options: Input/Output, Loops, Conditional Statements, Timing, and Matrices, 302 Input/Output, 302 Loops, 303 Conditional Statements, 303 Timing Information, 304 Matrices, 304 Matrix Multiplication, 304 Element by Element Calculations, 305 More Information, 306 Finding and Fixing Errors, 306 Eigenvalues of a Matrix, 307 Evaluate an Integral, 307 Spline Interpolation, 307 Interpolate Data, Evaluate the Polynomial, and Plot the Result, 308 Solve Algebraic Equations, 309 Using “fsolve”, 309 Solve Algebraic Equations Using “fzero” or “fminsearch” (Both in Standard MATLAB), 309 Integrate Ordinary Differential Equations that are Initial Value Problems, 309 Differential-Algebraic Equations, 311 Checklist for Using “ode45” and Other Integration Packages, 311 Plotting, 312 Simple Plots, 312 Add Data to an Existing Plot, 312 Dress Up Your Plot, 312 Multiple Plots, 313 3D Plots, 313 More Complicated Plots, 314 Use Greek Letters and Symbols in the Text, 314 Bold, Italics, and Subscripts, 314 Other Applications, 315 Plotting Results from Integration of Partial Differential Equations Using Method of Lines, 315 Import/Export Data, 315 Import/Export with Comsol Multiphysics, 318 Programming Graphical User Interfaces, 318 MATLAB Help, 318 Applications of MATLAB, 319 Appendix C Hints When Using Aspen Plus® 321 Introduction, 321 Flowsheet, 323 Model Library, 323 Place Units on Flowsheet, 324 Connect the Units with Streams, 324 Data, 324 Setup, 324 Data Entry, 325 Specify Components, 325 Specify Properties, 325 Specify Input Streams, 326 Specify Block Parameters, 326 Run the Problem, 326 Scrutinize the Stream Table, 327 Checking Your Results, 328 Change Conditions, 328 Report, 329 Transfer the Flowsheet and Mass and Energy Balance to a Word Processing Program, 329 Prepare Your Report, 329 Save Your Results, 330 Getting Help, 330 Advanced Features, 330 Flowsheet Sections, 330 Mass Balance Only Simulations and Inclusion of Solids, 331 Transfer Between Excel and Aspen, 331 Block Summary, 331 Calculator Blocks, 332 Aspen Examples, 334 Molecule Draw, 334 Applications of Aspen Plus, 334 Appendix D HintsWhen Using Comsol Multiphysics® 335 Basic Comsol Multiphysics Techniques, 336 Opening Screens, 336 Equations, 337 Specify the Problem and Parameters, 337 Physics, 339 Definitions, 339 Geometry, 339 Materials, 340 Discretization, 341 Boundary Conditions, 341 Mesh, 342 Solve and Examine the Solution, 342 Solve, 342 Plot, 342 Publication Quality Figures, 343 Results, 343 Probes, 344 Data Sets, 344 Advanced Features, 345 Mesh, 345 Transfer to Excel, 346 LiveLink with MATLAB, 347 Variables, 348 Animation, 349 Studies, 349 Help with Convergence, 349 Help with Time-Dependent Problems, 350 Jump Discontinuity, 350 Help, 351 Applications of Comsol Multiphysics, 351 Appendix E Mathematical Methods 353 Algebraic Equations, 354 Successive Substitution, 354 Newton–Raphson, 354 Ordinary Differential Equations as Initial Value Problems, 356 Euler’s Method, 356 Runge–Kutta Methods, 357 MATLAB and ode45 and ode15s, 357 Ordinary Differential Equations as Boundary Value Problems, 358 Finite Difference Method, 359 Finite Difference Method in Excel, 360 Finite Element Method in One Space Dimension, 361 Initial Value Methods, 363 Partial Differential Equations in time and One Space Dimension, 365 Problems with Strong Convection, 366 Partial Differential Equations in Two Space Dimensions, 367 Finite-Difference Method for Elliptic Equations in Excel, 367 Finite Element Method for Two-Dimensional Problems, 368 Summary, 370 Problems, 370 References 373 Index 379

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Book SynopsisWritten by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

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Book SynopsisOver 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.

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Book Synopsis

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Book SynopsisAn up-to-date, comprehensive treatment of a classic text on missing data in statisticsThe topic of missing data has gained considerable attention in recent decades. This new edition by two acknowledged experts on the subject offers an up-to-date account of practical methodology for handling missing data problems. Blending theory and application, authors Roderick Little and Donald Rubin review historical approaches to the subject and describe simple methods for multivariate analysis with missing values. They then provide a coherent theory for analysis of problems based on likelihoods derived from statistical models for the data and the missing data mechanism, and then they apply the theory to a wide range of important missing data problems.Statistical Analysis with Missing Data, Third Edition starts by introducing readers to the subject and approaches toward solving it. It looks at the patterns and mechanisms that create the missing data, as well asTable of ContentsPreface to the Third Edition xi Part I Overview and Basic Approaches 1 1 Introduction 3 1.1 The Problem of Missing Data 3 1.2 Missingness Patterns and Mechanisms 8 1.3 Mechanisms That Lead to Missing Data 13 1.4 A Taxonomy of Missing Data Methods 23 2 Missing Data in Experiments 29 2.1 Introduction 29 2.2 The Exact Least Squares Solution with Complete Data 30 2.3 The Correct Least Squares Analysis with Missing Data 32 2.4 Filling in Least Squares Estimates 33 2.4.1 Yates’s Method 33 2.4.2 Using a Formula for the Missing Values 34 2.4.3 Iterating to Find the Missing Values 34 2.4.4 ANCOVA with Missing Value Covariates 35 2.5 Bartlett’s ANCOVA Method 35 2.5.1 Useful Properties of Bartlett’s Method 35 2.5.2 Notation 36 2.5.3 The ANCOVA Estimates of Parameters and Missing Y-Values 36 2.5.4 ANCOVA Estimates of the Residual Sums of Squares and the Covariance Matrix of 𝛽̂ 37 2.6 Least Squares Estimates of Missing Values by ANCOVA Using Only Complete-Data Methods 38 2.7 Correct Least Squares Estimates of Standard Errors and One Degree of Freedom Sums of Squares 40 2.8 Correct Least-Squares Sums of Squares with More Than One Degree of Freedom 42 3 Complete-Case and Available-Case Analysis, Including Weighting Methods 47 3.1 Introduction 47 3.2 Complete-Case Analysis 47 3.3 Weighted Complete-Case Analysis 50 3.3.1 Weighting Adjustments 50 3.3.2 Poststratification and Raking to Known Margins 58 3.3.3 Inference from Weighted Data 60 3.3.4 Summary of Weighting Methods 61 3.4 Available-Case Analysis 61 4 Single Imputation Methods 67 4.1 Introduction 67 4.2 Imputing Means from a Predictive Distribution 69 4.2.1 Unconditional Mean Imputation 69 4.2.2 Conditional Mean Imputation 70 4.3 Imputing Draws from a Predictive Distribution 73 4.3.1 Draws Based on Explicit Models 73 4.3.2 Draws Based on Implicit Models – Hot Deck Methods 76 4.4 Conclusion 81 5 Accounting for Uncertainty from Missing Data 85 5.1 Introduction 85 5.2 Imputation Methods that Provide Valid Standard Errors from a Single Filled-in Data Set 86 5.3 Standard Errors for Imputed Data by Resampling 90 5.3.1 Bootstrap Standard Errors 90 5.3.2 Jackknife Standard Errors 92 5.4 Introduction to Multiple Imputation 95 5.5 Comparison of Resampling Methods and Multiple Imputation 100 Part II Likelihood-Based Approaches to the Analysis of Data with Missing Values 107 6 Theory of Inference Based on the Likelihood Function 109 6.1 Review of Likelihood-Based Estimation for Complete Data 109 6.1.1 Maximum Likelihood Estimation 109 6.1.2 Inference Based on the Likelihood 118 6.1.3 Large Sample Maximum Likelihood and Bayes Inference 119 6.1.4 Bayes Inference Based on the Full Posterior Distribution 126 6.1.5 Simulating Posterior Distributions 130 6.2 Likelihood-Based Inference with Incomplete Data 132 6.3 A Generally Flawed Alternative to Maximum Likelihood: Maximizing over the Parameters and the Missing Data 141 6.3.1 The Method 141 6.3.2 Background 142 6.3.3 Examples 143 6.4 Likelihood Theory for Coarsened Data 145 7 Factored Likelihood Methods When the Missingness Mechanism Is Ignorable 151 7.1 Introduction 151 7.2 Bivariate Normal Data with One Variable Subject to Missingness: ML Estimation 153 7.2.1 ML Estimates 153 7.2.2 Large-Sample Covariance Matrix 157 7.3 Bivariate Normal Monotone Data: Small-Sample Inference 158 7.4 Monotone Missingness with More Than Two Variables 161 7.4.1 Multivariate Data with One Normal Variable Subject to Missingness 161 7.4.2 The Factored Likelihood for a General Monotone Pattern 162 7.4.3 ML Computation for Monotone Normal Data via the Sweep Operator 166 7.4.4 Bayes Computation forMonotone Normal Data via the Sweep Operator 174 7.5 Factored Likelihoods for Special Nonmonotone Patterns 175 8 Maximum Likelihood for General Patterns of Missing Data: Introduction and Theory with Ignorable Nonresponse 185 8.1 Alternative Computational Strategies 185 8.2 Introduction to the EM Algorithm 187 8.3 The E Step and The M Step of EM 188 8.4 Theory of the EM Algorithm 193 8.4.1 Convergence Properties of EM 193 8.4.2 EM for Exponential Families 196 8.4.3 Rate of Convergence of EM 198 8.5 Extensions of EM 200 8.5.1 The ECM Algorithm 200 8.5.2 The ECME and AECM Algorithms 205 8.5.3 The PX-EM Algorithm 206 8.6 Hybrid Maximization Methods 208 9 Large-Sample Inference Based on Maximum Likelihood Estimates 213 9.1 Standard Errors Based on The Information Matrix 213 9.2 Standard Errors via Other Methods 214 9.2.1 The Supplemented EM Algorithm 214 9.2.2 Bootstrapping the Observed Data 219 9.2.3 Other Large-Sample Methods 220 9.2.4 Posterior Standard Errors from Bayesian Methods 221 10 Bayes and Multiple Imputation 223 10.1 Bayesian Iterative Simulation Methods 223 10.1.1 Data Augmentation 223 10.1.2 The Gibbs’ Sampler 226 10.1.3 Assessing Convergence of Iterative Simulations 230 10.1.4 Some Other Simulation Methods 231 10.2 Multiple Imputation 232 10.2.1 Large-Sample Bayesian Approximations of the Posterior Mean and Variance Based on a Small Number of Draws 232 10.2.2 Approximations Using Test Statistics or p-Values 235 10.2.3 Other Methods for Creating Multiple Imputations 238 10.2.4 Chained-Equation Multiple Imputation 241 10.2.5 Using Different Models for Imputation and Analysis 243 Part III Likelihood-Based Approaches to the Analysis of Incomplete Data: Some Examples 247 11 Multivariate Normal Examples, Ignoring the Missingness Mechanism 249 11.1 Introduction 249 11.2 Inference for a Mean Vector and Covariance Matrix with Missing Data Under Normality 249 11.2.1 The EM Algorithm for Incomplete Multivariate Normal Samples 250 11.2.2 Estimated Asymptotic Covariance Matrix of (𝜃 − ) 252 11.2.3 Bayes Inference and Multiple Imputation for the Normal Model 253 11.3 The Normal Model with a Restricted Covariance Matrix 257 11.4 Multiple Linear Regression 264 11.4.1 Linear Regression with Missingness Confined to the Dependent Variable 264 11.4.2 More General Linear Regression Problems with Missing Data 266 11.5 A General Repeated-Measures Model with Missing Data 269 11.6 Time Series Models 273 11.6.1 Introduction 273 11.6.2 Autoregressive Models for Univariate Time Series with Missing Values 273 11.6.3 Kalman Filter Models 276 11.7 Measurement Error Formulated as Missing Data 277 12 Models for Robust Estimation 285 12.1 Introduction 285 12.2 Reducing the Influence of Outliers by Replacing the Normal Distribution by a Longer-Tailed Distribution 286 12.2.1 Estimation for a Univariate Sample 286 12.2.2 Robust Estimation of the Mean and Covariance Matrix with Complete Data 288 12.2.3 Robust Estimation of the Mean and Covariance Matrix from Data with Missing Values 290 12.2.4 Adaptive Robust Multivariate Estimation 291 12.2.5 Bayes Inference for the t Model 292 12.2.6 Further Extensions of the t Model 294 12.3 Penalized Spline of Propensity Prediction 298 13 Models for Partially Classified Contingency Tables, Ignoring the Missingness Mechanism 301 13.1 Introduction 301 13.2 Factored Likelihoods for Monotone Multinomial Data 302 13.2.1 Introduction 302 13.2.2 ML and Bayes for Monotone Patterns 303 13.2.3 Precision of Estimation 312 13.3 ML and Bayes Estimation for Multinomial Samples with General Patterns of Missingness 313 13.4 Loglinear Models for Partially Classified Contingency Tables 317 13.4.1 The Complete-Data Case 317 13.4.2 Loglinear Models for Partially Classified Tables 320 13.4.3 Goodness-of-Fit Tests for Partially Classified Data 326 14 Mixed Normal and Nonnormal Data with Missing Values, Ignoring the Missingness Mechanism 329 14.1 Introduction 329 14.2 The General Location Model 329 14.2.1 The Complete-DataModel and Parameter Estimates 329 14.2.2 ML Estimation with Missing Values 331 14.2.3 Details of the E Step Calculations 334 14.2.4 Bayes’ Computation for the Unrestricted General Location Model 335 14.3 The General Location Model with Parameter Constraints 337 14.3.1 Introduction 337 14.3.2 Restricted Models for the Cell Means 340 14.3.3 LoglinearModels for the Cell Probabilities 340 14.3.4 Modifications to the Algorithms of Previous Sections to Accommodate Parameter Restrictions 340 14.3.5 SimplificationsWhen Categorical Variables are More Observed than Continuous Variables 343 14.4 Regression Problems InvolvingMixtures of Continuous and Categorical Variables 344 14.4.1 Normal Linear Regression with Missing Continuous or Categorical Covariates 344 14.4.2 Logistic Regression with Missing Continuous or Categorical Covariates 346 14.5 Further Extensions of the General Location Model 347 15 Missing Not at RandomModels 351 15.1 Introduction 351 15.2 Models with Known MNAR Missingness Mechanisms: Grouped and Rounded Data 355 15.3 Normal Models for MNAR Missing Data 362 15.3.1 Normal Selection and Pattern-Mixture Models for Univariate Missingness 362 15.3.2 Following up a Subsample of Nonrespondents 364 15.3.3 The Bayesian Approach 366 15.3.4 Imposing Restrictions on Model Parameters 369 15.3.5 Sensitivity Analysis 376 15.3.6 Subsample Ignorable Likelihood for Regression with Missing Data 379 15.4 Other Models and Methods for MNAR Missing Data 382 15.4.1 MNAR Models for Repeated-Measures Data 382 15.4.2 MNAR Models for Categorical Data 385 15.4.3 Sensitivity Analyses for Chained-Equation Multiple Imputations 391 15.4.4 Sensitivity Analyses in Pharmaceutical Applications 396 References 405 Author Index 429 Subject Index 437

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Book SynopsisComputational Colour Science Using MATLAB 2nd Edition offers a practical, problem-based approach to colour physics. The book focuses on the key issues encountered in modern colour engineering, including efficient representation of colour information, Fourier analysis of reflectance spectra and advanced colorimetric computation.Table of ContentsAcknowledgements About the Authors 1. Introduction 1 1.1 Preface 1 1.2 Why Base this Book on MATLAB? 2 1.3 A Brief Review of the CIE System of Colorimetry 4 2. Linear Algebra for Beginners 13 2.1 Some Basic Definitions 13 2.2 Solving Systems of Simultaneous Equations 14 2.3 Function Approximation 16 3. A Short Introduction to MATLAB 19 3.1 Matrices 19 3.2 Matrix Operations 21 3.3 Solving Linear Systems 23 3.4 M-Files 25 3.5 Using Functions in MATLAB 25 4. Computing CIE Tristimulus Values 27 4.1 Introduction 27 4.2 Colour-Matching Functions 28 4.3 Interpolation Methods 29 4.4 Extrapolation Methods 38 4.5 Correction for Spectral Bandpass 38 4.6 Tristimulus Values 39 4.7 Chromaticity Diagrams 43 5. CIELAB and Colour Difference 49 5.1 Introduction 49 5.2 ACIELAB and CIELUV Colour Space 50 5.2.1 A Representation of CIELAB Using MATLAB 56 5.3 CIELAB Colour Difference 60 5.4 Optimised Colour-Difference Formulae 64 5.4.1 CMC (l:c) 64 5.4.2 CIE 94 67 5.4.3 CIEDE 2000 68 6. Chromatic-Adaptation Transforms and Colour Appearance 75 6.1 Introduction 75 6.2 Chromatic-Adaptation Transforms (CATs) 76 6.2.1 A Brief History of CATs 80 6.2.2 CMCCAT97 80 6.2.3 CMCCAT2000 83 6.3 Colour-Appearance Models (CAMs) 86 6.3.1 CIECAM02 88 7. Physiological Colour Spaces 93 7.1 Introduction 93 7.2 Colour Vision 94 7.3 Cone-Excitation Space 96 7.4 MacLeod and Boynton Chromaticity Diagram 101 7.5 DKL Colour Space 106 8. Colour Management 119 8.1 The Need for Colour Management 119 8.1.1 Using MATLAB to Create Representations of Gamuts 121 8.2 RGB Colour Spaces 122 8.2.1 sRGB 123 8.2.2 Adobe RGB (1998) 125 8.3 The International Color Consortium 126 8.4 Characterisation and Calibration 127 8.4.1 Approaches to Characterisation 128 9. Display Characterisation 131 9.1 Introduction 131 9.2 Gamma 131 9.3 The GOG Model 132 9.4 Device-Independent Transformation 133 9.5 Example Characterisation of CRT Display 134 9.6 Beyond CRT Displays 140 10. Characterisation of Cameras 143 10.1 Introduction 143 10.2 Correction for Nonlinearity 144 10.3 Correction for Lack of Spatial Uniformity 146 10.4 Characterisation 146 10.5 Example Characterisation of a Digital Camera 149 11. Characterisation of Printers 159 11.1 Introduction 159 11.1.1 Physical Models 160 11.1.2 Neural Networks 161 11.2 Characterisation of Half-Tone Printers 162 11.2.1 Correction for Nonlinearity 162 11.2.2 Neugebauer Models 163 11.2.3 Example Characterisation of a Half-Tone Printer 165 11.3 Characterisation of Continuous-Tone Printers 169 11.3.1 Kubelka-Munk Models 169 11.3.2 Interpolation of 3D Look-Up Tables 172 11.3.3 General Linear and Nonlinear Transforms 173 11.3.4 Example Characterisation of a Half-Tone Printer 173 12. Multispectral Imaging 179 12.1 Introduction 179 12.2 Computational Colour Constancy and Linear Models 180 12.2.1 Example Using MATLAB 181 12.3 Properties of Reflectance Spectra 182 12.3.1 PCA and SVD 183 12.3.2 SVD Using MATLAB 12.4 Application of SVD to Reflectance Recovery 189 12.5 Techniques for Multispectral Imaging 191 12.5.1 Maloney-Wandell Method 191 12.5.2 Imai-Berns Method 192 12.5.3 Shi-Healey Method 192 12.5.4 Methods Based on Maximum Smoothness 193 12.5.5 Device Characterisation Revisited 193 12.5.6 Spectral Recovery Using Low-Dimensional Linear Models in MATLAB 193 12.6 Fourier Operations on Reflectance Spectra 193 A. Table of White Points of Illuminants used in r2xyz and Other Functions 197 B. Colour Toolbox 199 B.1 Where to Find the Toolbox 199 B.2 How to Install the Toolbox 199 B.3 Summary of Toolbox Files 199 B.3.1 Computing CIE Tristimulus Values 199 B.3.2 CIELAB and Colour Difference 200 B.3.3 Chromatic-Adaptation Transforms and Colour Appearance 200 B.3.4 Physiological Colour Spaces 200 B.3.5 Colour Management 200 B.3.6 Display Characterisation 200 B.3.7 Characterisation of Cameras 201 B.3.8 Characterisation of Printers 201 References 203 Index 213

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Book SynopsisTable of ContentsB-algebras. Bounded Normal Operators in Hilbert Space. Miscellaneous Operators in Hilbert Space. Unbounded Operators in Hilbert Space. Ordinary Differential Operators. Linear Partial Differential Equations and Operators. Appendix. References. Notation Index. Author Index. Subject Index.

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Book SynopsisPrize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.

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Book Synopsis

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Book Synopsis

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Book SynopsisPerfected over three editions and more than forty years, this field- and classroom-tested reference: * Uses the method of maximum likelihood to a large extent to ensure reasonable, and in some cases optimal procedures. * Treats all the basic and important topics in multivariate statistics. * Adds two new chapters, along with a number of new sections. * Provides the most methodical, up-to-date information on MV statistics available.Trade Review"…suitable for a graduate-level course on multivariate analysis…an important reference on the bookshelves of many scientific researchers and most practicing statisticians." (Journal of the American Statistical Association, September 2004) “…really well written. The edition will be certainly welcomed…” (Zentralblatt Math, Vo.1039, No.08, 2004) "…a wonderful textbook…that covers the mathematical theory of multivariate statistical analysis…" (Clinical Chemistry, Vol. 50, No. 2, May 2004) "...remains an authoritative work that can still be highly recommended..." (Short Book Reviews, 2004) "...still a very serious and comprehensive book on the statistical theory of multivariate analysis." (Technometrics, Vol. 46, No. 1, February 2004) “...remains a mathematically rigorous development of statistical methods for observations consisting of several measurements or characteristics of each subject and a study of their properties.” (Quarterly of Applied Mathematics, Vol. LXI, No. 4, December 2003)Table of ContentsPreface to the Third Edition. Preface to the Second Edition. Preface to the First Edition. 1. Introduction. 2. The Multivariate Normal Distribution. 3. Estimation of the Mean Vector and the Covariance Matrix. 4. The Distributions and Uses of Sample Correlation Coefficients. 5. The Generalized T2-Statistic. 6. Classification of Observations. 7. The Distribution of the Sample Covariance Matrix and the Sample Generalized Variance. 8. Testing the General Linear Hypothesis: Multivariate Analysis of Variance 9. Testing Independence of Sets of Variates. 10. Testing Hypotheses of Equality of Covariance Matrices and Equality of Mean Vectors and Covariance Matrices. 11. Principal Components. 12. Cononical Correlations and Cononical Variables. 13. The Distributions of Characteristic Roots and Vectors. 14. Factor Analysis. 15. Pattern of Dependence; Graphical Models. Appendix A: Matrix Theory. Appendix B: Tables. References. Index.

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Book SynopsisInthe tradition of Fermat’s Enigma and Pi, Marcus du Sautoy tells the illuminating, authoritative, and engagingstory of Bernhard Reimann and the ongoing quest tocapture the holy grail of mathematics—the formula to predict prime numbers.Oliver Sacks, author of The Man Who Mistook His Wife for a Hat, calls TheMusic of the Primes “an amazing book. . . . I could not put it down once Ihad started.” Simon Winchester, author of The Professor and the Madman,writes, “this fascinating account, decoding the inscrutable language of themathematical priesthood, is written like the purest poetry. Marcus du Sautoy''s enthusiasm shines through every line of this hymnto the joy of high intelligence, illuminating as it does so even the darkestcorners of his most arcane universe.”

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