Applied mathematics Books

Book SynopsisA #1 SUNDAY TIMES BESTSELLER Explore the life-changing magic of trigonometry with Matt Parker, stand-up mathematician and No. 1 bestselling author of Humble Pi Why can no two people ever see the same rainbow? What happens when you pull a pop song apart into pure sine waves and play it back on a piano? Why does the wake behind a duck always form an angle of exactly 39 degrees? And what did mathematicians have to do with the great pig stampede of 2012? The answer to each of these questions can be found in the triangle. In Love Triangle, stand-up comedian, ex-maths teacher and Sunday Times number one bestselling author Matt Parker is on a mission to prove why we should all show a lot more love for triangles, along with the useful trigonometry and geometry they enable. To make his point, he uses triangles to create his own digital avatar, survive a harrowing motorcycle ride, cut a sandwich into three equal parts, and measure tall bu

Read more less

Book Synopsis

Read more less

Book SynopsisAn accessible and contemporary introduction to the methods for determining cause and effect in the social sciencesTrade Review“A new guide to methods for determining cause and effect in the social sciences. In summarising, systematising and prioritising methodological tools for researchers, this book will be of use to all social scientists looking to validate their quantitative findings.”—Dr Simeon Mitropolitski, LSE Review of Books "Cunningham's brilliant book is that rare statistical treatise written for students and practitioners alike. Engaging language and vivid examples bring the tools of causal inference to a broad audience. Read the book, absorb its lessons, and you'll develop the skills you need to credibly assess whether a statistics class, a public policy, or a new business practice truly makes a difference."–Justin Wolfers, University of Michigan "Accessible and engaging. An excellent introduction to the statistics of causal inference."–Alberto Abadie, MIT “Learning about causal effects is the main goal of most empirical research in economics. In this engaging book, Scott Cunningham provides an accessible introduction to this area, full of wisdom and wit and with detailed coding examples for practitioners.”--Guido Imbens, coauthor of Causal Inference "This book will probably shock economics instructors with the clarity, insights, and tools that modern graphical models introduce to the teaching of econometrics. The benefits will outlast the shock."--Judea Pearl, University of California, Los Angeles “Causation versus correlation has been the basis of arguments—economic and otherwise—since the beginning of time. Causal Inference: The Mixtape uses legit real-world examples that I found genuinely thought-provoking. It’s rare that a book prompts readers to expand their outlook; this one did for me.”—Marvin Young (Young MC)

Read more less

Book SynopsisEvidence-Based Technical Analysis examines how you can apply the scientific method, and recently developed statistical tests, to determine the true effectiveness of technical trading signals. Throughout the book, expert David Aronson provides you with comprehensive coverage of this new methodology, which is specifically designed for evaluating the performance of rules/signals that are discovered by data mining.Trade Review"…his book is well written and contains a great deal of information that is of value…." (The Technical Analyst, May/June 2007)Table of ContentsAcknowledgments. About the Author. Introduction. PART I Methodological, Psychological, Philosophical, and Statistical Foundations. CHAPTER 1 Objective Rules and Their Evaluation. CHAPTER 2 The Illusory Validity of Subjective Technical Analysis. CHAPTER 3 The Scientific Method and Technical Analysis. CHAPTER 4 Statistical Analysis. CHAPTER 5 Hypothesis Tests and Confidence Intervals. CHAPTER 6 Data-Mining Bias: The Fool’s Gold of Objective TA. CHAPTER 7 Theories of Nonrandom Price Motion. PART II Case Study: Signal Rules for the S&P 500 Index. CHAPTER 8 Case Study of Rule Data Mining for the S&P 500. CHAPTER 9 Case Study Results and the Future of TA. APPENDIX Proof That Detrending Is Equivalent to Benchmarking Based on Position Bias. Notes. Index.

Read more less

Book SynopsisSoccer is the most mathematical of sports--riddled with numbers, patterns, and shapes. How to make sense of them? The answer lies in mathematical modeling, a science with applications in a host of biological systems. Soccermatics brings the two together in a fascinating, mind-bending synthesis. What''s the connection between an ant colony and Total Football, Dutch-style? How is the Barcelona midfield linked geometrically? And how can we relate the mechanics of a Mexican Wave to the singing of cicadas in an Australian valley? Welcome to the world of mathematical modeling, expressed brilliantly by David Sumpter through the prism of soccer. Soccer is indeed more than a game and this book is packed with game theory. After reading it, you will forever watch the game with new eyes.Trade ReviewSumpter's deconstruction of formations proved why maths and football can't live without each other. It's every football nerd's dream. * FourFourTwo *A fascinating and entertaining dive into the mathematics of the beautiful game. * The Guardian *...Highly readable... * The Irish Times *...You will love this book. * The Tribune *This is football looked at in a very different way. David Sumpter is mining a rich and deep seam here in Soccermatics, one that will become an increasingly important part of the game. -- Pat Nevin, former Chelsea and Everton star and football media analystA fascinating study of the structures and patterns that underpin football matches, with revealing and surprising conclusions. -- Michael Cox, editor of Zonal Marking and Guardian SportsSoccermatics provides fresh insight into a game we've been watching all of our lives. But it's more than a book about football and is all the better for it. -- Adam Bate, football features writer for Sky SportsDavid Sumpter brings together his two passions, mathematics and football, in a highly original and entertaining way. The beautiful game illustrated through the beauty of mathematics. -- Philip Maini FRS, Professor of Mathematical Biology, University of OxfordTable of ContentsPreface: The Kick-off Part I: On the Pitch Chapter 1: I Never Predict Anything and I Never Will Chapter 2: How Slime Moulds Built Barcelona Chapter 3: Check My Flow Chapter 4: Statistical Brilliance Chapter 5: Zlatan Ibrah Rocket Science Part II: In the Dugout Chapter 6: Three Points for the Bird-brained Manager Chapter 7: The Tactical Map CHapter 8: Total Cyber Dynamo Chapter 9: The World in Motion Part III: From the Crowd Chapter 10: You'll Never Walk Alone Chapter 11: Bet Against the Masses Chapter 12: Putting My Money Where My Mouth Is Chapter 13: The Results Are In The Full-Time Whistle Notes Acknowledgements Index

Read more less

Book SynopsisTable of ContentsBasic Math and Pre-Algebra For Dummies, 2nd Edition Introduction 1 Part 1: Getting Started with Basic Math and Pre-Algebra 5 CHAPTER 1: Playing the Numbers Game 7 CHAPTER 2: It’s All in the Fingers: Numbers and Digits 23 CHAPTER 3: The Big Four: Addition, Subtraction, Multiplication, and Division 29 Part 2: Getting a Handle on Whole Numbers 47 CHAPTER 4: Putting the Big Four Operations to Work 49 CHAPTER 5: A Question of Values: Evaluating Arithmetic Expressions 63 CHAPTER 6: Say What? Turning Words into Numbers 75 CHAPTER 7: Divisibility 87 CHAPTER 8: Fabulous Factors and Marvelous Multiples 95 Part 3: Parts of the Whole: Fractions, Decimals, and Percents 109 CHAPTER 9: Fooling with Fractions 111 CHAPTER 10: Parting Ways: Fractions and the Big Four Operations 125 CHAPTER 11: Dallying with Decimals 149 CHAPTER 12: Playing with Percents 171 CHAPTER 13: Word Problems with Fractions, Decimals, and Percents 183 Part 4: Picturing and Measuring — Graphs, Measures, Stats, and Sets 195 CHAPTER 14: A Perfect Ten: Condensing Numbers with Scientific Notation 197 CHAPTER 15: How Much Have You Got? Weights and Measures 205 CHAPTER 16: Picture This: Basic Geometry 217 CHAPTER 17: Seeing Is Believing: Graphing as a Visual Tool 239 CHAPTER 18: Solving Geometry and Measurement Word Problems 247 CHAPTER 19: Figuring Your Chances: Statistics and Probability 259 CHAPTER 20: Setting Things Up with Basic Set Theory 271 Part 5: The X-Files: Introduction to Algebra 279 CHAPTER 21: Enter Mr X: Algebra and Algebraic Expressions 281 CHAPTER 22: Unmasking Mr X: Algebraic Equations 299 CHAPTER 23: Putting Mr X to Work: Algebra Word Problems 311 Part 6: The Part of Tens 321 CHAPTER 24: Ten Little Math Demons That Trip People Up 323 CHAPTER 25: Ten Important Number Sets to Know 329 Index 337 Basic Math and Pre-Algebra Workbook For Dummies, 3rd Edition Introduction 1 Part 1: Getting Started with Basic Math and Pre-Algebra 5 CHAPTER 1: We've Got Your Numbers 7 CHAPTER 2: Smooth Operators: Working with the Big Four Operations 23 CHAPTER 3: Getting Down with Negative Numbers 37 CHAPTER 4: It's Just an Expression 49 CHAPTER 5: Dividing Attention: Divisibility, Factors, and Multiples 69 Part 2: Slicing Things Up: Fractions, Decimals, and Percents 89 CHAPTER 6: Fractions Are a Piece of Cake 91 CHAPTER 7: Fractions and the Big Four 109 CHAPTER 8: Getting to the Point with Decimals 143 CHAPTER 9: Playing the Percentages 165 Part 3: A Giant Step Forward: Intermediate Topics 177 CHAPTER 10: Seeking a Higher Power through Scientific Notation 179 CHAPTER 11: Weighty Questions on Weights and Measures 189 CHAPTER 12: Shaping Up with Geometry 203 CHAPTER 13: Getting Graphic: Xy-Graphs 223 Part 4: The X Factor: Introducing Algebra 235 CHAPTER 14: Expressing Yourself with Algebraic Expressions 237 CHAPTER 15: Finding the Right Balance: Solving Algebraic Equations 259 Part 5: The Part of Tens 277 CHAPTER 16: Ten Alternative Numeral and Number Systems 279 CHAPTER 17: Ten Curious Types of Numbers 287 Index 293

Read more less

Book SynopsisThis is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; coversTrade Review"The treasures [in the Princeton Companion to Applied Mathematics] go on and on."--Lloyd N. Trefethen, SIAM Review "[An] impressive volume... It has been a major project that eventually resulted in this amazing product."--Adhemar Bultheel, European Mathematical Society "Safe to say there is something for everyone in The Princeton Companion to Applied Mathematics."--Alan Stevens, Mathematics Today "[A] valuable addition to the mathematics library of any university or research institution."--Library Journal "Higham and his associate editors ... have produced an admirably readable and informative volume, which anyone interested in applied mathematics would be well advised to consult or--better still--to own!"--James Case, SIAM News "A unique work full of beautiful and interesting mathematics. It is surely a valuable resource for exposing young mathematicians to possible areas of applied mathematics for research and further study. Without a doubt PCAM is an important contribution to the mathematical literature."--Jason M. Graham, MathSciNet "[A]n excellent reference that successfully compiles into a readable and engaging form the broad range of topics that an applied mathematician might encounter in their career... As a reader, I find myself flipping through the pages and becoming engaged in new and interesting ideas from the world of applied math."--Joanna Bieri, MAA Reviews "A handy one-volume reference for applied mathematics that cuts across several disciplines within an academic framework."--Lesley S.J. Farmer, Reference ReviewsTable of Contents*Frontmatter, pg. i*Contents, pg. v*Preface, pg. ix*Contributors, pg. xiii*Part I. Introduction to Applied Mathematics, pg. 1*Part II. Concepts, pg. 81*Part III. Equations, Laws, and Functions of Applied Mathematics, pg. 135*Part IV. Areas of Applied Mathematics, pg. 173*Part V. Modeling, pg. 591*Part VI. Example Problems, pg. 733*Part VII. Application Areas, pg. 783*Part VIII. Final Perspectives, pg. 897*Index, pg. 963

Read more less

Book SynopsisTable of ContentsPart 1 Introduction to Programming Using MATLAB 1. Introduction to MATLAB 2. Vectors and Matrices 3. Introduction to MATLAB Programming 4. Selection Statements 5. Loop Statements and Vectorizing Code 6. MATLAB Programs 7. Text Manipulation 8. Data Structures Part 2 Advanced Topics for Problem Solving with MATLAB 9. Data Transfer 10. Advanced Functions 11. Introduction to Object-Oriented Programming and Graphics 12. Advanced Plotting Techniques 13. Sights and Sounds 14. Advanced Mathematics 15. Introduction to Machine Learning

Read more less

Book SynopsisThis book reveals glimpses of how the quantum physics of atoms and molecules influences, and even controls, the way our cells function and how we and our fellow animals interact with our environment. Simply put, how birds fly and why grass grows.Certainly, biochemistry and molecular biology are the foundations for the biology of living cells, but there is more—quantum coherence and entanglement influencing the functioning of proteins and enzymes, and strictly speaking, without the quantum phenomena we wouldn’t even be here.In the end, however, this book is based on the solid ground of science, presenting the many fascinating phenomena of how quantum physics makes life possible without any unwarranted mystification.Table of Contents1. Life and Quantum Physics 2. Our World Is Just a Small Part of the Whole 3. The Gecko and Life Upside Down 4. The Quantized World 5. Evolution: About the Origin of Life 6. From the Big Bang to Black Holes 7. As Time Goes By: The Arrow of Time 8. The Art of Finding Your Way Back Home 9. The Vision in New Light 10. Photosynthesis and the Golf Putt 11. The Respiratory Chain Sustains Our Lives 12. A Sense of Smell 13. DNA Repair: A Matter of Survival and Development 14. Quantum Physics in Diagnostics and Therapy 15. Not More Mysterious Than Necessary 16. Consciousness: The Greatest Mystery 17. A Glance at the Future of Quantum and Life

Read more less

Book SynopsisPraise for the First Edition An indispensable addition to any serious collection on lifetime data analysis and . . . a valuable contribution to the statistical literature. Highly recommended . . . -Choice This is an important book, which will appeal to statisticians working on survival analysis problems. -Biometrics A thorough, unified treatment of statistical models and methods used in the analysis of lifetime data . . . this is a highly competent and agreeable statistical textbook. -Statistics in Medicine The statistical analysis of lifetime or response time data is a key tool in engineering, medicine, and many other scientific and technological areas. This book provides a unified treatment of the models and statistical methods used to analyze lifetime data. Equally useful as a reference for individuals interested in the analysis of lifetime data and as a text for advanced students, Statistical Models and Methods for Lifetime Data, SecoTrade Review“...a welcome addition to the literature on survival analysis...for a unified and thorough reference of classical theory and models, this book is an excellent choice.” (Journal of the American Statistical Association, March 2004) "This book is a role-model for other who are planning to write books…every statistician and applied researcher ought to have this book in their collection." (Journal of Statistical Computation and Simulation, October 2003) "...expanded and updated with recent research...a valuable reference...this book...merits a place on the bookshelf of anyone concerned with the analysis of lifetime data from any field. (Technometrics, Vol. 45, No. 3, August 2003) "...updated version of the popular text...this excellent book will serve as either a reference or a graduate-level textbook." (Short Book Reviews, Vol. 23, No. 2, August 2003) "...excellent...provides a wealth of information for those familiar with the area." (Pharmaceutical Research, Vol. 20, No. 9, September 2003) "...the author's aim is to cover lifetime data analysis without concentrating exclusively on any field of applications...he succeeds quite well..." (Zentralblatt Math, 2003) “...rewritten to reflect new developments...” (Quarterly of Applied Mathematics, Vol. LXI, No. 2, June 2003) "Compared with the large number of other good textbooks in the this field, this is one of the best. I highly recommend that all applied statisticians add this volume to their libraries." (Applied Clinical Trials, May 2003)Table of ContentsBasic Concepts and Models. Observation Schemes, Censoring and Likelihood. Some Nonparametric and Graphical Procedures. Inference Procedures for Parametric Models. Inference procedures for Log-Location-Scale Distributions. Parametric Regression Models. Semiparametric Multiplicative Hazards Regression Models. Rank-Type and Other Semiparametric Procedures for Log-Location-Scale Models. Multiple Modes of Failure. Goodness of Fit Tests. Beyond Univariate Survival Analysis. Appendix A. Glossary of Notation and Abbreviations. Appendix B. Asymptotic Variance Formulas, Gamma Functions and Order Statistics. Appendix C. Large Sample Theory for Likelihood and Estimating Function Methods. Appendix D. Computational Methods and Simulation. Appendix E. Inference in Location-Scale Parameter Models. Appendix F. Martingales and Counting Processes. Appendix G. Data Sets. References.

Read more less

Book Synopsis

Read more less

Book SynopsisHugh Barker is a non-fiction author and editor; as the latter he has edited several successful popular maths books, including A Slice of Pi. Hugh is a keen amateur mathematician and was accepted to study maths at Cambridge University aged 16.

Read more less

Book SynopsisMatrix Differential Calculus With Applications in Statistics and Econometrics Revised Edition Jan R. Magnus, CentER, Tilburg University, The Netherlands and Heinz Neudecker, Cesaro, Schagen, The Netherlands .deals rigorously with many of the problems that have bedevilled the subject up to the present time. - Stephen Pollock, Econometric Theory I continued to be pleasantly surprised by the variety and usefulness of its contents - Isabella Verdinelli, Journal of the American Statistical Association Continuing the success of their first edition, Magnus and Neudecker present an exhaustive and self-contained revised text on matrix theory and matrix differential calculus. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioural sciences to econometrics. While the structure and successful elements of the first edition remain, this revised and updated edition contains many new examples and exercises. * CoTrade Review"...the best book to learn matrix and related ideas...statisticians, econometricians, computer scientists, engineers, and psychometricians will find this extremely useful." (Journal of Statistical Computation and Simulation, March 2006) "a most welcome revision" (Computational Statistics & Data Analysis, 28 August 2001)Table of ContentsPreface xv Preface to the first revised printing xvii Preface to the second revised printing xviii Part One- Matrices Part Two- Differentials: the theory Part Three- Differentials: the practice Part Four- Inequalities Part Five- The linear model Part Six- Applications to maximum likelihood estimation Bibliography 379 Index of Symbols 387 Subject Index 390

Read more less

Book SynopsisThis textbook is an introduction to the theory of solitons and its diverse applications to nonlinear systems that arise in the physical sciences. The authors explain the generation and properties of solitons, introducing the mathematical technique known as the Inverse Scattering Transform. Their aim is to present the essence of inverse scattering clearly, rather than rigorously or completely. Thus, the prerequisites (i.e., partial differential equations, calculus of variations, Fourier integrals, linear waves and SturmâLiouville theory), and more advanced material is explained in the text with useful references to further reading given at the end of each chapter. Worked examples are frequently used to help the reader follow the various ideas, and the exercises at the end of each chapter not only contain applications but also test understanding. Answers, or hints to the solution, are given at the end of the book. Sections and exercises that contain more difficult material are indicated Trade Review"...should find an enthusiastic following, and the author is to be congratulated on a job well done." American Scientist"...a fine book, certainly the one that I would choose as the text for an introductory course on solitons." SIAM Review"All things considered, I cannot think of a clearer introduction to the subject from a mathematical point of view." Physics Today"...an excellent book, achieving its goals both concisely and comprehensively." John G. Harris, Applied Mechanics ReviewTable of ContentsPreface; 1. The Kortewag–de Vries equation; 2. Elementary solutions of the Korteweg–de Vries equation; 3. The scattering and inverse scattering problems; 4. The initial-value problem for the Korteweg–de Vries equation; 5. Further properties of the Korteweg–de Vries equation; 6. More general inverse methods; 7. The Painlevé property, perturbations and numerical methods; 8. Epilogue; Answers and hints; Bibliography and author index; Motion picture index; Subject index.

Read more less

Book SynopsisThis book provides a detailed description of how Python can be used to give insight into the flow of groundwater based on analytic solutions. Starting with simple problems to illustrate the basic principles, complexity is added step by step to show how one-dimensional and two-dimensional models of one or two aquifers can be implemented. Steady and transient flow problems are discussed in confined, semi-confined, and unconfined aquifers that may include wells, rivers, and areal recharge. Special consideration is given to coastal aquifers, including the effect of tides and the simulation of interface flow.Application of Python allows for compact and readable code, and quick visualization of the solutions. Python scripts are provided to reproduce all results. The scripts are also available online so that they can be altered to meet site-specific conditions. This book is intended both as training material for the next generation of university students and as a useful resource forTrade Review 'This is a fantastic addition to the analytical solutions and analytic element modeling canon with a modern approach to programming with Python. I hope readers will use it to learn and explore groundwater theory, and to up their game on making simple reality checks of complex systems to improve all groundwater modeling.''The authors do an excellent job of describing practically important calculations, like determining the critical flowrate at which a pumped well starts to induce flow from a nearby river.'- Michael Fienen, Groundwater - NGWA, Book Review, 7 September 2022'This is a fantastic addition to the analytical solutions and analytic element modeling canon with a modern approach to programming with Python. I hope readers will use it to learn and explore groundwater theory, and to up their game on making simple reality checks of complex systems to improve all groundwater modeling.''The authors do an excellent job of describing practically important calculations, like determining the critical flowrate at which a pumped well starts to induce flow from a nearby river.'- Michael Fienen, Groundwater - NGWA, Book Review, 7 September 2022Table of Contents0. Basics of Groundwater Flow. 1. Steady One-dimensional Flow with Constant Transmissivity. 2. Steady One-dimensional Semi-confined Flow. 3. Steady One-dimensional Unconfined Flow with Variable Saturated Thickness. 4. Steady One-dimensional Flow in Coastal Aquifers. 5. Transient One-dimensional Flow. 6. Steady Two-dimensional Flow to Wells. 7. Steady Two-dimensional Flow to Wells in Uniform Background Flow. 8. Analytic Element Modeling of Steady Two-dimensional Flow. 9. Transient Two-dimensional Flow. 10. Steady Two-dimensional Flow in the Vertical Plane. 11. Appendix - Python Primer

Read more less

Book SynopsisComprehensively teaches the fundamentals of supply chain theory This book presents the methodology and foundations of supply chain management and also demonstrates how recent developments build upon classic models. The authors focus on strategic, tactical, and operational aspects of supply chain management and cover a broad range of topics from forecasting, inventory management, and facility location to transportation, process flexibility, and auctions. Key mathematical models for optimizing the design, operation, and evaluation of supply chains are presented as well as models currently emerging from the research frontier. Fundamentals of Supply Chain Theory, Second Edition contains new chapters on transportation (traveling salesman and vehicle routing problems), integrated supply chain models, and applications of supply chain theory. New sections have also been added throughout, on topics including machine learning models for forecasting, conic optimizaTable of ContentsList of Figures xxi List of Tables xxvii List of Algorithms xxix Preface xxxi 1 Introduction 1 1.1 The Evolution of Supply Chain Theory 1 1.2 Definitions and Scope 2 1.3 Levels of Decision Making in Supply Chain Management 4 2 Forecasting and Demand Modeling 5 2.1 Introduction 5 2.2 Classical Demand Forecasting Methods 6 2.3 Forecast Accuracy 15 2.4 Machine Learning in Demand Forecasting 17 2.5 Demand Modeling Techniques 23 2.6 Bass Diffusion Model 24 2.7 Leading Indicator Approach 30 2.8 Discrete Choice Models 33 Case Study: Semiconductor Demand Forecasting at Intel 38 Problems 39 3 Deterministic Inventory Models 45 3.1 Introduction to Inventory Modeling 45 3.2 Continuous Review: The Economic Order Quantity Problem 51 3.3 Power of Two Policies 57 3.4 The EOQ with Quantity Discounts 60 3.5 The EOQ with Planned Backorders 67 3.6 The Economic Production Quantity Model 70 3.7 Periodic Review: The Wagner–Whitin Model 72 Case Study: Ice Cream Production and Inventory at Scotsburn Dairy Group 76 Problems 77 4 Stochastic Inventory Models: Periodic Review 87 4.1 Inventory Policies 87 4.2 Demand Processes 89 4.3 Periodic Review with Zero Fixed Costs: Base-Stock Policies 89 4.4 Periodic Review with Nonzero Fixed Costs: (s; S) Policies 114 4.5 Policy Optimality 123 4.6 Lost Sales 136 Case Study: Optimization of Warranty Inventory at Hitachi 138 Problems 140 5 Stochastic Inventory Models: Continuous Review 155 5.1 (r; Q) Policies 155 5.2 Exact (r; Q) Problem with Continuous Demand Distribution 156 5.3 Approximations for (r; Q) Problem with Continuous Distribution 161 5.4 Exact (r; Q) Problem with Continuous Distribution: Properties of Optimal r and Q 170 5.5 Exact (r; Q) Problem with Discrete Distribution 177 Case Study: (r; Q) Inventory Optimization at Dell 180 Problems 182 6 Multiechelon Inventory Models 187 6.1 Introduction 187 6.2 Stochastic-Service Models 191 6.3 Guaranteed-Service Models 203 6.4 Closing Thoughts 217 Case Study: Multiechelon Inventory Optimization at Procter & Gamble 222 Problems 223 7 Pooling and Flexibility 229 7.1 Introduction 229 7.2 The Risk-Pooling Effect 230 7.3 Postponement 236 7.4 Transshipments 237 7.5 Process Flexibility 243 7.6 A Process Flexibility Optimization Model 253 Case Study: Risk Pooling and Inventory Management at Yedioth Group 257 Problems 259 8 Facility Location Models 267 8.1 Introduction 267 8.2 The Uncapacitated Fixed-Charge Location Problem 269 8.3 Other Minisum Models 295 8.4 Covering Models 305 8.5 Other Facility Location Problems 314 8.6 Stochastic and Robust Location Models 317 8.7 Supply Chain Network Design 321 Case Study: Locating Fire Stations in Istanbul 332 Problems 335 9 Supply Uncertainty 355 9.1 Introduction to Supply Uncertainty 355 9.2 Inventory Models with Disruptions 356 9.3 Inventory Models with Yield Uncertainty 365 9.4 A Multisupplier Model 372 9.5 The Risk-Diversification Effect 384 9.6 A Facility Location Model with Disruptions 387 Case Study: Disruption Management at Ford 395 Problems 396 10 The Traveling Salesman Problem 403 10.1 Supply Chain Transportation 403 10.2 Introduction to the TSP 404 10.3 Exact Algorithms for the TSP 408 10.4 Construction Heuristics for the TSP 416 10.5 Improvement Heuristics for the TSP 436 10.6 Bounds and Approximations for the TSP 442 10.7 World Records 452 Case Study: Routing Meals on Wheels Deliveries 453 Problems 455 11 The Vehicle Routing Problem 463 11.1 Introduction to the VRP 463 11.2 Exact Algorithms for the VRP 468 11.3 Heuristics for the VRP 475 11.4 Bounds and Approximations for the VRP 495 11.5 Extensions of the VRP 498 Case Study: ORION: Optimizing Delivery Routes at UPS 501 Problems 502 12 Integrated Supply Chain Models 511 12.1 Introduction 511 12.2 A Location–Inventory Model 512 12.3 A Location–Routing Model 529 12.4 An Inventory–Routing Model 531 Case Study: Inventory–Routing at Frito-Lay 534 Problems 535 13 The Bullwhip Effect 539 13.1 Introduction 539 13.2 Proving the Existence of the Bullwhip Effect 541 13.3 Reducing the Bullwhip Effect 552 13.4 Centralizing Demand Information 555 Case Study: Reducing the Bullwhip Effect at Philips Electronics 556 Problems 559 14 Supply Chain Contracts 563 14.1 Introduction 563 14.2 Introduction to Game Theory 564 14.3 Notation 565 14.4 Preliminary Analysis 566 14.5 The Wholesale Price Contract 568 14.6 The Buyback Contract 574 14.7 The Revenue Sharing Contract 578 14.8 The Quantity Flexibility Contract 581 Case Study: Designing a Shared-Savings Contract at McGriff Treading Company 584 Problems 586 15 Auctions 591 15.1 Introduction 591 15.2 The English Auction 593 15.3 Combinatorial Auctions 595 15.4 The Vickrey–Clarke–Groves Auction 599 Case Study: Procurement Auctions for Mars 608 Problems 610 16 Applications of Supply Chain Theory 615 16.1 Introduction 615 16.2 Electricity Systems 615 16.3 Health Care 625 16.4 Public Sector Operations 632 Case Study: Optimization of the Natural Gas Supply Chain in China 639 Problems 641 Appendix A: Multiple-Chapter Problems 643 Problems 643 Appendix B: How to Write Proofs: A Short Guide 651 B.1 How to Prove Anything 651 B.2 Types of Things You May Be Asked to Prove 653 B.3 Proof Techniques 655 B.4 Other Advice 657 Appendix C: Helpful Formulas 661 C.1 Positive and Negative Parts 661 C.2 Standard Normal Random Variables 662 C.3 Loss Functions 662 C.4 Differentiation of Integrals 665 C.5 Geometric Series 666 C.6 Normal Distributions in Excel and MATLAB 666 C.7 Partial Expectations 667 Appendix D: Integer Optimization Techniques 669 D.1 Lagrangian Relaxation 669 D.2 Column Generation 675 References 681 Subject Index 712 Author Index 725

Read more less

Book SynopsisOffering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling.Table of Contents1. Modeling Change. 2. The Modeling Process, Proportionality, and Geometric Similarity. 3. Model Fitting. 4. Experimental Modeling. 5. Simulation Modeling. 6. Discrete Probabilistic Modeling. 7. Optimization of Discrete Models. 8. Modeling with Graph Theory. 9. Modeling with Decision Theory. 10. Game Theory. 11. Modeling with a Differential Equation. 12. Modeling with Systems of Differential Equations. 13. Optimization of Continuous Modeling. 14. Dimensional Analysis and Similitude. 15. Graphs of Functions as Models. Appendix A: Problems from the Mathematics Contest in Modeling, 1985-2007. Appendix B: An Elevator Simulation Model. Appendix C: The Revised Simplex Method. Appendix D. Brief Review of Integration Techniques.

Read more less

Book SynopsisThe first edition of this award-winning book attracted a wide audience. This second edition is both a joy to read and a useful classroom tool. Unlike traditional textbooks, it requires no mathematical prerequisites and can be read around the mathematics presented. If used as a textbook, the mathematics can be prioritized, with a book both students and instructors will enjoy reading.Secret History: The Story of Cryptology, Second Edition incorporates new material concerning various eras in the long history of cryptology. Much has happened concerning the political aspects of cryptology since the first edition appeared. The still unfolding story is updated here.The first edition of this book contained chapters devoted to the cracking of German and Japanese systems during World War II. Now the other side of this cipher war is also told, that is, how the United States was able to come up with systems that were never broken.The text is in t

Read more less

Book SynopsisGives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. This book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables.Trade Review"The authors do a good job of deriving the mathematical models from physical considerations, and then showing how the equations can be solved by finite difference methods."--Choice "Where was this book when I was in university? ... I enjoyed this book very much and recommend it to students and researchers with an interest in this field."--Ray Wood, Leading EdgeTable of ContentsPreface xi Chapter 1: Modeling and Mathematical Concepts 1 Pros and Cons of Dynamical Models 2 An Important Modeling Assumption 4 Some Examples 4 Example I: Simulation of Chicxulub Impact and Its Consequences 5 Example II: Storm Surge of Hurricane Ivan in Escambia Bay 7 Steps in Model Building 8 Basic Definitions and Concepts 11 Nondimensionalization 13 A Brief Mathematical Review 14 Summary 22 Chapter 2: Basics of Numerical Solutions by Finite Difference 23 First Some Matrix Algebra 23 Solution of Linear Systems of Algebraic Equations 25 General Finite Difference Approach 26 Discretization 27 Obtaining Difference Operators by Taylor Series 28 Explicit Schemes 29 Implicit Schemes 30 How Good Is My Finite Difference Scheme? 33 Stability Is Not Accuracy 35 Summary 37 Modeling Exercises 38 Chapter 3: Box Modeling: Unsteady, Uniform Conservation of Mass 39 Translations 40 Example I: Radiocarbon Content of the Biosphere as a One-Box Model 40 Example II: The Carbon Cycle as a Multibox Model 48 Example III: One-Dimensional Energy Balance Climate Model 53 Finite Difference Solutions of Box Models 57 The Forward Euler Method 57 Predictor-Corrector Methods 59 Stiff Systems 60 Example IV: Rothman Ocean 61 Backward Euler Method 65 Model Enhancements 69 Summary 71 Modeling Exercises 71 Chapter 4: One-Dimensional Diffusion Problems 74 Translations 75 Example I: Dissolved Species in a Homogeneous Aquifer 75 Example II: Evolution of a Sandy Coastline 80 Example III: Diffusion of Momentum 83 Finite Difference Solutions to 1-D Diffusion Problems 86 Summary 86 Modeling Exercises 87 Chapter 5: Multidimensional Diffusion Problems 89 Translations 90 Example I: Landscape Evolution as a 2-D Diffusion Problem 90 Example II: Pollutant Transport in a Confined Aquifer 96 Example III: Thermal Considerations in Radioactive Waste Disposal 99 Finite Difference Solutions to Parabolic PDEs and Elliptic Boundary Value Problems 101 An Explicit Scheme 102 Implicit Schemes 103 Case of Variable Coefficients 107 Summary 108 Modeling Exercises 109 Chapter 6: Advection-Dominated Problems 111 Translations 112 Example I: A Dissolved Species in a River 112 Example II: Lahars Flowing along Simple Channels 116 Finite Difference Solution Schemes to the Linear Advection Equation 122 Summary 126 Modeling Exercises 128 Chapter 7: Advection and Diffusion (Transport) Problems 130 Translations 131 Example I: A Generic 1-D Case 131 Example II: Transport of Suspended Sediment in a Stream 134 Example III: Sedimentary Diagenes Influence of Burrows 138 Finite Difference Solutions to the Transport Equation 143 QUICK Scheme 144 QUICKEST Scheme 146 Summary 147 Modeling Exercises 147 Chapter 8: Transport Problems with a Twist: The Transport of Momentum 151 Translations 152 Example I: One-Dimensional Transport of Momentum in a Newtonian Fluid (Burgers' Equation) 152 An Analytic Solution to Burgers' Equation 157 Finite Difference Scheme for Burgers' Equation 158 Solution Scheme Accuracy 160 Diffusive Momentum Transport in Turbulent Flows 163 Adding Sources and Sinks of Momentum: The General Law of Motion 165 Summary 166 Modeling Exercises 167 Chapter 9: Systems of One-Dimensional Nonlinear Partial Differential Equations 169 Translations 169 Example I: Gradually Varied Flow in an Open Channel 169 Finite Difference Solution Schemes for Equation Sets 175 Explicit FTCS Scheme on a Staggered Mesh 175 Four-Point Implicit Scheme 177 The Dam-Break Problem: An Example 180 Summary 183 Modeling Exercises 185 Chapter 10: Two-Dimensional Nonlinear Hyperbolic Systems 187 Translations 188 Example I: The Circulation of Lakes, Estuaries, and the Coastal Ocean 188 An Explicit Solution Scheme for 2-D Vertically Integrated Geophysical Flows 197 Lake Ontario Wind-Driven Circulation: An Example 202 Summary 203 Modeling Exercises 206 Closing Remarks 209 References 211 Index 217

Read more less

Book SynopsisOffers an introduction to the modeling of infectious diseases in humans and animals. This book moves from modeling with simple differential equations to more complex models, where spatial structure, seasonal 'forcing', or stochasticity influence the dynamics, and where computer simulation needs to be used to generate theory.Trade Review"Matt Keeling and Pejman Rohani...have made important and original contributions to epidemiology...and are well qualified to deliver an authoritative, comprehensive and up-to-date review. [The authors] advocate...the use of mathematical models to help design disease-control programs. They recognize that modeling is a partnership between modelers and empiricists. For that reason, I hope that [readership] will extend beyond existing and new devotees of this challenging and exciting discipline."--Mark Woolhouse, Nature "This book represents a valuable step toward educating readers to have greater appreciation and understanding of the development of mathematical models in infectious diseases."--Carol Y. Lin, Biometrics Book Reviews "[T]he authors have created a well written and essential reference for epidemiologists, mathematicians and other scientists interested in the mathematical modeling of infectious diseases."--Michael Hohle, Biometrical JournalTable of ContentsAcknowledgments xiii Chapter 1: Introduction 1 1.1 Types of Disease 1 1.2 Characterization of Diseases 3 1.3 Control of Infectious Diseases 5 1.4 What Are Mathematical Models? 7 1.5 What Models Can Do 8 1.6 What Models Cannot Do 10 1.7 What Is a Good Model? 10 1.8 Layout of This Book 11 1.9 What Else Should You Know? 13 Chapter 2: Introduction to Simple Epidemic Models 15 2.1 Formulating the Deterministic SIR Model 16 2.1.1 The SIR Model Without Demography 19 2.1.1.1 The Threshold Phenomenon 19 2.1.1.2 Epidemic Burnout 21 2.1.1.3 Worked Example: Influenza in a Boarding School 26 2.1.2 The SIR Model With Demography 26 2.1.2.1 The Equilibrium State 28 2.1.2.2 Stability Properties 29 2.1.2.3 Oscillatory Dynamics 30 2.1.2.4 Mean Age at Infection 31 2.2 Infection-Induced Mortality and SI Models 34 2.2.1 Mortality Throughout Infection 34 2.2.1.1 Density-Dependent Transmission 35 2.2.1.2 Frequency Dependent Transmission 36 2.2.2 Mortality Late in Infection 37 2.2.3 Fatal Infections 38 2.3 Without Immunity: The SIS Model 39 2.4 Waning Immunity: The SIRS Model 40 2.5 Adding a Latent Period: The SEIR Model 41 2.6 Infections with a Carrier State 44 2.7 Discrete-Time Models 46 2.8 Parameterization 48 2.8.1 Estimating R0 from Reported Cases 50 2.8.2 Estimating R0 from Seroprevalence Data 51 2.8.3 Estimating Parameters in General 52 2.9 Summary 52 Chapter 3: Host Heterogeneities 54 3.1 Risk-Structure: Sexually Transmitted Infections 55 3.1.1 Modeling Risk Structure 57 3.1.1.1 High-Risk and Low-Risk Groups 57 3.1.1.2 Initial Dynamics 59 3.1.1.3 Equilibrium Prevalence 62 3.1.1.4 Targeted Control 63 3.1.1.5 Generalizing the Model 64 3.1.1.6 Parameterization 64 3.1.2 Two Applications of Risk Structure 69 3.1.2.1 Early Dynamics of HIV 71 3.1.2.2 Chlamydia Infections in Koalas 74 3.1.3 Other Types of Risk Structure 76 3.2 Age-Structure: Childhood Infections 77 3.2.1 Basic Methodology 78 3.2.1.1 Initial Dynamics 80 3.2.1.2 Equilibrium Prevalence 80 3.2.1.3 Control by Vaccination 81 3.2.1.3 Parameterization 82 3.2.2 Applications of Age Structure 84 3.2.2.1 Dynamics of Measles 84 3.2.2.2 Spread and Control of BSE 89 3.3 Dependence on Time Since Infection 93 3.3.1 SEIR and Multi-Compartment Models 94 3.3.2 Models with Memory 98 3.3.3 Application: SARS 100 3.4 Future Directions 102 3.5 Summary 103 Chapter 4: Multi-Pathogen/Multi-Host Models 105 4.1 Multiple Pathogens 106 4.1.1 Complete Cross-Immunity 107 4.1.1.1 Evolutionary Implications 109 4.1.2 No Cross-Immunity 112 4.1.2.1 Application: The Interaction of Measles and Whooping Cough 112 4.1.2.2 Application: Multiple Malaria Strains 115 4.1.3 Enhanced Susceptibility 116 4.1.4 Partial Cross-Immunity 118 4.1.4.1 Evolutionary Implications 120 4.1.4.2 Oscillations Driven by Cross-Immunity 122 4.1.5 A General Framework 125 4.2 Multiple Hosts 128 4.2.1 Shared Hosts 130 4.2.1.1 Application: Transmission of Foot-and-Mouth Disease 131 4.2.1.2 Application: Parapoxvirus and the Decline of the Red Squirrel 133 4.2.2 Vectored Transmission 135 4.2.2.1 Mosquito Vectors 136 4.2.2.2 Sessile Vectors 141 4.2.3 Zoonoses 143 4.2.3.1 Directly Transmitted Zoonoses 144 4.2.3.2 Vector-Borne Zoonoses: West Nile Virus 148 4.3 Future Directions 151 4.4 Summary 153 Chapter 5: Temporally Forced Models 155 5.1 Historical Background 155 5.1.1 Seasonality in Other Systems 158 5.2 Modeling Forcing in Childhood Infectious Diseases: Measles 159 5.2.1 Dynamical Consequences of Seasonality: Harmonic and Subharmonic Resonance 160 5.2.2 Mechanisms of Multi-Annual Cycles 163 5.2.3 Bifurcation Diagrams 164 5.2.4 Multiple Attractors and Their Basins 167 5.2.5 Which Forcing Function? 171 5.2.6 Dynamical Trasitions in Seasonally Forced Systems 178 5.3 Seasonality in Other Diseases 181 5.3.1 Other Childhood Infections 181 5.3.2 Seasonality in Wildlife Populations 183 5.3.2.1 Seasonal Births 183 5.3.2.2 Application: Rabbit Hemorrhagic Disease 185 5.4 Summary 187 Chapter 6: Stochastic Dynamics 190 6.1 Observational Noise 193 6.2 Process Noise 193 6.2.1 Constant Noise 195 6.2.2 Scaled Noise 197 6.2.3 Random Parameters 198 6.2.4 Summary 199 6.2.4.1 Contrasting Types of Noise 199 6.2.4.2 Advantages and Disadvantages 200 6.3 Event-Driven Approaches 200 6.3.1 Basic Methodology 201 6.3.1.1 The SIS Model 202 6.3.2 The General Approach 203 6.3.2.1 Simulation Time 203 6.3.3 Stochastic Extinctions and The Critical Community Size 205 6.3.3.1 The Importance of Imports 209 6.3.3.2 Measures of Persistence 212 6.3.3.3 Vaccination in a Stochastic Environment 213 6.3.4 Application: Porcine Reproductive and Respiratory Syndrome 214 6.3.5 Individual-Based Models 217 6.4 Parameterization of Stochastic Models 219 6.5 Interaction of Noise with Heterogeneities 219 6.5.1 Temporal Forcing 219 6.5.2 Risk Structure 220 6.5.3 Spatial Structure 221 6.6 Analytical Methods 222 6.6.1 Fokker-Plank Equations 222 6.6.2 Master Equations 223 6.6.3 Moment Equations 227 6.7 Future Directions 230 6.8 Summary 230 Chapter 7: Spatial Models 232 7.1 Concepts 233 7.1.1 Heterogeneity 233 7.1.2 Interaction 235 7.1.3 Isolation 236 7.1.4 Localized Extinction 236 7.1.5 Scale 236 7.2 Metapopulations 237 7.2.1 Types of Interaction 240 7.2.1.1 Plants 240 7.2.1.2 Animals 241 7.2.1.3 Humans 242 7.2.1.4 Commuter Approximations 243 7.2.2 Coupling and Synchrony 245 7.2.3 Extinction and Rescue Effects 246 7.2.4 Levins-Type Metapopulations 250 7.2.5 Application to the Spread of Wildlife Infections 251 7.2.5.1 Phocine Distemper Virus 252 7.2.5.2 Rabies in Raccoons 252 7.3 Lattice-Based Models 255 7.3.1 Coupled Lattice Models 255 7.3.2 Cellular Automata 257 7.3.2.1 The Contact Process 258 7.3.2.2 The Forest-Fire Model 259 7.3.2.3 Application: Power laws in Childhood Epidemic Data 260 7.4 Continuous-Space Continuous-Population Models 262 7.4.1 Reaction-Diffusion Equations 262 7.4.2 Integro-Differential Equations 265 7.5 Individual-Based Models 268 7.5.1 Application: Spatial Spread of Citrus Tristeza Virus 269 7.5.2 Applilcation: Spread of Foot-and-mouth Disease in the United Kingdom 274 7.6 Networks 276 7.6.1 Network Types 277 7.6.1.1 Random Networks 277 7.6.1.2 Lattices 277 7.6.1.3 Small World Networks 279 7.6.1.4 Spatial Networks 279 7.6.1.5 Scale-Free Networks 279 7.6.2 Simulation of Epidemics on Networks 280 7.7 Which Model to Use? 282 7.8 Approximations 283 7.8.1 Pair-Wise Models for Networks 283 7.8.2 Pair-Wise Models for Spatial Processes 286 7.9 Future Directions 287 7.10 Summary 288 Chapter 8: Controlling Infectious Diseases 291 8.1 Vaccination 292 8.1.1 Pediatric Vaccination 292 8.1.2 Wildlife Vaccination 296 8.1.3 Random Mass Vaccination 297 8.1.4 Imperfect Vaccines and Boosting 298 8.1.5 Pulse Vaccination 301 8.1.6 Age-Structured Vaccination 303 8.1.6.1 Application: Rubella Vaccination 304 8.1.7 Targeted Vaccination 306 8.2 Contact Tracing and Isolation 308 8.2.1 Simple Isolation 309 8.2.2 Contact Tracing to Find Infection 312 8.3 Case Study: Smallpox, Contact Tracing, and Isolation 313 8.4 Case Study: Foot-and-Mouth Disease, Spatial Spread, and Local Control 321 8.5 Case Study: Swine Fever Virus, Seasonal Dynamics, and Pulsed Control 327 8.5.1 Equilibrium Properties 329 8.5.2 Dynamical Properties 331 8.6 Future Directions 333 8.7 Summary 334 References 337 Index 361 Parameter Glossary 367

Read more less

Book SynopsisTrade ReviewOne of Choice's Outstanding Academic Titles for 2015 "The Fascinating World of Graph Theory shows its pedagogic value. Traditional courseware develops subject matter from the bottom on up, going from basic definitions to the more complex. [This book] is different, not starting with the simplest structures or algorithms but with interesting problems to be solved, puzzles that use graphs and networks... [It is] readable and 'student-friendly'--more so than the typical math textbook."--New York Journal of Books "[The authors] have set out to make graph theory not only accessible to people with a limited mathematics background, but also to make it interesting. They have--by virtue of very clear writing, combined with a greater-than-usual emphasis on the historical and personal side of the subject--succeeded admirably."--MAA Reviews "The book is written masterfully; the narrative in each chapter flows naturally, engagingly... [I]t's a popular but also comprehensive introduction into graph theory."--Alexander Bogomolny, Cut the Knot blog "A fun and interesting tour of graph theory, leaving each visitor with a feeling of accomplishment and a satisfying understanding of this unusual mathematical world... This is an entertaining book for those who enjoy solving problems, plus readers will learn about some powerful mathematical ideas along the way!"--Choice "Here is a book with an enjoyable mix of mathematics and its applications, spiced with liberal amounts of history and anecdote... The value of books like this is that they make mathematics come alive to a broad range of readers who might not look twice at a textbook or monograph."--Norman Biggs, London Mathematical Society Newsletter "Deftly written and dynamic...The Fascinating World of Graph Theoryis an aptly named book, able to present a wide variety of central topics in graph theory, including the history behind them... in a lively and entertaining manner... A superb example of approachable mathematical writing."--SIAM Review "The authors manage to motivate all topics with interesting applications, historical problems and discussion of concepts from an intuitive point of view."--Radu Trimbitas, Studia Mathematica "I am not going to try to list the topics that are covered, since there is a great variety. This breadth, along with the superb writing, make the book a must-have for anyone with serious interest in graph theory."--James M. Cargal, UMAP JournalTable of ContentsPreface vii Prologue xiii 1 Introducing Graphs 1 2 Classifying Graphs 22 3 Analyzing Distance 45 4 Constructing Trees 67 5 Traversing Graphs 91 6 Encircling Graphs 108 7 Factoring Graphs 125 8 Decomposing Graphs 143 9 Orienting Graphs 164 10 Drawing Graphs 183 11 Coloring Graphs 206 12 Synchronizing Graphs 226 Epilogue Graph Theory: A Look Back-The Road Ahead 251 Exercises 255 Selected References 309 Index of Names 317 Index of Mathematical Terms 319

Read more less

Book SynopsisRelax: no one understands technical mathematics without lengthy training but we all have an intuitive grasp of the ideas behind the symbols. To celebrate the 50th anniversary of the founding of the Institute of Mathematics and its Applications (IMA), this book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain. The book is a collection of 50 original essays contributed by a wide variety of authors. It contains articles by some of the best expositors of the subject (du Sautoy, Singh and Stewart for example) together with entertaining biographical pieces and articles of relevance to our everyday lives (such as Spiegelhalter on risk and Elwes on medical imaging). The topics covered are deliberately diverse and involve concepts from simple numerology to the very cutting edge of mathematics research. Each article is designed to be read in one sittinTrade ReviewMotorways; Sherlock Holmes; networks; mysterious numbers; sweets; champagne; interviews; mathematical poetry; ravens and even The Simpsons - this book has them all and more! Don't miss it! * Alan Stevens, Mathematics Today *The 50 essays in the book cover both pure and applied topics, and even the most esoteric subjects are addressed in an accessible way. * Physics World *Warmly recommended as recreational and stimulating reading to all mathematics aficionado! * Yuriy V. Rogovchenko, Zentralblatt MATH *Table of Contents1. What's the problem with mathematics? ; 2. The mathematics of messages ; 3. Decathlon: The art of scoring points ; 4. Queen Dido and the mathematics of the extreme ; 5. Can strings tie things together? ; 6. Grooves and knuckleballs ; 7. Pigs didn't fly but swine flu ; 8. Bill Tutte: Unsung Bletchley hero ; 9. What's the use of a quadratic equation? ; 10. Tony Hilton Royle Skyrme ; 11. The mathematics of obesity ; 12. It's a small world really ; 13. How does mathematics help at a murder scene? ; 14. Mathematics: The language of the universe ; 15. The troublesome geometry of CAT scanning ; 16. The mathematics of sports gambling ; Pythagoras's Theorem: a2 ; 17. A conversation with Freeman Dyson ; 18. A glass of bubbly ; 19. The influenza virus: It's all in the packaging ; 20. Mathematicians at the movies: Sherlock Holmes vs Professor Moriarty ; 21. Solving the Bristol bridge problem ; 22. All ravens are black: Puzzles and paradoxes in probability and statistics ; 23. The Tower of Hanoi: Where mathematics meets psychology ; 24. Career: A sample path ; 25. Sweets in the jar ; 26. Mary Cartwright ; 27. The fallibility of mathematics ; 28. Anecdotes of Dr Barrow ; 29. Finding Apollo ; 30. The golden ratio in astronomy and astrophysics ; 31. The high-power hypar ; 32. This is not a carrot: Paraconsistent mathematics ; 33. The mystery of Groombridge Place ; Pythagoras's Theorem: b2 ; 34. Mysterious number 6174 ; 35. Percolating possibilities ; 36. Milestones on a non-Euclidean journey ; 37. Simpson's rule ; 38. Risking your life ; 39. Networks and illusions ; 40. Emmy Noether: Against the odds ; 41. Of catastrophes and creodes: How maths benefits from collaboration with other fields ; 42. Conic section hide and seek ; 43. Sir James Lighthill: A life in waves ; 44. Fail safe or fail dangerous ; 45. Leapfrogging into the future: How child's play is at the heart of weather and climate models ; 46. Motorway mathematics ; 47. The philosophy of applied mathematics ; 48. Mighty Morphogenesis ; 49. Called to the barcode ; 50. Roughly fifty-fifty? ; Pythagoras's Theorem: c2

Read more less

Book SynopsisLinear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further than the Google search engine, which relies upon linear algebra to rank the results of a search with respect to relevance. The strength of the text is in the large number of examples and the step-by-step explanation of each topic as it is introduced. It is compiled in a way that allows distance learning, with explicit solutions to set problems freely available online. The miscellaneous exercises at the end of each chapter comprise questions from past exam papers from various universities, helping to reinforce the reader''s confidence. Also included, generally at the beginning of sections, are short historical biographies of the leading pTrade ReviewThis book gives an introduction to linear algebra for students with limited mathematical preparation. ... The steady pace of the book is so gentle that no student need be left behind. * Peter Macgregor, Mathematical Gazette *Table of Contents1. Linear Equations and Matrices ; 2. Euclidean Space ; 3. General Vector Spaces ; 4. Inner Product Spaces ; 5. Linear Transformation ; 6. Determinants ; 7. Eigenvalues and Eigenvectors

Read more less

Book SynopsisA graduate-level text utilizing exterior differential forms in the analysis of a variety of mathematical problems in the physical and engineering sciences. Includes 45 illustrations. Index.

Read more less

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

Read more less

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

Read more less

Book SynopsisProvides an account of complex adaptive social systems, by two of the field's leading authorities. This work focuses on the key tools and ideas that have emerged in the field since the mid-1990s, as well as the techniques needed to investigate such systems. It also demonstrates how the usual extremes used in modeling can be fruitfully transcended.Trade Review"The use of computational, especially agent-based, models has already shown its value in illuminating the study of economic and other social processes. Miller and Page have written an orientation to this field that is a model of motivation and insight, making clear the underlying thinking and illustrating it by varied and thoughtful examples. It conveys with remarkable clarity the essentials of the complex systems approach to the embarking researcher."—Kenneth J. Arrow, winner of the Nobel Prize in economics"In Complex Adaptive Systems, two masters of this burgeoning field provide a highly readable and novel restatement of the logic of social interactions, linking individually based micro processes to macrosocial outcomes, ranging from Adam Smith's invisible hand to Thomas Schelling's models of standing ovations. The book combines the vision of a new Santa Fe school of computational, social, and behavioral science with essential 'how to' advice for apprentice modelers."—Samuel Bowles, author of Microeconomics: Behavior, Institutions, Evolution"This is a wonderful book that will be read by graduate students, faculty, and policymakers. The authors write in an extraordinarily clear manner about topics that are very technical and difficult for many people. I sat down to begin thumbing through and found myself deeply engaged."—Elinor Ostrom, author of Understanding Institutional DiversityTable of ContentsList of Figures xiii List of Tables xv Preface xvii Part I: Introduction 1 Chapter 1: Introduction 3 Chapter 2: Complexity in Social Worlds 9 2.1 The Standing Ovation Problem 10 2.2 What's the Buzz? 14 2.2.1 Stay Cool 14 2.2.2 Attack of the Killer Bees 15 2.2.3 Averaging Out Average Behavior 16 2.3 A Tale of Two Cities 17 2.3.1 Adding Complexity 20 2.4 New Directions 26 2.5 Complex Social Worlds Redux 27 2.5.1 Questioning Complexity 27 Part II: Preliminaries 33 Chapter 3: Modeling 35 3.1 Models as Maps 36 3.2 A More Formal Approach to Modeling 38 3.3 Modeling Complex Systems 40 3.4 Modeling Modeling 42 Chapter 4: On Emergence 44 4.1 A Theory of Emergence 46 4.2 Beyond Disorganized Complexity 48 4.2.1 Feedback and Organized Complexity 50 Part III: Computational Modeling 55 Chapter 5: Computation as Theory 57 5.1 Theory versus Tools 59 5.1.1 Physics Envy: A Pseudo-Freudian Analysis 62 5.2 Computation and Theory 64 5.2.1 Computation in Theory 64 5.2.2 Computation as Theory 67 5.3 Objections to Computation as Theory 68 5.3.1 Computations Build in Their Results 69 5.3.2 Computations Lack Discipline 70 5.3.3 Computational Models Are Only Approximations to Specific Circumstances 71 5.3.4 Computational Models Are Brittle 72 5.3.5 Computational Models Are Hard to Test 73 5.3.6 Computational Models Are Hard to Understand 76 5.4 New Directions 76 Chapter 6: Why Agent-Based Objects? 78 6.1 Flexibility versus Precision 78 6.2 Process Oriented 80 6.3 Adaptive Agents 81 6.4 Inherently Dynamic 83 6.5 Heterogeneous Agents and Asymmetry 84 6.6 Scalability 85 6.7 Repeatable and Recoverable 86 6.8 Constructive 86 6.9 Low Cost 87 6.10 Economic E. coli (E. coni?) 88 Part IV: Models of Complex Adaptive Social Systems 91 Chapter 7: A Basic Framework 93 7.1 The Eightfold Way 93 7.1.1 Right View 94 7.1.2 Right Intention 95 7.1.3 Right Speech 96 7.1.4 Right Action 96 7.1.5 Right Livelihood 97 7.1.6 Right Effort 98 7.1.7 Right Mindfulness 100 7.1.8 Right Concentration 101 7.2 Smoke and Mirrors: The Forest Fire Model 102 7.2.1 A Simple Model of Forest Fires 102 7.2.2 Fixed, Homogeneous Rules 102 7.2.3 Homogeneous Adaptation 104 7.2.4 Heterogeneous Adaptation 105 7.2.5 Adding More Intelligence: Internal Models 107 7.2.6 Omniscient Closure 108 7.2.7 Banks 109 7.3 Eight Folding into One 110 7.4 Conclusion 113 Chapter 8: Complex Adaptive Social Systems in One Dimension 114 8.1 Cellular Automata 115 8.2 Social Cellular Automata 119 8.2.1 Socially Acceptable Rules 120 8.3 Majority Rules 124 8.3.1 The Zen of Mistakes in Majority Rule 128 8.4 The Edge of Chaos 129 8.4.1 Is There an Edge? 130 8.4.2 Computation at the Edge of Chaos 137 8.4.3 The Edge of Robustness 139 Chapter 9: Social Dynamics 141 9.1 A Roving Agent 141 9.2 Segregation 143 9.3 The Beach Problem 146 9.4 City Formation 151 9.5 Networks 154 9.5.1 Majority Rule and Network Structures 158 9.5.2 Schelling's Segregation Model and Network Structures 163 9.6 Self-Organized Criticality and Power Laws 165 9.6.1 The Sand Pile Model 167 9.6.2 A Minimalist Sand Pile 169 9.6.3 Fat-Tailed Avalanches 171 9.6.4 Purposive Agents 175 9.6.5 The Forest Fire Model Redux 176 9.6.6 Criticality in Social Systems 177 Chapter 10: Evolving Automata 178 10.1 Agent Behavior 178 10.2 Adaptation 180 10.3 A Taxonomy of 2 x 2 Games 185 10.3.1 Methodology 187 10.3.2 Results 189 10.4 Games Theory: One Agent, Many Games 191 10.5 Evolving Communication 192 10.5.1 Results 194 10.5.2 Furthering Communication 197 10.6 The Full Monty 198 Chapter 11: Some Fundamentals of Organizational Decision Making 200 11.1 Organizations and Boolean Functions 201 11.2 Some Results 203 11.3 Do Organizations Just Find Solvable Problems? 206 11.3.1 Imperfection 207 11.4 Future Directions 210 Part V: Conclusions 211 Chapter 12: Social Science in Between 213 12.1 Some Contributions 214 12.2 The Interest in Between 218 12.2.1 In between Simple and Strategic Behavior 219 12.2.2 In between Pairs and Infinities of Agents 221 12.2.3 In between Equilibrium and Chaos 222 12.2.4 In between Richness and Rigor 223 12.2.5 In between Anarchy and Control 225 12.3 Here Be Dragons 225 Epilogue 227 The Interest in Between 227 Social Complexity 228 The Faraway Nearby 230 Appendixes A An Open Agenda For Complex Adaptive Social Systems 231 A.1 Whither Complexity 231 A.2 What Does it Take for a System to Exhibit Complex Behavior? 233 A.3 Is There an Objective Basis for Recognizing Emergence and Complexity? 233 A.4 Is There a Mathematics of Complex Adaptive Social Systems? 234 A.5 What Mechanisms Exist for Tuning the Performance of Complex Systems? 235 A.6 Do Productive Complex Systems Have Unusual Properties? 235 A.7 Do Social Systems Become More Complex over Time 236 A.8 What Makes a System Robust? 236 A.9 Causality in Complex Systems? 237 A.10 When Does Coevolution Work? 237 A.11 When Does Updating Matter? 238 A.12 When Does Heterogeneity Matter? 238 A.13 How Sophisticated Must Agents Be Before They Are Interesting? 239 A.14 What Are the Equivalence Classes of Adaptive Behavior? 240 A.15 When Does Adaptation Lead to Optimization and Equilibrium? 241 A.16 How Important Is Communication to Complex Adaptive Social Systems? 242 A.17 How Do Decentralized Markets Equilibrate? 243 A.18 When Do Organizations Arise? 243 A.19 What Are the Origins of Social Life? 244 B Practices for Computational Modeling 245 B.1 Keep the Model Simple 246 B.2 Focus on the Science, Not the Computer 246 B.3 The Old Computer Test 247 B.4 Avoid Black Boxes 247 B.5 Nest Your Models 248 B.6 Have Tunable Dials 248 B.7 Construct Flexible Frameworks 249 B.8 Create Multiple Implementations 249 B.9 Check the Parameters 250 B.10 Document Code 250 B.11 Know the Source of Random Numbers 251 B.12 Beware of Debugging Bias 251 B.13 Write Good Code 251 B.14 Avoid False Precision 252 B.15 Distribute Your Code 253 B.16 Keep a Lab Notebook 253 B.17 Prove Your Results 253 B.18 Reward the Right Things 254 Bibliography 255 Index 261

Read more less

Book SynopsisAn essential introduction to discrete and computational geometryDiscrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only) Trade Review"Discrete and Computational Geometry meets an urgent need for an undergraduate text bridging the theoretical sides and the applied sides of the field. It is an excellent choice as a textbook for an undergraduate course in discrete and computational geometry! The presented material should be accessible for most mathematics or computer science majors in their second or third year in college. The book also is a valuable resource for graduate students and researchers."--Egon Schulte, Zentralblatt MATH "[W]e recommend this book for an undergraduate course on computational geometry. In fact, we hope to use this book ourselves when we teach such a class."--Brittany Terese Fasy and David L. Millman, SigAct News

Read more less

Book SynopsisProviding a systematic and self-contained treatment of excitation, propagation and re- emission of electromagnetic waves guided by density ducts in magnetized plasmas, this book describes in detail the theoretical basis of the electrodynamics of ducts. The classical dielectric-waveguide theory in open guiding systems in magnetoplasma is subjected to rigorous generalization. The authors emphasize the conceptual physical and mathematical aspects of the theory, while demonstrating its applications to problems encountered in actual practice. The opening chapters of the book discuss the underlying physical phenomena, outline some of the results obtained in natural and artificial density ducts, and describe the basic theory crucial to understanding the remainder of the book. The more specialized and complex topics dealt with in subsequent chapters include the theory of guided wave propagation along axially uniform ducts, finding the field excited by the source in the presence of a duct, excitation of guided modes, the asymptotic theory of wave propagation along axially nonuniform ducts, and mode re-emission from a duct. The full wave theory is used throughout most of the book to ensure consistency, and the authors start with simpler cases and gradually increase the complexity of the treatment.Table of Contents1. The Basic Equations 2. Integral Representation of Source-excited Fields on a Duct 3. Modal Representation of Source-excited Fields on a Duct 4. Wave Re-emission from a Density Duct 5. Modes in Axially Uniform Ducts 6. Radiation from Given Sources in a Uniform Unbounded Magnetoplasma 7. Wave Propagation Along Axially Non-uniform Ducts

Read more less

Book SynopsisThis monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. Wavelets are a mathematical development that many experts think may revolutionize the world of information storage and retrieval. They are a fairly simple mathematical tool now being applied to the compression of data, such as fingerprints, weather satellite photographs, and medical x-rays - that were previously thought to be impossible to condense without losing crucial details. The opening chapter provides an overview of the main problems presented in the book. Following chapters discuss the theoretical and practical aspects of wavelet theory, including wavelet transforms, orthonormal bases of wavelets, and characterization of functional spaces by means of wavelets. The last chapter presents several topics under active research, as multidimensional wavelets, wavelet packet bases, and a construction of wavelets tailored to decompose fun

Read more less

Book SynopsisTrade Review"A no-nonsense, clearly written graduate level textbook . . . . far more approachable than many other books on complex analysis"---Jonathan Shock, Mathemafrica"An excellent textbook. . . . Carefully and precisely written in a lively style."---Ali Abkar, zbMATH Open"Beautifully produced, beautifully written, on an incomparably beautiful area of mathematics, this is an inspirational book that I shall gratefully return to again and again."---Nick Lord, Mathematical Gazette

Read more less

Book SynopsisEverything You Need to Know about Mathematics for Science and EngineeringUpdated and expanded with new topics, The Mathematics Companion: Mathematical Methods for Physicists and Engineers, 2nd Edition presents the essential core of mathematical principles needed by scientists and engineers. Starting from the basic concepts of trigonometry, the book covers calculus, differential equations, and vector calculus. A new chapter on applications discusses how we see objects mathematically with the eye, how quantum mechanics works, and more.A Convenient, Student-Friendly Format Rich with Diagrams and Clear ExplanationsThe book presents essential mathematics ideas from basic to advanced level in a way that is useful to both students and practicing professionals. It offers a unique and educational approach that is the signature style of the author's companion books. The author explains mathematical concepts clearly, concisely, and visually, ilTrade Review"The book summarizes basic notions of mathematical methods for physicists and engineers in a schematic way. It is aimed both at science students and physicists who need a quick handy reference when they have to solve a specific mathematical problem."—Applications of Mathematics, 60, 2015Praise for the First Edition:"This is an interesting and useful little book … .it is very well done, and everything that might be expected to be there is there … . The book might also be invaluable for those undergraduate students in Mathematics, Science, or Engineering, who need to undertake first- and second-year courses in Mathematics, and it will serve those who wish to have quick access to all those formulae that seem to be so readily forgotten."—Australian Physics, March/April 2006Table of ContentsPart 1 Essential Mathematics: Basic mathematics. Differentiation. Integration. Exponentials and logarithms. Hyperbolic functions. Infinite series. Part 2 Advance Mathematics: Ordinary differential equations. Laplace transforms. Vector analysis. Partial derivatives. Multiple integrals. Fourier series. Special functions. Partial differential equations.

Read more less

Book SynopsisA book for anyone who wishes to illustrate their mathematical ideas. It is organised by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way.Table of Contents Drawings Paper & fiber arts Laser cutting Graphics Video & virtual reality 3D printing Mechanical constructions and other materials Multiple ways to illustrate the same thing Acknowledgments Image credits Index.

Read more less

Book SynopsisTough Test Questions? Missed Lectures? Not Enough Time?Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you Practice problems with full explanations that reinforce knowledge Coverage of the most up-to-date developments in your course field In-depth review of practices and applications Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!Schaum's Outlines-Problem Solved.Table of ContentsIntroductionFluid StatisticsMathematical Models of Fluid MotionDimensional Analysis and SimilitudeBoundary Layer Flow and Flow in Pipes and DuctsIncompressible Potential FlowOne-Dimensional Compressible FlowTwo-Dimensional Compressible Flow GasdynamicsIncompressible Turbulent FlowHypersonic Boundary Layer FlowMangetohydrodynamicsNon-Newtonian FluidsAppendix A: Some Properties of FluidsAppendix B: Units and DimensionsAppendix C: Some Basic Equations in Various Coordinate SystemsAppendix D: Tables for Compressible FlowAppendix E: Cartesian TensorsAppendix F: Vector IdentitiesAppendix G: Flow Measuring Techniques

Read more less

Book SynopsisApplied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition provides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, economics, and the life and social sciences. Students achieve success using this text as a result of the author''s applied and real-world orientation to concepts, problem-solving approach, straight forward and concise writing style, and comprehensive exercise sets. More than 100,000 students worldwide have studied from this text!Table of ContentsChapter 1: Functions, Graphs, and Limits1.1 Functions1.2 The Graph of a Function1.3 Linear Functions1.4 Functional Models1.5 Limits1.6 One-Sided Limits and ContinuityChapter 2: Differentiation: Basic Concepts2.1 The Derivative2.2 Techniques of Differentiation2.3 Product and Quotient Rules; Higher-Order Derivatives2.4 The Chain Rule2.5 Marginal Analysis and Approximations Using Increments2.6 Implicit Differentiation and Related RatesChapter 3: Additional Applications of the Derivative3.1 Increasing and Decreasing Functions; Relative Extrema3.2 Concavity and Points of Inflection3.3 Curve Sketching3.4 Optimization; Elasticity of Demand3.5 Additional Applied OptimizationChapter 4: Exponential and Logarithmic Functions4.1 Exponential Functions; Continuous Compounding4.2 Logarithmic Functions4.3 Differentiation of Exponential and Logarithmic Functions4.4 Applications; Exponential ModelsChapter 5: Integration5.1 Indefinite Integration with Applications5.2 Integration by Substitution5.3 The Definite Integral and the Fundamental Theorem of Calculus5.4 Applying Definite Integration: Area Between Curves and Average Value5.5 Additional Applications to Business and Economics5.6 Additional Applications to the Life and Social SciencesChapter 6: Additional Topics in Integration6.1 Integration by Parts; Integral Tables6.2 Numerical Integration6.3 Improper IntegralsChapter 7: Calculus of Several Variables7.1 Functions of Several Variables7.2 Partial Derivatives7.3 Optimizing Functions of Two Variables7.4 The Method of Least-Squares7.5 Constrained Optimization: The Method of Lagrange Multipliers7.6 Double IntegralsChapter 8: Trigonometric Functions8.1 Angle Measurement; Trigonometric Functions8.2 Derivatives of Trigonometric Functions8.3 Integrals of Trigonometric FunctionsChapter 9: Differential Equations9.1 Introduction to Differential Equations9.2 First-Order Linear Differential Equations9.3 Additional Applications of Differential Equations9.4 Approximate Solutions of Differential Equations9.5 Difference Equations; The Cobweb ModelChapter 10: Probability and Calculus10.1 Continuous Probability Distributions10.2 Expected Value and Variance10.3 Normal DistributionsChapter 11: Infinite Series and Taylor Series Approximations11.1 Infinite Series; Geometric Series11.2 Tests for Convergence11.3 Functions as Power Series; Taylor SeriesAppendix A: Algebra ReviewA.1 A Brief Review of AlgebraA.2 Factoring Polynomials and Solving Systems of EquationsA.3 Evaluating Limits with L’Hopital’s RuleA.4 The Summation Notation

Read more less

Book Synopsis Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition provides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, economics, and the life and social sciences. Students achieve success using this text as a result of the author's applied and real-world orientation to concepts, problem-solving approach, straight forward and concise writing style, and comprehensive exercise sets. More than 100,000 students worldwide have studied from this text!Table of ContentsChapter 1: Functions, Graphs, and Limits1.1Functions1.2The Graph of a Function1.3Lines and Linear Functions1.4Functional Models1.5Limits1.6One-Sided Limits and ContinuityChapter 2: Differentiation: Basic Concepts2.1The Derivative2.2Techniques of Differentiation2.3Product and Quotient Rules; Higher-Order Derivatives2.4The Chain Rule2.5Marginal Analysis and Approximations Using Increments2.6Implicit Differentiation and Related RatesChapter 3: Additional Applications of the Derivative3.1 Increasing and Decreasing Functions; Relative Extrema3.2 Concavity and Points of Inflection3.3 Curve Sketching3.4 Optimization; Elasticity of Demand3.5 Additional Applied OptimizationChapter 4: Exponential and Logarithmic Functions4.1 Exponential Functions; Continuous Compounding4.2 Logarithmic Functions4.3 Differentiation of Exponential and Logarithmic Functions4.4 Additional Applications; Exponential ModelsChapter 5: Integration5.1 Indefinite Integration and Differential Equations5.2 Integration by Substitution5.3 The Definite Integral and the Fundamental Theorem of Calculus5.4 Applying Definite Integration: Distribution of Wealth and Average Value5.5 Additional Applications to Business and Economics5.6 Additional Applications to the Life and Social SciencesChapter 6: Additional Topics in Integration6.1 Integration by Parts; Integral Tables6.2 Numerical Integration6.3 Improper IntegralsChapter 7: Calculus of Several Variables7.1 Functions of Several Variables7.2 Partial Derivatives7.3 Optimizing Functions of Two Variables7.4 The Method of Least-Squares7.5 Constrained Optimization: The Method of Lagrange Multipliers7.6 Double IntegralsChapter 8: Trigonometric Functions8.1 Angle Measurement; Trigonometric Functions8.2 Trigonometric Applications Involving Differentiation8.3 Trigonometric Applications Involving IntegrationChapter 9: Differential Equations9.1 Modeling with Differential Equations9.2 First-Order Linear Differential Equations9.3 Additional Applications of Differential Equations9.4 Approximate Solutions of Differential Equations9.5 Difference Equations; The Cobweb ModelChapter 10: Infinite Series and Taylor Series Approximations10.1 Infinite Series; Geometric Series10.2 Tests for Convergence10.3 Functions as Power Series; Taylor SeriesChapter 11: Probability and Calculus11.1 Introduction to Probability; Discrete Random Variables11.2 Continuous Probability Distributions11.3 Expected Value and Variance of Continuous Random Variables10.4 Normal and Poisson Probability DistributionsAppendix A: Algebra ReviewA.1 A Brief Review of AlgebraA.2 Factoring Polynomials and Solving Systems of EquationsA.3 Evaluating Limits with L’Hopital’s RuleA.4 The Summation Notation

Read more less

Book Synopsis Calculus for Business, Economics, and the Social and Life Sciences, Brief Edition provides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, economics, and the life and social sciences. Students achieve success using this text as a result of the author's applied and real-world orientation to concepts, problem-solving approach, straight forward and concise writing style, and comprehensive exercise sets. More than 100,000 students worldwide have studied from this text!Table of ContentsChapter 1: Functions, Graphs, and Limits1.1Functions1.2The Graph of a Function1.3Lines and Linear Functions1.4Functional Models1.5Limits1.6One-Sided Limits and ContinuityChapter 2: Differentiation: Basic Concepts2.1The Derivative2.2Techniques of Differentiation2.3Product and Quotient Rules; Higher-Order Derivatives2.4The Chain Rule2.5Marginal Analysis and Approximations Using Increments2.6Implicit Differentiation and Related RatesChapter 3: Additional Applications of the Derivative3.1 Increasing and Decreasing Functions; Relative Extrema3.2 Concavity and Points of Inflection3.3 Curve Sketching3.4 Optimization; Elasticity of Demand3.5 Additional Applied OptimizationChapter 4: Exponential and Logarithmic Functions4.1 Exponential Functions; Continuous Compounding4.2 Logarithmic Functions4.3 Differentiation of Exponential and Logarithmic Functions4.4 Additional Applications; Exponential ModelsChapter 5: Integration5.1 Indefinite Integration and Differential Equations5.2 Integration by Substitution5.3 The Definite Integral and the Fundamental Theorem of Calculus5.4 Applying Definite Integration: Distribution of Wealth and Average Value5.5 Additional Applications to Business and Economics5.6 Additional Applications to the Life and Social SciencesChapter 6: Additional Topics in Integration6.1 Integration by Parts; Integral Tables6.2 Numerical Integration6.3 Improper Integrals6.4 Introduction to Continuous ProbabilityChapter 7: Calculus of Several Variables7.1 Functions of Several Variables7.2 Partial Derivatives7.3 Optimizing Functions of Two Variables7.4 The Method of Least-Squares7.5 Constrained Optimization: The Method of Lagrange Multipliers7.6 Double IntegralsAppendix A: Algebra ReviewA.1 A Brief Review of AlgebraA.2 Factoring Polynomials and Solving Systems of EquationsA.3 Evaluating Limits with L’Hopital’s RuleA.4 The Summation Notation

Read more less

Book Synopsis

Read more less

Book SynopsisTrade Review"Both textbook and practical guide, this work is an accessible account of Bayesian data analysis starting from the basics…This edition is truly an expanded work and includes all new programs in JAGS and Stan designed to be easier to use than the scripts of the first edition, including when running the programs on your own data sets." --MAA Reviews "fills a gaping hole in what is currently available, and will serve to create its own market" --Prof. Michael Lee, U. of Cal., Irvine; pres. Society for Mathematical Psych "has the potential to change the way most cognitive scientists and experimental psychologists approach the planning and analysis of their experiments" --Prof. Geoffrey Iverson, U. of Cal., Irvine; past pres. Society for Mathematical Psych. "better than others for reasons stylistic.... buy it -- it’s truly amazin’!" --James L. (Jay) McClelland, Lucie Stern Prof. & Chair, Dept. of Psych., Stanford U. "the best introductory textbook on Bayesian MCMC techniques" --J. of Mathematical Psych. "potential to change the methodological toolbox of a new generation of social scientists" --J. of Economic Psych. "revolutionary" --British J. of Mathematical and Statistical Psych. "writing for real people with real data. From the very first chapter, the engaging writing style will get readers excited about this topic" --PsycCritiquesTable of Contents1. What’s in This Book (Read This First!) PART I The Basics: Models, Probability, Bayes’ Rule, and R 2. Introduction: Credibility, Models, and Parameters 3. The R Programming Language 4. What Is This Stuff Called Probability? 5. Bayes’ Rule PART II All the Fundamentals Applied to Inferring a Binomial Probability 6. Inferring a Binomial Probability via Exact Mathematical Analysis 7. Markov Chain Monte Carlo 8. JAGS 9. Hierarchical Models 10. Model Comparison and Hierarchical Modeling 11. Null Hypothesis Significance Testing 12. Bayesian Approaches to Testing a Point ("Null") Hypothesis 13. Goals, Power, and Sample Size 14. Stan PART III The Generalized Linear Model 15. Overview of the Generalized Linear Model 16. Metric-Predicted Variable on One or Two Groups 17. Metric Predicted Variable with One Metric Predictor 18. Metric Predicted Variable with Multiple Metric Predictors 19. Metric Predicted Variable with One Nominal Predictor 20. Metric Predicted Variable with Multiple Nominal Predictors 21. Dichotomous Predicted Variable 22. Nominal Predicted Variable 23. Ordinal Predicted Variable 24. Count Predicted Variable 25. Tools in the Trunk

Read more less

Book SynopsisTable of ContentsCHAPTER 1 Introduction to statistics CHAPTER 2 Descriptive statistics CHAPTER 3 Elements of probability CHAPTER 4 Random variables and expectation CHAPTER 5 Special random variables CHAPTER 6 Distributions of sampling statistics CHAPTER 7 Parameter estimation CHAPTER 8 Hypothesis testing CHAPTER 9 Regression CHAPTER 10 Analysis of variance CHAPTER 11 Goodness of fit tests and categorical data analysis CHAPTER 12 Nonparametric hypothesis tests CHAPTER 13 Quality control CHAPTER 14 Life testing CHAPTER 15 Simulation, bootstrap statistical methods, and permutation tests CHAPTER 16 Machine learning and big data

Read more less

Book SynopsisIn About Time: Einstein''s Unfinished Revolution Paul Davies confronts the puzzles and paradoxes of time that have bemused the world''s greatest thinkers throughout the ages.When Albert Einstein formulated his theory of relativity it brought about a revolution in our understanding of time, yet also presented a new set of mysteries. Einstein''s time can be warped, leading to bizarre possibilities such as black holes and time travel, while making a nonsense of our perception of a ''now'' or a division of time into past, present and future.In About Time Paul Davies tackles the tough questions about time, including the strange relationship between physical time and our psychological perception of it. He gives straightforward descriptions of topics such as the theory of relativity, the relation between time dilation and the speed of light and Hawking''s ''imaginary time''. He concludes that, despite decades of progress in unravelling the mysteries of Table of ContentsA very brief history of time; time for a change; timewarps; black holes - gateways to the end of time; the beginning of time - when exactly was it?; Einstein's greatest triumph?; quantum time; imaginary time; the arrow of time; backwards in time; time travel - fact or fantasy?; but what time is it now?; experimenting with time; the unfinished revolution.

Read more less

Book SynopsisTHE INTERNATIONAL BESTSELLER''An entertaining tour that will change how you see the world'' Sean Carroll, author of Something Deeply HiddenIs there a secret formula for improving your life? For making something a viral hit? For deciding how long to stick with your current job, Netflix series, or even relationship?This book is all about the equations that make our world go round. Ten of them, in fact. They are integral to everything from investment banking to betting companies and social media giants. And they can help you to increase your chance of success, guard against financial loss, live more healthily and see through scaremongering. They are known only by mathematicians - until now.With wit and clarity, mathematician David Sumpter shows that it isn''t the technical details which make these formulas so successful. It is the way they allow mathematicians to view problems from a different angle - a way of seeing the world that anyone cTrade ReviewSometimes books about numbers come along and we're so ecstatic that we just pop with delight. One such book is The Ten Equations that Rule The World -- Tim Harford * More or Less BBC4 *Hugely entertaining, erudite and at times genuinely witty . . . it's nice to be spoken to in grown-up language by a genius. You will come away from Sumpter's book with a much clearer idea of why the world is less messy than it appears * E&T Magazine *These aren't the equations of Newton or Einstein -- crisp relations describing the evolution of a clockwork universe. These are the equations of randomness, expectation, and imperfect information. The equations, in other words, of the real world. David Sumpter provides an entertaining tour that will change how you see the world -- Sean Carroll author of Something Deeply HiddenSumpter writes fascinatingly about his experiences as a consulting mathematician. . . I will encourage my mathematics undergraduates to read this book since it will inspire them by showing the relevance of mathematics to today's world and make them think about the moral issues they will face as mathematicians * Times Higher Education *

Read more less

Book SynopsisThis text provides an introduction to the methods of parallel optimization by introducing parallel computing ideas and techniques into both optimization theory and numerical algorithms for large-scale optimization problems.Trade Review"This book presents a domain that arises where two different branches of science, namely parallel computations and the theory of constrained optimization, intersect with real life problems. This domain, called parallel optimization, has been developing rapidly under the stimulus of progress in computer technology. The book focuses on parallel optimization methods for large-scale constrained optimization problems and structured linear problems. . . . [It] covers a vast portion of parallel optimization, though full coverage of this domain, as the authors admit, goes far beyond the capacity of a single monograph. This book, however, in over 500 pages brings an excellent and in-depth presentation of all the major aspects of a process which matches theory and methods of optimization with modern computers. The volume can be recommended for graduate students, faculty, and researchers in any of those fields."--Mathematical Reviews "This book presents a domain that arises where two different branches of science, namely parallel computations and the theory of constrained optimization, intersect with real life problems. This domain, called parallel optimization, has been developing rapidly under the stimulus of progress in computer technology. The book focuses on parallel optimization methods for large-scale constrained optimization problems and structured linear problems. . . . [It] covers a vast portion of parallel optimization, though full coverage of this domain, as the authors admit, goes far beyond the capacity of a single monograph. This book, however, in over 500 pages brings an excellent and in-depth presentation of all the major aspects of a process which matches theory and methods of optimization with modern computers. The volume can be recommended for graduate students, faculty, and researchers in any of those fields."--Mathematical ReviewsTable of ContentsForeword ; Preface ; Glossary of Symbols ; 1. Introduction ; Part I Theory ; 2. Generalized Distances and Generalized Projections ; 3. Proximal Minimization with D-Functions ; Part II Algorithms ; 4. Penalty Methods, Barrier Methods and Augmented Lagrangians ; 5. Iterative Methods for Convex Feasibility Problems ; 6. Iterative Algorithms for Linearly Constrained Optimization Problems ; 7. Model Decomposition Algorithms ; 8. Decompositions in Interior Point Algorithms ; Part III Applications ; 9. Matrix Estimation Problems ; 10. Image Reconsturction from Projections ; 11. The Inverse Problem in Radiation Therapy Treatment Planning ; 12. Multicommodity Network Flow Problems ; 13. Planning Under Uncertainty ; 14. Decompositions for Parallel Computing ; 15. Numerical Investigations

Read more less

Book SynopsisProviding an overview of computational mathematics and a series of key economics problems using "higher mathematics", this book presents a mix of classical and contemporary economic theory. It also covers the problems of uncertainty, continuous-time dynamics, comparative statistics, and the applications of optimization methods to economics.Table of Contents0. Review of Mathematics ; 1. Economic Applications of One-Variable Calculus ; 2. Economic Applications of Multivariate Calculus ; COMPARATIVE STATICS 1: ONE AND TWO VARIABLES WITH AND WITHOUT OPTIMIZATION ; 4. Integration, Time and Uncertainty in Economics ; 5. Introduction to Continuous-Time Dynamics in One and Two Dimensions ; 6. Matrices and Economic Theory ; 7. Comparative Statics 2: n Variables with and without Optimization ; 8. Comparative Statics 3: Optimization under Constraint ; 9. Inequality Constraints in Optimization Theory

Read more less

Book SynopsisThis book brings together an impressive group of leading scholars in the sciences of complexity, and a few workers on the interface of science and religion, to explore the wider implications of complexity studies. It includes an introduction to complexity studies and explores the concept of information in physics and biology and various philosophical and religious perspectives. Chapter authors include Paul Davies, Greg Chaitin, Charles Bennett, Werner Loewenstein, Paul Dembski, Ian Stewart, Stuart Kauffman, Harold Morowitz, Arthur Peacocke, and Niels H. Gregersen.Trade ReviewMelanie Mitchell's book is most enjoyable, truly inspiring, skillfully written, and, above all, beautifully clear. The author's enthusiasm and passion for the field make the book fascinating to read. Her rigor, clarity, and healthy skepticism make the book sound and the field scientifically stronger. It is an excellent and rigorous account of the scientific field of complexity. She proves by example that it is possible to explain complex systems science with rigor, breadth, depth, and - above all - exquisite clarity * Artificial Life *Table of ContentsPart 1: Introduction ; 1. Towards an Emergentist Worldview ; Part 2: Defining Complexity ; 2. Randomness and Mathematical Proof ; 3. "How to define Complexity in Physics, and Why?" ; Part 3: The Concept of Information in Physics and Biology ; 4. The Emergence of Autonomous Agents ; 5. Complexity and The Arrow of Time ; 6. Can Evolutionary Algorithms Generate Specified Complexity? ; 7. The Second Law of Thermodynamics and the Fourth Law of Thermodynamics ; 8. Two Arrows from a Mighty Bow ; Part 4: Philosophical and Religious Perspectives ; 9. Emergence of Transcendence ; 10. Complexity, Emergence and Divine Creativity ; 11. From Anthropic Design to Self-Organized Complexity

Read more less

Book SynopsisDesigned for the many applied mathematicians and engineers who wish to explore computerized numerical methods, this text communicates an enthusiasm for the power of C++, an object-oriented language, as a tool for this kind of work. This revision of the successful first edition includes for the first time information on programming in Windows-based environments. In addition this revision includes new topics and methods throughout the text that clarify and enhance the treatment of the subject. From reviews of the first edition: ''If you are interested in numerical methods or are looking for a course text this book is worth your attention.'''' Journal of the Association of C and C++ UsersTable of Contents1. Preliminaries ; 2. Expressions, statements and functions ; 3. Errors, theorems and speed ; 4. Roots of non-linear equations ; 5. Classes ; 6. Derived classes and streams ; 7. Integer arithmetic ; 8. Tests of randomness ; 9. Vectors and matrices ; 10. Direct solution of linear equations ; 11. Errors in matrix manipulation ; 12. Iterative solutions of systems of equations ; 13. Matrix eigenvalue problems ; 14. Interpolation and data fitting ; 15. Graphics ; 16. Differentiation and integration ; 17. Orthogonal polynomials ; 18. Differential equations ; 19. More about differential equations ; 20. Recursive data types - lists ; 21. Elements of Fourier analysis

Read more less

Book SynopsisSpin glasses are magnetic materials. Statistical mechanics, a subfield of physics, has been a powerful tool to theoretically analyse various unique properties of spin glasses. A number of new analytical techniques have been developed to establish a theory of spin glasses. Surprisingly, these techniques have turned out to offer new tools and viewpoints for the understanding of information processing problems, including neural networks, error-correcting codes, image restoration, and optimization problems. This book is one of the first publications of the past ten years that provide a broad overview of this interdisciplinary field. Most of the book is written in a self-contained manner, assuming only a general knowledge of statistical mechanics and basic probability theory. It provides the reader with a sound introduction to the field and to the analytical techniques necessary to follow its most recent developments.Trade Review... very enjoyable to read and often opening the reader's eye to new possibilities. This is a perfect introduction to the field for students and researchers who want to study problems in information science, including the use of physics in information processing * Butsuri *Table of Contents1. Mean-field theory of phase transitions ; 2. Mean-field theory of spin glasses ; 3. Replica symmetry breaking ; 4. Gauge theory of spin glasses ; 5. Error-correcting codes ; 6. Image restoration ; 7. Associative memory ; 8. Learning in perceptron ; 9. Optimization problems ; A. Eigenvalues of the Hessian ; B. Parisi equation ; C. Channel coding theorem ; D. Distribution and free energy of K-Sat ; References ; Index

Read more less