Mathematics Books

Book SynopsisA First Course on Numerical Methods is designed for students and researchers who seek practical knowledge of modern techniques in scientific computing. Avoiding encyclopaedic and heavily theoretical exposition, the book provides an in-depth treatment of fundamental issues and methods, the reasons behind the success and failure of numerical software, and fresh and easy-to-follow approaches and techniques. The authors focus on current methods, issues and software while providing a comprehensive theoretical foundation, enabling those who need to apply the techniques to successfully design solutions to nonstandard problems. The book also illustrates algorithms using the programming environment of MATLAB , with the expectation that the reader will gradually become proficient in it while learning the material covered in the book. The book takes an algorithmic approach, focusing on techniques that have a high level of applicability to engineering, computer science and industrial mathematics.

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Book SynopsisThis thorough book collects methods and strategies to analyze proteomics data. It is intended to describe how data obtained by gel-based or gel-free proteomics approaches can be inspected, organized, and interpreted to extrapolate biological information. Organized into four sections, the volume explores strategies to analyze proteomics data obtained by gel-based approaches, different data analysis approaches for gel-free proteomics experiments, bioinformatic tools for the interpretation of proteomics data to obtain biological significant information, as well as methods to integrate proteomics data with other omics datasets including genomics, transcriptomics, metabolomics, and other types of data. Written for the highly successful Methods in Molecular Biology series, chapters include the kind of detailed implementation advice that will ensure high quality results in the lab. Authoritative and practical, Proteomics Data Analysis serves as an ideal Table of ContentsPart I: Data Analysis for Gel-Based Proteomics 1. Two-Dimensional Gel Electrophoresis Image Analysis Elisa Robotti, Elisa Calà, and Emilio Marengo 2. Chemometric Tools for 2D-PAGE Data Analysis Elisa Robotti, Elisa Calà, and Emilio Marengo Part II: Data Analysis for Gel-Free Proteomics 3. Software Options for the Analysis of MS Proteomic Data Avinash Yadav, Federica Marini, Alessandro Cuomo, and Tiziana Bonaldi 4. Analysis of Label-Based Quantitative Proteomics Data Using IsoProt Johannes Griss and Veit Schwämmle 5. Quantification of Changes in Protein Expression Using SWATH Proteomics Clarissa Braccia, Nara Liessi, and Andrea Armirotti 6. Data Processing and Analysis for DIA-Based Phosphoproteomics Using Spectronaut Ana Martinez-Val, Dorte Breinholdt Bekker-Jensen, Alexander Hogrebe, and Jesper Velgaard Olsen 7. Enhanced Glycopeptide Identification Using a GlyConnect Compozitor-Derived Glycan Composition File Julien Mariethoz, Catherine Hayes, and Frédérique Lisacek 8. Elaboration Pipeline for the Management of MALDI-MS Imaging Datasets Andrew Smith, Isabella Piga, Vanna Denti, Clizia Chinello, and Fulvio Magni 9. Features Selection and Extraction in Statistical Analysis of Proteomics Datasets Marta Lualdi and Mauro Fasano Part III: Proteomics Data Interpretation 10. ORA, FCS, and PT Strategies in Functional Enrichment Analysis Marco Fernandes and Holger Husi 11. A Strategy for the Annotation and GO Enrichment Analysis of a List of Differentially Expressed Proteins Using ProteoRE Florence Combes, Valentin Loux, and Yves Vandenbrouck 12. Protein Subcellular Localization Prediction Elettra Barberis, Emilio Marengo, and Marcello Manfredi 13. Protein Secretion Prediction Tools and Extracellular Vesicles Databases Daniela Cecconi, Claudia Di Carlo, and Jessica Brandi 14. Databases for Protein-Protein Interactions Natsu Nakajima, Tatsuya Akutsu, and Ryuichiro Nakato 15. Machine and Deep Learning for Prediction of Subcellular Localization Gaofeng Pan, Chao Sun, Zijun Liao, and Jijun Tang 16. Deep Learning for Protein-Protein Interaction Site Prediction Arian R. Jamasb, Ben Day, Cătălina Cangea, Pietro Liò, and Tom L. Blundell Part IV: Proteomics Data Integration with Other -Omics 17. Integrative Analysis of Incongruous Cancer Genomics and Proteomics Datasets Karla Cervantes-Gracia, Richard Chahwan, and Holger Husi 18. Integration of Proteomics and Other Omics Data Mengyun Wu, Yu Jiang, and Shuangge Ma

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Book SynopsisThe Bulletin of Mathematical Biology, the official journal of the Society for Mathematical Biology, disseminates original research findings and other information relevant to the interface of biology and the mathematical sciences. Contributions should have relevance to both fields. In order to accommodate the broad scope of new developments, the journal accepts a variety of contributions, including: Original research articles focused on new biological insights gained with the help of tools from the mathematical sciences or new mathematical tools and methods with demonstrated applicability to biological investigations Research in mathematical biology education Reviews Commentaries Perspectives, and contributions that discuss issues important to the profession All contributions are peer-reviewed. 

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Book SynopsisDifferent linear mathematical methods can be used to solve these models analytically, such as the Inverse Scattering Transformation (IST), Adomian Decomposition Method, Variational Iteration Method (VIM), Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM).Table of ContentsNonlinear Water Waves and Nonlinear Evolution Equations with ApplicationsInverse Scattering Transform and the Theory of SolitonsKorteweg-de Vries Equation (KdV), Different Analytical Methods for Solving theKorteweg-de Vries Equation (KdV), History, Exact N-Soliton Solutions and Further Properties of theSemi-analytical Methods for Solving the KdV and mKdV EquationsKorteweg-de Vries Equation (KdV), Some Numerical Methods for Solving theNonlinear Internal WavesPartial Differential Equations that Lead to SolitonsShallow Water Waves and Solitary WavesSoliton PerturbationSolitons and CompactonsSolitons: Historical and Physical IntroductionSolitons InteractionsSolitons, Introduction toSolitons, Tsunamis and Oceanographical Applications ofWater Waves and the Korteweg-de Vries EquationSoliton Solutions for Some Nonlinear Water Wave Dynamical ModelsAnalytical Soliton Solutions for Some Nonlinear Dynamical Water Waves ModelsSoliton Propagation in Solids: Advances and ApplicationsApplications of lump and interaction soliton solutions to the model of liquid crystals and nerve fibersPeriodic cross-kink, rogue-waves, and lump interaction soliton solutions with kink and periodic waves for fractional Bogoyavlenskii equationDouble Tchebyshev spectral tau algorithm for solving KdV equation, with soliton application

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Book SynopsisBasic Notions of Probability Theory.- Calculation of Expectations.- Convexity, Optimization, and Inequalities.- Combinatorics.- Combinatorial Optimization.- Poisson Processes.- Discrete-Time Markov Chains.- Continuous-Time Markov Chains.- Branching Processes.- Martingales.- Diffusion Processes.- Asymptotic Methods.- Numerical Methods.- Poisson Approximation.- Number Theory.- Entropy.- Appendix: Mathematical Review.

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Book SynopsisA comprehensive guidebook to the current methodologies and practices used in health surveys A unique and self-contained resource, Handbook of Health Survey Methods presents techniques necessary for confronting challenges that are specific to health survey research.Trade Review“The extensive and analytical coverage will make the book an extremely valuable resource: the new handbook will certainly emerge as essential reading for anyone deals with health surveys.” (Ann Ist Super Sanità, 1 October 2015)Table of ContentsList of Contributors xvii Preface xxi Acknowledgments xxiii 1 Origins and Development of Health Survey Methods 1Timothy P. Johnson 1.1 Introduction 1 1.2 Precursors of Modern Health Surveys 1 1.3 The First Modern Health Surveys 4 1.4 The Emergence of National Health Surveys 5 1.5 Post-WWII Advances 6 1.6 Current Developments 7 References 9 Online Resources 17 Part I Design and Sampling Issues2 Sampling For Community Health Surveys 21Michael P. Battaglia 2.1 Introduction 21 2.2 Background 22 2.3 Theory and Applications 24 2.4 Subpopulation Surveys 30 2.5 Sample Size Considerations 32 2.6 Summary 32 References 33 Online Resources 34 3 Developing a Survey Sample Design for Population-Based Case–Control Studies 37Ralph DiGaetano 3.1 Introduction 37 3.2 A “Classic” Sample Design for a Population-Based Case–Control Study 39 3.3 Sample Design Concepts and Issues Related to Case–Control Studies 40 3.4 Basic Sample Design Considerations 49 3.5 Sample Selection of Cases 56 3.6 Sample Selection of Controls 57 3.7 Sample Weighting for Population-Based Case–Control Studies 62 3.8 The Need to Account for Analytic Plans When Developing a Sample Design: An Example 65 3.9 Sample Designs for Population-Based Case–Control Studies: When Unweighted Analyses Are Planned 66 3.10 Mimicking the Classic Design Using RDD-Based Sampling of Population-Based Controls 66 3.11 Examples of the Development of Complex Sample Designs for Population-Based Case–Control Studies Using Weighted Analyses Where Cases Serve as the Reference Population and Variance Estimates Reflect the Sample Design 69 3.12 Summary 71 References 71 Online Resources 75 4 Sampling Rare Populations 77James Wagner and Sunghee Lee 4.1 Introduction 77 4.2 Traditional Probability Sampling Approaches 80 4.3 Nontraditional and Nonprobability Sampling Approaches 84 4.4 Conclusion 95 References 97 Online Resources 103 Part II Design and Measurement Issues 5 Assessing Physical Health 107Todd Rockwood 5.1 Introduction 107 5.2 Assessing Health: Response Formation and Accuracy 110 5.3 Conceptual Framework for Developing and Assessing Health 118 5.4 Measurement Theory 124 5.5 Error and Methodology 129 5.6 Conclusion 132 References 134 Online Resources 141 6 Developing and Selecting Mental Health Measures 143Ronald C. Kessler and Beth-Ellen Pennell 6.1 Introduction 143 6.2 Historical Background 144 6.3 Fully Structured Diagnostic Interviews 147 6.4 Dimensional Measures of Symptom Severity 148 6.5 Emerging Issues in Survey Assessments of Mental Disorders 156 6.6 Conclusion 159 References 159 Online Resources 169 7 Developing Measures of Health Behavior and Health Service Utilization 171Paul Beatty 7.1 Introduction 171 7.2 The Conceptual Phase of Questionnaire Development 172 7.3 Development of Particular Questions 173 7.4 Overall Questionnaire Construction 184 7.5 Questionnaire Testing and Evaluation 186 7.6 Using Questions from Previously Administered Questionnaires 187 7.7 Conclusion 187 References 188 Online Resources 190 8 Self-Rated Health in Health Surveys 193Sunghee Lee 8.1 Introduction 193 8.2 Utility of Self-Rated Health 195 8.3 Theoretical Evidence: Cognitive Processes Pertinent to Responding to SRH in Surveys 198 8.4 Measurement Issues for Self-Rated Health 201 8.5 Conclusion 206 References 207 Online Resources 216 9 Pretesting of Health Survey Questionnaires: Cognitive Interviewing Usability Testing and Behavior Coding 217Gordon Willis 9.1 Introduction 217 9.2 Historical Background and Theory of Pretesting 218 9.3 Cognitive Interviewing 220 9.4 Usability Testing 229 9.5 Behavior Coding 232 9.6 Summary 236 References 238 Online Resources 241 10 Cross-Cultural Considerations in Health Surveys 243Brad Edwards 10.1 Introduction 243 10.2 Theory and Practice 255 10.3 Conclusion 266 References 266 Online Resources 274 11 Survey Methods for Social Network Research 275Benjamin Cornwell and Emily Hoagland 11.1 Introduction 275 11.2 Respondents as Social Network Informants 277 11.3 Whole, Egocentric, and Mixed Designs 277 11.4 Name Generators 282 11.5 Free Versus Fixed Choice 286 11.6 Name Interpreters 287 11.7 Social Network Measures 288 11.8 Other Approaches to Collecting Network-Like Data 292 11.9 Modes of Data Collection and Survey Logistics 295 11.10 Avoiding Endogeneity in Survey-Based Network Data 296 11.11 Selection Issues 300 11.12 New Directions: Measuring Social Network Dynamics 301 11.13 Further Reading 304 References 304 Online Resources 312 12 New Technologies for Health Survey Research 315Joe Murphy, Elizabeth Dean, Craig A. Hill, and Ashley Richards 12.1 Introduction 315 12.2 Background 316 12.3 Theory and Applications 318 12.4 Summary 329 References 331 Online Resources 337 Part III Field Issues 13 Using Survey Data to Improve Health: Community Outreach and Collaboration 341Steven Whitman, Ami M. Shah, Maureen R. Benjamins, and Joseph West 13.1 Introduction 341 13.2 Our Motivation 342 13.3 Our Process 343 13.4 A Few Findings 344 13.5 Case Studies of Community Engagement 349 13.6 Some Lessons Learned 361 References 363 Online Resources 365 14 Proxy Reporting in Health Surveys 367Joseph W. Sakshaug 14.1 Introduction 367 14.2 Background 367 14.3 Proxy Interviews for Children 370 14.4 Proxy Interviews for the Elderly 372 14.5 Proxy Interviews for the Disabled 374 14.6 Summary 375 References 376 Online Resources 381 15 The Collection of Biospecimens in Health Surveys 383Joseph W. Sakshaug, Mary Beth, Ofstedal Heidi Guyer, and Timothy J. Beebe 15.1 Introduction 383 15.2 Background 384 15.3 Biomeasure Selection 387 15.4 Methodological and Operational Considerations 397 15.5 Quality Control 402 15.6 Ethical and Legal Considerations 408 15.7 Methods of Data Dissemination 411 15.8 Summary 412 References 413 Online Resources 419 16 Collecting Contextual Health Survey Data Using Systematic Observation 421Shannon N. Zenk, Sandy Slater, and Safa Rashid 16.1 Introduction 421 16.2 Background 423 16.3 Data Collection 426 16.4 Reliability and Validity Assessment 429 16.5 Data Analysis 432 16.6 Theory and Applications 432 16.7 BTG-COMP: Evaluating the Impact of the Built Environment on Adolescent Obesity 432 16.8 Evaluating the Impact of a Policy Change on the Retail Fruit and Vegetable Supply 436 16.9 Summary 440 References 441 Online Resources 445 17 Collecting Survey Data on Sensitive Topics: Substance Use 447Joe Gfroerer and Joel Kennet 17.1 Introduction 447 17.2 Background 448 17.3 Theory and Applications 450 17.4 Validation 463 17.5 Alternative Estimation Methods 464 17.6 Summary 466 References 467 Online Resources 472 18 Collecting Survey Data on Sensitive Topics: Sexual Behavior 473Tom W. Smith 18.1 Introduction 473 18.2 Sampling 474 18.3 Nonobservation 475 18.4 Observation/Measurement Error 475 18.5 Summary 479 References 479 Online Resources 485 19 Ethical Considerations in Collecting Health Survey Data 487Emily E. Anderson 19.1 Introduction 487 19.2 Background: Ethical Principles and Federal Regulations for Research 488 19.3 Defining, Evaluating, and Minimizing Risk 491 19.4 Ethical Review of Health Survey Research 497 19.5 Informed Consent for Survey Participation 500 19.6 Considerations for Data Collection 504 19.7 Summary 505 References 506 Online Resources 510 Part IV Health Surveys of Special Populations 20 Surveys of Physicians 515Jonathan B. VanGeest, Timothy J. Beebe, and Timothy P. Johnson 20.1 Introduction 515 20.2 Why Physicians do not Respond 517 20.3 Theory and Applications: Improving Physician Participation 518 20.4 Sampling 518 20.5 Design-Based Interventions to Improve Response 523 20.6 Incentive-Based Interventions 530 20.7 Supporting Evidence from Other Health Professions 532 20.8 Conclusion 533 References 534 Online Resources 543 21 Surveys of Health Care Organizations 545John D. Loft, Joe Murphy, and Craig A. Hill 21.1 Introduction 545 21.2 Examples of Health Care Organizations Surveys 548 21.3 Surveys of Health Care Organizations as Establishment Surveys 548 21.4 Conclusions 556 References 558 Online Resources 560 22 Surveys of Patient Populations 561Francis Fullam and Jonathan B. VanGeest 22.1 Introduction 561 22.2 Patients and Care Settings 563 22.3 Overview of Common Patient Survey Methodologies 564 22.4 Key Issues in Patient Survey Design and Administration 565 22.5 Strategies for Developing Effective Patient Surveys 570 22.6 Conclusion 573 References 574 Online Resources 583 23 Surveying Sexual and Gender Minorities 585Melissa A. Clark, Samantha Rosenthal, and Ulrike Boehmer 23.1 Introduction 585 23.2 Prevalence Estimates of Sexual and Gender Minorities 592 23.3 Sampling and Recruitment 597 23.4 Data Collection 606 23.5 Conclusions 608 References 609 Online Resources 617 24 Surveying People with Disabilities: Moving Toward Better Practices and Policies 619Rooshey Hasnain, Carmit-Noa Shpigelman, Mike Scott, Jon R. Gunderson, Hadi B. Rangin, Ashmeet Oberoi, and Liam McKeever 24.1 Introduction 620 24.2 Setting a Foundation:The Importance of Inclusion for Web-Based Surveys 623 24.3 Promoting Participation with Web Accessibility 624 24.4 Testing the Accessibility of Some Web-Based Survey Tools 626 24.5 Ensuring Web Accessibility at Various Levels of Disability 629 24.6 Problems Posed By Inaccessible Web-Based Surveys for People with Disabilities 633 24.7 Applications: How to Ensure that Web-Based Surveys are Accessible 634 24.8 Summary and Conclusions 637 References 638 Online Resources 641 Part V Data Management and Analysis 25 Assessing the Quality of Health Survey Data Through Modern Test Theory 645Adam C. Carle 25.1 Introduction 645 25.2 Internal Validity and Dimensionality 647 25.3 Dimensionality and Bifactor Model Example 650 25.4 Dimensionality Discussion 652 25.5 Measurement Bias 653 25.6 Multiple Group Multiple Indicator Multiple Cause Models 655 25.7 Additional Challenges to Health Survey Data Quality 664 25.8 Overall Conclusion 664 References 665 Online Resources 667 26 Sample Weighting for Health Surveys 669Kennon R. Copeland and Nadarajasundaram Ganesh 26.1 Objectives of Sample Weighting 669 26.2 Sample Weighting Stages (Probability Sample Designs) 670 26.3 Calculating Base Weights 671 26.4 Accounting for Noncontact and Nonresponse 672 26.5 Adjusting to Independent Population Controls 677 26.6 SampleWeighting for Nonprobability Sample Designs 680 26.7 Issues in Sample Weighting 680 26.8 Estimation 682 26.9 Variance Estimation 683 26.10 Special Topics 683 26.11 Example: Weighting for the 2010 National Immunization Survey 685 26.12 Summary 692 References 692 Online Resources 694 27 Merging Survey Data with Administrative Data for Health Research Purposes 695Michael Davern Marc Roemer and Wendy Thomas 27.1 Introduction 695 27.2 Potential Uses of Linked Data 696 27.3 Limitations and Strengths of Survey Data 699 27.4 Limitations and Strengths of Administrative Data 700 27.5 A Research Agenda into Linked Data File Quality 701 27.6 Conclusions 712 References 713 Online Resources 716 28 Merging Survey Data with Aggregate Data from Other Sources: Opportunities and Challenges 717Jarvis T. Chen 28.1 Background 717 28.2 Geocoding and Linkage to Area-Based Data 719 28.3 Geographic Levels of Aggregation 720 28.4 Types of Area-Level Measures 723 28.5 Sources of Aggregated Data 724 28.6 Aggregate Data Measures as Proxies for Individual Data 730 28.7 Aggregate Measures as Contextual Variables 731 28.8 The Components of Ecological Bias 732 28.9 Analytic Approaches to the Analysis of Survey Data with Linked Area-Based Measures 742 28.10 Summary 746 References 748 Online Resources 754 29 Analysis of Complex Health Survey Data 755Stanislav Kolenikov and Jeff Pitblado 29.1 Introduction 755 29.2 Inference with Complex Survey Data 760 29.3 Substantive Analyses 784 29.4 Quality Control Analyses 795 29.5 Discussion 798 References 798 Online Resources 804 Index 805

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Book SynopsisLearn how quantitative models can help fight client problems head-on Before financial problems can be solved, they need to be fully understood. Since in-depth quantitative modeling techniques are a powerful tool to understanding the drivers associated with financial problems, one would need a solid grasp of these techniques before being able to unlock their full potential of the methods used. In The Mathematics of Financial Models, the author presents real world solutions to the everyday problems facing financial professionals. With interactive tools such as spreadsheets for valuation, pricing, and modeling, this resource combines highly mathematical quantitative analysis with useful, practical methodologies to create an essential guide for investment and risk-management professionals facing modeling issues in insurance, derivatives valuation, and pension benefits, among others. In addition to this, this resource also provides the relevant tools like matrices, calculuTable of ContentsPreface ix Acknowledgments xi Chapter 1 Setting the Stage 1 Why is This Book Different? 2 Road Map of the Book 3 References 5 Chapter 2 Building Zero Curves 7 Market Instruments 8 Linear Interpolation 16 Cubic Splining 25 Appendix: Finding Swap Rates Using a Floating Coupon Bond Approach 41 References 43 Chapter 3 Valuing Vanilla Options 45 Black-Scholes Formulae 47 Adaptations of the Black-Scholes Formulae 53 Limitations of the Black-Scholes Formulae 70 Application in Currency Risk Management 74 Appendix 78 References 80 Chapter 4 Simulations 81 Uniform Number Generation 82 Non-Uniform Number Generation 86 Applications of Simulations 93 Variance Reduction Techniques 100 References 104 Chapter 5 Valuing Exotic Options 107 Valuing Path-Independent, European-Style Options on a Single Variable 108 Valuing Path-Dependent, European-Style Options on a Single Variable 114 Valuing Path-Independent, European-Style Options on Two Variables 135 Valuing Path-Dependent, European-Style Options on Multiple Variables 152 References 157 Chapter 6 Estimating Model Parameters 159 Calibration of Parameters in the Black-Scholes Model 161 Using Implied Black-Scholes Volatility Surface and Zero Rate Term Structure to Value Options 169 Using Volatility Surface 178 Calibration of Interest Rate Option Model Parameters 190 Statistical Estimation 196 References 203 Chapter 7 The Effectiveness of Hedging Strategies 205 Delta Hedging 206 Assumptions Underlying Delta Hedging 216 Beyond Delta Hedging 223 Testing Hedging Strategies 230 Analysis Associated with the Hedging of a European-Style Vanilla Put Option 235 References 244 Chapter 8 Valuing Variable Annuity Guarantees 245 Basic GMDB 246 Death Benefit Riders 261 Other Details Associated with GMDB Products 269 Improving Modeling Assumptions 273 Living Benefit Riders 276 References 279 Chapter 9 Real Options 281 Surrendering a GMAB Rider 282 Adding Servers in a Queue 300 References 314 Chapter 10 Parting Thoughts 315 About the Author 317 About the Website 319 Index 321

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Book SynopsisCOVERS THE FUNDAMENTAL TOPICS IN MATHEMATICS, STATISTICS, AND FINANCIAL MANAGEMENT THAT ARE REQUIRED FOR A THOROUGH STUDY OF FINANCIAL MARKETS This comprehensive yet accessible book introduces students to financial markets and delves into more advanced material at a steady pace while providing motivating examples, poignant remarks, counterexamples, ideological clashes, and intuitive traps throughout. Tempered by real-life cases and actual market structures, An Introduction to Financial Markets: A Quantitative Approach accentuates theory through quantitative modeling whenever and wherever necessary. It focuses on the lessons learned from timely subject matter such as the impact of the recent subprime mortgage storm, the collapse of LTCM, and the harsh criticism on risk management and innovative finance. The book also provides the necessary foundations in stochastic calculus and optimization, alongside financial modeling concepts that are illustrated with relevantTable of ContentsPreface xv About the Companion Website xix Part I Overview 1 Financial Markets: Functions, Institutions, and Traded Assets 1 1.1 What is the purpose of finance? 2 1.2 Traded assets 12 1.2.1 The balance sheet 15 1.2.2 Assets vs. securities 20 1.2.3 Equity 22 1.2.4 Fixed income 24 1.2.5 FOREX markets 27 1.2.6 Derivatives 29 1.3 Market participants and their roles 46 1.3.1 Commercial vs. investment banks 48 1.3.2 Investment funds and insurance companies 49 1.3.3 Dealers and brokers 51 1.3.4 Hedgers, speculators, and arbitrageurs 51 1.4 Market structure and trading strategies 53 1.4.1 Primary and secondary markets 53 1.4.2 Over-the-counter vs. exchange-traded derivatives 53 1.4.3 Auction mechanisms and the limit order book 53 1.4.4 Buying on margin and leverage 55 1.4.5 Short-selling 58 1.5 Market indexes 60 Problems 63 Further reading 65 Bibliography 65 2 Basic Problems in Quantitative Finance 67 2.1 Portfolio optimization 68 2.1.1 Static portfolio optimization: Mean–variance efficiency 70 2.1.2 Dynamic decision-making under uncertainty: A stylized consumption–saving model 75 2.2 Risk measurement and management 80 2.2.1 Sensitivity of asset prices to underlying risk factors 81 2.2.2 Risk measures in a non-normal world: Value-atrisk 84 2.2.3 Risk management: Introductory hedging examples 93 2.2.4 Financial vs. nonfinancial risk factors 100 2.3 The no-arbitrage principle in asset pricing 102 2.3.1 Why do we need asset pricing models? 103 2.3.2 Arbitrage strategies 104 2.3.3 Pricing by no-arbitrage 108 2.3.4 Option pricing in a binomial model 112 2.3.5 The limitations of the no-arbitrage principle 116 2.4 The mathematics of arbitrage 117 2.4.1 Linearity of the pricing functional and law of one price 119 2.4.2 Dominant strategies 120 2.4.3 No-arbitrage principle and risk-neutral measures 125 S2.1 Multiobjective optimization 129 S2.2 Summary of LP duality 133 Problems 137 Further reading 139 Bibliography 139 Part II Fixed income assets 3 Elementary Theory of Interest Rates 143 3.1 The time value of money: Shifting money forward in time 146 3.1.1 Simple vs. compounded rates 147 3.1.2 Quoted vs. effective rates: Compounding frequencies 150 3.2 The time value of money: Shifting money backward in time 153 3.2.1 Discount factors and pricing a zero-coupon bond 154 3.2.2 Discount factors vs. interest rates 158 3.3 Nominal vs. real interest rates 161 3.4 The term structure of interest rates 163 3.5 Elementary bond pricing 165 3.5.1 Pricing coupon-bearing bonds 165 3.5.2 From bond prices to term structures, and vice versa 168 3.5.3 What is a risk-free rate, anyway? 171 3.5.4 Yield-to-maturity 174 3.5.5 Interest rate risk 180 3.5.6 Pricing floating rate bonds 188 3.6 A digression: Elementary investment analysis 190 3.6.1 Net present value 191 3.6.2 Internal rate of return 192 3.6.3 Real options 193 3.7 Spot vs. forward interest rates 193 3.7.1 The forward and the spot rate curves 197 3.7.2 Discretely compounded forward rates 197 3.7.3 Forward discount factors 198 3.7.4 The expectation hypothesis 199 3.7.5 A word of caution: Model risk and hidden assumptions 202 S3.1 Proof of Equation (3.42) 203 Problems 203 Further reading 205 Bibliography 205 4 Forward Rate Agreements, Interest Rate Futures, and Vanilla Swaps 207 4.1 LIBOR and EURIBOR rates 208 4.2 Forward rate agreements 209 4.2.1 A hedging view of forward rates 210 4.2.2 FRAs as bond trades 214 4.2.3 A numerical example 215 4.3 Eurodollar futures 216 4.4 Vanilla interest rate swaps 220 4.4.1 Swap valuation: Approach 1 221 4.4.2 Swap valuation: Approach 2 223 4.4.3 The swap curve and the term structure 225 Problems 226 Further reading 226 Bibliography 226 5 Fixed-Income Markets 229 5.1 Day count conventions 230 5.2 Bond markets 231 5.2.1 Bond credit ratings 233 5.2.2 Quoting bond prices 233 5.2.3 Bonds with embedded options 235 5.3 Interest rate derivatives 237 5.3.1 Swap markets 237 5.3.2 Bond futures and options 238 5.4 The repo market and other money market instruments 239 5.5 Securitization 240 Problems 244 Further reading 244 Bibliography 244 6 Interest Rate Risk Management 247 6.1 Duration as a first-order sensitivity measure 248 6.1.1 Duration of fixed-coupon bonds 250 6.1.2 Duration of a floater 254 6.1.3 Dollar duration and interest rate swaps 255 6.2 Further interpretations of duration 257 6.2.1 Duration and investment horizons 258 6.2.2 Duration and yield volatility 260 6.2.3 Duration and quantile-based risk measures 260 6.3 Classical duration-based immunization 261 6.3.1 Cash flow matching 262 6.3.2 Duration matching 263 6.4 Immunization by interest rate derivatives 265 6.4.1 Using interest rate swaps in asset–liability management 266 6.5 A second-order refinement: Convexity 266 6.6 Multifactor models in interest rate risk management 269 Problems 271 Further reading 272 Bibliography 273 Part III Equity portfolios 7 Decision-Making under Uncertainty: The Static Case 277 7.1 Introductory examples 278 7.2 Should we just consider expected values of returns and monetary outcomes? 282 7.2.1 Formalizing static decision-making under uncertainty 283 7.2.2 The flaw of averages 284 7.3 A conceptual tool: The utility function 288 7.3.1 A few standard utility functions 293 7.3.2 Limitations of utility functions 297 7.4 Mean–risk models 299 7.4.1 Coherent risk measures 300 7.4.2 Standard deviation and variance as risk measures 302 7.4.3 Quantile-based risk measures: V@R and CV@R 303 7.4.4 Formulation of mean–risk models 309 7.5 Stochastic dominance 310 S7.1 Theorem proofs 314 S7.1.1 Proof of Theorem 7.2 314 S7.1.2 Proof of Theorem 7.4 315 Problems 315 Further reading 317 Bibliography 317 8 Mean–Variance Efficient Portfolios 319 8.1 Risk aversion and capital allocation to risky assets 320 8.1.1 The role of risk aversion 324 8.2 The mean–variance efficient frontier with risky assets 325 8.2.1 Diversification and portfolio risk 325 8.2.2 The efficient frontier in the case of two risky assets 326 8.2.3 The efficient frontier in the case of n risky assets 329 8.3 Mean–variance efficiency with a risk-free asset: The separation property 332 8.4 Maximizing the Sharpe ratio 337 8.4.1 Technical issues in Sharpe ratio maximization 340 8.5 Mean–variance efficiency vs. expected utility 341 8.6 Instability in mean–variance portfolio optimization 343 S8.1 The attainable set for two risky assets is a hyperbola 345 S8.2 Explicit solution of mean–variance optimization in matrix form 346 Problems 348 Further reading 349 Bibliography 349 9 Factor Models 351 9.1 Statistical issues in mean–variance portfolio optimization 352 9.2 The single-index model 353 9.2.1 Estimating a factor model 354 9.2.2 Portfolio optimization within the single-index model 356 9.3 The Treynor–Black model 358 9.3.1 A top-down/bottom-up optimization procedure 362 9.4 Multifactor models 365 9.5 Factor models in practice 367 S9.1 Proof of Equation (9.17) 368 Problems 369 Further reading 371 Bibliography 371 10 Equilibrium Models: CAPM and APT 373 10.1 What is an equilibrium model? 374 10.2 The capital asset pricing model 375 10.2.1 Proof of the CAPM formula 377 10.2.2 Interpreting CAPM 378 10.2.3 CAPM as a pricing formula and its practical relevance 380 10.3 The Black–Litterman portfolio optimization model 381 10.3.1 Black–Litterman model: The role of CAPM and Bayesian Statistics 382 10.3.2 Black-Litterman model: A numerical example 386 10.4 Arbitrage pricing theory 388 10.4.1 The intuition 389 10.4.2 A not-so-rigorous proof of APT 391 10.4.3 APT for Well-Diversified Portfolios 392 10.4.4 APT for Individual Assets 393 10.4.5 Interpreting and using APT 394 10.5 The behavioral critique 398 10.5.1 The efficient market hypothesis 400 10.5.2 The psychology of choice by agents with limited rationality 400 10.5.3 Prospect theory: The aversion to sure loss 401 S10.1Bayesian statistics 404 S10.1.1 Bayesian estimation 405 S10.1.2 Bayesian learning in coin flipping 407 S10.1.3 The expected value of a normal distribution 408 Problems 411 Further reading 413 Bibliography 413 Part IV Derivatives 11 Modeling Dynamic Uncertainty 417 11.1 Stochastic processes 420 11.1.1 Introductory examples 422 11.1.2 Marginals do not tell the whole story 428 11.1.3 Modeling information: Filtration generated by a stochastic process 430 11.1.4 Markov processes 433 11.1.5 Martingales 436 11.2 Stochastic processes in continuous time 438 11.2.1 A fundamental building block: Standard Wiener process 438 11.2.2 A generalization: Lévy processes 440 11.3 Stochastic differential equations 441 11.3.1 A deterministic differential equation: The bank account process 442 11.3.2 The generalized Wiener process 443 11.3.3 Geometric Brownian motion and Itô processes 445 11.4 Stochastic integration and Itô’s lemma 447 11.4.1 A digression: Riemann and Riemann–Stieltjes integrals 447 11.4.2 Stochastic integral in the sense of Itô 448 11.4.3 Itô’s lemma 453 11.5 Stochastic processes in financial modeling 457 11.5.1 Geometric Brownian motion 457 11.5.2 Generalizations 460 11.6 Sample path generation 462 11.6.1 Monte Carlo sampling 463 11.6.2 Scenario trees 465 S11.1Probability spaces, measurability, and information 468 Problems 476 Further reading 478 Bibliography 478 12 Forward and Futures Contracts 481 12.1 Pricing forward contracts on equity and foreign currencies 482 12.1.1 The spot–forward parity theorem 482 12.1.2 The spot–forward parity theorem with dividend income 485 12.1.3 Forward contracts on currencies 487 12.1.4 Forward contracts on commodities or energy: Contango and backwardation 489 12.2 Forward vs. futures contracts 490 12.3 Hedging with linear contracts 493 12.3.1 Quantity-based hedging 493 12.3.2 Basis risk and minimum variance hedging 494 12.3.3 Hedging with index futures 496 12.3.4 Tailing the hedge 499 Problems 501 Further reading 502 Bibliography 502 13 Option Pricing: Complete Markets 505 13.1 Option terminology 506 13.1.1 Vanilla options 507 13.1.2 Exotic options 508 13.2 Model-free price restrictions 510 13.2.1 Bounds on call option prices 511 13.2.2 Bounds on put option prices: Early exercise and continuation regions 514 13.2.3 Parity relationships 517 13.3 Binomial option pricing 519 13.3.1 A hedging argument 520 13.3.2 Lattice calibration 523 13.3.3 Generalization to multiple steps 524 13.3.4 Binomial pricing of American-style options 527 13.4 A continuous-time model: The Black–Scholes–Merton pricing formula 530 13.4.1 The delta-hedging view 532 13.4.2 The risk-neutral view: Feynman–Ka¡c representation theorem 539 13.4.3 Interpreting the factors in the BSM formula 543 13.5 Option price sensitivities: The Greeks 545 13.5.1 Delta and gamma 546 13.5.2 Theta 550 13.5.3 Relationship between delta, gamma, and theta 551 13.5.4 Vega 552 13.6 The role of volatility 553 13.6.1 The implied volatility surface 553 13.6.2 The impact of volatility on barrier options 555 13.7 Options on assets providing income 556 13.7.1 Index options 557 13.7.2 Currency options 558 13.7.3 Futures options 559 13.7.4 The mechanics of futures options 559 13.7.5 A binomial view of futures options 560 13.7.6 A risk-neutral view of futures options 562 13.8 Portfolio strategies based on options 562 13.8.1 Portfolio insurance and the Black Monday of 1987 563 13.8.2 Volatility trading 564 13.8.3 Dynamic vs. Static hedging 566 13.9 Option pricing by numerical methods 569 Problems 570 Further reading 575 Bibliography 576 14 Option Pricing: Incomplete Markets 579 14.1 A PDE approach to incomplete markets 581 14.1.1 Pricing a zero-coupon bond in a driftless world 584 14.2 Pricing by short-rate models 588 14.2.1 The Vasicek short-rate model 589 14.2.2 The Cox–Ingersoll–Ross short-rate model 594 14.3 A martingale approach to incomplete markets 595 14.3.1 An informal approach to martingale equivalent measures 598 14.3.2 Choice of numeraire: The bank account 600 14.3.3 Choice of numeraire: The zero-coupon bond 601 14.3.4 Pricing options with stochastic interest rates: Black’s model 602 14.3.5 Extensions 603 14.4 Issues in model calibration 603 14.4.1 Bias–variance tradeoff and regularized least-squares 604 14.4.2 Financial model calibration 609 Further reading 612 Bibliography 612 Part V Advanced optimization models 15 Optimization Model Building 617 15.1 Classification of optimization models 618 15.2 Linear programming 625 15.2.1 Cash flow matching 627 15.3 Quadratic programming 628 15.3.1 Maximizing the Sharpe ratio 629 15.3.2 Quadratically constrained quadratic programming 631 15.4 Integer programming 632 15.4.1 A MIQP model to minimize TEV under a cardinality constraint 634 15.4.2 Good MILP model building: The role of tight model formulations 636 15.5 Conic optimization 642 15.5.1 Convex cones 644 15.5.2 Second-order cone programming 650 15.5.3 Semidefinite programming 653 15.6 Stochastic optimization 655 15.6.1 Chance-constrained LP models 656 15.6.2 Two-stage stochastic linear programming with recourse 657 15.6.3 Multistage stochastic linear programming with recourse 663 15.6.4 Scenario generation and stability in stochastic programming 670 15.7 Stochastic dynamic programming 675 15.7.1 The dynamic programming principle 676 15.7.2 Solving Bellman’s equation: The three curses of dimensionality 679 15.7.3 Application to pricing options with early exercise features 680 15.8 Decision rules for multistage SLPs 682 15.9 Worst-case robust models 686 15.9.1 Uncertain LPs: Polyhedral uncertainty 689 15.9.2 Uncertain LPs: Ellipsoidal uncertainty 690 15.10Nonlinear programming models in finance 691 15.10.1 Fixed-mix asset allocation 692 Problems 693 Further reading 695 Bibliography 696 16 Optimization Model Solving 699 16.1 Local methods for nonlinear programming 700 16.1.1 Unconstrained nonlinear programming 700 16.1.2 Penalty function methods 703 16.1.3 Lagrange multipliers and constraint qualification conditions 707 16.1.4 Duality theory 713 16.2 Global methods for nonlinear programming 715 16.2.1 Genetic algorithms 716 16.2.2 Particle swarm optimization 717 16.3 Linear programming 719 16.3.1 The simplex method 720 16.3.2 Duality in linear programming 723 16.3.3 Interior-point methods: Primal-dual barrier method for LP 726 16.4 Conic duality and interior-point methods 728 16.4.1 Conic duality 728 16.4.2 Interior-point methods for SOCP and SDP 731 16.5 Branch-and-bound methods for integer programming 732 16.5.1 A matheuristic approach: Fix-and-relax 735 16.6 Optimization software 736 16.6.1 Solvers 737 16.6.2 Interfacing through imperative programming languages 738 16.6.3 Interfacing through non-imperative algebraic languages 738 16.6.4 Additional interfaces 739 Problems 739 Further reading 740 Bibliography 741 Index 743

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Book SynopsisWith a focus on Unbound Register Machines (URMs), this book introduces new ideas and topics using real computer-related examples to help readers gain the skills and intuition that are key to successful programming.Trade Review“This is an outstanding book, and I recommend it highly to students and practitioners alike.” (Computing Reviews, 8 April 2013) Table of ContentsPreface xi 1. Mathematical Foundations 1 1.1 Sets and Logic; Naïvely 1 1.2 Relations and Functions 40 1.3 Big and Small Infinite Sets; Diagonalization 52 1.4 Induction from a User’s Perspective 61 1.5 Why Induction Ticks 68 1.6 Inductively Defined Sets 1.7 Recursive Definitions of Functions 1.8 Additional Exercises 85 2. Algorithms, Computable Functions and Computations 91 2.1 A Theory of Computability 91 2.2 A programming Formalism for the Primitive Recursive Functions Function Class 147 2.3 URM Computations and their Arithmetization 141 2.4 A double-recursion that leads outside the Primitive Recursive Function Class 2.5 Semi-computable Relations: Unsolvability 2.6 The Iteration Theorem of Kleene 172 2.7 Diagonalization Revisited; Unsolvability via Reductions 175 2.8 Productive and Creative Sets 209 2.9 The Recursion Theorem 214 2. 10 Completeness 217 2.11 Unprovability from Unsolvability 221 2.12 Additional Exercises 234 3. A Subset of the URM Language; FA and NFA 241 3.1 Deterministic Finite Automata and their Languages 243 3.2 Nondeterministic Finite Automata 3.3 Regular Expressions 266 3.4 Regular Grammars and Languages 277 3.5 Additional Exercises 287 4. Adding a stack of a NFA: Pushdown Automata 4.1 The PDA 294 4.2 PDA Computations 294 4.3 The PDA-acceptable Languages are the Context Free Languages 305 4.4 Non-Context Free Languages; Another Pumping Lemma 312 4.5 Additional Exercise 322 5. Computational Complexity 325 5.1 Adding a second stack; Turning Machines 325 5.2 Axt, loop program, and Grzegorczyk hierarchies 5.3 Additional Exercised

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Book SynopsisA modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momeTrade Review “The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.” (Zentralblatt MATH, 2012) Table of ContentsPreface xiii I Nonlinear Continuum Mechanics 1 1 Kinematics of Deformable Bodies 3 1.1 Motion 4 1.2 Strain and Deformation Tensors 7 1.3 Rates of Motion 10 1.4 Rates of Deformation 13 1.5 The Piola Transformation 15 1.6 The Polar Decomposition Theorem 19 1.7 Principal Directions and Invariants of Deformation and Strain 20 1.8 The Reynolds' Transport Theorem 23 2 Mass and Momentum 25 2.1 Local Forms of the Principle of Conservation of Mass 26 2.2 Momentum 28 3 Force and Stress in Deformable Bodies 29 4 The Principles of Balance of Linear and Angular Momentum 35 4.1 Cauchy's Theorem: The Cauchy Stress Tensor 36 4.2 The Equations of Motion (Linear Momentum) 38 4.3 The Equations of Motion Referred to the Reference Configuration: The Piola-Kirchhoff Stress Tensors 40 4.4 Power 42 5 The Principle of Conservation of Energy 45 5.1 Energy and the Conservation of Energy 45 5.2 Local Forms of the Principle of Conservation of Energy 47 6 Thermodynamics of Continua and the Second Law 49 7 Constitutive Equations 53 7.1 Rules and Principles for Constitutive Equations 54 7.2 Principle of Material Frame Indifference 57 7.2.1 Solids 57 7.2.2 Fluids 59 7.3 The Coleman-Noll Method: Consistency with the Second Law of Thermodynamics 60 8 Examples and Applications 63 8.1 The Navier-Stokes Equations for Incompressible Flow 63 8.2 Flow of Gases and Compressible Fluids: The Compressible Navier-Stokes Equations 66 8.3 Heat Conduction 67 8.4 Theory of Elasticity 69 II Electromagnetic Field Theory and Quantum Mechanics 73 9 Electromagnetic Waves 75 9.1 Introduction 75 9.2 Electric Fields 75 9.3 Gauss's Law 79 9.4 Electric Potential Energy 80 9.4.1 Atom Models 80 9.5 Magnetic Fields 81 9.6 Some Properties of Waves 84 9.7 Maxwell's Equations 87 9.8 Electromagnetic Waves 91 10 Introduction to Quantum Mechanics 93 10.1 Introductory Comments 93 10.2 Wave and Particle Mechanics 94 10.3 Heisenberg's Uncertainty Principle 97 10.4 Schrödinger's Equation 99 10.4.1 The Case of a Free Particle 99 10.4.2 Superposition in Rn 101 10.4.3 Hamiltonian Form 102 10.4.4 The Case of Potential Energy 102 10.4.5 Relativistic Quantum Mechanics 102 10.4.6 General Formulations of Schrödinger's Equation 103 10.4.7 The Time-Independent Schrödinger Equation 104 10.5 Elementary Properties of the Wave Equation 104 10.5.1 Review 104 10.5.2 Momentum 106 10.5.3 Wave Packets and Fourier Transforms 109 10.6 The Wave-Momentum Duality 110 10.7 Appendix: A Brief Review of Probability Densities 111 11 Dynamical Variables and Observables in Quantum Mechanics: The Mathematical Formalism 115 11.1 Introductory Remarks 115 11.2 The Hilbert Spaces L2(R) (or L2(Rd)) and H1(R) (or H1(Rd)) 116 11.3 Dynamical Variables and Hermitian Operators 118 11.4 Spectral Theory of Hermitian Operators: The Discrete Spectrum 121 11.5 Observables and Statistical Distributions 125 11.6 The Continuous Spectrum 127 11.7 The Generalized Uncertainty Principle for Dynamical Variables 128 11.7.1 Simultaneous Eigenfunctions 130 12 Applications: The Harmonic Oscillator and the Hydrogen Atom 131 12.1 Introductory Remarks 131 12.2 Ground States and Energy Quanta: The Harmonic Oscillator 131 12.3 The Hydrogen Atom 133 12.3.1 Schrödinger Equation in Spherical Coordinates 135 12.3.2 The Radial Equation 136 12.3.3 The Angular Equation 138 12.3.4 The Orbitals of the Hydrogen Atom 140 12.3.5 Spectroscopic States 140 13 Spin and Pauli's Principle 145 13.1 Angular Momentum and Spin 145 13.2 Extrinsic Angular Momentum 147 13.2.1 The Ladder Property: Raising and Lowering States 149 13.3 Spin 151 13.4 Identical Particles and Pauli's Principle 155 13.5 The Helium Atom 158 13.6 Variational Principle 161 14 Atomic and Molecular Structure 165 14.1 Introduction 165 14.2 Electronic Structure of Atomic Elements 165 14.3 The Periodic Table 169 14.4 Atomic Bonds and Molecules 173 14.5 Examples of Molecular Structures 180 15 Ab Initio Methods: Approximate Methods and Density Functional Theory 189 15.1 Introduction 189 15.2 The Born-Oppenheimer Approximation 190 15.3 The Hartree and the Hartree-Fock Methods 194 15.3.1 The Hartree Method 196 15.3.2 The Hartree-Fock Method 196 15.3.3 The Roothaan Equations 199 15.4 Density Functional Theory 200 15.4.1 Electron Density 200 15.4.2 The Hohenberg-Kohn Theorem 205 15.4.3 The Kohn-Sham Theory 208 III Statistical Mechanics 213 16 Basic Concepts: Ensembles, Distribution Functions, and Averages 215 16.1 Introductory Remarks 215 16.2 Hamiltonian Mechanics 216 16.2.1 The Hamiltonian and the Equations of Motion 218 16.3 Phase Functions and Time Averages 219 16.4 Ensembles, Ensemble Averages, and Ergodic Systems 220 16.5 Statistical Mechanics of Isolated Systems 224 16.6 The Microcanonical Ensemble 228 16.6.1 Composite Systems 230 16.7 The Canonical Ensemble 234 16.8 The Grand Canonical Ensemble 239 16.9 Appendix: A Brief Account of Molecular Dynamics 240 16.9.1 Newtonian's Equations of Motion 241 16.9.2 Potential Functions 242 16.9.3 Numerical Solution of the Dynamical System 245 17 Statistical Mechanics Basis of Classical Thermodynamics 249 17.1 Introductory Remarks 249 17.2 Energy and the First Law of Thermodynamics 250 17.3 Statistical Mechanics Interpretation of the Rate of Work in Quasi-Static Processes 251 17.4 Statistical Mechanics Interpretation of the First Law of Thermodynamics 254 17.4.1 Statistical Interpretation of Q 256 17.5 Entropy and the Partition Function 257 17.6 Conjugate Hamiltonians 259 17.7 The Gibbs Relations 261 17.8 Monte Carlo and Metropolis Methods 262 17.8.1 The Partition Function for a Canonical Ensemble 263 17.8.2 The Metropolis Method 264 17.9 Kinetic Theory: Boltzmann's Equation of Nonequilibrium Statistical Mechanics 265 17.9.1 Boltzmann's Equation 265 17.9.2 Collision Invariants 268 17.9.3 The Continuum Mechanics of Compressible Fluids and Gases: The Macroscopic Balance Laws 269 Exercises 273 Bibliography 317 Index 325

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Book SynopsisDiscover how mathematics and science have propelled history From Ancient Greece to the Enlightenment and then on to modern times, Shifting the Earth: The Mathematical Quest to Understand the Motion of the Universe takes readers on a journey motivated by the desire to understand the universe and the motion of the heavens. The author presents a thought-provoking depiction of the sociopolitical environment in which some of the most prominent scientists in history lived and then provides a mathematical account of their contributions. From Eudoxus to Einstein, this fascinating book describes how, beginning in ancient times, pioneers in the sciences and mathematics have dramatically changed our vision of who we are as well as our place in the universe. Readers will discover how Ptolemy''s geocentric model evolved into Kepler''s heliocentric model, with Copernicus as the critical intermediary. The author explains how one scientific breakthrough set the stage for the next one, anTrade Review“Summing Up: Recommended. Upper-division undergraduates through researchers/faculty; general readers.” (Choice, 1 June 2012) Table of ContentsPREFACE ix ACKNOWLEDGMENTS xv 1 PERFECTION 1 2 PERFECTIONISTS 5 A Tour of Athens / 5 Plato’s Challenge / 8 Eudoxus’ Universe / 10 The Math (a mathematical presentation requiring linear algebra) / 14 3 THE ICONOCLAST 24 Insanity / 24 A Disturbing Insight / 29 Aristarchus and On the Sizes and Distances of the Sun and Moon (a mathematical presentation requiring trigonometry) / 29 4 INSTIGATORS 38 A Heavy Hand / 38 Patriarchs / 41 The Irony / 43 Fun / 44 Apollonius’ Osculating Circle and the Ellipse (a mathematical presentation requiring calculus) / 46 Fun’s Harvest / 62 5 RETROGRADE 63 The Imperial Theocracy / 63 Ptolemy’s Universe / 67 Ptolemy and The Almagest (a mathematical presentation requiring trigonometry) / 70 Inspiration / 91 6 REVOLUTIONARY 93 Possibilities / 93 Copernicus’ On Revolutions, the Pursuit of Elegance / 103 The Model (a mathematical presentation requiring trigonometry) / 106 An Elegant Result / 116 7 RENEGADES 117 Countering the Reformation / 117 The Trio: Tycho, Kepler, and Rudolf / 119 Meanwhile in Italy / 131 New Astronomy, in Kepler’s Own Likeness / 134 A Path Strewn with Casualties / 136 The Physicist’s Law / 142 Tycho’s Gift / 145 Mars’ Bed / 147 Configuring the Ellipse: The Second Law (a mathematical presentation requiring trigonometry) / 149 The Mentor / 167 8 THE AUTHORITY 168 Louis XIV, the Sun King / 168 Newton, the Math King / 172 The Influential Principia / 181 Without Fluxions (a mathematical presentation of Newton’s laws of motion and the ellipse requiring high school algebra) / 184 Newton’s Laws, Kepler’s Laws, and Calculus (a calculus-based presentation of Newton’s laws of motion and the ellipse) / 207 Newton’s Agenda / 224 9 RULE BREAKERS 225 Beginnings / 225 Debunking the Ether / 232 The Established and the Unknown / 240 Trouble / 246 Exiting the Quantum Universe / 249 Bending the Light / 251 An Ergodic Life / 252 Victory / 254 The Experiment / 259 The Famous and the Infamous / 260 Exodus / 264 The End / 267 Relativity / 268 Special Relativity (a mathematical presentation requiring high school algebra) / 271 EPILOGUE 293 BIBLIOGRAPHY 295 INDEX 301

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Book SynopsisDemonstrates the application of DSM to solve a broad range of operator equations The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method''s underlying logic and its numerous applications. Dynamical Systems Method and Applications begins with a general introduction and then sets forth the scope of DSM in Part One. Part Two introduces the discrepancy principle, and Part Three offers examples of numerical applications of DSM to solve a broad range of problems in science and engineering. Additional featured topics include: General nonlinear operator equations Operators satisfying a spectral assumption <Trade Review“The book is well organized and presents the DSM method to solve a broad range of operator equations. Suitable for senior under graduate and under graduate students as well as practical engineers and researchers interested in dynamical systems methods and application for operator equations”. (Zentralblatt MATH, 1 December 2012) Table of ContentsPART I 1 Introduction 3 2 Ill-posed problems 11 3 DSM for well-posed problems 57 4 DSM and linear ill-posed problems 71 5 Some inequalities 93 6 DSM for monotone operators 133 7 DSM for general nonlinear operator equations 145 8 DSM for operators satisfying a spectral assumption 155 9 DSM in Banach spaces 161 10 DSM and Newton-type methods without inversion of the derivative 169 11 DSM and unbounded operators 177 12 DSM and nonsmooth operators 181 13 DSM as a theoretical tool 195 14 DSM and iterative methods 201 15 Numerical problems arising in applications 213 PART II 16 Solving linear operator equations by a Newton-type DSM 255 17 DSM of gradient type for solving linear operator equations 269 18 DSM for solving linear equations with finite-rank operators 281 19 A discrepancy principle for equations with monotone continuous operators 295 20 DSM of Newton-type for solving operator equations with minimal smoothness assumptions 307 21 DSM of gradient type 347 22 DSM of simple iteration type 373 23 DSM for solving nonlinear operator equations in Banach spaces 409 PART III 24 Solving linear operator equations by the DSM 423 25 Stable solutions of Hammerstein-type integral equations 441 26 Inversion of the Laplace transform from the real axis using an adaptive iterative method 455

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Book SynopsisA how to guide for applying statistical methods to biomarker data analysis Presenting a solid foundation for the statistical methods that are used to analyze biomarker data, Analysis of Biomarker Data: A Practical Guide features preferred techniques for biomarker validation. The authors provide descriptions of select elementary statistical methods that are traditionally used to analyze biomarker data with a focus on the proper application of each method, including necessary assumptions, software recommendations, and proper interpretation of computer output. In addition, the book discusses frequently encountered challenges in analyzing biomarker data and how to deal with them, methods for the quality assessment of biomarkers, and biomarker study designs. Covering a broad range of statistical methods that have been used to analyze biomarker data in published research studies, Analysis of Biomarker Data: A Practical Guide also features: ATable of ContentsPreface xiii Acknowledgements xvii 1 Introduction 1 1.1 What is a Biomarker? 1 1.2 Biomarkers Versus Surrogate Endpoints 2 1.3 Organization of This Book 3 2 Designing Biomarker Studies 5 2.1 Introduction 5 2.2 Designing the Study 6 2.2.1 The Exposure–Disease Association 6 2.2.2 Cross-sectional Studies 7 2.2.3 Case–Control Studies 7 2.2.4 Retrospective Cohort Studies 9 2.2.5 Prospective Cohort Studies 9 2.2.6 Observational Studies 10 2.2.7 Randomized Controlled Trials 11 2.3 Designing the Analysis 13 2.3.1 Choosing the Appropriate Measure of Association 15 2.3.1.1 Odds Ratio versus Risk Ratio 15 2.3.1.2 Consequences of Not Choosing the Appropriate Measure of Association 16 2.3.2 Choosing the Appropriate Statistical Analysis 16 2.3.3 Choosing the Appropriate Sample Size 17 2.4 Presenting Statistical Results 18 Problems 20 3 Elementary Statistical Methods for Analyzing Biomarker Data 21 3.1 Introduction 21 3.2 Graphical and Tabular Summaries 21 3.3 Descriptive Statistics 26 3.4 Describing the Shape of Distributions 31 3.5 Sampling Distributions 33 3.6 Introduction to Statistical Inference 34 3.6.1 Point Estimation and Confidence Interval Estimation 34 3.6.2 Hypothesis Testing 38 3.7 Comparing Means Across Groups 43 3.7.1 Two Group Comparisons 44 3.7.2 Multiple-Group Comparisons 45 3.8 Correlation Analysis 50 3.9 Regression Analysis 52 3.9.1 Simple Linear Regression 52 3.9.2 Multiple Regression 55 3.9.3 Analysis of Covariance 58 3.10 Analyzing Cross-Classified Data 61 3.10.1 Testing for Independence 61 3.10.2 Comparison of Proportions 65 Problems 69 4 Frequently Encountered Challenges in Analyzing Biomarker Data and How to Deal with Them 72 4.1 Introduction 72 4.2 Non-Normally Distributed Data 73 4.2.1 The Effects of Non-Normality 73 4.2.2 Testing Distributional Assumptions 74 4.2.2.1 Graphical Methods for Assessing Normality 74 4.2.2.2 Measures of Skewness and Kurtosis 81 4.2.2.3 Formal Hypothesis Tests of the Normality Assumption 83 4.2.3 Remedial Measures for Violation of a Distributional Assumption 86 4.2.3.1 Choosing a Transformation 86 4.2.3.2 Using a Robust Statistical Procedure 92 4.2.3.3 Distribution-Free Alternatives 93 4.3 Heterogeneity of Variance 113 4.3.1 The Effects of Heterogeneity 113 4.3.2 The Importance of Heterogeneity in the Comparison of Means 113 4.3.2.1 Comparisons of Two Groups 113 4.3.2.2 Comparisons of More Than Two Groups 116 4.3.2.3 Multiple Comparisons 118 4.4 Dependent Groups 122 4.4.1 The Consequences of Ignoring Dependence Among Groups 122 4.4.2 Comparing Two Dependent Means 124 4.4.2.1 Paired t-test 124 4.4.2.2 Wilcoxon Signed Ranks Test 127 4.4.2.3 Sign Test 128 4.4.3 Tests of Dependent Proportions 134 4.4.3.1 McNemar’s Test 134 4.4.3.2 Cochran’s Q test 138 4.4.3.3 Sample Size and Power Considerations 142 4.5 Correlated Outcomes 144 4.5.1 Choosing the Appropriate Measure of Association 144 4.5.1.1 Spearman’s rho 144 4.5.1.2 Kendall’s tau-b 146 4.5.2 Recommended Methods of Statistical Analysis for Correlation Coefficients 148 4.5.3 Recommended Methods for Interpreting Correlation Coefficient Results 156 4.5.4 Sample Size Issues in Correlation Analysis 157 4.5.5 Comparison of Correlation Coefficients 171 4.5.5.1 Comparison of Independent Correlation Coefficients 172 4.5.5.2 Comparison of Dependent Correlation Coefficients 174 4.5.6 Sample Size Issues When Comparing Two Correlation Coefficients 181 4.5.6.1 Sample Size Issues When Comparing Independent Correlation Coefficients 181 4.5.6.2 Sample Size Issues When Comparing Dependent Correlation Coefficients 183 4.6 Clustered Data 184 4.7 Outliers 199 4.7.1 The Effects of Outliers 199 4.7.2 Detection of Outliers 199 4.7.3 Methods for Accommodating Outliers 207 4.8 Limits of Detection and Non-Detected Observations 208 4.8.1 Statistical Inference When NDs Are Present 210 4.8.2 Maximum Likelihood Estimation of a Correlation Coefficient When Both X and Y Are Subject to Non-Detects 210 4.8.3 Comparison of Confidence Interval Methods for Correlation Coefficients When Both Variables Are Subject to Limits of Detection 212 4.9 The Analysis of Cross-Classified Categorical Data 221 4.9.1 Choosing the Appropriate Measure of Association 221 4.9.1.1 The Odds Ratio 221 4.9.1.2 Risk Ratio 223 4.9.1.3 Risk Difference 224 4.9.1.4 Odds Ratio for Paired Data 225 4.9.2 Choosing the Appropriate Statistical Analysis 225 4.9.3 Choosing the Appropriate Sample Size 226 4.9.4 Choosing a Statistical Method When Both the Predictor and the Outcome Are Dichotomous 226 4.9.4.1 Comparing Two Independent Groups in Terms of a Binomial Proportion 226 4.9.4.2 Exact Test for Independence of Rows and Columns in a 2 × 2 Table 230 4.9.4.3 Exact Inference for Odds Ratios 232 4.9.4.4 Inference for the Odds Ratio for Paired Data 234 4.9.5 Choice of a Statistical Method When the Predictor is Ordinal and the Outcome is Dichotomous 237 4.9.5.1 Tests for a Significant Trend in Proportions 237 4.9.6 Choice of a Statistical Method When Both the Predictor and the Outcome are Ordinal 240 4.9.6.1 Test for Linear-by-Linear Association 240 4.9.7 Choice of a Statistical Method When Both the Predictor and the Outcome are Nominal 243 4.9.7.1 Fisher–Freeman–Halton Test 243 Problems 246 5 Validation of Biomarkers 255 5.1 Overview of Methods for Assessing Characteristics of Biomarkers 255 5.2 General Description of Measures of Agreement 257 5.2.1 Discrete Variables 257 5.2.1.1 Cohen’s Kappa 257 5.2.1.2 Extensions of Coefficient Kappa 265 5.2.1.3 Weighted Kappa 273 5.2.2 Continuous Variables 275 5.2.2.1 Pearson’s Correlation Coefficient 275 5.2.2.2 Alternatives to Pearson’s Correlation Coefficient 277 5.3 Assessing Reliability of a Biomarker 287 5.3.1 General Considerations 287 5.3.2 Assessing Reliability of a Dichotomous Biomarker 287 5.3.2.1 Dichotomous Biomarker, More Than Two Raters 289 5.3.3 Assessing Reliability of a Continuous Biomarker 291 5.3.4 Assessing Inter-Subject, Intra-Subject, and Analytical Measurement Variability 292 5.4 Assessing Validity 294 5.4.1 General Considerations 294 5.4.2 Assessing Validity When a Gold Standard is Available 295 5.4.2.1 Dichotomous Biomarkers 295 5.4.2.2 Comparing Several Dichotomous Biomarkers 302 5.4.2.3 Continuous Biomarkers 304 5.4.3 Assessing Validity When a Gold Standard is Not Available 314 5.4.3.1 Dichotomous Biomarkers 315 5.4.3.2 Continuous Biomarkers 319 5.4.4 Assessing Criterion Validity in Method Comparison Studies 328 5.4.5 Assessing Construct Validity in Method Comparison Studies 329 Problems 329 References 332 Solutions to Problems 348 Index 391

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Book SynopsisMethods for estimating sparse and large covariance matrices Covariance and correlation matrices play fundamental roles in every aspect of the analysis of multivariate data collected from a variety of fields including business and economics, health care, engineering, and environmental and physical sciences. High-Dimensional Covariance Estimation provides accessible and comprehensive coverage of the classical and modern approaches for estimating covariance matrices as well as their applications to the rapidly developing areas lying at the intersection of statistics and machine learning. Recently, the classical sample covariance methodologies have been modified and improved upon to meet the needs of statisticians and researchers dealing with large correlated datasets. High-Dimensional Covariance Estimation focuses on the methodologies based on shrinkage, thresholding, and penalized likelihood with applications to Gaussian graphical models, prediction,Table of ContentsPreface xi PART I MOTIVATION AND THE BASICS 1 Introduction 3 1.1 Least-Squares and Regularized Regression 4 1.2 Lasso: Survival of the Bigger 6 1.3 Thresholding the Sample Covariance Matrix 9 1.4 Sparse PCA and Regression 10 1.5 Graphical Models: Nodewise Regression 12 1.6 Cholesky Decomposition and Regression 13 1.7 The Bigger Picture: Latent Factor Models 14 1.8 Further Reading 16 2 Data, Sparsity and Regularization 21 2.1 Data Matrix: Examples 22 2.2 Shrinking the Sample Covariance Matrix 26 2.3 Distribution of the Sample Eigenvalues 29 2.4 Regularizing Covariances Like a Mean 30 2.5 The Lasso Regression 32 2.6 Lasso, Variable Selection and Prediction 36 2.7 Lasso, Degrees of Freedom and BIC 37 2.8 Some Alternatives to the Lasso Penalty 38 3 Covariance Matrices 45 3.1 Definition and Basic Properties 46 3.2 The Spectral Decomposition 49 3.3 Structured Covariance Matrices 52 3.4 Functions of a Covariance Matrix 55 3.5 PCA: The Maximum Variance Property 59 3.6 Modified Cholesky Decomposition 61 3.7 Latent Factor Models 65 3.8 GLM for Covariance Matrices 71 3.9 GLM via the Cholesky Decomposition 73 3.10 The GLM for Incomplete Longitudinal Data 76 3.11 A Data Example: Fruit Fly Mortality Rate 81 3.12 Simulating Random Correlation Matrices 85 3.13 Bayesian Analysis of Covariance Matrices 88 PART II COVARIANCE ESTIMATION: REGULARIZATION 4 Regularizing the Eigenstructure 95 4.1 Shrinking the Eigenvalues 96 4.2 Regularizing The Eigenvectors 101 4.3 A Duality between PCA and SVD 103 4.4 Implementing Sparse PCA: A Data Example 106 4.5 Sparse Singular Value Decomposition (SSVD) 108 4.6 Consistency of PCA 109 4.7 Principal Subspace Estimation 113 4.8 Further Reading 114 5 Sparse Gaussian Graphical Models 115 5.1 Covariance Selection Models: Two Examples 116 5.2 Regression Interpretation of Entries of ∑-1 118 5.3 Penalized Likelihood and Graphical Lasso 120 5.4 Penalized Quasi-Likelihood Formulation 126 5.5 Penalizing the Cholesky Factor 127 5.6 Consistency and Sparsistency 130 5.7 Joint Graphical Models 130 5.8 Further Reading 132 6 Banding, Tapering and Thresholding 135 6.1 Banding the Sample Covariance Matrix 136 6.2 Tapering the Sample Covariance Matrix 137 6.3 Thresholding the Sample Covariance Matrix 138 6.4 Low-Rank Plus Sparse Covariance Matrices 142 6.5 Further Reading 143 7 Multivariate Regression: Accounting for Correlation 145 7.1 Multivariate Regression & LS Estimators 146 7.2 Reduced Rank Regressions (RRR) 148 7.3 Regularized Estimation of B 150 7.4 Joint Regularization of (B;) 152 7.5 Implementing MRCE: Data Examples 155 7.5.1 Intraday Electricity Prices 155 7.5.2 Predicting Asset Returns 158 7.6 Further Reading 161

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Book SynopsisPraise for the First Edition . . .will certainly fascinate anyone interested in abstract algebra: a remarkable book! Monatshefte fur Mathematik Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel's theory of Abelian equations, casus irreducibili, and the Galois theory of origami. In addition, this book features detailed treatments of several topics not covered in standard texts on Galois theory, including: The contributions of Lagrange, Galois, and Kronecker How to compute Galois groups Galois''s results about irreducible polynomials of prime orprime-squared degreTrade Review“There is barely a better introduction to the subject, in all its theoretical and practical aspects, than the book under review.” (Zentralblatt MATH, 1 December 2012)"the great merit of this book (one of many expositions of the subject) is that everything is taken at a slow pace, with many examples to illustrate every idea. You get the (probably true) impression that the author loves this material, has taught it to undergraduates at Amherst College many times, has learned by experience the ideas which students find difficult, and has then taken great trouble to dissect these ideas and to pick out exactly the right examples and exercises to make them part of the reader’s mental equipment." (The Mathematical Gazette 2016) Table of ContentsPreface to the First Edition xvii Preface to the Second Edition xxi Notation xxiii 1 Basic Notation xxiii 2 Chapter-by-Chapter Notation xxv PART I POLYNOMIALS 1 Cubic Equations 3 1.1 Cardan's Formulas 4 1.2 Permutations of the Roots 10 1.3 Cubic Equations over the Real Numbers 15 2 Symmetric Polynomials 25 2.1 Polynomials of Several Variables 25 2.2 Symmetric Polynomials 30 2.3 Computing with Symmetric Polynomials (Optional) 42 2.4 The Discriminant 46 3 Roots of Polynomials 55 3.1 The Existence of Roots 55 3.2 The Fundamental Theorem of Algebra 62 PART II FIELDS 4 Extension Fields 73 4.1 Elements of Extension Fields 73 4.2 Irreducible Polynomials 81 4.3 The Degree of an Extension 89 4.4 Algebraic Extensions 95 5 Normal and Separable Extensions 101 5.1 Splitting Fields 101 5.2 Normal Extensions 107 5.3 Separable Extensions 109 5.4 Theorem of the Primitive Element 119 6 The Galois Group 125 6.1 Definition of the Galois Group 125 6.2 Galois Groups of Splitting Fields 130 6.3 Permutations of the Roots 132 6.4 Examples of Galois Groups 136 6.5 Abelian Equations (Optional) 143 7 The Galois Correspondence 147 7.1 Galois Extensions 147 7.2 Normal Subgroups and Normal Extensions 154 7.3 The Fundamental Theorem of Galois Theory 161 7.4 First Applications 167 7.5 Automorphisms and Geometry (Optional) 173 PART III APPLICATIONS 8 Solvability by Radicals 191 8.1 Solvable Groups 191 8.2 Radical and Solvable Extensions 196 8.3 Solvable Extensions and Solvable Groups 201 8.4 Simple Groups 210 8.5 Solving Polynomials by Radicals 215 8.6 The Casus Irreducbilis (Optional) 220 9 Cyclotomic Extensions 229 9.1 Cyclotomic Polynomials 229 9.2 Gauss and Roots of Unity (Optional) 238 10 Geometric Constructions 255 10.1 Constructible Numbers 255 10.2 Regular Polygons and Roots of Unity 270 10.3 Origami (Optional) 274 11 Finite Fields 291 11.1 The Structure of Finite Fields 291 11.2 Irreducible Polynomials over Finite Fields (Optional) 301 PART IV FURTHER TOPICS 12 Lagrange, Galois, and Kronecker 315 12.1 Lagrange 315 12.2 Galois 334 12.3 Kronecker 347 13 Computing Galois Groups 357 13.1 Quartic Polynomials 357 13.2 Quintic Polynomials 368 13.3 Resolvents 386 13.4 Other Methods 400 14 Solvable Permutation Groups 413 14.1 Polynomials of Prime Degree 413 14.2 Imprimitive Polynomials of Prime-Squared Degree 419 14.3 Primitive Permutation Groups 429 14.4 Primitive Polynomials of Prime-Squared Degree 444 15 The Lemniscate 463 15.1 Division Points and Arc Length 464 15.2 The Lemniscatic Function 470 15.3 The Complex Lemniscatic Function 482 15.4 Complex Multiplication 489 15.5 Abel's Theorem 504 A Abstract Algebra 515 A.1 Basic Algebra 515 A.2 Complex Numbers 524 A.3 Polynomials with Rational Coefficients 528 A.4 Group Actions 530 A.5 More Algebra 532 Index 557

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Book SynopsisA powerful, unified approach to mathematical and computational modeling in science and engineering Mathematical and computational modeling makes it possible to predict the behavior of a broad range of systems across a broad range of disciplines. This text guides students and professionals through the axiomatic approach, a powerful method that will enable them to easily master the principle types of mathematical and computational models used in engineering and science. Readers will discover that this axiomatic approach not only enables them to systematically construct effective models, it also enables them to apply these models to any macroscopic physical system. Mathematical Modeling in Science and Engineering focuses on models in which the processes to be modeled are expressed as systems of partial differential equations. It begins with an introductory discussion of the axiomatic formulation of basic models, setting the foundation for further topics such as:Table of ContentsPreface xiii 1 AXIOMATIC FORMULATION OF THE BASIC MODELS 1 1.1 Models 1 1.2 Microscopic and macroscopic physics 2 1.3 Kinematics of continuous systems 3 1.3.1 Intensive properties 6 1.3.2 Extensive properties 8 1.4 Balance equations of extensive and intensive properties 9 1.4.1 Global balance equations 9 1.4.2 The local balance equations 10 1.4.3 The role of balance conditions in the modeling of continuous systems 13 1.4.4 Formulation of motion restrictions by means of balance equations 14 1.5 Summary 16 2 MECHANICS OF CLASSICAL CONTINUOUS SYSTEMS 23 2.1 One-phase systems 23 2.2 The basic mathematical model of one-phase systems 24 2.3 The extensive/intensive properties of classical mechanics 25 2.4 Mass conservation 26 2.5 Linear momentum balance 27 2.6 Angular momentum balance 29 2.7 Energy concepts 32 2.8 The balance of kinetic energy 33 2.9 The balance of internal energy 34 2.10 Heat equivalent of mechanical work 35 2.11 Summary of basic equations for solid and fluid mechanics 35 2.12 Some basic concepts of thermodynamics 36 2.12.1 Heat transport 36 2.13 Summary 38 3 MECHANICS OF NON-CLASSICAL CONTINUOUS SYSTEMS 45 3.1 Multiphase systems 45 3.2 The basic mathematical model of multiphase systems 46 3.3 Solute transport in a free fluid 47 3.4 Transport by fluids in porous media 49 3.5 Flow of fluids through porous media 51 3.6 Petroleum reservoirs: the black-oil model 52 3.6.1 Assumptions of the black-oil model 53 3.6.2 Notation 53 3.6.3 Family of extensive properties 54 3.6.4 Differential equations and jump conditions 55 3.7 Summary 57 4 SOLUTE TRANSPORT BY A FREE FLUID 63 4.1 The general equation of solute transport by a free fluid 64 4.2 Transport processes 65 4.2.1 Advection 65 4.2.2 Diffusion processes 65 4.3 Mass generation processes 66 4.4 Differential equations of diffusive transport 67 4.5 Well-posed problems for diffusive transport 69 4.5.1 Time-dependent problems 70 4.5.2 Steady state 71 4.6 First-order irreversible processes 71 4.7 Differential equations of non-diffusive transport 73 4.8 Well-posed problems for non-diffusive transport 73 4.8.1 Well-posed problems in one spatial dimension 74 4.8.2 Well-posed problems in several spatial dimensions 79 4.8.3 Well-posed problems for steady-state models 80 4.9 Summary 80 5 FLOW OF A FLUID IN A POROUS MEDIUM 85 5.1 Basic assumptions of the flow model 85 5.2 The basic model for the flow of a fluid through a porous medium 86 5.3 Modeling the elasticity and compressibility 87 5.3.1 Fluid compressibility 87 5.3.2 Pore compressibility 88 5.3.3 The storage coefficient 90 5.4 Darcy's law 90 5.5 Piezometric level 92 5.6 General equation governing flow through a porous medium 94 5.6.1 Special forms of the governing differential equation 95 5.7 Applications of the jump conditions 96 5.8 Well-posed problems 96 5.8.1 Steady-state models 97 5.8.2 Time-dependent problems 99 5.9 Models with a reduced number of spatial dimensions 99 5.9.1 Theoretical derivation of a 2-D model for a confined aquifer 100 5.9.2 Leaky aquitard method 102 5.9.3 The integrodifferential equations approach 104 5.9.4 Other 2-D aquifer models 108 5.10 Summary 111 6 SOLUTE TRANSPORT IN A POROUS MEDIUM 117 6.1 Transport processes 118 6.1.1 Advection 118 6.2 Non-conservative processes 118 6.2.1 First-order irreversible processes 119 6.2.2 Adsorption 119 6.3 Dispersion-diffusion 121 6.4 The equations for transport of solutes in porous media 123 6.5 Well-posed problems 125 6.6 Summary 125 7 MULTIPHASE SYSTEMS 129 7.1 Basic model for the flow of multiple-species transport in a multiple-fluid- phase porous medium 129 7.2 Modeling the transport of species i in phase a 130 7.3 The saturated flow case 133 7.4 The air-water system 137 7.5 The immobile air unsaturated flow model 142 7.6 Boundary conditions 143 7.7 Summary 145 8 ENHANCED OIL RECOVERY 149 8.1 Background on oil production and reservoir modeling 149 8.2 Processes to be modeled 151 8.3 Unified formulation of EOR models 151 8.4 The black-oil model 152 8.5 The Compositional Model 156 8.6 Summary 160 9 LINEAR ELASTICITY 165 9.1 Introduction 165 9.2 Elastic Solids 166 9.3 The Linear Elastic Solid 167 9.4 More on the Displacement Field Decomposition 170 9.5 Strain Analysis 171 9.6 Stress Analysis 173 9.7 Isotropic materials 175 9.8 Stress-strain relations for isotropic materials 177 9.9 The governing differential equations 179 9.9.1 Elastodynamics 180 9.9.2 Elastostatics 180 9.10 Well-posed problems 181 9.10.1 Elastostatics 181 9.10.2 Elastodynamics 181 9.11 Representation of solutions for isotropic elastic solids 182 9.12 Summary 183 10 FLUID MECHANICS 189 10.1 Introduction 189 10.2 Newtonian fluids: Stokes' constitutive equations 190 10.3 Navier-Stokes equations 192 10.4 Complementary constitutive equations 193 10.5 The concepts of incompressible and inviscid fluids 193 10.6 Incompressible fluids 194 10.7 Initial and boundary conditions 195 10.8 Viscous incompressible fluids: steady states 196 10.9 Linearized theory of incompressible fluids 196 10.10 Ideal fluids 197 10.11 Irrotational flows 198 10.12 Extension of Bernoulli's relations to compressible fluids 199 10.13 Shallow-water theory 200 10.14 Inviscid compressible fluids 202 10.14.1 Small perturbations in a compressible fluid: the theory of sound 203 10.14.2 Initiation of motion 204 10.14.3 Discontinuous models and shock conditions 206 10.15 Summary 208 A: PARTIAL DIFFERENTIAL EQUATIONS 211 A. 1 Classification 211 A.2 Canonical forms 213 A.3 Well-posed problems 213 A.3.1 Boundary-value problems: the elliptic case 214 A.3.2 Initial-boundary-value problems 214 B: SOME RESULTS FROM THE CALCULUS 217 B.l Notation 217 B.2 Generalized Gauss Theorem 218 C: PROOF OF THEOREM 221 D: THE BOUNDARY LAYER INCOMPRESSIBILITY APPROXIMATION 225 E: INDICIAL NOTATION 229 E.l General 229 E.2 Matrix algebra 230 E.3 Applications to differential calculus 232 Index 235

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Book SynopsisFeatures recent advances and new applications in graph edge coloring Reviewing recent advances in the Edge Coloring Problem, Graph Edge Coloring: Vizing''s Theorem and Goldberg''s Conjecture provides an overview of the current state of the science, explaining the interconnections among the results obtained from important graph theory studies. The authors introduce many new improved proofs of known results to identify and point to possible solutions for open problems in edge coloring. The book begins with an introduction to graph theory and the concept of edge coloring. Subsequent chapters explore important topics such as: Use of Tashkinov trees to obtain an asymptotic positive solution to Goldberg''s conjecture Application of Vizing fans to obtain both known and new results Kierstead paths as an alternative to Vizing fans Classification problem of simple graphs Generalized Trade Review “College mathematics collections need just this sort of rarity-accounts of major unsolved problems, elementary but still comprehensive. Summing Up: Recommended. Upper-division undergraduates.” (Choice, 1 September 2012) Table of ContentsPreface xi 1 Introduction 1 1.1 Graphs 1 1.2 Coloring Preliminaries 2 1.3 Critical Graphs 5 1.4 Lower Bounds and Elementary Graphs 6 1.5 Upper Bounds and Coloring Algorithms 11 1.6 Notes 15 2 Vizing Fans 19 2.1 The Fan Equation and the Classical Bounds 19 2.2 Adjacency Lemmas 24 2.3 The Second Fan Equation 26 2.4 The Double Fan 31 2.5 The Fan Number 32 2.6 Notes 39 3 Kierstead Paths 43 3.1 Kierstead's Method 43 3.2 Short Kierstead's Paths 46 3.3 Notes 49 4 Simple Graphs and Line Graphs 51 4.1 Class One and Class Two Graphs 51 4.2 Graphs whose Core has Maximum Degree Two 54 4.3 Simple Overfull Graphs 63 4.4 Adjacency Lemmas for Critical Class Two Graphs 73 4.5 Average Degree of Critical Class Two Graphs 84 4.6 Independent Vertices in Critical Class Two Graphs 89 4.7 Constructions of Critical Class Two Graphs 93 4.8 Hadwiger's Conjecture for Line Graphs 101 4.9 Simple Graphs on Surfaces 105 4.10 Notes 110 5 Tashkinov Trees 115 5.1 Tashkinov's Method 115 5.2 Extended Tashkinov Trees 127 5.3 Asymptotic Bounds 139 5.4 Tashkinov's Coloring Algorithm 144 5.5 Polynomial Time Algorithms 148 5.6 Notes 152 6 Goldberg's Conjecture 155 6.1 Density and Fractional Chromatic Index 155 6.2 Balanced Tashkinov Trees 160 6.3 Obstructions 162 6.4 Approximation Algorithms 183 6.5 Goldberg's Conjecture for Small Graphs 185 6.6 Another Classification Problem for Graphs 186 6.7 Notes 193 7 Extreme Graphs 197 7.1 Shannon's Bound and Ring Graphs 197 7.2 Vizing's Bound and Extreme Graphs 201 7.3 Extreme Graphs and Elementary Graphs 203 7.4 Upper Bounds for ÷' Depending on Ä and ì 205 7.5 Notes 209 8 Generalized Edge Colorings of Graphs 213 8.1 Equitable and Balanced Edge Colorings 213 8.2 Full Edge Colorings and the Cover Index 222 8.3 Edge Colorings of Weighted Graphs 224 8.4 The Fan Equation for the Chromatic Index X'f 228 8.5 Decomposing Graphs into Simple Graphs 239 8.6 Notes 243 9 Twenty Pretty Edge Coloring Conjectures 245 Appendix A: Vizing's Two Fundamental Papers 269 A. 1 On an Estimate of the Chromatic Class of a p-Graph 269 References 272 A.2 Critical Graphs with a Given Chromatic Class 273 References 278 Appendix B: Fractional Edge Colorings 281 B. 1 The Fractional Chromatic Index 281 B.2 The Matching Polytope 284 B.3 A Formula for X'f 290 References 295 Symbol Index 312 Name Index 314 Subject Index 318

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Book SynopsisWith a focus on one central theme (the Impossibility Theorem) throughout, this highly accessible introduction to Galois theory presents a classical treatment of the topic and poses questions related to the solvability of polynomial equations by radicals. Modern points of view are also discussed in contrast to the historical development and context.Table of ContentsPreface xi 1 Classical Formulas 1 1.1 Quadratic Polynomials 3 1.2 Cubic Polynomials 5 1.3 Quartic Polynomials 11 2 Polynomials and Field Theory 15 2.1 Divisibility 16 2.2 Algebraic Extensions 24 2.3 Degree of Extensions 25 2.4 Derivatives 29 2.5 Primitive Element Theorem 30 2.6 Isomorphism Extension Theorem and Splitting Fields 35 3 Fundamental Theorem on Symmetric Polynomials and Discriminants 41 3.1 Fundamental Theorem on Symmetric Polynomials 41 3.2 Fundamental Theorem on Symmetric Rational Functions 48 3.3 Some Identities Based on Elementary Symmetric Polynomials 50 3.4 Discriminants 53 3.5 Discriminants and Subfields of the Real Numbers 60 4 Irreducibility and Factorization 65 4.1 Irreducibility Over the Rational Numbers 65 4.2 Irreducibility and Splitting Fields 69 4.3 Factorization and Adjunction 72 5 Roots of Unity and Cyclotomic Polynomials 80 5.1 Roots of Unity 80 5.2 Cyclotomic Polynomials 82 6 Radical Extensions and Solvability by Radicals 89 6.1 Basic Results on Radical Extensions 89 6.2 Gauss’s Theorem on Cyclotomic Polynomials 93 6.3 Abel’s Theorem on Radical Extensions 104 6.4 Polynomials of Prime Degree 109 7 General Polynomials and the Beginnings of Galois Theory 117 7.1 General Polynomials 117 7.2 The Beginnings of Galois Theory 124 8 Classical Galois Theory According to Galois 135 9 Modern Galois Theory 151 9.1 Galois Theory and Finite Extensions 152 9.2 Galois Theory and Splitting Fields 156 10 Cyclic Extensions and Cyclotomic Fields 171 10.1 Cyclic Extensions 171 10.2 Cyclotomic Fields 179 11 Galois’s Criterion for Solvability of Polynomials by Radicals 185 12 Polynomials of Prime degree 192 13 Periods of Roots of Unity 200 14 Denesting Radicals 225 15 Classical Formulas Revisited 231 15.1 General Quadratic Polynomial 231 15.2 General Cubic Polynomial 233 15.3 General Quartic Polynomial 236 Appendix A Cosets and Group Actions 245 Appendix B Cyclic Groups 249 Appendix C Solvable Groups 254 Appendix D Permutation Groups 261 Appendix E Finite fields and Number Theory 270 Appendix F Further Reading 274 References 277 Index 281

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Book Synopsis". this edition is useful and effective in teaching Bayesian inference at both elementary and intermediate levels. It is a well-written book on elementary Bayesian inference, and the material is easily accessible.Table of ContentsPreface xiii 1 Introduction to Statistical Science 1 1.1 The Scientic Method: A Process for Learning 3 1.2 The Role of Statistics in the Scientic Method 5 1.3 Main Approaches to Statistics 5 1.4 Purpose and Organization of This Text 8 2 Scientic Data Gathering 13 2.1 Sampling from a Real Population 14 2.2 Observational Studies and Designed Experiments 17 Monte Carlo Exercises 23 3 Displaying and Summarizing Data 31 3.1 Graphically Displaying a Single Variable 32 3.2 Graphically Comparing Two Samples 39 3.3 Measures of Location 41 3.4 Measures of Spread 44 3.5 Displaying Relationships Between Two or More Variables 46 3.6 Measures of Association for Two or More Variables 49 Exercises 52 4 Logic, Probability, and Uncertainty 59 4.1 Deductive Logic and Plausible Reasoning 60 4.2 Probability 62 4.3 Axioms of Probability 64 4.4 Joint Probability and Independent Events 65 4.5 Conditional Probability 66 4.6 Bayes' Theorem 68 4.7 Assigning Probabilities 74 4.8 Odds and Bayes Factor 75 4.9 Beat the Dealer 76 Exercises 80 5 Discrete Random Variables 83 5.1 Discrete Random Variables 84 5.2 Probability Distribution of a Discrete Random Variable 86 5.3 Binomial Distribution 90 5.4 Hypergeometric Distribution 92 5.5 Poisson Distribution 93 5.6 Joint Random Variables 96 5.7 Conditional Probability for Joint Random Variables 100 Exercises 104 6 Bayesian Inference for Discrete Random Variables 109 6.1 Two Equivalent Ways of Using Bayes' Theorem 114 6.2 Bayes' Theorem for Binomial with Discrete Prior 116 6.3 Important Consequences of Bayes' Theorem 119 6.4 Bayes' Theorem for Poisson with Discrete Prior 120 Exercises 122 Computer Exercises 126 7 Continuous Random Variables 129 7.1 Probability Density Function 131 7.2 Some Continuous Distributions 135 7.3 Joint Continuous Random Variables 143 7.4 Joint Continuous and Discrete Random Variables 144 Exercises 147 8 Bayesian Inference for Binomial Proportion 149 8.1 Using a Uniform Prior 150 8.2 Using a Beta Prior 151 8.3 Choosing Your Prior 154 8.4 Summarizing the Posterior Distribution 158 8.5 Estimating the Proportion 161 8.6 Bayesian Credible Interval 162 Exercises 164 Computer Exercises 167 9 Comparing Bayesian and Frequentist Inferences for Proportion 169 9.1 Frequentist Interpretation of Probability and Parameters 170 9.2 Point Estimation 171 9.3 Comparing Estimators for Proportion 174 9.4 Interval Estimation 175 9.5 Hypothesis Testing 178 9.6 Testing a One-Sided Hypothesis 179 9.7 Testing a Two-Sided Hypothesis 182 Exercises 187 Monte Carlo Exercises 190 10 Bayesian Inference for Poisson 193 10.1 Some Prior Distributions for Poisson 194 10.2 Inference for Poisson Parameter 200 Exercises 207 Computer Exercises 208 11 Bayesian Inference for Normal Mean 211 11.1 Bayes' Theorem for Normal Mean with a Discrete Prior 211 11.2 Bayes' Theorem for Normal Mean with a Continuous Prior 218 11.3 Choosing Your Normal Prior 222 11.4 Bayesian Credible Interval for Normal Mean 224 11.5 Predictive Density for Next Observation 227 Exercises 230 Computer Exercises 232 12 Comparing Bayesian and Frequentist Inferences for Mean 237 12.1 Comparing Frequentist and Bayesian Point Estimators 238 12.2 Comparing Condence and Credible Intervals for Mean 241 12.3 Testing a One-Sided Hypothesis about a Normal Mean 243 12.4 Testing a Two-Sided Hypothesis about a Normal Mean 247 Exercises 251 13 Bayesian Inference for Di erence Between Means 255 13.1 Independent Random Samples from Two Normal Distributions 256 13.2 Case 1: Equal Variances 257 13.3 Case 2: Unequal Variances 262 13.4 Bayesian Inference for Dierence Between Two Proportions Using Normal Approximation 265 13.5 Normal Random Samples from Paired Experiments 266 Exercises 272 14 Bayesian Inference for Simple Linear Regression 283 14.1 Least Squares Regression 284 14.2 Exponential Growth Model 288 14.3 Simple Linear Regression Assumptions 290 14.4 Bayes' Theorem for the Regression Model 292 14.5 Predictive Distribution for Future Observation 298 Exercises 303 Computer Exercises 312 15 Bayesian Inference for Standard Deviation 315 15.1 Bayes' Theorem for Normal Variance with a Continuous Prior 316 15.2 Some Specic Prior Distributions and the Resulting Posteriors 318 15.3 Bayesian Inference for Normal Standard Deviation 326 Exercises 332 Computer Exercises 335 16 Robust Bayesian Methods 337 16.1 Eect of Misspecied Prior 338 16.2 Bayes' Theorem with Mixture Priors 340 Exercises 349 Computer Exercises 351 17 Bayesian Inference for Normal with Unknown Mean and Variance 355 17.1 The Joint Likelihood Function 358 17.2 Finding the Posterior when Independent Jeffreys' Priors for μ and σ2 Are Used 359 17.3 Finding the Posterior when a Joint Conjugate Prior for μ and σ2 Is Used 361 17.4 Difference Between Normal Means with Equal Unknown Variance 367 17.5 Difference Between Normal Means with Unequal Unknown Variances 377 Computer Exercises 383 Appendix: Proof that the Exact Marginal Posterior Distribution of μ is Student's t 385 18 Bayesian Inference for Multivariate Normal Mean Vector 393 18.1 Bivariate Normal Density 394 18.2 Multivariate Normal Distribution 397 18.3 The Posterior Distribution of the Multivariate Normal Mean Vector when Covariance Matrix Is Known 398 18.4 Credible Region for Multivariate Normal Mean Vector when Covariance Matrix Is Known 400 18.5 Multivariate Normal Distribution with Unknown Covariance Matrix 402 Computer Exercises 406 19 Bayesian Inference for the Multiple Linear Regression Model 411 19.1 Least Squares Regression for Multiple Linear Regression Model 412 19.2 Assumptions of Normal Multiple Linear Regression Model 414 19.3 Bayes' Theorem for Normal Multiple Linear Regression Model 415 19.4 Inference in the Multivariate Normal Linear Regression Model 419 19.5 The Predictive Distribution for a Future Observation 425 Computer Exercises 428 20 Computational Bayesian Statistics Including Markov Chain Monte Carlo 431 20.1 Direct Methods for Sampling from the Posterior 436 20.2 Sampling - Importance - Resampling 450 20.3 Markov Chain Monte Carlo Methods 454 20.4 Slice Sampling 470 20.5 Inference from a Posterior Random Sample 473 20.6 Where to Next? 475 A Introduction to Calculus 477 B Use of Statistical Tables 497 C Using the Included Minitab Macros 523 D Using the Included R Functions 543 E Answers to Selected Exercises 565 References 591 Index 595

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Book SynopsisPraise for the First Edition This book will serve to greatly complement the growing number of texts dealing with mixed models, and I highly recommend including it in one's personal library. Journal of the American Statistical Association Mixed modeling is a crucial area of statistics, enabling the analysis of clustered and longitudinal data. Mixed Models: Theory and Applications with R, Second Edition fills a gap in existing literature between mathematical and applied statistical books by presenting a powerful examination of mixed model theory and application with special attention given to the implementation in R. The new edition provides in-depth mathematical coverage of mixed models' statistical properties and numerical algorithms, as well as nontraditional applications, such as regrowth curves, shapes, and images. The book features the latest topics in statistics including modeling of complex clustered or longitudinal dataTable of ContentsPreface xvii Preface to the Second Edition xix R software and Functions xx Data Sets xxii Open Problems in Mixed Models xxiii 1 Introduction: Why Mixed Models? 1 1.1 Mixed effects for clustered data 2 1.2 ANOVA, variance components, and the mixed model 4 1.3 Other special cases of the mixed effects model 6 1.4 A compromise between Bayesian and frequentist approaches 7 1.5 Penalized likelihood and mixed effects 9 1.6 Healthy Akaike information criterion 11 1.7 Penalized smoothing 13 1.8 Penalized polynomial fitting 16 1.9 Restraining parameters, or what to eat 18 1.10 Ill-posed problems, Tikhonov regularization, and mixed effects 20 1.11 Computerized tomography and linear image reconstruction 23 1.12 GLMM for PET 26 1.13 Maple shape leaf analysis 29 1.14 DNA Western blot analysis 31 1.15 Where does the wind blow? 33 1.16 Software and books 36 1.17 Summary points 37 2 MLE for LME Model 41 2.1 Example: Weight versus height 42 2.2 The model and log-likelihood functions 45 2.3 Balanced random-coefficient model 60 2.4 LME model with random intercepts 64 2.5 Criterion for the MLE existence 72 2.6 Criterion for positive definiteness of matrix D 74 2.7 Preestimation bounds for variance parameters 77 2.8 Maximization algorithms 79 2.9 Derivatives of the log-likelihood function 81 2.10 Newton—Raphson algorithm 83 2.11 Fisher scoring algorithm 85 2.12 EM algorithm 88 2.13 Starting point 93 2.14 Algorithms for restricted MLE 96 2.15 Optimization on nonnegative definite matrices 97 2.16 lmeFS and lme in R 108 2.17 Appendix: Proof of the MLE existence 112 2.18 Summary points 115 3 Statistical Properties of the LME Model 119 3.1 Introduction 119 3.2 Identifiability of the LME model 119 3.3 Information matrix for variance parameters 122 3.4 Profile-likelihood confidence intervals 133 3.5 Statistical testing of the presence of random effects 135 3.6 Statistical properties of MLE 139 3.7 Estimation of random effects 148 3.8 Hypothesis and membership testing 153 3.9 Ignoring random effects 157 3.10 MINQUE for variance parameters 160 3.11 Method of moments 169 3.12 Variance least squares estimator 173 3.13 Projection on D+ space 178 3.14 Comparison of the variance parameter estimation 178 3.15 Asymptotically efficient estimation for β 182 3.16 Summary points 183 4 Growth Curve Model and Generalizations 187 4.1 Linear growth curve model 187 4.2 General linear growth curve model 203 4.3 Linear model with linear covariance structure 221 4.4 Robust linear mixed effects model 235 4.5 Appendix: Derivation of the MM estimator 243 4.6 Summary points 244 5 Meta-analysis Model 247 5.1 Simple meta-analysis model 248 5.2 Meta-analysis model with covariates 275 5.3 Multivariate meta-analysis model 280 5.4 Summary points 291 6 Nonlinear Marginal Model 293 6.1 Fixed matrix of random effects 294 6.2 Varied matrix of random effects 307 6.3 Three types of nonlinear marginal models 318 6.4 Total generalized estimating equations approach 323 6.5 Summary points 330 7 Generalized Linear Mixed Models 333 7.1 Regression models for binary data 334 7.2 Binary model with subject-specific intercept 357 7.3 Logistic regression with random intercept 364 7.4 Probit model with random intercept 384 7.5 Poisson model with random intercept 388 7.6 Random intercept model: overview 403 7.7 Mixed models with multiple random effects 404 7.8 GLMM and simulation methods 413 7.9 GEE for clustered marginal GLM 418 7.10 Criteria for MLE existence for binary model 426 7.11 Summary points 431 8 Nonlinear Mixed Effects Model 435 8.1 Introduction 435 8.2 The model 436 8.3 Example: Height of girls and boys 439 8.4 Maximum likelihood estimation 441 8.5 Two-stage estimator 444 8.6 First-order approximation 450 8.7 Lindstrom—Bates estimator 452 8.8 Likelihood approximations 457 8.9 One-parameter exponential model 460 8.10 Asymptotic equivalence of the TS and LB estimators 467 8.11 Bias-corrected two-stage estimator 469 8.12 Distribution misspecification 471 8.13 Partially nonlinear marginal mixed model 474 8.14 Fixed sample likelihood approach 475 8.15 Estimation of random effects and hypothesis testing 478 8.16 Example (continued) 479 8.17 Practical recommendations 481 8.18 Appendix: Proof of theorem on equivalence 482 8.19 Summary points 485 9 Diagnostics and Influence Analysis 489 9.1 Introduction 489 9.2 Influence analysis for linear regression 490 9.3 The idea of infinitesimal influence 493 9.4 Linear regression model 495 9.5 Nonlinear regression model 512 9.6 Logistic regression for binary outcome 517 9.7 Influence of correlation structure 526 9.8 Influence of measurement error 527 9.9 Influence analysis for the LME model 530 9.10 Appendix: MLE derivative with respect to σ2 536 9.11 Summary points 537 10 Tumor Regrowth Curves 541 10.1 Survival curves 543 10.2 Double—exponential regrowth curve 545 10.3 Exponential growth with fixed regrowth time 559 10.4 General regrowth curve 565 10.5 Double—exponential transient regrowth curve 566 10.6 Gompertz transient regrowth curve 573 10.7 Summary points 576 11 Statistical Analysis of Shape 579 11.1 Introduction 579 11.2 Statistical analysis of random triangles 581 11.3 Face recognition 584 11.4 Scale-irrelevant shape model 585 11.5 Gorilla vertebrae analysis 589 11.6 Procrustes estimation of the mean shape 591 11.7 Fourier descriptor analysis 598 11.8 Summary points 607 12 Statistical Image Analysis 609 12.1 Introduction 609 12.2 Testing for uniform lighting 612 12.3 Kolmogorov—Smirnov image comparison 616 12.4 Multinomial statistical model for images 620 12.5 Image entropy 623 12.6 Ensemble of unstructured images 627 12.7 Image alignment and registration 640 12.8 Ensemble of structured images 652 12.9 Modeling spatial correlation 654 12.10 Summary points 660 13 Appendix: Useful Facts and Formulas 663 13.1 Basic facts of asymptotic theory 663 13.2 Some formulas of matrix algebra 670 13.3 Basic facts of optimization theory 674 References 683 Index 713

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Book SynopsisThis introductory guide provides a fresh approach to integrating design and statistics in a hands-on fashion that incorporates the power of SPSS (R) software to solve real-world problems.Trade Review“This is a good book on designing good research studies and using statistical and analytical tools to measure their results accurately.” (Biz India, 22 April 2013) Table of ContentsPreface xvii Acknowledgments xix PART I WHEEL OF SCIENCE: PREMISES OF RESEARCH 1 1 "DUH" SCIENCE VERSUS "HUH" SCIENCE 3 2 THEORIES AND HYPOTHESES 21 3 OBSERVATION AND EMPIRICAL GENERALIZATION 35 4 ETHICS 52 PART II WHEEL OF SCIENCE: PROCEDURES OF RESEARCH 63 5 MEASUREMENT 65 6 USING SPSS IN RESEARCH 83 7 CHI-SQUARE AND CONTINGENCY TABLE ANALYSIS 90 8 LEARNING FROM POPULATIONS: CENSUSES AND SAMPLES 102 9 CORRELATION 127 10 REGRESSION 146 11 CAUSATION 162 PART III WHEEL OF SCIENCE: DESIGNS OF RESEARCH 203 12 SURVEY RESEARCH 205 13 AGGREGATE RESEARCH 234 14 EXPERIMENTS 251 15 STATISTICAL METHODS OF DIFFERENCE: T TEST 270 16 ANALYSIS OF VARIANCE 280 17 FIELD RESEARCH 301 18 CONTENT ANALYSIS 316 PART IV STATISTICS AND DATA MANAGEMENT 327 STATISTICAL PROCEDURES UNIT A: WRITING THE STATISTICAL RESEARCH SUMMARY 329 STATISTICAL PROCEDURES UNIT B: THE NATURE OF INFERENTIAL STATISTICS 333 DATA MANAGEMENT UNIT A: USE AND FUNCTIONS OF SPSS 343 DATA MANAGEMENT UNIT B: USING SPSS TO RECODE FOR T TEST 357 DATA MANAGEMENT UNIT C: DESCRIPTIVE STATISTICS 364 STATISTICAL PROCEDURES UNIT C: Z SCORES 389 Glossary 397 Bibliography 411 Index 416

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Book SynopsisAn easily accessible introduction to over three centuries of innovations in geometry Praise for the First Edition . . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained. CHOICE This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics. Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible,Table of ContentsPreface ix Acknowledgments xiii 1 Informal Topology 1 2 Graphs 13 2.1 Nodes and Arcs 13 2.2 Traversability 16 2.3 Colorings 21 2.4 Planarity 25 2.5 Graph Homeomorphisms 31 3 Surfaces 41 3.1 Polygonal Presentations 42 3.2 Closed Surfaces 50 3.3 Operations on Surfaces 71 3.4 Bordered Surfaces 79 3.5 Riemann Surfaces 94 4 Graphs and Surfaces 103 4.1 Embeddings and Their Regions 103 4.2 Polygonal Embeddings 113 4.3 Embedding a Fixed Graph 118 4.4 Voltage Graphs and Their Coverings 128 Appendix: 141 5 Knots and Links 143 5.1 Preliminaries 144 5.2 Labelings 147 5.3 From Graphs to Links and on to Surfaces 158 5.4 The Jones Polynomial 169 5.5 The Jones Polynomial and Alternating Diagrams 187 5.6 Knots and surfaces 194 6 The Differential Geometry of Surfaces 205 6.1 Surfaces, Normals, and Tangent Planes 205 6.2 The Gaussian Curvature 212 6.3 The First Fundamental Form 219 6.4 Normal Curvatures 229 6.5 The Geodesic Polar Parametrization 236 6.6 Polyhedral Surfaces I 242 6.7 Gauss’s Total Curvature Theorem 247 6.8 Polyhedral Surfaces II 252 7 Riemann Geometries 259 8 Hyperbolic Geometry 275 8.1 Neutral Geometry 275 8.2 The Upper Half Plane 287 8.3 The HalfPlane Theorem of Pythagoras 295 8.4 HalfPlane Isometries 305 9 The Fundamental Group 317 9.1 Definitions and the Punctured Plane 317 9.2 Surfaces 325 9.3 3Manifolds 332 9.4 The Poincar´e Conjecture 357 10 General Topology 361 10.1 Metric and Topological Spaces 361 10.2 Continuity and Homeomorphisms 367 10.3 Connectedness 377 10.4 Compactness 379 11 Polytopes 387 11.1 Introduction to Polytopes 387 11.2 Graphs of Polytopes 401 11.3 Regular Polytopes 405 11.4 Enumerating Faces 415 Appendix A Curves 429 A.1 Parametrization of Curves and Arclength 429 Appendix B A Brief Survey of Groups 441 B.1 The General Background 441 B.2 Abelian Groups 446 B.3 Group Presentations 447 Appendix C Permutations 457 Appendix D Modular Arithmetic 461 Appendix E Solutions and Hints to Selected Exercises 465 References and Resources 497

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Book SynopsisTable of ContentsStatistical Methods for Reliability Data i Preface to the Second Edition iii Preface to First Edition viii Acknowledgments xii 1 Reliability Concepts and an Introduction to Reliability Data 1 1.1 Introduction 1 1.2 Examples of Reliability Data 3 1.3 General Models for Reliability Data 11 1.4 Models for Time to Event Versus Models for Recurrences in a Sequence of Events 13 1.5 Strategy for Data Collection, Modeling, and Analysis 15 2 Models, Censoring, and Likelihood for Failure-Time Data 19 2.1 Models for Continuous Failure-Time Processes 19 2.2 Models for Discrete Data from a Continuous Process 25 2.3 Censoring 27 2.4 Likelihood 28 3 Nonparametric Estimation for Failure-Time Data 37 3.1 Estimation from Complete Data 38 3.2 Estimation from Singly-Censored Interval Data 38 3.3 Basic Ideas of Statistical Inference 40 3.4 Confidence Intervals from Complete or Singly-Censored Data 41 3.5 Estimation from Multiply-Censored Data 43 3.6 Pointwise Confidence Intervals from Multiply-Censored Data 45 3.7 Estimation from Multiply-Censored Data with Exact Failures 47 3.8 Nonparametric Simultaneous Confidence Bands 49 3.9 Arbitrary Censoring 52 4 Some Parametric Distributions Used in Reliability Applications 60 4.1 Introduction 61 4.2 Quantities of Interest in Reliability Applications 61 4.3 Location-Scale and Log-Location-Scale Distributions 62 4.4 Exponential Distribution 63 4.5 Normal Distribution 64 4.6 Lognormal Distribution 65 4.7 Smallest Extreme Value Distribution 67 4.8 Weibull Distribution 68 4.9 Largest Extreme Value Distribution 70 4.10 Frechet Distribution 71 4.11 Logistic Distribution 73 4.12 Loglogistic Distribution 74 4.13 Generalized Gamma Distribution 75 4.14 Distributions with a Threshold Parameter 76 4.15 Other Methods of Deriving Failure-Time Distributions 78 4.16 Parameters and Parameterization 80 4.17 Generating Pseudorandom Observations from a Specified Distribution 80 5 System Reliability Concepts and Methods 87 5.1 Non-Repairable System Reliability Metrics 88 5.2 Series Systems 88 5.3 Parallel Systems 91 5.4 Series-Parallel Systems 93 5.5 Other System Structures 94 5.6 Multistate System Reliability Models 96 6 Probability Plotting 102 6.1 Introduction 103 6.2 Linearizing Location-Scale-Based Distributions 103 6.3 Graphical Goodness of Fit 105 6.4 Probability Plotting Positions 106 6.5 Notes on the Application of Probability Plotting 111 7 Parametric Likelihood Fitting Concepts: Exponential Distribution 119 7.1 Introduction 120 7.2 Parametric Likelihood 122 7.3 Likelihood Confidence Intervals for θ 123 7.4 Wald (Normal-Approximation) Confidence Intervals for θ 125 7.5 Confidence Intervals for Functions of θ 126 7.6 Comparison of Confidence Interval Procedures 127 7.7 Likelihood for Exact Failure Times 128 7.8 Effect of Sample Size on Confidence Interval Width and the Likelihood Shape 130 7.9 Exponential Distribution Inferences with No Failures 131 8 Maximum Likelihood Estimation for Log-Location-Scale Distributions 138 8.1 Likelihood Definition 139 8.2 Likelihood Confidence Regions and Intervals 142 8.3 Wald Confidence Intervals 146 8.4 The ML Estimate May Not Go Through the Points 151 8.5 Estimation with a Given Shape Parameter 152 9 Parametric Bootstrap and Other Simulation-Based Confidence Interval Methods 164 9.1 Introduction 165 9.2 Methods for Generating Bootstrap Samples and Obtaining Bootstrap Estimates 165 9.3 Bootstrap Confidence Interval Methods 171 9.4 Bootstrap Confidence Intervals Based on Pivotal Quantities 176 9.5 Confidence Intervals Based on Generalized Pivotal Quantities 181 10 An Introduction to Bayesian Statistical Methods for Reliability 189 10.1 Bayesian Inference: Overview 190 10.2 Bayesian Inference: an Illustrative Example 194 10.3 More About Prior Information and Specification of a Prior Distribution 202 10.4 Implementing Bayesian Analyses Using MCMC Simulation 205 10.5 Using Prior Information to Estimate the Service-Life Distribution of a Rocket Motor 210 11 Special Parametric Models 219 11.1 Extending ML Methods 219 11.2 Fitting the Generalized Gamma Distribution 220 11.3 Fitting the Birnbaum–Saunders Distribution 223 11.4 The Limited Failure Population Model 225 11.5 Truncated Data and Truncated Distributions 227 11.6 Fitting Distributions that Have a Threshold Parameter 232 12 Comparing Failure-Time Distributions 243 12.1 Background and Motivation 243 12.2 Nonparametric Comparisons 244 12.3 Parametric Comparison of Two Groups by Fitting Separate Distributions 247 12.4 Parametric Comparison of Two Groups by Fitting Separate Distributions With Equal σ values 248 12.5 Parametric Comparison of More than Two Groups 250 13 Planning Life Tests for Estimation 261 13.1 Introduction 261 13.2 Simple Formulas to Determine the Needed Sample Size 263 13.3 Use of Simulation in Test Planning 267 13.4 Approximate Variance of ML Estimators and Computing Variance Factors 274 13.5 Variance Factors for (Log-)Location-Scale Distributions 275 13.6 Some Extensions 278 14 Planning Reliability Demonstration Tests 282 14.1 Introduction to Demonstration Testing 282 14.2 Finding the Required Sample Size n or Test-Length Factor k 284 14.3 Probability of Successful Demonstration 288 15 Prediction of Failure Times and the Number of Future Field Failures 293 15.1 Basic Concepts of Statistical Prediction 294 15.2 Probability Prediction Intervals (_ Known) 295 15.3 Statistical Prediction Intervals (_ Estimated) 296 15.4 Plug-In Prediction and Calibration 297 15.5 Computing and Using Predictive Distributions 301 15.6 Prediction of the Number of Future Failures from a Single Group of Units in the Field 304 15.7 Predicting the Number of Future Failures from Multiple Groups of Units in the Field with Staggered Entry into the Field 307 15.8 Bayesian Prediction Methods 311 15.9 Choosing a Distribution for Making Predictions 313 16 Analysis of Data with More than One Failure Mode 321 16.1 An Introduction to Multiple Failure Modes 321 16.2 Model for Multiple Failure Modes Data 323 16.3 Competing-Risk Estimation 324 16.4 The Effect of Eliminating a Failure Mode 328 16.5 Subdistribution Functions and Prediction for Individual Failure Modes 331 16.6 More About the Non-Identifiability of Dependence Among Failure Modes 332 17 Failure-Time Regression Analysis 340 17.1 Introduction 341 17.2 Simple Linear Regression Models 342 17.3 Standard Errors and Confidence Intervals for Regression Models 345 17.4 Regression Model with Quadratic μ and Nonconstant σ 347 17.5 Checking Model Assumptions 351 17.6 Empirical Regression Models and Sensitivity Analysis 354 17.7 Models with Two or More Explanatory Variables 359 18 Analysis of Accelerated Life Test Data 369 18.1 Introduction to Accelerated Life Tests 369 18.2 Overview of ALT Data Analysis Methods 371 18.3 Temperature-Accelerated Life Tests 372 18.4 Bayesian Analysis of a Temperature-Accelerated Life Test 380 18.5 Voltage-Accelerated Life Test 381 19 More Topics on Accelerated Life Testing 396 19.1 ALTs with Interval-Censored Data 396 19.2 ALTs with Two Accelerating Variables 401 19.3 Multifactor Experiments with a Single Accelerating Variable 405 19.4 Practical Suggestions for Drawing Conclusions from ALT Data 409 19.5 Pitfalls of Accelerated Life Testing 410 19.6 Other Kinds of Accelerated Tests 412 20 Degradation Modeling and Destructive Degradation Data Analysis 421 20.1 Degradation Reliability Data and Degradation Path Models: Introduction and Background422 20.2 Description and Mechanistic Motivation for Degradation Path Models 423 20.3 Models Relating Degradation and Failure 427 20.4 DDT Background, Motivating Examples, and Estimation 427 20.5 Failure-Time Distributions Induced from DDT Models and Failure-Time Inferences 431 20.6 ADDT Model Building 433 20.7 Fitting an Acceleration Model to ADDT Data 435 20.8 ADDT Failure-Time Inferences 437 20.9 ADDT Analysis Using an Informative Prior Distribution 438 20.10 An ADDT with an Asymptotic Model 439 21 Repeated-Measures Degradation Modeling and Analysis 448 21.1 RMDT Models and Data 448 21.2 RMDT Parameter Estimation 451 21.3 The Relationship Between Degradation and Failure-Time for RMDT Models 454 21.4 Estimation of a Failure-Time cdf from RMDT Data 457 21.5 Models for ARMDT Data 458 21.6 ARMDT Estimation 459 21.7 ARMDT with Multiple Accelerating Variables 462 22 Analysis of Repairable System and Other Recurrent Events Data 469 22.1 Introduction 469 22.2 Nonparametric Estimation of the MCF 471 22.3 Comparison of Two Samples of Recurrent Events Data 474 22.4 Recurrent Events Data with Multiple Event Types 475 23 Case Studies and Further Applications 481 23.1 Analysis of Hard Drive Field Data 481 23.2 Reliability in the Presence of Stress-Strength Interference 484 23.3 Predicting Field Failures with a Limited Failure Population 487 23.4 Analysis of Accelerated Life Test Data When There is a Batch Effect 494 Epilogue 499 A Notation and Acronyms 503 B Other Useful Distributions and Probability Distribution Computations 509 B.1 Important Characteristics of Distribution Functions 509 B.2 Distributions and R Computations 511 B.3 Continuous Distributions 511 B.4 Discrete Distributions 519 B.4.1 Binomial Distribution 519 C Some Results from Statistical Theory 522 C.1 The cdfs and pdfs of Functions of Random Variables 522 C.2 Statistical Error Propagation—The Delta Method 527 C.3 Likelihood and Fisher Information Matrices 528 C.4 Regularity Conditions 529 C.5 Convergence in Distribution 530 C.6 Convergence in Probability 531 C.7 Outline of General ML Theory 532 C.8 Inference with Zero or Few Failures 534 C.9 The Bonferroni Inequality 536 D Tables 538 References 549

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Book SynopsisINTRODUCTION TO CULTURAL MATHEMATICS Challenges readers to think creatively about mathematics and ponder its role in their own daily lives Cultural mathematics, or ethnomathematics as it is also known, studies the relationship between mathematics and culturewith the ultimate goal of contributing to an appreciation of the connection between the two. Introduction to Cultural Mathematics: With Case Studies in the Otomies and Incas integrates both theoretical and applied aspects of the topic, promotes discussions on the development of mathematical concepts, and provides a comprehensive reference for teaching and learning about multicultural mathematical practices. This illuminating book provides a nontraditional, evidence-based approach to mathematics that promotes diversity and respect for cultural heritages. Part One covers such major concepts as cultural aspects of mathematics, numeration and number symbols, kinship relations, art and decoration, games, divTable of ContentsPreface ix Introduction xi PART I General Concepts 1 Understanding the Culture in Mathematics 3 2 Numeration S ystems 24 3 Number Gestures and N umber S ymbols 39 4 Kinship and S ocial R elations 57 5 Art and D ecoration 73 6 Divination 103 7 Games 123 8 Calendars 142 PART II Case S tudies 9 Hñähñu Math: T he O tomies 181 10 Tawantinsuyu Math: T he Incas 211 Hints to S elected E xercises 253 Bibliography 273 Index 281

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Book SynopsisConcepts and applications in trigonometry In Analytic Trigonometry, almost every concept is illustrated by an example followed by a matching problem to encourage an active involvement in the learning process, and concept development proceeds from the concrete to the abstract. Extensive chapter review summaries, chapter and cumulative review exercises with answers keyed to the corresponding text sections, effective use of color comments and annotations, and prominent displays of important material to help master the subject.Table of ContentsChapter 1 Right Triangle Ratios 1 Chapter 2 Trigonometric Functions 31 Chapter 3 Graphing Trigonometric Functions 65 Cumulative Review Chapters 1—3 113 Chapter 4 Identities 129 Chapter 5 Inverse Trigonometric Functions; Trigonometric Equations and Inequalities 199 Cumulative Review Chapters 1—5 255 Chapter 6 Additional Topics: Triangles and Vectors 281 Chapter 7 Polar Coordinates; Complex Numbers 327 Cumulative Review Chapters 1—7 361 Appendices 387

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Book SynopsisEnables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world problems in engineering and the physical sciences. With its easy-to-follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus theory and its applications. The first five chapters introduce underlying concepts such as algebra, geometry, coordinate geometry, and trigonometry. Subsequent chapters present a broad range of theories, methods, and applications in differential calculus, including: Concepts of function, continuity, and derivative Properties of expoTrade Review “The book is addressed mainly to students studying non-mathematical subjects. It will be also helpful for those who want to understand why it is important to study Calculus and how to apply it.” (Zentralblatt MATH, 1 December 2012) Table of ContentsForeword xiii Preface xvii Biographies xxv Introduction xxvii Acknowledgments xxix 1 From Arithmetic to Algebra (What must you know to learn Calculus?) 1 1.1 Introduction 1 1.2 The Set of Whole Numbers 1 1.3 The Set of Integers 1 1.4 The Set of Rational Numbers 1 1.5 The Set of Irrational Numbers 2 1.6 The Set of Real Numbers 2 1.7 Even and Odd Numbers 3 1.8 Factors 3 1.9 Prime and Composite Numbers 3 1.10 Coprime Numbers 4 1.11 Highest Common Factor (H.C.F.) 4 1.12 Least Common Multiple (L.C.M.) 4 1.13 The Language of Algebra 5 1.14 Algebra as a Language for Thinking 7 1.15 Induction 9 1.16 An Important Result: The Number of Primes is Infinite 10 1.17 Algebra as the Shorthand of Mathematics 10 1.18 Notations in Algebra 11 1.19 Expressions and Identities in Algebra 12 1.20 Operations Involving Negative Numbers 15 1.21 Division by Zero 16 2 The Concept of a Function (What must you know to learn Calculus?) 19 2.1 Introduction 19 2.2 Equality of Ordered Pairs 20 2.3 Relations and Functions 20 2.4 Definition 21 2.5 Domain, Codomain, Image, and Range of a Function 23 2.6 Distinction Between “f ” and “f(x)” 23 2.7 Dependent and Independent Variables 24 2.8 Functions at a Glance 24 2.9 Modes of Expressing a Function 24 2.10 Types of Functions 25 2.11 Inverse Function f 1 29 2.12 Comparing Sets without Counting their Elements 32 2.13 The Cardinal Number of a Set 32 2.14 Equivalent Sets (Definition) 33 2.15 Finite Set (Definition) 33 2.16 Infinite Set (Definition) 34 2.17 Countable and Uncountable Sets 36 2.18 Cardinality of Countable and Uncountable Sets 36 2.19 Second Definition of an Infinity Set 37 2.20 The Notion of Infinity 37 2.21 An Important Note About the Size of Infinity 38 2.22 Algebra of Infinity (1) 38 3 Discovery of Real Numbers: Through Traditional Algebra (What must you know to learn Calculus?) 41 3.1 Introduction 41 3.2 Prime and Composite Numbers 42 3.3 The Set of Rational Numbers 43 3.4 The Set of Irrational Numbers 43 3.5 The Set of Real Numbers 43 3.6 Definition of a Real Number 44 3.7 Geometrical Picture of Real Numbers 44 3.8 Algebraic Properties of Real Numbers 44 3.9 Inequalities (Order Properties in Real Numbers) 45 3.10 Intervals 46 3.11 Properties of Absolute Values 51 3.12 Neighborhood of a Point 54 3.13 Property of Denseness 55 3.14 Completeness Property of Real Numbers 55 3.15 (Modified) Definition II (l.u.b.) 60 3.16 (Modified) Definition II (g.l.b.) 60 4 From Geometry to Coordinate Geometry (What must you know to learn Calculus?) 63 4.1 Introduction 63 4.2 Coordinate Geometry (or Analytic Geometry) 64 4.3 The Distance Formula 69 4.4 Section Formula 70 4.5 The Angle of Inclination of a Line 71 4.6 Solution(s) of an Equation and its Graph 76 4.7 Equations of a Line 83 4.8 Parallel Lines 89 4.9 Relation Between the Slopes of (Nonvertical) Lines that are Perpendicular to One Another 90 4.10 Angle Between Two Lines 92 4.11 Polar Coordinate System 93 5 Trigonometry and Trigonometric Functions (What must you know to learn Calculus?) 97 5.1 Introduction 97 5.2 (Directed) Angles 98 5.3 Ranges of sin and cos 109 5.4 Useful Concepts and Definitions 111 5.5 Two Important Properties of Trigonometric Functions 114 5.6 Graphs of Trigonometric Functions 115 5.7 Trigonometric Identities and Trigonometric Equations 115 5.8 Revision of Certain Ideas in Trigonometry 120 6 More About Functions (What must you know to learn Calculus?) 129 6.1 Introduction 129 6.2 Function as a Machine 129 6.3 Domain and Range 130 6.4 Dependent and Independent Variables 130 6.5 Two Special Functions 132 6.6 Combining Functions 132 6.7 Raising a Function to a Power 137 6.8 Composition of Functions 137 6.9 Equality of Functions 142 6.10 Important Observations 142 6.11 Even and Odd Functions 143 6.12 Increasing and Decreasing Functions 144 6.13 Elementary and Nonelementary Functions 147 7a The Concept of Limit of a Function (What must you know to learn Calculus?) 149 7a.1 Introduction 149 7a.2 Useful Notations 149 7a.3 The Concept of Limit of a Function: Informal Discussion 151 7a.4 Intuitive Meaning of Limit of a Function 153 7a.5 Testing the Definition [Applications of the «, d Definition of Limit] 163 7a.6 Theorem (B): Substitution Theorem 174 7a.7 Theorem (C): Squeeze Theorem or Sandwich Theorem 175 7a.8 One-Sided Limits (Extension to the Concept of Limit) 175 7b Methods for Computing Limits of Algebraic Functions (What must you know to learn Calculus?) 177 7b.1 Introduction 177 7b.2 Methods for Evaluating Limits of Various Algebraic Functions 178 7b.3 Limit at Infinity 187 7b.4 Infinite Limits 190 7b.5 Asymptotes 192 8 The Concept of Continuity of a Function, and Points of Discontinuity (What must you know to learn Calculus?) 197 8.1 Introduction 197 8.2 Developing the Definition of Continuity “At a Point” 204 8.3 Classification of the Points of Discontinuity: Types of Discontinuities 214 8.4 Checking Continuity of Functions Involving Trigonometric, Exponential, and Logarithmic Functions 215 8.5 From One-Sided Limit to One-Sided Continuity and its Applications 224 8.6 Continuity on an Interval 224 8.7 Properties of Continuous Functions 225 9 The Idea of a Derivative of a Function 235 9.1 Introduction 235 9.2 Definition of the Derivative as a Rate Function 239 9.3 Instantaneous Rate of Change of y [=f(x)] at x=x1 and the Slope of its Graph at x=x1 239 9.4 A Notation for Increment(s) 246 9.5 The Problem of Instantaneous Velocity 246 9.6 Derivative of Simple Algebraic Functions 259 9.7 Derivatives of Trigonometric Functions 263 9.8 Derivatives of Exponential and Logarithmic Functions 264 9.9 Differentiability and Continuity 264 9.10 Physical Meaning of Derivative 270 9.11 Some Interesting Observations 271 9.12 Historical Notes 273 10 Algebra of Derivatives: Rules for Computing Derivatives of Various Combinations of Differentiable Functions 275 10.1 Introduction 275 10.2 Recalling the Operator of Differentiation 277 10.3 The Derivative of a Composite Function 290 10.4 Usefulness of Trigonometric Identities in Computing Derivatives 300 10.5 Derivatives of Inverse Functions 302 11a Basic Trigonometric Limits and Their Applications in Computing Derivatives of Trigonometric Functions 307 11a.1 Introduction 307 11a.2 Basic Trigonometric Limits 308 11a.3 Derivatives of Trigonometric Functions 314 11b Methods of Computing Limits of Trigonometric Functions 325 11b.1 Introduction 325 11b.2 Limits of the Type (I) 328 11b.3 Limits of the Type (II) [ lim f(x), where a&rae;0] 332 11b.4 Limits of Exponential and Logarithmic Functions 335 12 Exponential Form(s) of a Positive Real Number and its Logarithm(s): Pre-Requisite for Understanding Exponential and Logarithmic Functions (What must you know to learn Calculus?) 339 12.1 Introduction 339 12.2 Concept of Logarithmic 339 12.3 The Laws of Exponent 340 12.4 Laws of Exponents (or Laws of Indices) 341 12.5 Two Important Bases: “10” and “e” 343 12.6 Definition: Logarithm 344 12.7 Advantages of Common Logarithms 346 12.8 Change of Base 348 12.9 Why were Logarithms Invented? 351 12.10 Finding a Common Logarithm of a (Positive) Number 351 12.11 Antilogarithm 353 12.12 Method of Calculation in Using Logarithm 355 13a Exponential and Logarithmic Functions and Their Derivatives (What must you know to learn Calculus?) 359 13a.1 Introduction 359 13a.2 Origin of e 360 13a.3 Distinction Between Exponential and Power Functions 362 13a.4 The Value of e 362 13a.5 The Exponential Series 364 13a.6 Properties of e and Those of Related Functions 365 13a.7 Comparison of Properties of Logarithm(s) to the Bases 10 and e 369 13a.8 A Little More About e 371 13a.9 Graphs of Exponential Function(s) 373 13a.10 General Logarithmic Function 375 13a.11 Derivatives of Exponential and Logarithmic Functions 378 13a.12 Exponential Rate of Growth 383 13a.13 Higher Exponential Rates of Growth 383 13a.14 An Important Standard Limit 385 13a.15 Applications of the Function ex: Exponential Growth and Decay 390 13b Methods for Computing Limits of Exponential and Logarithmic Functions 401 13b.1 Introduction 401 13b.2 Review of Logarithms 401 13b.3 Some Basic Limits 403 13b.4 Evaluation of Limits Based on the Standard Limit 410 14 Inverse Trigonometric Functions and Their Derivatives 417 14.1 Introduction 417 14.2 Trigonometric Functions (With Restricted Domains) and Their Inverses 420 14.3 The Inverse Cosine Function 425 14.4 The Inverse Tangent Function 428 14.5 Definition of the Inverse Cotangent Function 431 14.6 Formula for the Derivative of Inverse Secant Function 433 14.7 Formula for the Derivative of Inverse Cosecant Function 436 14.8 Important Sets of Results and their Applications 437 14.9 Application of Trigonometric Identities in Simplification of Functions and Evaluation of Derivatives of Functions Involving Inverse Trigonometric Functions 441 15a Implicit Functions and Their Differentiation 453 15a.1 Introduction 453 15a.2 Closer Look at the Difficulties Involved 455 15a.3 The Method of Logarithmic Differentiation 463 15a.4 Procedure of Logarithmic Differentiation 464 15b Parametric Functions and Their Differentiation 473 15b.1 Introduction 473 15b.2 The Derivative of a Function Represented Parametrically 477 15b.3 Line of Approach for Computing the Speed of a Moving Particle 480 15b.4 Meaning of dy/dx with Reference to the Cartesian Form y = f(x) and Parametric Forms x = f(t), y = g(t) of the Function 481 15b.5 Derivative of One Function with Respect to the Other 483 16 Differentials “dy” and “dx”: Meanings and Applications 487 16.1 Introduction 487 16.2 Applying Differentials to Approximate Calculations 492 16.3 Differentials of Basic Elementary Functions 494 16.4 Two Interpretations of the Notation dy/dx 498 16.5 Integrals in Differential Notation 499 16.6 To Compute (Approximate) Small Changes and Small Errors Caused in Various Situations 503 17 Derivatives and Differentials of Higher Order 511 17.1 Introduction 511 17.2 Derivatives of Higher Orders: Implicit Functions 516 17.3 Derivatives of Higher Orders: Parametric Functions 516 17.4 Derivatives of Higher Orders: Product of Two Functions (Leibniz Formula) 517 17.5 Differentials of Higher Orders 521 17.6 Rate of Change of a Function and Related Rates 523 18 Applications of Derivatives in Studying Motion in a Straight Line 535 18.1 Introduction 535 18.2 Motion in a Straight Line 535 18.3 Angular Velocity 540 18.4 Applications of Differentiation in Geometry 540 18.5 Slope of a Curve in Polar Coordinates 548 19a Increasing and Decreasing Functions and the Sign of the First Derivative 551 19a.1 Introduction 551 19a.2 The First Derivative Test for Rise and Fall 556 19a.3 Intervals of Increase and Decrease (Intervals of Monotonicity) 557 19a.4 Horizontal Tangents with a Local Maximum/Minimum 565 19a.5 Concavity, Points of Inflection, and the Sign of the Second Derivative 567 19b Maximum and Minimum Values of a Function 575 19b.1 Introduction 575 19b.2 Relative Extreme Values of a Function 576 19b.3 Theorem A 580 19b.4 Theorem B: Sufficient Conditions for the Existence of a Relative Extrema—In Terms of the First Derivative 584 19b.5 Sufficient Condition for Relative Extremum (In Terms of the Second Derivative) 588 19b.6 Maximum and Minimum of a Function on the Whole Interval (Absolute Maximum and Absolute Minimum Values) 593 19b.7 Applications of Maxima and Minima Techniques in Solving Certain Problems Involving the Determination of the Greatest and the Least Values 597 20 Rolle’s Theorem and the Mean Value Theorem (MVT) 605 20.1 Introduction 605 20.2 Rolle’s Theorem (A Theorem on the Roots of a Derivative) 608 20.3 Introduction to the Mean Value Theorem 613 20.4 Some Applications of the Mean Value Theorem 622 21 The Generalized Mean Value Theorem (Cauchy’s MVT), L’ Hospital’s Rule, and their Applications 625 21.1 Introduction 625 21.2 Generalized Mean Value Theorem (Cauchy’s MVT) 625 21.3 Indeterminate Forms and L’Hospital’s Rule 627 21.4 L’Hospital’s Rule (First Form) 630 21.5 L’Hospital’s Theorem (For Evaluating Limits(s) of the Indeterminate Form 0/0.) 632 21.6 Evaluating Indeterminate Form of the Type ∞/∞ 638 21.7 Most General Statement of L’Hospital’s Theorem 644 21.8 Meaning of Indeterminate Forms 644 21.9 Finding Limits Involving Various Indeterminate Forms (by Expressing them to the Form 0/0 or ∞/∞) 646 22 Extending the Mean Value Theorem to Taylor’s Formula: Taylor Polynomials for Certain Functions 653 22.1 Introduction 653 22.2 The Mean Value Theorem For Second Derivatives: The First Extended MVT 654 22.3 Taylor’s Theorem 658 22.4 Polynomial Approximations and Taylor’s Formula 658 22.5 From Maclaurin Series To Taylor Series 667 22.6 Taylor’s Formula for Polynomials 669 22.7 Taylor’s Formula for Arbitrary Functions 672 23 Hyperbolic Functions and Their Properties 677 23.1 Introduction 677 23.2 Relation Between Exponential and Trigonometric Functions 680 23.3 Similarities and Differences in the Behavior of Hyperbolic and Circular Functions 682 23.4 Derivatives of Hyperbolic Functions 685 23.5 Curves of Hyperbolic Functions 686 23.6 The Indefinite Integral Formulas for Hyperbolic Functions 689 23.7 Inverse Hyperbolic Functions 689 23.8 Justification for Calling sinh and cosh as Hyperbolic Functions Just as sine and cosine are Called Trigonometric Circular Functions 699 Appendix A (Related To Chapter-2) Elementary Set Theory 703 Appendix B (Related To Chapter-4) 711 Appendix C (Related To Chapter-20) 735 Index 739

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Book SynopsisAn accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences I ntegration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The authors provide a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. With logical organization coupled with clear, simple explanations, the authors reinforce new concepts to progressively build skills and knowledge, and numerous real-world examples as well as intriguing applications help readers to better understand the connections between the theory of calculus and practical problem solving. The first six chapters address the prerequisites needed to understand the principlesTrade Review“Introduction to Integral Calculus is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner.” (Zentralblatt MATH, 2012) “Long on examples but often short of exercises, this work might best be used as a reference source. Summing Up: Recommended. Lower-and upper-division undergraduates.” (Choice, 1 September 2012) Table of ContentsFOREWORD ix PREFACE xiii BIOGRAPHIES xxi INTRODUCTION xxiii ACKNOWLEDGMENT xxv 1 Antiderivative(s) [or Indefinite Integral(s)] 1 1.1 Introduction 1 1.2 Useful Symbols, Terms, and Phrases Frequently Needed 6 1.3 Table(s) of Derivatives and their corresponding Integrals 7 1.4 Integration of Certain Combinations of Functions 10 1.5 Comparison Between the Operations of Differentiation and Integration 15 2 Integration Using Trigonometric Identities 17 2.1 Introduction 17 2.2 Some Important Integrals Involving sin x and cos x 34 2.3 Integrals of the Form ? (d/( a sin + b cos x)), where a, b ϵ r 37 3a Integration by Substitution: Change of Variable of Integration 43 3b Further Integration by Substitution: Additional Standard Integrals 67 4a Integration by Parts 97 4b Further Integration by Parts: Where the Given Integral Reappears on Right-Hand Side 117 5 Preparation for the Definite Integral: The Concept of Area 139 5.1 Introduction 139 5.2 Preparation for the Definite Integral 140 5.3 The Definite Integral as an Area 143 5.4 Definition of Area in Terms of the Definite Integral 151 5.5 Riemann Sums and the Analytical Definition of the Definite Integral 151 6a The Fundamental Theorems of Calculus 165 6b The Integral Function Ð x 1 1 t dt, (x > 0) Identified as ln x or loge x 183 7a Methods for Evaluating Definite Integrals 197 7b Some Important Properties of Definite Integrals 213 8a Applying the Definite Integral to Compute the Area of a Plane Figure 249 8b To Find Length(s) of Arc(s) of Curve(s), the Volume(s) of Solid(s) of Revolution, and the Area(s) of Surface(s) of Solid(s) of Revolution 295 9a Differential Equations: Related Concepts and Terminology 321 9a.4 Definition: Integral Curve 332 9b Methods of Solving Ordinary Differential Equations of the First Order and of the First Degree 361 INDEX 399

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Book SynopsisA one-stop guide for the theories, applications, and statistical methodologies essential to operational risk Providing a complete overview of operational risk modeling and relevant insurance analytics, Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk offers a systematic approach that covers the wide range of topics in this area. Written by a team of leading experts in the field, the handbook presents detailed coverage of the theories, applications, and models inherent in any discussion of the fundamentals of operational risk, with a primary focus on Basel II/III regulation, modeling dependence, estimation of risk models, and modeling the data elements. Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk begins with coverage on the four data elements used in operational risk framework as well as processing risk taxonomy. The book then goes further Table of ContentsPreface xvii Acronyms xix List of Distributions xxi 1 OpRisk in Perspective 1 1.1 Brief History 1 1.2 Risk-Based Capital Ratios for Banks 5 1.3 The Basic Indicator and Standardized Approaches for OpRisk 9 1.4 The Advanced Measurement Approach 10 1.4.1 Internal Measurement Approach 11 1.4.2 Score Card Approach 11 1.4.3 Loss Distribution Approach 12 1.4.4 Requirements for AMA 13 1.5 General Remarks and Book Structure 16 2 OpRisk Data and Governance 17 2.1 Introduction 17 2.2 OpRisk Taxonomy 17 2.2.1 Execution, Delivery, and Process Management 19 2.2.2 Clients, Products, and Business Practices 21 2.2.3 Business Disruption and System Failures 22 2.2.4 External Frauds 23 2.2.5 Internal Fraud 23 2.2.6 Employment Practices and Workplace Safety 24 2.2.7 Damage to Physical Assets 25 2.3 The Elements of the OpRisk Framework 25 2.3.1 Internal Loss Data 26 2.3.2 Setting a Collection Threshold and Possible Impacts 26 2.3.3 Completeness of Database (Under-reporting Events) 27 2.3.4 Recoveries and Near Misses 27 2.3.5 Time Period for Resolution of Operational Losses 28 2.3.6 Adding Costs to Losses 28 2.3.7 Provisioning Treatment of Expected Operational Losses 28 2.4 Business Environment and Internal Control Environment Factors (BEICFs) 29 2.4.1 Risk Control Self-Assessment (RCSA) 29 2.4.2 Key Risk Indicators 31 2.5 External Databases 33 2.6 Scenario Analysis 34 2.7 OpRisk Profile in Different Financial Sectors 37 2.7.1 Trading and Sales 37 2.7.2 Corporate Finance 38 2.7.3 Retail Banking 38 2.7.4 Insurance 39 2.7.5 Asset Management 40 2.7.6 Retail Brokerage 42 2.8 Risk Organization and Governance 43 2.8.1 Organization of Risk Departments 44 2.8.2 Structuring a Firm Wide Policy: Example of an OpRisk Policy 46 2.8.3 Governance 47 3 Using OpRisk Data for Business Analysis 48 3.1 Cost Reduction Programs in Financial Firms 49 3.2 Using OpRisk Data to Perform Business Analysis 53 3.2.1 The Risk of Losing Key Talents: OpRisk in Human Resources 53 3.2.2 OpRisk in Systems Development and Transaction Processing 54 3.3 Conclusions 58 4 Stress-Testing OpRisk Capital and the Comprehensive Capital Analysis and Review (CCAR) 59 4.1 The Need for Stressing OpRisk Capital Even Beyond 99.9% 59 4.2 Comprehensive Capital Review and Analysis (CCAR) 60 4.3 OpRisk and Stress Tests 68 4.4 OpRisk in CCAR in Practice 70 4.5 Reverse Stress Test 75 4.6 Stressing OpRisk Multivariate Models—Understanding the Relationship Among Internal Control Factors and Their Impact on Operational Losses 76 5 Basic Probability Concepts in Loss Distribution Approach 79 5.1 Loss Distribution Approach 79 5.2 Quantiles and Moments 85 5.3 Frequency Distributions 88 5.4 Severity Distributions 89 5.4.1 Simple Parametric Distributions 90 5.4.2 Truncated Distributions 92 5.4.3 Mixture and Spliced Distributions 93 5.5 Convolutions and Characteristic Functions 94 5.6 Extreme Value Theory 97 5.6.1 EVT—Block Maxima 98 5.6.2 EVT—Random Number of Losses 99 5.6.3 EVT—Threshold Exceedances 100 6 Risk Measures and Capital Allocation 102 6.1 Development of Capital Accords Base I, II and III 103 6.2 Measures of Risk 106 6.2.1 Coherent and Convex Risk Measures 107 6.2.2 Comonotonic Additive Risk Measures 109 6.2.3 Value-at-Risk 109 6.2.4 Expected Shortfall 114 6.2.5 Spectral Risk Measure 120 6.2.6 Higher-Order Risk Measures 122 6.2.7 Distortion Risk Measures 125 6.2.8 Elicitable Risk Measures 126 6.2.9 Risk Measure Accounting for Parameter Uncertainty 130 6.3 Capital Allocation 133 6.3.1 Coherent Capital Allocation 134 6.3.2 Euler Allocation 136 6.3.3 Standard Deviation 138 6.3.4 Expected Shortfall 139 6.3.5 Value-at-Risk 140 6.3.6 Allocation by Marginal Contributions 142 6.3.7 Numerical Example 143 7 Estimation of Frequency and Severity Models 146 7.1 Frequentist Estimation 146 7.1.1 Parameteric Maximum Likelihood Method 149 7.1.2 Maximum Likelihood Method for Truncated and Censored Data 151 7.1.3 Expectation Maximization and Parameter Estimation 152 7.1.4 Bootstrap for Estimation of Parameter Accuracy 156 7.1.5 Indirect Inference–Based Likelihood Estimation 157 7.2 Bayesian Inference Approach 159 7.2.1 Conjugate Prior Distributions 161 7.2.2 Gaussian Approximation for Posterior (Laplace Type) 161 7.2.3 Posterior Point Estimators 162 7.2.4 Restricted Parameters 163 7.2.5 Noninformative Prior 163 7.3 Mean Square Error of Prediction 164 7.4 Standard Markov Chain Monte Carlo (MCMC) Methods 166 7.4.1 Motivation for Markov Chain Methods 167 7.4.2 Metropolis–Hastings Algorithm 177 7.4.3 Gibbs Sampler 178 7.4.4 Random Walk Metropolis–Hastings within Gibbs 179 7.5 Standard MCMC Guidelines for Implementation 180 7.5.1 Tuning, Burn-in, and Sampling Stages 180 7.5.2 Numerical Error 185 7.5.3 MCMC Extensions: Reducing Sample Autocorrelation 187 7.6 Advanced MCMC Methods 188 7.6.1 Auxiliary Variable MCMC Methods: Slice Sampling 189 7.6.2 Generic Univariate Auxiliary Variable Gibbs Sampler: Slice Sampler 189 7.6.3 Adaptive MCMC 192 7.6.4 Riemann–Manifold Hamiltonian Monte Carlo Sampler (Automated Local Adaption) 196 7.7 Sequential Monte Carlo (SMC) Samplers and Importance Sampling 201 7.7.1 Motivating OpRisk Applications for SMC Samplers 202 7.7.2 SMC Sampler Methodology and Components 210 7.7.3 Incorporating Partial Rejection Control into SMC Samplers 216 7.7.4 Finite Sample (Nonasymptotic) Accuracy for Particle Integration 219 7.8 Approximate Bayesian Computation (ABC) Methods 220 7.9 OpRisk Estimation and Modeling for Truncated Data 223 7.9.1 Constant Threshold - Poisson Process 224 7.9.2 Negative Binomial and Binomial Frequencies 227 7.9.3 Ignoring Data Truncation 228 7.9.4 Threshold Varying in Time 232 7.9.5 Unknown and Stochastic Truncation Level 236 8 Model Selection and Goodness-of-Fit Testing for Frequency and Severity Models 238 8.1 Qualitative Model Diagnostic Tools 238 8.2 Tail Diagnostics 240 8.3 Information Criterion for Model Selection 242 8.3.1 Akaike Information Criterion for LDA Model Selection 242 8.3.2 Deviance Information Criterion 245 8.4 Goodness-of-Fit Testing for Model Choice (How to Account for Heavy Tails!) 246 8.4.1 Convergence Results of the Empirical Process for GOF Testing 247 8.4.2 Overview of Generic GOF Tests—Omnibus Distributional Tests 256 8.4.3 Kolmogorov–Smirnov Goodness-of-Fit Test and Weighted Variants: Testing in the Presence of Heavy Tails 260 8.4.4 Cramer-von-Mises Goodness-of-Fit Tests and Weighted Variants: Testing in the Presence of Heavy Tails 271 8.5 Bayesian Model Selection 283 8.5.1 Reciprocal Importance Sampling Estimator 284 8.5.2 Chib Estimator for Model Evidence 285 8.6 SMC Sampler Estimators of Model Evidence 286 8.7 Multiple Risk Dependence Structure Model Selection: Copula Choice 287 8.7.1 Approaches to Goodness-of-Fit Testing for Dependence Structures 293 8.7.2 Double Parameteric Bootstrap for Copula GOF 297 9 Flexible Parametric Severity Models: Basics 300 9.1 Motivation for Flexible Parametric Severity Loss Models 300 9.2 Context of Flexible Heavy-Tailed Loss Models in OpRisk and Insurance LDA Models 301 9.3 Empirical Analysis Justifying Heavy-Tailed Loss Models in OpRisk 303 9.4 Quantile Function Heavy-Tailed Severity Models 305 9.4.1 g-and-h Severity Model Family in OpRisk 311 9.4.2 Tail Properties of the g-and-h, g, h, and h–h Severity in OpRisk 321 9.4.3 Parameter Estimation for the g-and-h Severity in OpRisk 324 9.4.4 Bayesian Models for the g-and-h Severity in OpRisk 328 9.5 Generalized Beta Family of Heavy-Tailed Severity Models 333 9.5.1 Generalized Beta Family Type II Severity Models in OpRisk 333 9.5.2 Sub families of the Generalized Beta Family Type II Severity Models 336 9.5.3 Mixture Representations of the Generalized Beta Family Type II Severity Models 337 9.5.4 Estimation in the Generalized Beta Family Type II Severity Models 339 9.6 Generalized Hyperbolic Families of Heavy-Tailed Severity Models 340 9.6.1 Tail Properties and Infinite Divisibility of the Generalized Hyperbolic Severity Models 342 9.6.2 Subfamilies of the Generalized Hyperbolic Severity Models 344 9.6.3 Normal Inverse Gaussian Family of Heavy-Tailed Severity Models 346 9.7 Halphen Family of Flexible Severity Models: GIG and Hyperbolic 350 9.7.1 Halphen Type A: Generalized Inverse Gaussian Family of Flexible Severity Models 355 9.7.2 Halphen Type B and IB Families of Flexible Severity Models 361 10 Dependence Concepts 365 10.1 Introduction to Concepts in Dependence for OpRisk and Insurance 365 10.2 Dependence Modeling Within and Between LDA Model Structures 366 10.2.1 Where Can One Introduce Dependence Between LDA Model Structures? 368 10.2.2 Understanding Basic Impacts of Dependence Modeling Between LDA Components in Multiple Risks 369 10.3 General Notions of Dependence 372 10.4 Dependence Measures 387 10.4.1 Linear Correlation 390 10.4.2 Rank Correlation Measures 393 10.5 Tail Dependence Parameters, Functions, and Tail Order Functions 398 10.5.1 Tail Dependence Coefficients 398 10.5.2 Tail Dependence Functions and Orders 407 10.5.3 A Link Between Orthant Extreme Dependence and Spectral Measures: Tail Dependence 410 11 Dependence Models 414 11.1 Introduction to Parametric Dependence Modeling Through a Copula 414 11.2 Copula Model Families for OpRisk 422 11.2.1 Gaussian Copula 428 11.2.2 t-Copula 430 11.2.3 Archimedean Copulas 435 11.2.4 Archimedean Copula Generators and the Laplace Transform of a Non-Negative Random Variable 439 11.2.5 Archimedean Copula Generators, l1-Norm Symmetric Distributions and the Williamson Transform 441 11.2.6 Hierarchical and Nested Archimedean Copulae 452 11.2.7 Mixtures of Archimedean Copulae 454 11.2.8 Multivariate Archimedean Copula Tail Dependence 456 11.3 Copula Parameter Estimation in Two Stages: Inference for the Margins 457 11.3.1 MPLE: Copula Parameter Estimation 458 11.3.2 Inference Functions for Margins (IFM): Copula Parameter Estimation 459 12 Examples of LDA Dependence Models 462 12.1 Multiple Risk LDA Compound Poisson Processes and Lévy Copula 462 12.2 Multiple Risk LDA: Dependence Between Frequencies via Copula 468 12.3 Multiple Risk LDA: Dependence Between the k-th Event Times/Losses 468 12.3.1 Common Shock Processes 469 12.3.2 Max-Stable and Self-Chaining Copula Models 470 12.4 Multiple Risk LDA: Dependence Between Aggregated Losses via Copula 474 12.5 Multiple Risk LDA: Structural Model with Common Factors 477 12.6 Multiple Risk LDA: Stochastic and Dependent Risk Profiles 478 12.7 Multiple Risk LDA: Dependence and Combining Different Data Sources 482 12.7.1 Bayesian Inference Using MCMC 484 12.7.2 Numerical Example 485 12.7.3 Predictive Distribution 487 12.8 A Note on Negative Diversification and Dependence Modeling 489 13 Loss Aggregation 492 13.1 Analytic Solution 492 13.1.1 Analytic Solution via Convolutions 493 13.1.2 Analytic Solution via Characteristic Functions 494 13.1.3 Moments of Compound Distribution 496 13.1.4 Value-at-Risk and Expected Shortfall 499 13.2 Monte Carlo Method 499 13.2.1 Quantile Estimate 500 13.2.2 Expected Shortfall Estimate 502 13.3 Panjer Recursion 503 13.4 Panjer Extensions 509 13.5 Fast Fourier Transform 511 13.6 Closed-Form Approximation 514 13.7 Capital Charge Under Parameter Uncertainty 519 13.7.1 Predictive Distributions 520 13.7.2 Calculation of Predictive Distributions 521 13.8 Special Advanced Topics on Loss Aggregation 523 13.8.1 Discretisation Errors and Extrapolation Methods 524 13.8.2 Classes of Discrete Distributions: Discrete Infinite Divisibility and Discrete Heavy Tails 527 13.8.3 Recursions for Convolutions (Partial Sums) with Discretised Severity Distributions (Fixed n) 535 13.8.4 Alternatives to Panjer Recursions: Recursions for Compound Distributions with Discretised Severity Distributions 543 13.8.5 Higher Order Recursions for Discretised Severity Distributions in Compound LDA Models 545 13.8.6 Recursions for Discretised Severity Distributions in Compound Mixed Poisson LDA Models 547 13.8.7 Continuous Versions of the Panjer Recursion 550 14 Scenario Analysis 556 14.1 Introduction 556 14.2 Examples of Expert Judgments 559 14.3 Pure Bayesian Approach (Estimating Prior) 561 14.4 Expert Distribution and Scenario Elicitation: Learning from Bayesian Methods 563 14.5 Building Models for Elicited Opinions: Hierarchical Dirichlet Models 566 14.6 Worst-Case Scenario Framework 568 14.7 Stress Test Scenario Analysis 571 14.8 Bow-Tie Diagram 574 14.9 Bayesian Networks 576 14.9.1 Definition and Examples 577 14.9.2 Constructing and Simulating a Bayesian Net 580 14.9.3 Combining Expert Opinion and Data in a Bayesian Net 581 14.9.4 Bayesian Net and Operational Risk 582 14.10 Discussion 584 15 Combining Different Data Sources 585 15.1 Minimum Variance Principle 586 15.2 Bayesian Method to Combine Two Data Sources 588 15.2.1 Estimating Prior: Pure Bayesian Approach 590 15.2.2 Estimating Prior: Empirical Bayesian Approach 592 15.2.3 Poisson Frequency 593 15.2.4 The LogNormal Severity 597 15.2.5 Pareto Severity 601 15.3 Estimation of the Prior Using Data 606 15.3.1 The Maximum Likelihood Estimator 606 15.3.2 Poisson Frequencies 607 15.4 Combining Expert Opinions with External and Internal Data 609 15.4.1 Conjugate Prior Extension 610 15.4.2 Modeling Frequency: Poisson Model 611 15.4.3 LogNormal Model for Severities 618 15.4.4 Pareto Model 620 15.5 Combining Data Sources Using Credibility Theory 625 15.5.1 Bühlmann–Straub Model 626 15.5.2 Modeling Frequency 628 15.5.3 Modeling Severity 631 15.5.4 Numerical Example 633 15.5.5 Remarks and Interpretation 634 15.6 Nonparametric Bayesian Approach via Dirichlet Process 635 15.7 Combining Using Dempster–Shafer Structures and p-Boxes 638 15.7.1 Dempster–Shafer Structures and p-Boxes 639 15.7.2 Dempster’s Rule 641 15.7.3 Intersection Method 643 15.7.4 Envelope Method 644 15.7.5 Bounds for the Empirical Data Distribution 645 15.8 General Remarks 647 16 Multifactor Modeling and Regression for Loss Processes 649 16.1 Generalized Linear Model Regressions and the Exponential Family 649 16.1.1 Basic Components of a Generalized Linear Model Regression in the Exponential Family 650 16.1.2 Basis Function Regression 654 16.2 Maximum Likelihood Estimation for Generalized Linear Models 655 16.2.1 Iterated Weighted Least Squares Maximum Likelihood for Generalised Linear Models 655 16.2.2 Model Selection via the Deviance in a GLM Regression 657 16.3 Bayesian Generalized Linear Model Regressions and Regularization Priors 659 16.3.1 Bayesian Model Selection for Regularlized GLM Regression 665 16.4 Bayesian Estimation and Model Selection via SMC Samplers 666 16.4.1 Proposed SMC Sampler Solution 667 16.5 Illustrations of SMC Samplers Model Estimation and Selection for Bayesian GLM Regressions 668 16.5.1 Normal Regression Model 668 16.5.2 Poisson Regression Model 669 16.6 Introduction to Quantile Regression Methods for OpRisk 672 16.6.1 Nonparametric Quantile Regression Models 674 16.6.2 Parametric Quantile Regression Models 675 16.7 Factor Modeling for Industry Data 681 16.8 Multifactor Modeling under EVT Approach 683 17 Insurance and Risk Transfer: Products and Modeling 685 17.1 Motivation for Insurance and Risk Transfer in OpRisk 685 17.2 Fundamentals of Insurance Product Structures for OpRisk 688 17.3 Single Peril Policy Products for OpRisk 692 17.4 Generic Insurance Product Structures for OpRisk 694 17.4.1 Generic Deterministic Policy Structures 694 17.4.2 Generic Stochastic Policy Structures: Accounting for Coverage Uncertainty 700 17.5 Closed-Form LDA Models with Insurance Mitigations 705 17.5.1 Insurance Mitigation Under the Poisson-Inverse-Gaussian Closed-Form LDA Models 705 17.5.2 Insurance Mitigation and Poisson-α-Stable Closed-Form LDA Models 712 17.5.3 Large Claim Number Loss Processes: Generic Closed-Form LDA Models with Insurance Mitigation 719 17.5.4 Generic Closed-Form Approximations for Insured LDA Models 734 18 Insurance and Risk Transfer: Pricing Insurance-Linked Derivatives, Reinsurance, and CAT Bonds for OpRisk 750 18.1 Insurance-Linked Securities and CAT Bonds for OpRisk 751 18.1.1 Background on Insurance-Linked Derivatives and CAT Bonds for Extreme Risk Transfer 755 18.1.2 Triggers for CAT Bonds and Their Impact on Risk Transfer 760 18.1.3 Recent Trends in CAT Bonds 763 18.1.4 Management Strategies for Utilization of Insurance-Linked Derivatives and CAT Bonds in OpRisk 763 18.2 Basics of Valuation of ILS and CAT Bonds for OpRisk 765 18.2.1 Probabilistic Pricing Frameworks: Complete and Incomplete Markets, Real-World Pricing, Benchmark Approach, and Actuarial Valuation 771 18.2.2 Risk Assessment for Reinsurance: ILS and CAT Bonds 794 18.3 Applications of Pricing ILS and CAT Bonds 796 18.3.1 Probabilistic Framework for CAT Bond Market 796 18.3.2 Framework 1: Assuming Complete Market and Arbitrage-Free Pricing 798 18.3.3 Framework 2: Assuming Incomplete Arbitrage-Free Pricing 809 18.4 Sidecars, Multiple Peril Baskets, and Umbrellas for OpRisk 815 18.4.1 Umbrella Insurance 816 18.4.2 OpRisk Loss Processes Comprised of Multiple Perils 817 18.5 Optimal Insurance Purchase Strategies for OpRisk Insurance via Multiple Optimal Stopping Times 823 18.5.1 Examples of Basic Insurance Policies 826 18.5.2 Objective Functions for Rational and Boundedly Rational Insurees 828 18.5.3 Closed-Form Multiple Optimal Stopping Rules for Multiple Insurance Purchase Decisions 830 18.5.4 Aski-Polynomial Orthogonal Series Approximations 835 A Miscellaneous Definitions and List of Distributions 842 A.1 Indicator Function 842 A.2 Gamma Function 842 A.3 Discrete Distributions 842 A.3.1 Poisson Distribution 842 A.3.2 Binomial Distribution 843 A.3.3 Negative Binomial Distribution 843 A.3.4 Doubly Stochastic Poisson Process (Cox Process) 844 A.4 Continuous Distributions 844 A.4.1 Uniform Distribution 844 A.4.2 Normal (Gaussian) Distribution 844 A.4.3 Inverse Gaussian Distribution 845 A.4.4 LogNormal Distribution 845 A.4.5 Student’s t Distribution 846 A.4.6 Gamma Distribution 846 A.4.7 Weibull Distribution 846 A.4.8 Inverse Chi-Squared Distribution 847 A.4.9 Pareto Distribution (One-Parameter) 847 A.4.10 Pareto Distribution (Two-Parameter) 847 A.4.11 Generalized Pareto Distribution 848 A.4.12 Beta Distribution 848 A.4.13 Generalized Inverse Gaussian Distribution 849 A.4.14 d-variate Normal Distribution 849 A.4.15 d-variate t-Distribution 850 Bibliography 851 Index 892

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Book SynopsisINTRODUCTION TO PROBABILITY Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite. This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to teTable of ContentsPreface xi Acknowledgments xv 1 Two-Dimensional Discrete Random Variables and Distributions 1 1.1 Introduction 2 1.2 Joint Probability Function 2 1.3 Marginal Distributions 15 1.4 Expectation of a Function 24 1.5 Conditional Distributions and Expectations 32 1.6 Basic Concepts and Formulas 41 1.7 Computational Exercises 42 1.8 Self-assessment Exercises 46 1.8.1 True–False Questions 46 1.8.2 Multiple Choice Questions 47 1.9 Review Problems 50 1.10 Applications 54 1.10.1 Mixture Distributions and Reinsurance 54 Key Terms 57 2 Two-Dimensional Continuous Random Variables and Distributions 59 2.1 Introduction 60 2.2 Joint Density Function 60 2.3 Marginal Distributions 73 2.4 Expectation of a Function 79 2.5 Conditional Distributions and Expectations 82 2.6 Geometric Probability 91 2.7 Basic Concepts and Formulas 98 2.8 Computational Exercises 100 2.9 Self-assessment Exercises 107 2.9.1 True–False Questions 107 2.9.2 Multiple Choice Questions 109 2.10 Review Problems 111 2.11 Applications 114 2.11.1 Modeling Proportions 114 Key Terms 119 3 Independence and Multivariate Distributions 121 3.1 Introduction 122 3.2 Independence 122 3.3 Properties of Independent Random Variables 137 3.4 Multivariate Joint Distributions 142 3.5 Independence of More Than Two Variables 156 3.6 Distribution of an Ordered Sample 165 3.7 Basic Concepts and Formulas 176 3.8 Computational Exercises 178 3.9 Self-assessment Exercises 185 3.9.1 True–False Questions 185 3.9.2 Multiple Choice Questions 186 3.10 Review Problems 189 3.11 Applications 194 3.11.1 Acceptance Sampling 194 Key Terms 200 4 Transformations of Variables 201 4.1 Introduction 202 4.2 Joint Distribution for Functions of Variables 202 4.3 Distributions of sum, difference, product and quotient 210 4.4 𝜒2, t and F Distributions 223 4.5 Basic Concepts and Formulas 236 4.6 Computational Exercises 237 4.7 Self-assessment Exercises 242 4.7.1 True–False Questions 242 4.7.2 Multiple Choice Questions 243 4.8 Review Problems 246 4.9 Applications 250 4.9.1 Random Number Generators Coverage – Planning Under Random Event Occurrences 250 Key Terms 255 5 Covariance and Correlation 257 5.1 Introduction 258 5.2 Covariance 258 5.3 Correlation Coefficient 272 5.4 Conditional Expectation and Variance 281 5.5 Regression Curves 293 5.6 Basic Concepts and Formulas 307 5.7 Computational Exercises 308 5.8 Self-assessment Exercises 314 5.8.1 True–False Questions 314 5.8.2 Multiple Choice Questions 316 5.9 Review Problems 320 5.10 Applications 326 5.10.1 Portfolio Optimization Theory 326 Key Terms 330 6 Important Multivariate Distributions 331 6.1 Introduction 332 6.2 Multinomial Distribution 332 6.3 Multivariate Hypergeometric Distribution 344 6.4 Bivariate Normal Distribution 358 6.5 Basic Concepts and Formulas 371 6.6 Computational Exercises 373 6.7 Self-Assessment Exercises 378 6.7.1 True–False Questions 378 6.7.2 Multiple Choice Questions 380 6.8 Review Problems 383 6.9 Applications 387 6.9.1 The Effect of Dependence on the Distribution of the Sum 387 Key Terms 390 7 Generating Functions 391 7.1 Introduction 392 7.2 Moment Generating Function 392 7.3 Moment Generating Functions of Some Important Distributions 401 7.3.1 Binomial Distribution 401 7.3.2 Negative Binomial Distribution 402 7.3.3 Poisson Distribution 403 7.3.4 Uniform Distribution 403 7.3.5 Normal Distribution 403 7.3.6 Gamma Distribution 404 7.4 Moment Generating Functions for Sum of Variables 407 7.5 Probability Generating Function 416 7.6 Characteristic Function 428 7.7 Generating Functions for Multivariate Case 433 7.8 Basic Concepts and Formulas 441 7.9 Computational Exercises 443 7.10 Self-assessment Exercises 446 7.10.1 True–False Questions 446 7.10.2 Multiple Choice Questions 448 7.11 Review Problems 452 7.12 Applications 460 7.12.1 Random Walks 460 Key Terms 465 8 Limit Theorems 467 8.1 Introduction 468 8.2 Laws of Large Numbers 468 8.3 Central Limit Theorem 476 8.4 Basic Concepts and Formulas 492 8.5 Computational Exercises 493 8.6 Self-assessment Exercises 497 8.6.1 True–False Questions 497 8.6.2 Multiple Choice Questions 498 8.7 Review Problems 501 8.8 Applications 504 8.8.1 Use of the CLT for Capacity Planning 504 Key Terms 507 Appendix A Tail Probability Under Standard Normal Distribution 509 Appendix B Critical Values Under Chi-Square Distribution 511 Appendix C Student’s t-Distribution 515 Appendix D F-Distribution: 5% (Lightface Type) and 1% (Boldface Type) Points for the F-Distribution 517 Appendix E Generating Functions 521 Bibliography 525 Index 527

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Book SynopsisAn essential guide to the concepts of probability theory that puts the focus on models and applications Introduction to Probability offers an authoritative text that presents the main ideas and concepts, as well as the theoretical background, models, and applications of probability. The authorsnoted experts in the fieldinclude a review of problems where probabilistic models naturally arise, and discuss the methodology to tackle these problems.A wide-range of topics are covered that include the concepts of probability and conditional probability, univariate discrete distributions, univariate continuous distributions, along with a detailed presentation of the most important probability distributions used in practice, with their main properties and applications. Designed as a useful guide, the text contains theory of probability, de finitions, charts, examples with solutions, illustrations, self-assessment exercises, computational exercises,Table of ContentsPreface xi 1 The Concept of Probability 1 1.1 Chance Experiments – Sample Spaces 2 1.2 Operations Between Events 11 1.3 Probability as Relative Frequency 27 1.4 Axiomatic Definition of Probability 38 1.5 Properties of Probability 45 1.6 The Continuity Property of Probability 54 1.7 Basic Concepts and Formulas 60 1.8 Computational Exercises 61 1.9 Self-assessment Exercises 63 1.9.1 True–False Questions 63 1.9.2 Multiple Choice Questions 64 1.10 Review Problems 67 1.11 Applications 71 1.11.1 System Reliability 71 Key Terms 77 2 Finite Sample Spaces – Combinatorial Methods 79 2.1 Finite Sample Spaces with Events of Equal Probability 80 2.2 Main Principles of Counting 89 2.3 Permutations 96 2.4 Combinations 105 2.5 The Binomial Theorem 123 2.6 Basic Concepts and Formulas 132 2.7 Computational Exercises 133 2.8 Self-Assessment Exercises 139 2.8.1 True–False Questions 139 2.8.2 Multiple Choice Questions 140 2.9 Review Problems 143 2.10 Applications 150 2.10.1 Estimation of Population Size: Capture–Recapture Method 150 Key Terms 152 3 Conditional Probability – Independent Events 153 3.1 Conditional Probability 154 3.2 The Multiplicative Law of Probability 166 3.3 The Law of Total Probability 174 3.4 Bayes’ Formula 183 3.5 Independent Events 189 3.6 Basic Concepts and Formulas 206 3.7 Computational Exercises 207 3.8 Self-assessment Exercises 210 3.8.1 True–False Questions 210 3.8.2 Multiple Choice Questions 211 3.9 Review Problems 214 3.10 Applications 220 3.10.1 Diagnostic and Screening Tests 220 Key Terms 223 4 Discrete Random Variables and Distributions 225 4.1 Random Variables 226 4.2 Distribution Functions 232 4.3 Discrete Random Variables 247 4.4 Expectation of a Discrete Random Variable 261 4.5 Variance of a Discrete Random Variable 281 4.6 Some Results for Expectation and Variance 293 4.7 Basic Concepts and Formulas 302 4.8 Computational Exercises 303 4.9 Self-Assessment Exercises 309 4.9.1 True–False Questions 309 4.9.2 Multiple Choice Questions 310 4.10 Review Problems 313 4.11 Applications 317 4.11.1 Decision Making Under Uncertainty 317 Key Terms 320 5 Some Important Discrete Distributions 321 5.1 Bernoulli Trials and Binomial Distribution 322 5.2 Geometric and Negative Binomial Distributions 337 5.3 The Hypergeometric Distribution 358 5.4 The Poisson Distribution 371 5.5 The Poisson Process 385 5.6 Basic Concepts and Formulas 394 5.7 Computational Exercises 395 5.8 Self-Assessment Exercises 399 5.8.1 True–False Questions 399 5.8.2 Multiple Choice Questions 401 5.9 Review Problems 403 5.10 Applications 411 5.10.1 Overbooking 411 Key Terms 414 6 Continuous Random Variables 415 6.1 Density Functions 416 6.2 Distribution for a Function of a Random Variable 431 6.3 Expectation and Variance 442 6.4 Additional Useful Results for the Expectation 451 6.5 Mixed Distributions 459 6.6 Basic Concepts and Formulas 468 6.7 Computational Exercises 469 6.8 Self-Assessment Exercises 474 6.8.1 True–False Questions 474 6.8.2 Multiple Choice Questions 476 6.9 Review Problems 479 6.10 Applications 486 6.10.1 Profit Maximization 486 Key Terms 490 7 Some Important Continuous Distributions 491 7.1 The Uniform Distribution 492 7.2 The Normal Distribution 501 7.3 The Exponential Distribution 531 7.4 Other Continuous Distributions 542 7.4.1 The Gamma Distribution 543 7.4.2 The Beta Distribution 548 7.5 Basic Concepts and Formulas 555 7.6 Computational Exercises 557 7.7 Self-Assessment Exercises 561 7.7.1 True–False Questions 561 7.7.2 Multiple Choice Questions 562 7.8 Review Problems 565 7.9 Applications 573 7.9.1 Transforming Data: The Lognormal Distribution 573 Key Terms 578 Appendix A Sums and Products 579 Appendix B Distribution Function of the Standard Normal Distribution 593 Appendix C Simulation 595 Appendix D Discrete and Continuous Distributions 599 Bibliography 603 Index 605

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Book SynopsisTheories and practices to assess critical information in a complex adaptive system Organized for readers to follow along easily, The Fitness of Information: Quantitative Assessments of Critical Evidence provides a structured outline of the key challenges in assessing crucial information in a complex adaptive system. Illustrating a variety of computational and explanatory challenges, the book demonstrates principles and practical implications of exploring and assessing the fitness of information in an extensible framework of adaptive landscapes. The book's first three chapters introduce fundamental principles and practical examples in connection to the nature of aesthetics, mental models, and the subjectivity of evidence. In particular, the underlying question is how these issues can be addressed quantitatively, not only computationally but also explanatorily. The next chapter illustrates how one can reduce the level of complexity in undTable of ContentsPreface ix 1. Attention and Aesthetics 1 1.1. Attention, 1 1.1.1. What Is It That Attracts Our Attention? 2 1.1.2. Negative Information Attracts More Attention, 2 1.1.3. The Myths of Prehistoric Civilization, 5 1.2. Gestalt Principles, 6 1.2.1. Closure and Completeness, 6 1.2.2. Continuity and Smoothness, 8 1.2.3. Missing the Obvious, 9 1.3. Aesthetics, 11 1.3.1. The Golden Ratio, 11 1.3.2. Simplicity, 12 1.3.3. Regularity, 14 1.3.4. Beauty, 15 1.4. The Index of the Interesting, 17 1.4.1. Belief Updates, 18 1.4.2. Proteus Phenomenon, 18 1.4.3. Surprises, 19 1.4.4. Connecting the Dots, 23 1.5. Summary, 24 Bibliography, 25 2. Mental Models 27 2.1. Mental Models, 27 2.1.1. Pitfalls, 29 2.1.2. Communicating with Aliens, 31 2.1.3. Boundary Objects, 32 2.1.4. Wrong Models, 33 2.1.5. Competing Hypotheses, 41 2.2. Creativity, 47 2.2.1. Divergent Thinking, 49 2.2.2. Blind Variation and Selective Retention, 51 2.2.3. Binding Free-Floating Elements of Knowledge, 52 2.2.4. Janusian Thinking, 54 2.2.5. TRIZ, 57 2.2.6. Reasoning by Analogy, 59 2.2.7. Structural Holes, Brokerage, and Boundary Spanning, 59 2.3. Foresights, 61 2.3.1. Information Foraging, 61 2.3.2. Identifying Priorities, 63 2.3.3. Hindsight on Foresight, 65 2.4. Summary, 66 Bibliography, 67 3. Subjectivity of Evidence 71 3.1. The Value of Information, 71 3.2. Causes Célèbre, 74 3.2.1. The Sacco and Vanzetti Case, 74 3.2.2. The O.J. Simpson Case, 79 3.2.3. Ward Edwards’s Defense of Bayesian Thinking, 86 3.3. The Da Vinci Code, 87 3.3.1. Positive and Negative Reviews, 88 3.3.2. Decision Trees, 90 3.4. Supreme Court Opinions, 93 3.5. Apple versus Samsung, 100 3.6. Summary, 101 Bibliography, 101 4. Visualizing the Growth of Knowledge 103 4.1. Progressive Knowledge Domain Visualization, 105 4.1.1. The Structure of a Knowledge Domain, 106 4.1.2. Research Fronts and Intellectual Bases, 108 4.1.3. Strategies of Scientific Discoveries, 111 4.2. CiteSpace, 116 4.2.1. Design Rationale, 117 4.2.2. Basic Procedure, 119 4.2.3. Advanced Cocitation Analysis, 122 4.2.4. Toward a Tightly Connected Community, 128 4.3. Examples, 132 4.3.1. Terrorism Research, 132 4.3.2. Mass Extinctions, 136 4.3.3. Developing Expertise in Analytics and Topic Areas, 140 4.3.4. U.S. Supreme Court Landmark Cases, 142 4.4. Summary, 143 Bibliography, 143 5. Fitness Landscapes 147 5.1. Cognitive Maps, 147 5.1.1. The Legibility of Cognitive Maps, 147 5.1.2. Spatial Knowledge, 148 5.2. Fitness Landscapes, 149 5.2.1. Wright’s Adaptive Landscapes, 150 5.2.2. Fisher’s Geometric Model of Adaptation, 153 5.2.3. The Holey Landscape, 155 5.2.4. Kauffman’s NK Model, 156 5.2.5. Local Search and Adaptation, 157 5.2.6. Criticisms, 158 5.3. Applications of Fitness Landscapes, 159 5.3.1. Structure–Activity Relationship Landscapes, 159 5.3.2. Landscapes Beyond Evolutionary Biology, 161 5.4. Summary, 169 Bibliography, 170 6. Structural Variation 173 6.1. Complex Adaptive Systems, 173 6.1.1. Early Signs of Critical Transitions, 173 6.1.2. Early Signs of Great Ideas, 175 6.1.3. The Structural Variation Theory, 176 6.2. Radical Patents, 181 6.2.1. Patentability, 181 6.2.2. NK Models of Recombinant Patents, 182 6.2.3. Recombinant Search for High-Impact Radical Ideas, 184 6.2.4. Radical Inventions, 188 6.2.5. Genetically Evolved Patentable Ideas, 189 6.3. Bridging the Gaps, 192 6.3.1. The Principle of Boundary Spanning, 192 6.3.2. Baseline Networks, 193 6.3.3. Structural Variation Metrics, 195 6.3.4. Statistical Models, 198 6.4. Applications, 199 6.4.1. Small-World Networks, 200 6.4.2. Complex Network Analysis (1996–2004), 201 6.4.3. National Cancer Institute’s Patent Portfolio, 203 6.4.4. A Follow-Up Study, 211 6.5. Summary, 212 Bibliography, 212 7. Gap Analytics 217 7.1. Portfolio Analysis and Risk Assessment, 218 7.1.1. Portfolios of Grant Proposals, 219 7.2. Interactive Overlays, 225 7.2.1. Single-Map Overlays, 225 7.2.2. Dual-Map Overlays, 226 7.3. Examples of Dual-Map Overlays, 231 7.3.1. Portfolios of a Single Source, 231 7.3.2. Portfolios of Organizations, 234 7.3.3. Portfolios of Subject Matters, 239 7.3.4. Patterns in Trajectories, 243 7.4. Summary, 246 7.5. Conclusion, 247 Bibliography, 250 Index 253

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Book SynopsisExplore the essential steps for data collection, reporting, and analysis in business research Understanding Business Research offers a comprehensive introduction to the entire process of designing, conducting, interpreting, and reporting findings in the business environment.Table of ContentsPreface xiii Part I: Overview of the Research Process 1 1 Research and Business 3 Introduction 4 Why is Understanding Research Methods so Important? 4 The Role of Science in Business and Everyday Life 4 The Scientific Method 5 Brief History of the Science of Behavior in the Workplace 6 Bacon’s Legacy 10 Other Important Historical Figures 10 Assumptions of Science 12 Requirements for Scientific Research 13 Chapter Summary 18 Chapter Glossary for Review 20 References 21 2 Ethics and Research 23 Introduction 23 What is Ethics? 24 Approaches to Ethical Analysis 26 Making Ethical Decisions 29 Ethical Business Research 30 Components of an Ethical Research Plan 32 Research in Action: Ethical Dilemmas 37 Chapter Glossary for Review 40 References 40 3 The Foundations of Research 41 Introduction 41 The Hypothesis in Research 42 Types of Hypotheses 46 Measurement 52 Reliability of Measurement 57 Validity of Measurement 59 Populations and Samples 61 Research in Action: Credit or Cash? 65 Chapter Summary 68 Chapter Glossary for Review 69 References 71 4 An Overview of Empirical Methods 73 Introduction 74 Internal, Statistical, and External Validity 74 Survey of Empirical Methods 83 Intact Groups Designs and Quasi-Experimental Studies 87 Surveys 90 Correlational Studies 90 Interviews and Case Studies 92 Meta-Analysis 93 Computers and Statistics 94 Research in Action: Price Matters 95 Chapter Summary 99 Chapter Glossary for Review 101 References 103 Part II: Nuts and Bolts of Research 105 5 Writing the Research Report 107 Introduction 107 What Do Readers Appreciate in Good Writing? 109 Elements of Style 109 Special Grammatical Issues 113 Academic Integrity 117 Parts of the Research Report 122 Chapter Summary 135 References 136 6 Reviewing the Literature and Forming Hypotheses 137 Introduction 138 Bibliographic Research 138 The Internet as a Source 141 Developing a Search Strategy 143 Searching the Literature: The Library 144 Research in Action: Does Listening to Mozart Make You Smarter? 148 Statistical Inference and Testing Hypotheses 150 Chapter Summary 154 Chapter Glossary for Review 155 References 156 7 Sampling: The First Steps in Research 157 Introduction 158 The Nature of Samples 159 Probability Sampling 160 Sampling Methods 162 Nonprobability Sampling 165 Central Limit Theorem 167 Applications of the Central Limit Theorem 170 Sources of Bias and Error: A Reprise 176 Research in Action: Sampling Matters 178 Chapter Summary 180 Chapter Glossary for Review 181 References 182 8 Creating and Using Assessments, Surveys, and Objective Measures 183 Introduction 184 Purpose of Measurement 184 Caveat Assessor 184 Creating a Measurement Scale and Developing a Data-Collection Strategy 186 Interviews, Questionnaires, and Attitude Surveys 187 Question Response Formats 190 Writing Good Survey Items 194 Determining the Sample Size for a Survey 199 Naturalistic Observation 201 Research in Action: Analysis of Assaults 207 Chapter Summary 212 Chapter Glossary for Review 212 References 215 9 A Model for Research Design 215 Introduction 216 A Model for Research Design 216 What is the Independent Variable? 221 What is the Dependent Variable? 223 Are There Confounding Variables? 224 What are the Research Hypotheses? 227 Mathematical Hypotheses 228 Evaluating Hypotheses 229 Evaluating Hypotheses: Practical Matters 232 Research in Action: Sex Differences and Shopping Behavior 236 Research in Action: Changing Attitudes by Writing Essays 236 Chapter Summary 237 Chapter Glossary for Review 239 References 240 Part III: Common Research Designs 243 10 Correlational Research 245 Introduction 246 Conceptual Review of Correlation 246 Pearson’s r 248 Interpreting the Correlation Coefficient 248 Factors that Corrupt a Correlation Coefficient 250 Sample Size and the Correlation Coefficient 253 Applications of the Correlation Coefficient 255 Regression Analysis 259 Introduction to Mediation and Moderation 261 Regression to the Mean 262 Research in Action: Education and Income 264 Chapter Summary 268 Chapter Glossary for Review 269 References 270 11 Between-Subjects Designs 271 Introduction 271 Student’s t-Ratio for Independent Groups 272 Review of Hypothesis Testing 274 Testing Statistical Hypotheses 276 Common Errors in the Interpretation of p 282 The Power of a Test 284 Estimating the Sample Size 289 Statistics Behind The Research 291 Chapter Summary 295 Chapter Glossary for Review 296 References 296 12 Single-Variable Between-Subjects Research 297 Introduction 298 Independent Variable 298 Cause and Effect 301 Gaining Control Over the Variables 301 The General Linear Model 303 Components of Variance 306 The F-Ratio 307 H0 and H1 310 F-Ratio Sampling Distribution 310 Summarizing and Interpreting ANOVA Results 312 Effect Size and Power 313 Multiple Comparisons of the Means 315 Research in Action 318 Chapter Summary 320 Chapter Glossary for Review 321 References 322 13 Between-Subjects Factorial Designs 325 Introduction 326 The Logic of the Two-Variable Design 326 Advantages of the Two-Variable Design 327 Factorial Designs: Variables, Levels, and Cells 331 Examples of Factorial Designs 332 Main Effects and Interaction 334 Designing a Factorial Study 342 Identifying Samples and Estimating Sample Size 344 Interpreting the Interaction: Advanced Considerations 346 Chapter Summary 348 Chapter Glossary for Review 348 References 349 14 Correlated-Groups Designs 351 Introduction 351 Logic of the Correlated-Groups Research Design 352 Repeated-Measures Design 353 Longitudinal Designs 362 Matched-Groups Design 365 Mixed-Model Design 367 Research in Action 368 Chapter Summary 370 Chapter Glossary for Review 370 References 371 Part IV: Special Research Designs 373 15 Research with Categorical Data 375 Introduction 375 Goodness-of-Fit Test 377 χ2 Test of Independence 381 χ2 Test of Homogeneity 384 Further Analysis of the χ2 385 McNemar Test 388 Research in Action: Gambling and Productivity 391 Chapter Summary 393 Chapter Glossary for Review 394 References 394 16 Qualitative and Mixed-Methods Research 397 Introduction 398 Qualitative Versus Quantitative Research 398 Theory and Perspectives Guiding Qualitative Research 399 Mixing Methods: Quantitative and Qualitative Combined 400 Qualitative and Mixed-Methods Data Collection and Analysis 402 Benefits and Challenges of Mixed-Methods Research 408 Sources of Published Qualitative and Mixed-Methods Research 411 Research in Action: Gender- and Job-Based Differences in Work Stress 412 Chapter Summary 414 Chapter Glossary for Review 415 References 415 Appendix A: Statistics Behind the Research, or, ‘‘What Was I Supposed to Remember from My Statistics Class Anyway?’’ 417 Appendix B: Statistical Tables 435 Index 485

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Book SynopsisPraise for the Third Edition . . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . .Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book''s unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The pTrade Review “This could also be an excellent adjunct to more theoretically oriented textbooks used in more intensive courses.” (Computing Reviews, 5 November 2012) Table of ContentsPREFACE ix ACKNOWLEDGMENTS xvii NOTATION USED IN THE TEXT xix A SKETCH OF THE HISTORY OF ALGEBRA TO 1929 xxiii 0 Preliminaries 1 0.1 Proofs / 1 0.2 Sets / 5 0.3 Mappings / 9 0.4 Equivalences / 17 1 Integers and Permutations 23 1.1 Induction / 24 1.2 Divisors and Prime Factorization / 32 1.3 Integers Modulo n / 42 1.4 Permutations / 53 1.5 An Application to Cryptography / 67 2 Groups 69 2.1 Binary Operations / 70 2.2 Groups / 76 2.3 Subgroups / 86 2.4 Cyclic Groups and the Order of an Element / 90 2.5 Homomorphisms and Isomorphisms / 99 2.6 Cosets and Lagrange’s Theorem / 108 2.7 Groups of Motions and Symmetries / 117 2.8 Normal Subgroups / 122 2.9 Factor Groups / 131 2.10 The Isomorphism Theorem / 137 2.11 An Application to Binary Linear Codes / 143 3 Rings 159 3.1 Examples and Basic Properties / 160 3.2 Integral Domains and Fields / 171 3.3 Ideals and Factor Rings / 180 3.4 Homomorphisms / 189 3.5 Ordered Integral Domains / 199 4 Polynomials 202 4.1 Polynomials / 203 4.2 Factorization of Polynomials Over a Field / 214 4.3 Factor Rings of Polynomials Over a Field / 227 4.4 Partial Fractions / 236 4.5 Symmetric Polynomials / 239 4.6 Formal Construction of Polynomials / 248 5 Factorization in Integral Domains 251 5.1 Irreducibles and Unique Factorization / 252 5.2 Principal Ideal Domains / 264 6 Fields 274 6.1 Vector Spaces / 275 6.2 Algebraic Extensions / 283 6.3 Splitting Fields / 291 6.4 Finite Fields / 298 6.5 Geometric Constructions / 304 6.6 The Fundamental Theorem of Algebra / 308 6.7 An Application to Cyclic and BCH Codes / 310 7 Modules over Principal Ideal Domains 324 7.1 Modules / 324 7.2 Modules Over a PID / 335 8 p-Groups and the Sylow Theorems 349 8.1 Products and Factors / 350 8.2 Cauchy’s Theorem / 357 8.3 Group Actions / 364 8.4 The Sylow Theorems / 371 8.5 Semidirect Products / 379 8.6 An Application to Combinatorics / 382 9 Series of Subgroups 388 9.1 The Jordan–H¨older Theorem / 389 9.2 Solvable Groups / 395 9.3 Nilpotent Groups / 401 10 Galois Theory 412 10.1 Galois Groups and Separability / 413 10.2 The Main Theorem of Galois Theory / 422 10.3 Insolvability of Polynomials / 434 10.4 Cyclotomic Polynomials and Wedderburn’s Theorem / 442 11 Finiteness Conditions for Rings and Modules 447 11.1 Wedderburn’s Theorem / 448 11.2 The Wedderburn–Artin Theorem / 457 Appendices 471 Appendix A Complex Numbers / 471 Appendix B Matrix Algebra / 478 Appendix C Zorn’s Lemma / 486 Appendix D Proof of the Recursion Theorem / 490 BIBLIOGRAPHY 492 SELECTED ANSWERS 495 INDEX 523

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Book SynopsisOffers an introduction to behavioral and social science research methods in the health sciences. This book provides complete coverage of the process behind these research methods, including information-gathering, decision formation, and results presentation.Table of ContentsPreface ix Part One Overview of the Research Process 1 Behavioral and Social Research in the Health Sciences 3 2 Ethics and Research 25 3 The Foundations of Research 45 4 An Overview of Empirical Methods 79 Part Two Nuts and Bolts of Research 5 Writing the Research Report 113 6 Reviewing the Literature 139 7 Sampling 161 8 Assessments, Surveys, and Objective Measurement 191 9 A Model for Research Design 225 Part Three Common Research Designs 10 Correlational Research 255 11 Between-Subjects Designs 285 12 Single-Variable Between-Subjects Research 315 13 Between-Subjects Factorial Designs 345 14 Correlated-Groups Designs 367 Part Four Special Research Designs 15 Single-Participant Experiments, Longitudinal Studies, and Quasi-Experimental Designs 393 16 Research with Categorical Data 415 17 Qualitative and Mixed-Methods Research 439 Appendix A Reviewing the Statistics behind the Research 461 Appendix B Statistical Tables 479 Index 521

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Book SynopsisAn Integrated Approach to Product Development Reliability Engineering presents an integrated approach to the design, engineering, and management of reliability activities throughout the life cycle of a product, including concept, research and development, design, manufacturing, assembly, sales, and service.Table of ContentsPreface xv 1 Reliability Engineering in the Twenty-First Century 1 1.1 What Is Quality? 1 1.2 What Is Reliability? 2 1.2.1 The Ability to Perform as Intended 4 1.2.2 For a Specified Time 4 1.2.3 Life-Cycle Conditions 5 1.2.4 Reliability as a Relative Measure 5 1.3 Quality, Customer Satisfaction, and System Effectiveness 6 1.4 Performance, Quality, and Reliability 7 1.5 Reliability and the System Life Cycle 8 1.6 Consequences of Failure 12 1.6.1 Financial Loss 12 1.6.2 Breach of Public Trust 13 1.6.3 Legal Liability 15 1.6.4 Intangible Losses 15 1.7 Suppliers and Customers 16 1.8 Summary 16 Problems 17 2 Reliability Concepts 19 2.1 Basic Reliability Concepts 19 2.1.1 Concept of Probability Density Function 23 2.2 Hazard Rate 26 2.2.1 Motivation and Development of Hazard Rate 27 2.2.2 Some Properties of the Hazard Function 28 2.2.3 Conditional Reliability 31 2.3 Percentiles Product Life 33 2.4 Moments of Time to Failure 35 2.4.1 Moments about Origin and about the Mean 35 2.4.2 Expected Life or Mean Time to Failure 36 2.4.3 Variance or the Second Moment about the Mean 36 2.4.4 Coefficient of Skewness 37 2.4.5 Coefficient of Kurtosis 37 2.5 Summary 39 Problems 40 3 Probability and Life Distributions for Reliability Analysis 45 3.1 Discrete Distributions 45 3.1.1 Binomial Distribution 46 3.1.2 Poisson Distribution 50 3.1.3 Other Discrete Distributions 50 3.2 Continuous Distributions 51 3.2.1 Weibull Distribution 55 3.2.2 Exponential Distribution 61 3.2.3 Estimation of Reliability for Exponential Distribution 64 3.2.4 The Normal (Gaussian) Distribution 67 3.2.5 The Lognormal Distribution 73 3.2.6 Gamma Distribution75 3.3 Probability Plots 77 3.4 Summary 83 Problems 84 4 Design for Six Sigma 89 4.1 What Is Six Sigma? 89 4.2 Why Six Sigma? 90 4.3 How Is Six Sigma Implemented? 91 4.3.1 Steps in the Six Sigma Process 92 4.3.2 Summary of the Six Sigma Steps 97 4.4 Optimization Problems in the Six Sigma Process 98 4.4.1 System Transfer Function 99 4.4.2 Variance Transmission Equation 100 4.4.3 Economic Optimization and Quality Improvement 101 4.4.4 Tolerance Design Problem 102 4.5 Design for Six Sigma 103 4.5.1 Identify (I) 105 4.5.2 Characterize (C) 106 4.5.3 Optimize (O) 106 4.5.4 Verify (V) 106 4.6 Summary 108 Problems 108 5 Product Development 111 5.1 Product Requirements and Constraints 112 5.2 Product Life Cycle Conditions 113 5.3 Reliability Capability 114 5.4 Parts and Materials Selection 114 5.5 Human Factors and Reliability 115 5.6 Deductive versus Inductive Methods 117 5.7 Failure Modes, Effects, and Criticality Analysis 117 5.8 Fault Tree Analysis 119 5.8.1 Role of FTA in Decision-Making 121 5.8.2 Steps of Fault Tree Analysis 122 5.8.3 Basic Paradigms for the Construction of Fault Trees 122 5.8.4 Definition of the Top Event 122 5.8.5 Faults versus Failures 122 5.8.6 Minimal Cut Sets 127 5.9 Physics of Failure 128 5.9.1 Stress Margins 128 5.9.2 Model Analysis of Failure Mechanisms 129 5.9.3 Derating 129 5.9.4 Protective Architectures 130 5.9.5 Redundancy 131 5.9.6 Prognostics 131 5.10 Design Review 131 5.11 Qualification 132 5.12 Manufacture and Assembly 134 5.12.1 Manufacturability 134 5.12.2 Process Verification Testing 136 5.13 Analysis, Product Failure, and Root Causes 137 5.14 Summary 138 Problems 138 6 Product Requirements and Constraints 141 6.1 Defining Requirements 141 6.2 Responsibilities of the Supply Chain 142 6.2.1 Multiple-Customer Products 142 6.2.2 Single-Customer Products 143 6.2.3 Custom Products 144 6.3 The Requirements Document 144 6.4 Specifications 144 6.5 Requirements Tracking 146 6.6 Summary 147 Problems 147 7 Life-Cycle Conditions 149 7.1 Defining the Life-Cycle Profile 149 7.2 Life-Cycle Events 150 7.2.1 Manufacturing and Assembly 151 7.2.2 Testing and Screening 151 7.2.3 Storage 151 7.2.4 Transportation 151 7.2.5 Installation 151 7.2.6 Operation 152 7.2.7 Maintenance 152 7.3 Loads and Their Effects 152 7.3.1 Temperature 152 7.3.2 Humidity 155 7.3.3 Vibration and Shock 156 7.3.4 Solar Radiation 156 7.3.5 Electromagnetic Radiation 157 7.3.6 Pressure 157 7.3.7 Chemicals 158 7.3.8 Sand and Dust 159 7.3.9 Voltage 159 7.3.10 Current 159 7.3.11 Human Factors 160 7.4 Considerations and Recommendations for LCP Development 160 7.4.1 Extreme Specifications-Based Design (Global and Local Environments) 160 7.4.2 Standards-Based Profiles 161 7.4.3 Combined Load Conditions 161 7.4.4 Change in Magnitude and Rate of Change of Magnitude 165 7.5 Methods for Estimating Life-Cycle Loads 165 7.5.1 Market Studies and Standards Based Profiles as Sources of Data 165 7.5.2 In Situ Monitoring of Load Conditions 166 7.5.3 Field Trial Records, Service Records, and Failure Records 166 7.5.4 Data on Load Histories of Similar Parts, Assemblies, or Products 166 7.6 Summary 166 Problems 167 8 Reliability Capability 169 8.1 Capability Maturity Models 169 8.2 Key Reliability Practices 170 8.2.1 Reliability Requirements and Planning 170 8.2.2 Training and Development 171 8.2.3 Reliability Analysis 172 8.2.4 Reliability Testing 172 8.2.5 Supply-Chain Management 173 8.2.6 Failure Data Tracking and Analysis 173 8.2.7 Verification and Validation 174 8.2.8 Reliability Improvement 174 8.3 Summary 175 Problems 175 9 Parts Selection and Management 177 9.1 Part Assessment Process 177 9.1.1 Performance Assessment 178 9.1.2 Quality Assessment 179 9.1.3 Process Capability Index 179 9.1.4 Average Outgoing Quality 182 9.1.5 Reliability Assessment 182 9.1.6 Assembly Assessment 185 9.2 Parts Management 185 9.2.1 Supply Chain Management 185 9.2.2 Part Change Management 186 9.2.3 Industry Change Control Policies 187 9.3 Risk Management 188 9.4 Summary 190 Problems 191 10 Failure Modes, Mechanisms, and Effects Analysis 193 10.1 Development of FMMEA 193 10.2 Failure Modes, Mechanisms, and Effects Analysis 195 10.2.1 System Definition, Elements, and Functions 195 10.2.2 Potential Failure Modes 196 10.2.3 Potential Failure Causes 197 10.2.4 Potential Failure Mechanisms 197 10.2.5 Failure Models 197 10.2.6 Life-Cycle Profile 198 10.2.7 Failure Mechanism Prioritization 198 10.2.8 Documentation 200 10.3 Case Study 201 10.4 Summary 205 Problems 206 11 Probabilistic Design for Reliability and the Factor of Safety 207 11.1 Design for Reliability 207 11.2 Design of a Tension Element 208 11.3 Reliability Models for Probabilistic Design 209 11.4 Example of Probabilistic Design and Design for a Reliability Target 211 11.5 Relationship between Reliability, Factor of Safety, and Variability 212 11.6 Functions of Random Variables 215 11.7 Steps for Probabilistic Design 219 11.8 Summary 219 Problems 220 12 Derating and Uprating 223 12.1 Part Ratings 223 12.1.1 Absolute Maximum Ratings 224 12.1.2 Recommended Operating Conditions 224 12.1.3 Factors Used to Determine Ratings 225 12.2 Derating 225 12.2.1 How Is Derating Practiced? 225 12.2.2 Limitations of the Derating Methodology 231 12.2.3 How to Determine These Limits 238 12.3 Uprating 239 12.3.1 Parts Selection and Management Process 241 12.3.2 Assessment for Uprateability 241 12.3.3 Methods of Uprating 242 12.3.4 Continued Assurance 245 12.4 Summary 245 Problems 246 13 Reliability Estimation Techniques 247 13.1 Tests during the Product Life Cycle 247 13.1.1 Concept Design and Prototype 247 13.1.2 Performance Validation to Design Specification 248 13.1.3 Design Maturity Validation 248 13.1.4 Design and Manufacturing Process Validation 248 13.1.5 Preproduction Low Volume Manufacturing 248 13.1.6 High Volume Production 249 13.1.7 Feedback from Field Data 249 13.2 Reliability Estimation 249 13.3 Product Qualification and Testing 250 13.3.1 Input to PoF Qualification Methodology 250 13.3.2 Accelerated Stress Test Planning and Development 255 13.3.3 Specimen Characterization 257 13.3.4 Accelerated Life Tests 259 13.3.5 Virtual Testing 260 13.3.6 Virtual Qualification 261 13.3.7 Output 262 13.4 Case Study: System-in-Package Drop Test Qualification 263 13.4.1 Step 1: Accelerated Test Planning and Development 263 13.4.2 Step 2: Specimen Characterization 265 13.4.3 Step 3: Accelerated Life Testing 266 13.4.4 Step 4: Virtual Testing 270 13.4.5 Global FEA 271 13.4.6 Strain Distributions Due to Modal Contributions 272 13.4.7 Acceleration Curves 273 13.4.8 Local FEA 273 13.4.9 Step 5: Virtual Qualification 274 13.4.10 PoF Acceleration Curves 275 13.4.11 Summary of the Methodology for Qualification 276 13.5 Basic Statistical Concepts 276 13.5.1 Confidence Interval 277 13.5.2 Interpretation of the Confidence Level 277 13.5.3 Relationship between Confidence Interval and Sample Size 279 13.6 Confidence Interval for Normal Distribution 279 13.6.1 Unknown Mean with a Known Variance for Normal Distribution 279 13.6.2 Unknown Mean with an Unknown Variance for Normal Distribution 280 13.6.3 Differences in Two Population Means with Variances Known 281 13.7 Confidence Intervals for Proportions 282 13.8 Reliability Estimation and Confidence Limits for Success–Failure Testing 283 13.8.1 Success Testing 286 13.9 Reliability Estimation and Confidence Limits for Exponential Distribution 287 13.10 Summary 292 Problems 292 14 Process Control and Process Capability 295 14.1 Process Control System 295 14.1.1 Control Charts: Recognizing Sources of Variation 297 14.1.2 Sources of Variation 297 14.1.3 Use of Control Charts for Problem Identification 297 14.2 Control Charts 299 14.2.1 Control Charts for Variables 306 14.2.2 X-Bar and R Charts 306 14.2.3 Moving Range Chart Example 308 14.2.4 X-Bar and S Charts 311 14.2.5 Control Charts for Attributes 312 14.2.6 p Chart and np Chart 312 14.2.7 np Chart Example 313 14.2.8 c Chart and u Chart 314 14.2.9 c Chart Example 315 14.3 Benefits of Control Charts 316 14.4 Average Outgoing Quality 317 14.4.1 Process Capability Studies 318 14.5 Advanced Control Charts 323 14.5.1 Cumulative Sum Control Charts 323 14.5.2 Exponentially Weighted Moving Average Control Charts 324 14.5.3 Other Advanced Control Charts 325 14.6 Summary 325 Problems 326 15 Product Screening and Burn-In Strategies 331 15.1 Burn-In Data Observations 332 15.2 Discussion of Burn-In Data 333 15.3 Higher Field Reliability without Screening 334 15.4 Best Practices 335 15.5 Summary 336 Problems 337 16 Analyzing Product Failures and Root Causes 339 16.1 Root-Cause Analysis Processes 341 16.1.1 Preplanning 341 16.1.2 Collecting Data for Analysis and Assessing Immediate Causes 343 16.1.3 Root-Cause Hypothesization 344 16.1.4 Analysis and Interpretation of Evidence 348 16.1.5 Root-Cause Identification and Corrective Actions 348 16.1.6 Assessment of Corrective Actions 350 16.2 No-Fault-Found 351 16.2.1 An Approach to Assess NFF 353 16.2.2 Common Mode Failure 355 16.2.3 Concept of Common Mode Failure 356 16.2.4 Modeling and Analysis for Dependencies for Reliability Analysis 360 16.2.5 Common Mode Failure Root Causes 362 16.2.6 Common Mode Failure Analysis 364 16.2.7 Common Mode Failure Occurrence and Impact Reduction 366 16.3 Summary 373 Problems 374 17 System Reliability Modeling 375 17.1 Reliability Block Diagram 375 17.2 Series System 376 17.3 Products with Redundancy 381 17.3.1 Active Redundancy 381 17.3.2 Standby Systems 385 17.3.3 Standby Systems with Imperfect Switching 387 17.3.4 Shared Load Parallel Models 390 17.3.5 (k, n) Systems 391 17.3.6 Limits of Redundancy 393 17.4 Complex System Reliability 393 17.4.1 Complete Enumeration Method 393 17.4.2 Conditional Probability Method 395 17.4.3 Concept of Coherent Structures 396 17.5 Summary 401 Problems 402 18 Health Monitoring and Prognostics 409 18.1 Conceptual Model for Prognostics 410 18.2 Reliability and Prognostics 412 18.3 PHM for Electronics 414 18.4 PHM Concepts and Methods 417 18.4.1 Fuses and Canaries 418 18.5 Monitoring and Reasoning of Failure Precursors 420 18.5.1 Monitoring Environmental and Usage Profiles for Damage Modeling 424 18.6 Implementation of PHM in a System of Systems 429 18.7 Summary 431 Problems 431 19 Warranty Analysis 433 19.1 Product Warranties 434 19.2 Warranty Return Information 435 19.3 Warranty Policies 436 19.4 Warranty and Reliability 437 19.5 Warranty Cost Analysis 439 19.5.1 Elements of Warranty Cost Models 440 19.5.2 Failure Distributions 440 19.5.3 Cost Modeling Calculation 440 19.5.4 Modeling Assumptions and Notation 441 19.5.5 Cost Models Examples 442 19.5.6 Information Needs 444 19.5.7 Other Cost Models 446 19.6 Warranty and Reliability Management 448 19.7 Summary 449 Problems 449 Appendix A: Some Useful Integrals 451 Appendix B: Table for Gamma Function 453 Appendix C: Table for Cumulative Standard Normal Distribution 455 Appendix D: Values for the Percentage Points tα,ν of the t-Distribution 457 Appendix E: Percentage Points χ2α,ν of the Chi-Square Distribution 461 Appendix F: Percentage Points for the F-Distribution 467 Bibliography 473 Index 487

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Book SynopsisA comprehensive introduction to social network analysis that hones in on basic centrality measures, social links, subgroup analysis, data sources, and more Written by military, industry, and business professionals, this book introduces readers to social network analysis, the new and emerging topic that has recently become of significant use for industry, management, law enforcement, and military practitioners for identifying both vulnerabilities and opportunities in collaborative networked organizations. Focusing on models and methods for the analysis of organizational risk, Social Network Analysis with Applications provides easily accessible, yet comprehensive coverage of network basics, centrality measures, social link theory, subgroup analysis, relational algebra, data sources, and more. Examples of mathematical calculations and formulas for social network measures are also included. Along with practice problems and exercises, this easily accessible boTable of ContentsList of Figures xi List of Tables xv Foreword xvii Preface xix Acknowledgments xxi Introduction xxv Part I Network Basics Chapter 1 What is a Network? 3 1.1 Basic Network Concepts 4 1.2 Adjacency Matrices, Graphs, and Notation 4 1.3 Nodes and Links 6 1.4 Good Will Hunting Problem 9 1.5 Formal and Informal Networks 13 1.6 Summary 18 Chapter 2 Centrality Measures 29 2.1 What is “Centrality” and Why do we Study It? 29 2.2 Calculating Nodal Centrality Measures 33 2.3 Directed Networks and Centrality Measures 46 2.4 Location in the Network 46 2.5 Summary 52 Chapter 3 Graph Level Measures 69 3.1 Density 70 3.2 Diameter 71 3.3 Centralization 73 3.4 Average Centralities 77 3.5 Network Topology 78 3.6 Summary 86 Part II Social Theory Chapter 4 Social Links 109 4.1 Individual Actors 110 4.2 Social Exchange Theory 111 4.3 Social Forces 113 4.4 Graph Structure 120 4.5 Agent Optimization Strategies in Networks 121 4.6 Hierarchy of Social Link Motivation 124 4.7 Summary Chapter 5 Subgroup Analysis 129 5.1 Subgroups 129 5.2 Organizational Theory 130 5.3 Random Groups 133 5.4 Heuristics for Subgroup Identification 133 5.5 Analysis Methods 135 5.6 Summary 143 Chapter 6 Diffusion and Influence 149 6.1 Applications for Social Diffusion 149 6.2 Strain Theory 151 6.3 Social Context 152 6.4 Group Impacts on Diffusion 156 6.5 Network Structure and Diffusion 158 6.6 Group Influence Strategies and Bases of Power 160 6.7 Summary 165 Part III Data Chapter 7 Meta-Networks and Relational Algebra 173 7.1 Modes of Data 174 7.2 Source, Target, Direction 174 7.3 Mulitmode Networks 176 7.4 Bridging a Meta-Network 180 7.5 Strength of Ties 182 7.6 Summary 183 Chapter 8 Sources of Data 189 8.1 Network Sampling 189 8.2 Measuring Links 191 8.3 Data Quality 195 8.4 Additional Ethnographic Data Collection Methods 196 8.5 Anonymity Issues 198 8.6 Summary 199 Part IV Organizational Risk Chapter 9 Organizational Risk 205 9.1 What is risk? 205 9.2 Measures of Centrality and Risk 207 9.3 Other Risk Measures 216 9.4 The Right Network: Efficient Versus Learning/Adaptive 220 9.5 Network Threats and Vulnerabilities 223 9.6 Thickening a Network 226 9.7 Thinning a Network 227 9.8 Process of Organizational Risk Analysis 228 9.9 Summary of Main Points 231 Appendix A: Matrix Algebra Primer 235 Appendix B: Tables of Data and Networks 241 Appendix C: Five Points of a Graph 273 Index 281

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Book SynopsisPraise for the Second Edition An amazing assemblage of worldwide contributions in mathematics and, in addition to use as a course book, a valuable resource . . . essential. CHOICE This Third Edition of The History of Mathematics examines the elementary arithmetic, geometry, and algebra of numerous cultures, tracing their usage from Mesopotamia, Egypt, Greece, India, China, and Japan all the way to Europe during the Medieval and Renaissance periods where calculus was developed. Aimed primarily at undergraduate students studying the history of mathematics for science, engineering, and secondary education, the book focuses on three main ideas: the facts of who, what, when, and where major advances in mathematics took place; the type of mathematics involved at the time; and the integration of this information into a coherent picture of the development of mathematics. In addition, the book features carefully designed problems Table of ContentsPREFACE xxiii Changes from the Second Edition xxiii Elementary Texts on the History of Mathematics xxiv PART I. WHAT IS MATHEMATICS? Contents of Part I 1 1. Mathematics and its History 3 1.1. Two Ways to Look at the History of Mathematics 3 1.2. The Origin of Mathematics 5 1.3. The Philosophy of Mathematics 8 1.4. Our Approach to the History of Mathematics 11 2. Proto-mathematics 14 2.1. Number 14 2.2. Shape 16 2.3. Symbols 18 2.4. Mathematical Reasoning 20 PART II. THE MIDDLE EAST, 2000–1500 BCE Contents of Part II 25 3. Overview of Mesopotamian Mathematics 27 3.1. A Sketch of Two Millennia of Mesopotamian History 27 3.2. Mathematical Cuneiform Tablets 29 3.3. Systems of Measuring and Counting 30 3.4. The Mesopotamian Numbering System 31 4. Computations in Ancient Mesopotamia 38 4.1. Arithmetic 38 4.2. Algebra 40 5. Geometry in Mesopotamia 46 5.1. The Pythagorean Theorem 46 5.2. Plane Figures 48 5.3. Volumes 49 5.4. Plimpton 322 49 6. Egyptian Numerals and Arithmetic 56 6.1. Sources 56 6.2. The Rhind Papyrus 58 6.3. Egyptian Arithmetic 58 6.4. Computation 59 7. Algebra and Geometry in Ancient Egypt 66 7.1. Algebra Problems in the Rhind Papyrus 66 7.2. Geometry 68 7.3. Areas 69 PART III. GREEK MATHEMATICS FROM 500 BCE TO 500 CE Contents of Part III 77 8. An Overview of Ancient Greek Mathematics 79 8.1. Sources 80 8.2. General Features of Greek Mathematics 82 8.3. Works and Authors 87 9. Greek Number Theory 91 9.1. The Euclidean Algorithm 92 9.2. The Arithmetica of Nicomachus 93 9.3. Euclid’s Number Theory 97 9.4. The Arithmetica of Diophantus 97 10. Fifth-Century Greek Geometry 103 10.1. “Pythagorean” Geometry 103 10.2. Challenge No. 1: Unsolved Problems 106 10.3. Challenge No. 2: The Paradoxes of Zeno of Elea 107 10.4. Challenge No. 3: Irrational Numbers and Incommensurable Lines 108 11. Athenian Mathematics I: The Classical Problems 115 11.1. Squaring the Circle 116 11.2. Doubling the Cube 117 11.3. Trisecting the Angle 122 12. Athenian Mathematics II: Plato and Aristotle 128 12.1. The Influence of Plato 128 12.2. Eudoxan Geometry 130 12.3. Aristotle 134 13. Euclid of Alexandria 140 13.1. The Elements 140 13.2. The Data 144 14. Archimedes of Syracuse 148 14.1. The Works of Archimedes 149 14.2. The Surface of a Sphere 150 14.3. The Archimedes Palimpsest 153 14.4. Quadrature of the Parabola 155 15. Apollonius of Perga 160 15.1. History of the Conics 161 15.2. Contents of the Conics 162 15.3. Foci and the Three- and Four-Line Locus 165 16. Hellenistic and Roman Geometry 169 16.1. Zenodorus 169 16.2. The Parallel Postulate 171 16.3. Heron 172 16.4. Roman Civil Engineering 174 17. Ptolemy’s Geography and Astronomy 177 17.1. Geography 177 17.2. Astronomy 180 17.3. The Almagest 184 18. Pappus and the Later Commentators 190 18.1. The Collection of Pappus 190 18.2. The Later Commentators: Theon and Hypatia 196 PART IV. INDIA, CHINA, AND JAPAN 500 BCE–1700 CE Contents of Part IV 201 19. Overview of Mathematics in India 203 19.1. The Sulva Sutras 205 19.2. Buddhist and Jain Mathematics 206 19.3. The Bakshali Manuscript 206 19.4. The Siddhantas 206 19.5. Hindu–Arabic Numerals 206 19.6. Aryabhata I 207 19.7. Brahmagupta 208 19.8. Bhaskara II 209 19.9. Muslim India 210 19.10. Indian Mathematics in the Colonial Period and After 210 20. From the Vedas to Aryabhata I 213 20.1. Problems from the Sulva Sutras 213 20.2. Aryabhata I: Geometry and Trigonometry 219 21. Brahmagupta, the Kuttaka, and Bhaskara II 227 21.1. Brahmagupta’s Plane and Solid Geometry 227 21.2. Brahmagupta’s Number Theory and Algebra 228 21.3. The Kuttaka 230 21.4. Algebra in the Works of Bhaskara II 233 21.5. Geometry in the Works of Bhaskara II 235 22. Early Classics of Chinese Mathematics 239 22.1. Works and Authors 240 22.2. China’s Encounter with Western Mathematics 243 22.3. The Chinese Number System 244 22.4. Algebra 246 22.5. Contents of the Jiu Zhang Suan Shu 247 22.6. Early Chinese Geometry 249 23. Later Chinese Algebra and Geometry 255 23.1. Algebra 255 23.2. Later Chinese Geometry 262 24. Traditional Japanese Mathematics 267 24.1. Chinese Influence and Calculating Devices 267 24.2. Japanese Mathematicians and Their Works 268 24.3. Japanese Geometry and Algebra 270 24.4. Sangaku 277 PART V. ISLAMIC MATHEMATICS, 800–1500 Contents of Part V 281 25. Overview of Islamic Mathematics 283 25.1. A Brief Sketch of the Islamic Civilization 283 25.2. Islamic Science in General 285 25.3. Some Muslim Mathematicians and Their Works 287 26. Islamic Number Theory and Algebra 292 26.1. Number Theory 292 26.2. Algebra 294 27. Islamic Geometry 302 27.1. The Parallel Postulate 302 27.2. Thabit ibn-Qurra 302 27.3. Al-Biruni: Trigonometry 304 27.4. Al-Kuhi 305 27.5. Al-Haytham and Ibn-Sahl 305 27.6. Omar Khayyam 307 27.7. Nasir al-Din al-Tusi 308 PART VI. EUROPEAN MATHEMATICS, 500–1900 Contents of Part VI 311 28. Medieval and Early Modern Europe 313 28.1. From the Fall of Rome to the Year 1200 313 28.2. The High Middle Ages 318 28.3. The Early Modern Period 321 28.4. Northern European Advances 322 29. European Mathematics: 1200–1500 324 29.1. Leonardo of Pisa (Fibonacci) 324 29.2. Hindu–Arabic Numerals 328 29.3. Jordanus Nemorarius 329 29.4. Nicole d’Oresme 330 29.5. Trigonometry: Regiomontanus and Pitiscus 331 29.6. A Mathematical Skill: Prosthaphæresis 333 29.7. Algebra: Pacioli and Chuquet 335 30. Sixteenth-Century Algebra 338 30.1. Solution of Cubic and Quartic Equations 338 30.2. Consolidation 340 30.3. Logarithms 343 30.4. Hardware: Slide Rules and Calculating Machines 345 31. Renaissance Art and Geometry 348 31.1. The Greek Foundations 348 31.2. The Renaissance Artists and Geometers 349 31.3. Projective Properties 350 32. The Calculus Before Newton and Leibniz 358 32.1. Analytic Geometry 358 32.2. Components of the Calculus 363 33. Newton and Leibniz 373 33.1. Isaac Newton 373 33.2. Gottfried Wilhelm von Leibniz 375 33.3. The Disciples of Newton and Leibniz 379 33.4. Philosophical Issues 379 33.5. The Priority Dispute 381 33.6. Early Textbooks on Calculus 382 34. Consolidation of the Calculus 386 34.1. Ordinary Differential Equations 387 34.2. Partial Differential Equations 390 34.3. Calculus of Variations 391 34.4. Foundations of the Calculus 397 PART VII. SPECIAL TOPICS Contents of Part VII 404 35. Women Mathematicians 405 35.1. Sof’ya Kovalevskaya 406 35.2. Grace Chisholm Young 408 35.3. Emmy Noether 411 36. Probability 417 36.1. Cardano 418 36.2. Fermat and Pascal 419 36.3. Huygens 420 36.4. Leibniz 420 36.5. The Ars Conjectandi of James Bernoulli 421 36.6. De Moivre 423 36.7. The Petersburg Paradox 424 36.8. Laplace 425 36.9. Legendre 426 36.10. Gauss 426 36.11. Philosophical Issues 427 36.12. Large Numbers and Limit Theorems 428 37. Algebra from 1600 to 1850 433 37.1. Theory of Equations 433 37.2. Euler, D’Alembert, and Lagrange 437 37.3. The Fundamental Theorem of Algebra and Solution by Radicals 439 38. Projective and Algebraic Geometry and Topology 448 38.1. Projective Geometry 448 38.2. Algebraic Geometry 453 38.3. Topology 456 39. Differential Geometry 464 39.1. Plane Curves 464 39.2. The Eighteenth Century: Surfaces 468 39.3. Space Curves: The French Geometers 469 39.4. Gauss: Geodesics and Developable Surfaces 469 39.5. The French and British Geometers 473 39.6. Grassmann and Riemann: Manifolds 473 39.7. Differential Geometry and Physics 476 39.8. The Italian Geometers 477 40. Non-Euclidean Geometry 481 40.1. Saccheri 482 40.2. Lambert and Legendre 484 40.3. Gauss 485 40.4. The First Treatises 486 40.5. Lobachevskii’s Geometry 487 40.6. J´anos B´olyai 489 40.7. The Reception of Non-Euclidean Geometry 489 40.8. Foundations of Geometry 491 41. Complex Analysis 495 41.1. Imaginary and Complex Numbers 495 41.2. Analytic Function Theory 500 41.3. Comparison of the Three Approaches 508 42. Real Numbers, Series, and Integrals 511 42.1. Fourier Series, Functions, and Integrals 512 42.2. Fourier Series 514 42.3. Fourier Integrals 516 42.4. General Trigonometric Series 518 43. Foundations of Real Analysis 521 43.1. What is a Real Number? 521 43.2. Completeness of the Real Numbers 525 43.3. Uniform Convergence and Continuity 525 43.4. General Integrals and Discontinuous Functions 526 43.5. The Abstract and the Concrete 527 43.6. Discontinuity as a Positive Property 529 44. Set Theory 532 44.1. Technical Background 532 44.2. Cantor's Work on Trigonometric Series 533 44.3. The Reception of Set Theory 536 44.4. Existence and the Axiom of Choice 537 45. Logic 542 45.1. From Algebra to Logic 542 45.2. Symbolic Calculus 545 45.3. Boole’s Mathematical Analysis of Logic 546 45.4. Boole’s Laws of Thought 547 45.5. Jevons 548 45.6. Philosophies of Mathematics 548 45.7. Doubts About Formalized Mathematics: Gödel’s Theorems 554 Literature 559 Name Index 575 Subject Index

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Book SynopsisThis book details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems.Table of ContentsPreface xiii 1 Basics of Linear Algebra 1 1.1 Notation and Terminology 1 1.2 Vector and Matrix Norms 4 1.3 Dot Product and Orthogonality 8 1.4 Special Matrices 9 1.5 Vector Spaces 21 1.6 Linear Independence and Basis 24 1.7 Orthogonalization and Direct Sums 30 1.8 Column Space, Row Space and Null Space 34 1.9 Orthogonal Projections 43 1.10 Eigenvalues and Eigenvectors 47 1.11 Similarity 56 1.12 Bezier Curves Postscript Fonts 59 1.13 Final Remarks and Further Reading 68 Exercises 69 2 Ranking Web Pages 79 2.1 The Power Method 80 2.2 Stochastic, Irreducible and Primitive Matrices 84 2.3 Google’s PageRank Algorithm 92 2.4 Alternatives to Power Method 106 2.5 Final Remarks and Further Reading 120 Exercises 121 3 Matrix Factorizations 131 3.1 LU Factorization 132 3.2 QR Factorization 142 3.3 Singular Value Decomposition (SVD) 155 3.4 Schur Factorization 166 3.5 Information Retrieval 186 3.6 Partition of Simple Substitution Cryptograms 194 3.7 Final Remarks and Further Reading 203 Exercises 205 4 Least Squares 215 4.1 Projections and Normal Equations 215 4.2 Least Squares and QR Factorization 224 4.3 Lagrange Multipliers 228 4.4 Final Remarks and Further Reading 231 Exercises 231 5 Image Compression 235 5.1 Compressing with Discrete Cosine Transform 236 5.2 Huffman Coding 260 5.3 Compression with SVD 267 5.4 Final Remarks and Further Reading 269 Exercises 271 6 Ordinary Differential Equations 277 6.1 One-Dimensional Differential Equations 278 6.2 Linear Systems of Differential Equations 307 6.3 Solutions via Eigenvalues and Eigenvectors 307 6.4 Fundamentals Matrix Solution 312 6.5 Final Remarks and Further Reading 316 Exercises 316 7 Dynamical Systems 325 7.1 Linear Dynamical Systems 326 7.2 Nonlinear Dynamical Systems 340 7.3 Predator-Prey Models with Harvesting 374 7.4 Final Remarks and Further Reading 385 Exercises 385 8 Mathematical Models 395 8.1 Optimization of a Waste Management System 396 8.2 Grouping Problem in Networks 404 8.3 American Cutaneous Leishmaniasis 410 8.4 Variable Population Interactions 420 References 431 Index 435

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Book SynopsisThe book transitions smoothly from first-order to higher-order equations, featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology. In addition to plentiful exercises and examples throughout, each chapter concludes with a summary that outlines key concepts and techniques.Trade Review“It is clearly written, well illustrated and it could be useful for applied mathematicians, physicists, engineers and other related professionals and also for students who are interested in the applications of ordinary differential equations.” (Zentralblatt MATH, 1 June 2013)Table of ContentsPreface viii 1. First-Order Differential Equations 1 1.1 Motivation and Overview 1 1.2 Linear First-Order Equations 11 1.3 Applications of Linear First-Order Equations 24 1.4 Nonlinear First-Order Equations That Are Separable 43 1.5 Existence and Uniqueness 50 1.6 Applications of Nonlinear First-Order Equations 59 1.7 Exact Equations and Equations That Can Be Made Exact 71 1.8 Solution by Substitution 81 1.9 Numerical Solution by Euler’s Method 87 2. Higher-Order Linear Equations 99 2.1 Linear Differential Equations of Second Order 99 2.2 Constant-Coefficient Equations 103 2.3 Complex Roots 113 2.4 Linear Independence; Existence, Uniqueness, General Solution 118 2.5 Reduction of Order 128 2.6 Cauchy-Euler Equations 134 2.7 The General Theory for Higher-Order Equations 142 2.8 Nonhomogeneous Equations 149 2.9 Particular Solution by Undetermined Coefficients 155 2.10 Particular Solution by Variation of Parameters 163 3. Applications of Higher-Order Equations 173 3.1 Introduction 173 3.2 Linear Harmonic Oscillator; Free Oscillation 174 3.3 Free Oscillation with Damping 186 3.4 Forced Oscillation 193 3.5 Steady-State Diffusion; A Boundary Value Problem 202 3.6 Introduction to the Eigenvalue Problem; Column Buckling 211 4. Systems of Linear Differential Equations 219 4.1 Introduction, and Solution by Elimination 219 4.2 Application to Coupled Oscillators 230 4.3 N-Space and Matrices 238 4.4 Linear Dependence and Independence of Vectors 247 4.5 Existence, Uniqueness, and General Solution 253 4.6 Matrix Eigenvalue Problem 261 4.7 Homogeneous Systems with Constant Coefficients 270 4.8 Dot Product and Additional Matrix Algebra 283 4.9 Explicit Solution of x’ = Ax and the Matrix Exponential Function 297 4.10 Nonhomogeneous Systems 307 5. Laplace Transform 317 5.1 Introduction 317 5.2 The Transform and Its Inverse 319 5.3 Applications to the Solution of Differential Equations 334 5.4 Discontinuous Forcing Functions; Heaviside Step Function 347 5.5 Convolution 358 5.6 Impulsive Forcing Functions; Dirac Delta Function 366 6. Series Solutions 379 6.1 Introduction 379 6.2 Power Series and Taylor Series 380 6.3 Power Series Solution About a Regular Point 387 6.4 Legendre and Bessel Equations 395 6.5 The Method of Frobenius 408 7. Systems of Nonlinear Differential Equations 423 7.1 Introduction 423 7.2 The Phase Plane 424 7.3 Linear Systems 435 7.4 Nonlinear Systems 447 7.5 Limit Cycles 463 7.6 Numerical Solution of Systems by Euler’s Method 468 Appendix A. Review of Partial Fraction Expansions 479 Appendix B. Review of Determinants 483 Appendix C. Review of Gauss Elimination 491 Appendix D. Review of Complex Numbers and the Complex Plane 497 Answers to Exercises 501 Index 521

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Book SynopsisAn introduction to probability at the undergraduate level Chance and randomness are encountered on a daily basis. Authored by a highly qualified professor in the field, Probability: With Applications and R delves into the theories and applications essential to obtaining a thorough understanding of probability.Table of ContentsPreface xi Acknowledgments xiv Introduction xv 1 First Principles 1 1.1 Random Experiment, Sample Space, Event 1 1.2 What Is a Probability? 3 1.3 Probability Function 4 1.4 Properties of Probabilities 7 1.5 Equally Likely Outcomes 10 1.6 Counting I 12 1.7 Problem-Solving Strategies: Complements, Inclusion–Exclusion 14 1.8 Random Variables 18 1.9 A Closer Look at Random Variables 21 1.10 A First Look at Simulation 22 1.11 Summary 26 Exercises 27 2 Conditional Probability 34 2.1 Conditional Probability 34 2.2 New Information Changes the Sample Space 39 2.3 Finding P(A and B) 40 2.4 Conditioning and the Law of Total Probability 49 2.5 Bayes Formula and Inverting a Conditional Probability 57 2.6 Summary 61 Exercises 62 3 Independence and Independent Trials 68 3.1 Independence and Dependence 68 3.2 Independent Random Variables 76 3.3 Bernoulli Sequences 77 3.4 Counting II 79 3.5 Binomial Distribution 88 3.6 Stirling’s Approximation 95 3.7 Poisson Distribution 96 3.8 Product Spaces 105 3.9 Summary 107 Exercises 109 4 Random Variables 117 4.1 Expectation 118 4.2 Functions of Random Variables 121 4.3 Joint Distributions 125 4.4 Independent Random Variables 130 4.5 Linearity of Expectation 135 4.6 Variance and Standard Deviation 140 4.7 Covariance and Correlation 149 4.8 Conditional Distribution 156 4.9 Properties of Covariance and Correlation 162 4.10 Expectation of a Function of a Random Variable 164 4.11 Summary 165 Exercises 168 5 A Bounty of Discrete Distributions 176 5.1 Geometric Distribution 176 5.2 Negative Binomial—Up from the Geometric 184 5.3 Hypergeometric—Sampling Without Replacement 189 5.4 From Binomial to Multinomial 194 5.5 Benford’s Law 201 5.6 Summary 203 Exercises 205 6 Continuous Probability 211 6.1 Probability Density Function 213 6.2 Cumulative Distribution Function 216 6.3 Uniform Distribution 220 6.4 Expectation and Variance 222 6.5 Exponential Distribution 224 6.6 Functions of Random Variables I 229 6.7 Joint Distributions 235 6.8 Independence 243 6.9 Covariance, Correlation 249 6.10 Functions of Random Variables II 251 6.11 Geometric Probability 256 6.12 Summary 262 Exercises 265 7 Continuous Distributions 273 7.1 Normal Distribution 273 7.2 Gamma Distribution 290 7.3 Poisson Process 296 7.4 Beta Distribution 304 7.5 Pareto Distribution, Power Laws, and the 80-20 Rule 308 7.6 Summary 312 Exercises 315 8 Conditional Distribution, Expectation, and Variance 322 8.1 Conditional Distributions 322 8.2 Discrete and Continuous: Mixing it up 328 8.3 Conditional Expectation 332 8.4 Computing Probabilities by Conditioning 342 8.5 Conditional Variance 346 8.6 Summary 352 Exercises 353 9 Limits 359 9.1 Weak Law of Large Numbers 361 9.2 Strong Law of Large Numbers 367 9.3 Monte Carlo Integration 372 9.4 Central Limit Theorem 376 9.5 Moment-Generating Functions 385 9.6 Summary 391 Exercises 392 10 Additional Topics 399 10.1 Bivariate Normal Distribution 399 10.2 Transformations of Two Random Variables 407 10.3 Method of Moments 411 10.4 Random Walk on Graphs 413 10.5 Random Walks on Weighted Graphs and Markov Chains 421 10.6 From Markov Chain to Markov Chain Monte Carlo 429 10.7 Summary 440 Exercises 442 Appendix A Getting Started with R 447 Appendix B Probability Distributions in R 458 Appendix C Summary of Probability Distributions 459 Appendix D Reminders from Algebra and Calculus 462 Appendix E More Problems for Practice 464 Solutions to Exercises 469 References 487 Index 491

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Book SynopsisThis is the student Solutions Manual to accompanyAdvanced Engineering Mathematics, Volume 2, Tenth Edition.This market-leading text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self contained subject matter parts for maximum flexibility. The new edition continues with the tradition of providing instructors and students with a comprehensive and up-to-date resource for teaching and learning engineering mathematics, that is, applied mathematics for engineers and physicists, mathematicians and computer scientists, as well as members of other disciplines.Table of ContentsPART D: COMPLEX ANALYSIS…257 Chapter 13. Numbers and Functions. Complex Differentiation…257 13.1 Complex Numbers and Their Geometric Representation…258 13.2 Polar Form of Complex Numbers. Powers and Roots…261 13.3 Derivative. Analytic Function…267 13.4 Cauchy–Riemann Equations. Laplace’s Equation…269 13.5 Exponential Function…274 13.6 Trigonometric and Hyperbolic Functions. Euler’s Formula…277 13.7 Logarithm. General Power. Principal Value…279 Chapter 14: Complex Integration…283 14.1 Line Integral in the Complex Plane…283 14.2 Cauchy’s Integral Theorem…288 14.3 Cauchy’s Integral Formula…291 14.4 Derivatives of Analytic Functions…295 Chapter 15: Power Series, Taylor Series…298 15.1 Sequences, Series, Convergence Tests…298 15.2 Power Series…303 15.3 Functions Given by Power Series…306 15.4 Taylor and Maclaurin Series…309 15.5 Uniform Convergence. Optional…312 Chapter 16: Laurent Series. Residue Integration…316 16.1 Laurent Series…316 16.2 Singularities and Zeros. Infinity…320 16.3 Residue Integration Method…322 16.4 Residue Integration of Real Integrals…326 Chapter 17: Conformal Mapping…332 17.1 Geometry of Analytic Functions: Conformal Mapping…333 17.2 Linear Fractional Transformations. (Möbius Transformations)…339 17.3 Special Linear Fractional Transformations…343 17.4 Conformal Mapping by Other Functions…347 17.5 Riemann Surfaces. Optional…352 Chapter 18: Complex Analysis and Potential Theory…353 18.1 Electrostatic Fields…354 18.2 Use of Conformal Mapping. Modeling…358 18.3 Heat Problems…359 18.4 Fluid Flow…361 18.5 Poisson’s Integral Formula for Potentials…364 18.6 General Properties of Harmonic Functions. Uniqueness Theorem for the Dirchlet Problem…367 PART E: NUMERIC ANALYSIS…373 Chapter 19: Numerics in General…373 19.1 Introduction…374 19.2 Solution of Equations by Iteration…379 19.3 Interpolation…384 19.4 Spline Interpolation…389 19.5 Numeric Integration and Differentiation…393 Chapter 20: Numeric Linear Algebra…400 20.1 Linear Systems: Gauss Elimination…400 20.2 Linear Systems: LU-Factorization, Matrix Inversion…404 20.3 Linear Systems: Solution by Iteration…410 20.4 Linear Systems: Ill-Conditioning, Norms…415 20.5 Least Squares Method…419 20.6 Matrix Eigenvalue Problems: Introduction…424 20.7 Inclusion of Matrix Eigenvalues…424 20.8 Power Method for Eigenvalues…429 20.9 Tridiagonalization and QR-Factorization…434 Chapter 21: Numerics for ODEs and PDEs…442 21.1 Methods for First-Order ODEs…442 21.2 Multistep Methods…445 21.3 Methods for Systems and Higher Order ODEs…446 21.4 Methods for Elliptic PDEs…452 21.5 Neumann and Mixed Problems. Irregular Boundary…454 21.6 Methods for Parabolic PDEs…459 21.7 Method for Hyperbolic PDEs…462 PART F: OPTIMIZATION, GRAPHS…465 Chapter 22: Unconstrained Optimization. Linear Programming…465 22.1 Basic Concepts. Unconstrained Optimization: Method of Steepest Descent…465 22.2 Linear Programming…471 22.3 Simplex Method…474 22.4 Simplex Method. Difficulties…479 Chapter 23: Graphs. Combinatorial Optimization…482 23.1 Graphs and Digraphs…482 23.2 Shortest Path Problems. Complexity…484 23.3 Bellman’s Principle. Dijkstra’s Algorithm…487 23.4 Shortest Spanning Trees: Greedy Algorithm…490 23.5 Shortest Spanning Trees: Prim’s Algorithm…493 23.6 Flows in Networks 23.7 Maximum Flow: Ford–Fulkerson Algorithm…497 23.8 Bipartite Graphs. Assignment Problems…499 PART G: PROBABILITY, STATISTICS…502 Chapter 24: Data Analysis, Probability Theory…502 24.1 Data Representation. Average. Spread…502 24.2 Experiments, Outcomes, Events…507 24.3 Probability…509 24.4 Permutations and Combinations…512 24.5 Random Variables. Probability Distributions…516 24.6 Mean and Variance of a Distribution…520 24.7 Binomial, Poisson, and Hypergeometric Distributions…523 24.8 Normal Distribution…526 24.9 Distribution of Several Random Variables…530 Chapter 25: Mathematical Statistics…533 25.1 Introduction. Random Sampling…533 25.2 Point Estimation of Parameters…533 25.3 Confidence Intervals…536 25.4 Testing of Hypotheses. Decisions…540 25.5 Quality Control…543 25.6 Acceptance Sampling…544 25.7 Goodness of Fit. Chi-Square Test…547 25.8 Nonparametric Tests…549 25.9 Regression. Fitting Straight Lines. Correlation…551

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Book SynopsisThis is a self-contained introduction to the basic structures of abstract algebra and its applications. Classroom-tested over several decades, the book is self-contained and is ideal for self-study. The author has thoroughly reviewed and revised the book and has also significantly added to the discussion on modules over principle ideal domains.Trade Review“This could also be an excellent adjunct to more theoretically oriented textbooks used in more intensive courses.” (Computing Reviews, 5 November 2012) Table of Contents0 Preliminaries 1 0.1 Proofs 1 0.2 Sets 2 0.3 Mappings 3 0.4 Equivalences 4 1 Integers and Permutations 6 1.1 Induction 6 1.2 Divisors and Prime Factorization 8 1.3 Integers Modulo 11 1.4 Permutations 13 2 Groups 17 2.1 Binary Operations 17 2.2 Groups 19 2.3 Subgroups 21 2.4 Cyclic Groups and the Order of an Element 24 2.5 Homomorphisms and Isomorphisms 28 2.6 Cosets and Lagrange's Theorem 30 2.7 Groups of Motions and Symmetries 32 2.8 Normal Subgroups 34 2.9 Factor Groups 36 2.10 The Isomorphism Theorem 38 2.11 An Application to Binary Linear Codes 43 3 Rings 47 3.1 Examples and Basic Properties 47 3.2 Integral Domains and Fields 52 3.3 Ideals and Factor Rings 55 3.4 Homomorphisms 59 3.5 Ordered Integral Domains 62 4 Polynomials 64 4.1 Polynomials 64 4.2 Factorization of Polynomials over a Field 67 4.3 Factor Rings of Polynomials over a Field 70 4.4 Partial Fractions 76 4.5 Symmetric Polynomials 76 5 Factorization in Integral Domains 81 5.1 Irreducibles and Unique Factorization 81 5.2 Principal Ideal Domains 84 6 Fields 88 6.1 Vector Spaces 88 6.2 Algebraic Extensions 90 6.3 Splitting Fields 94 6.4 Finite Fields 96 6.5 Geometric Constructions 98 6.7 An Application to Cyclic and BCH Codes 99 7 Modules over Principal Ideal Domains 102 7.1 Modules 102 7.2 Modules over a Principal Ideal Domain 105 8 p-Groups and the Sylow Theorems 108 8.1 Products and Factors 108 8.2 Cauchy’s Theorem 111 8.3 Group Actions 114 8.4 The Sylow Theorems 116 8.5 Semidirect Products 118 8.6 An Application to Combinatorics 119 9 Series of Subgroups 122 9.1 The Jordan-H¨older Theorem 122 9.2 Solvable Groups 124 9.3 Nilpotent Groups 127 10 Galois Theory 130 10.1 Galois Groups and Separability 130 10.2 The Main Theorem of Galois Theory 134 10.3 Insolvability of Polynomials 138 10.4 Cyclotomic Polynomials and Wedderburn's Theorem 140 11 Finiteness Conditions for Rings and Modules 142 11.1 Wedderburn's Theorem 142 11.2 The Wedderburn-Artin Theorem 143 Appendices 147 Appendix A: Complex Numbers 147 Appendix B: Matrix Arithmetic 148 Appendix C: Zorn's Lemma 149

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Book SynopsisPraise for Common Errors in Statistics (and How to Avoid Them) A very engaging and valuable book for all who use statistics in any setting. ?CHOICE Addresses popular mistakes often made in data collection and provides an indispensable guide to accurate statistical analysis and reporting. The authors'' emphasis on careful practice, combined with a focus on the development of solutions, reveals the true value of statistics when applied correctly in any area of research. ?MAA Reviews Common Errors in Statistics (and How to Avoid Them), Fourth Edition provides a mathematically rigorous, yet readily accessible foundation in statistics for experienced readers as well as students learning to design and complete experiments, surveys, and clinical trials. Providing a consistent level of coherency throughout, the highly readable Fourth Edition focuses on debunking popular myths, analyzing common mistakes, and instructiTrade Review“Presented in an easy-to-follow style, this textbook is thought for students and professionals in industry, government, medicine, and the social sciences.” (Zentralblatt MATH, 1 December 2013)Table of ContentsPreface xi PART I FOUNDATIONS 1 1. Sources of Error 3 Prescription 4 Fundamental Concepts 5 Surveys and Long-Term Studies 9 Ad-Hoc, Post-Hoc Hypotheses 9 To Learn More 13 2. Hypotheses: The Why of Your Research 15 Prescription 15 What Is a Hypothesis? 16 How Precise Must a Hypothesis Be? 17 Found Data 18 Null or Nil Hypothesis 19 Neyman–Pearson Theory 20 Deduction and Induction 25 Losses 26 Decisions 27 To Learn More 28 3. Collecting Data 31 Preparation 31 Response Variables 32 Determining Sample Size 37 Fundamental Assumptions 46 Experimental Design 47 Four Guidelines 49 Are Experiments Really Necessary? 53 To Learn More 54 PART II STATISTICAL ANALYSIS 57 4. Data Quality Assessment 59 Objectives 60 Review the Sampling Design 60 Data Review 62 To Learn More 63 5. Estimation 65 Prevention 65 Desirable and Not-So-Desirable Estimators 68 Interval Estimates 72 Improved Results 77 Summary 78 To Learn More 78 6. Testing Hypotheses: Choosing a Test Statistic 79 First Steps 80 Test Assumptions 82 Binomial Trials 84 Categorical Data 85 Time-To-Event Data (Survival Analysis) 86 Comparing the Means of Two Sets of Measurements 90 Do Not Let Your Software Do Your Thinking For You 99 Comparing Variances 100 Comparing the Means of K Samples 105 Higher-Order Experimental Designs 108 Inferior Tests 113 Multiple Tests 114 Before You Draw Conclusions 115 Induction 116 Summary 117 To Learn More 117 7. Strengths and Limitations of Some Miscellaneous Statistical Procedures 119 Nonrandom Samples 119 Modern Statistical Methods 120 Bootstrap 121 Bayesian Methodology 123 Meta-Analysis 131 Permutation Tests 135 To Learn More 137 8. Reporting Your Results 139 Fundamentals 139 Descriptive Statistics 144 Ordinal Data 149 Tables 149 Standard Error 151 p-Values 155 Confidence Intervals 156 Recognizing and Reporting Biases 158 Reporting Power 160 Drawing Conclusions 160 Publishing Statistical Theory 162 A Slippery Slope 162 Summary 163 To Learn More 163 9. Interpreting Reports 165 With a Grain of Salt 165 The Authors 166 Cost–Benefit Analysis 167 The Samples 167 Aggregating Data 168 Experimental Design 168 Descriptive Statistics 169 The Analysis 169 Correlation and Regression 171 Graphics 171 Conclusions 172 Rates and Percentages 174 Interpreting Computer Printouts 175 Summary 178 To Learn More 178 10. Graphics 181 Is a Graph Really Necessary? 182 KISS 182 The Soccer Data 182 Five Rules for Avoiding Bad Graphics 183 One Rule for Correct Usage of Three-Dimensional Graphics 194 The Misunderstood and Maligned Pie Chart 196 Two Rules for Effective Display of Subgroup Information 198 Two Rules for Text Elements in Graphics 201 Multidimensional Displays 203 Choosing Effective Display Elements 209 Oral Presentations 209 Summary 210 To Learn More 211 PART III BUILDING A MODEL 213 11. Univariate Regression 215 Model Selection 215 Stratification 222 Further Considerations 226 Summary 233 To Learn More 234 12. Alternate Methods of Regression 237 Linear Versus Nonlinear Regression 238 Least-Absolute-Deviation Regression 238 Quantile Regression 243 Survival Analysis 245 The Ecological Fallacy 246 Nonsense Regression 248 Reporting the Results 248 Summary 248 To Learn More 249 13. Multivariable Regression 251 Caveats 251 Dynamic Models 256 Factor Analysis 256 Reporting Your Results 258 A Conjecture 260 Decision Trees 261 Building a Successful Model 264 To Learn More 265 14. Modeling Counts and Correlated Data 267 Counts 268 Binomial Outcomes 268 Common Sources of Error 269 Panel Data 270 Fixed- and Random-Effects Models 270 Population-Averaged Generalized Estimating Equation Models (GEEs) 271 Subject-Specific or Population-Averaged? 272 Variance Estimation 272 Quick Reference for Popular Panel Estimators 273 To Learn More 275 15. Validation 277 Objectives 277 Methods of Validation 278 Measures of Predictive Success 283 To Learn More 285 Glossary 287 Bibliography 291 Author Index 319 Subject Index 329

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Book SynopsisPraise for the Third Edition . . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . .Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book''s unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The pTrade Review “This could also be an excellent adjunct to more theoretically oriented textbooks used in more intensive courses.” (Computing Reviews, 5 November 2012) Table of ContentsPreface ix Acknowledgment xv Notations Used in the Text xvii A Sketch of the History of Algebra to 1929 xxi Preliminaries 1 Proofs 1 Sets 5 Mappings 9 Equivalences 17 Integers and Permutations 22 Induction 22 Divisors and Prime Factorization 30 Integers Modulo n 41 Permutations 51 An Application to Cryptography 63 Groups 66 Binary Operations 66 Groups 73 Subgroups 82 Cyclic Groups and the Order of an Element 87 Homomorphisms and Isomorphisms 95 Cosets and Lagrange's Theorem 105 Groups of Motions and Symmetries 114 Normal Subgroups 119 Factor Groups 127 The Isomorphism Theorem 133 An Application to Binary Linear Codes 140 Rings 155 Examples and Basic Properties 155 Integral Domains and Fields 166 Ideals and Factor Rings 174 Homomorphisms 183 Ordered Integral Domains 193 Polynomials 196 Polynomials 196 Factorization of Polynomials over a Field 209 Factor Rings of Polynomials over a Field 222 Partial Fractions 231 Symmetric Polynomials 233 Formal Construction of Polynomials 243 Factorization in Integral Domains 246 Irreducibles and Unique Factorization 247 Principal Ideal Domains 259 Fields 268 Vector Spaces 269 Algebraic Extensions 277 Splitting Fields 285 Finite Fields 293 Geometric Constructions 299 The Fundamental Theorem of Algebra 304 An Application to Cyclic and BCH Codes 305 Modules over Principal Ideal Domains 318 Modules 318 Modules over a PID 327 p-Groups and the Sylow Theorems 341 Factors and Products 341 Cauchy's Theorem 349 Group Actions 356 The Sylow Theorems 364 Semidirect Products 371 An Application to Combinatorics 375 Series of Subgroups 381 The Jordan-Holder Theorem 382 Solvable Groups 387 Nilpotent Groups 394 Galois Theory 401 Galois Groups and Separability 402 The Main Theorem of Galois Theory 410 Insolvability of Polynomials 423 Cyclotomic Polynomials and Wedderburn's Theorem 430 Finiteness Conditions for Rings and Modules 435 Wedderburn's Theorem 435 The Wedderburn-Artin Theorem 444 Appendices Complex Numbers 455 Matrix Arithmetic 462 Zorn's Lemma 467 Proof of the Recursion Theorem 471 Bibliography 473 Selected Answers 475 Index 499

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Book SynopsisMethods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods includes updates of established literature from the Wiley Encyclopedia of Clinical Trials as well as original material based on the latest developments in clinical trials. Prepared by a leading expert, the second volume includes numerous contributions from current prominent experts in the field of medical research. In addition, the volume features: Multiple new articles exploring emerging topics, such as evaluation methods with threshold, empirical likelihood methods, nonparametric ROC analysis, over- and under-dispersed models, and multi-armed bandit problems Up-to-date research on the Cox proportional hazard model, frailty models, trial reports, intrarater reliability, conditional power, and the kappa index Key qualitative issues including cost-effectiveness analysis, publication bias, and regulatory issues, which are crucial to the planniTrade Review“This book provides a good overview on most relevant topics for clinical trials.” (Biometrical Journal, 1 October 2015) Table of ContentsContributors xix Preface xxiii 1 Analysis of Over- and Underdispersed Data 1 2 Analysis of Variance (ANOVA) 10 3 Assessment of Health-Related Quality of Life 26 4 Bandit Processes and Response-Adaptive Clinical Trials: The Art of Exploration Versus Exploitation 40 5 Bayesian Dose-Finding Designs in Healthy Volunteers 51 6 Bootstrap 62 7 Conditional Power in Clinical Trial Monitoring 102 8 Cost-Effectiveness Analysis 111 9 Cox-Type Proportional Hazards Models 126 10 Empirical Likelihood Methods in Clinical Experiments 146 11 Frailty Models 166 12 Futility Analysis 174 13 Imaging Science in Medicine I: Overview 187 14 Imaging Science in Medicine, II: Basics of X-Ray Imaging 213 15 Imaging Science in Medicine, III: Digital (21st Century) X-Ray Imaging 264 16 Intention-to-Treat Analysis 313 17 Interim Analyses 323 18 Interrater Reliability 334 19 Intrarater Reliability 340 20 Kaplan-Meier Plot 357 21 Logistic Regression 365 22 Metadata 380 23 Microarray 392 24 Multi-Armed Bandits, Gittins Index, and Its Calculation 416 25 Multiple Comparisons 436 26 Multiple Evaluators 446 27 Noncompartmental Analysis 457 28 Nonparametric ROC Analysis for Diagnostic Trials 483 29 Optimal Biological Dose for Molecularly Targeted Therapies 496 30 Over- and Underdispersion Models 506 31 Permutation Tests in Clinical Trials 527 32 Pharmacoepidemiology, Overview 536 33 Population Pharmacokinetic and Pharmacodynamic Methods 551 34 Proportions: Inferences and Comparisons 570 35 Publication Bias 595 36 Quality of Life 608 37 Relative Risk Modeing 622 38 Sample Size Considerations for Morbidity/Mortality Trials 633 39 Sample Size for Comparing Means 642 40 Sample Size for Comparing Proportions 653 41 Sample Size for Comparing Time-to-Event Data 664 42 Sample Size for Comparing Variabilities 672 43 Screening, Models of 689 44 Screening Trials 721 45 Secondary Efficacy End Points 731 46 Sensitivity, Specificity, and Receiver Operator Characteristic (ROC) Methods 740 47 Software for Genetics/Genomics 752 48 Stability Study Designs 778 49 Subgroup Analysis 793 50 Survival Analysis, Overview 802 51 The FDA and Regulatory Issues 815 52 The Kappa Index 836 53 Treatment Interruption 846 54 Trial Reports: Improving Reporting, Minimizing Bias, and Producing Better Evidence-Based Practice 860 55 U.S. Department of Veterans Affairs Cooperative Studies Program 876 56 Women's Health Initiative: Statistical Aspects and Selected Early Results 901 57 World Health Organization (WHO): Global Health Situation 914 Index 925

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Book SynopsisThis textbook introduces chemistry and chemical engineering students to molecular descriptions of thermodynamics, chemical systems, and biomolecules. Equips students with the ability to apply the method to their own systems, as today''s research is microscopic and molecular and articles are written in that language Provides ample illustrations and tables to describe rather difficult concepts Makes use of plots (charts) to help students understand the mathematics necessary for the contents Includes practice problems and answers Table of ContentsPreface xiii Acknowledgments xvii About the Companion Website xix Symbols and Constants xxi 1 Introduction 1 1.1 Classical Thermodynamics and Statistical Thermodynamics 1 1.2 Examples of Results Obtained from Statistical Thermodynamics 2 1.2.1 Heat Capacity of Gas of Diatomic Molecules 2 1.2.2 Heat Capacity of a Solid 3 1.2.3 Blackbody Radiation 3 1.2.4 Adsorption 4 1.2.5 Helix–Coil Transition 5 1.2.6 Boltzmann Factor 6 1.3 Practices of Notation 6 2 Review of Probability Theory 9 2.1 Probability 9 2.2 Discrete Distributions 11 2.2.1 Binomial Distribution 12 2.2.2 Poisson Distribution 13 2.2.3 Multinomial Distribution 14 2.3 Continuous Distributions 15 2.3.1 Uniform Distribution 19 2.3.2 Exponential Distribution 19 2.3.3 Normal Distribution 21 2.3.4 Distribution of a Dihedral Angle 21 2.4 Means and Variances 22 2.4.1 Discrete Distributions 22 2.4.2 Continuous Distributions 26 2.4.3 Central Limit Theorem 27 2.5 Uncertainty 28 Problems 31 3 Energy and Interactions 35 3.1 Kinetic Energy and Potential Energy of Atoms and Ions 35 3.1.1 Kinetic Energy 35 3.1.2 Gravitational Potential 36 3.1.3 Ion in an Electric Field 36 3.1.4 Total Energy of Atoms and Ions 37 3.2 Kinetic Energy and Potential Energy of Diatomic Molecules 37 3.2.1 Kinetic Energy (Translation, Rotation, Vibration) 37 3.2.2 Dipolar Potential 42 3.2.2.1 Potential of a Permanent Dipole 42 3.2.2.2 Potential of an Induced Dipole 44 3.3 Kinetic Energy of Polyatomic Molecules 46 3.3.1 Linear Polyatomic Molecule 46 3.3.2 Nonlinear Polyatomic Molecule 48 3.4 Interactions Between Molecules 50 3.4.1 Excluded-Volume Interaction 52 3.4.2 Coulomb Interaction 52 3.4.3 Dipole–Dipole Interaction 53 3.4.4 van der Waals Interaction 54 3.4.5 Lennard-Jones Potential 55 3.5 Energy as an Extensive Property 57 3.6 Kinetic Energy of a Gas Molecule in Quantum Mechanics 58 3.6.1 Quantization of Translational Energy 58 3.6.2 Quantization of Rotational Energy 61 3.6.3 Quantization of Vibrational Energy 63 3.6.4 Electronic Energy Levels 65 3.6.5 Comparison of Energy Level Spacings 66 Problems 67 4 Statistical Mechanics 69 4.1 Basic Assumptions, Microcanonical Ensembles, and Canonical Ensembles 69 4.1.1 Basic Assumptions 69 4.1.2 Microcanonical Ensembles 73 4.1.3 Canonical Ensembles 75 4.2 Probability Distribution in Canonical Ensembles and Partition Functions 77 4.2.1 Probability Distribution 77 4.2.2 Partition Function for a System with Discrete States 79 4.2.3 Partition Function for a System with Continuous States 81 4.2.4 Energy Levels and States 83 4.3 Internal Energy 88 4.4 Identification of 𝛽 89 4.5 Equipartition Law 91 4.6 Other Thermodynamic Functions 93 4.7 Another View of Entropy 97 4.8 Fluctuations of Energy 99 4.9 Grand Canonical Ensembles 100 4.10 Cumulants of Energy 107 Problems 110 5 Canonical Ensemble of Gas Molecules 113 5.1 Velocity of Gas Molecules 113 5.2 Heat Capacity of a Classical Gas 116 5.2.1 Point Mass 117 5.2.2 Rigid Dumbbell 117 5.2.3 Elastic Dumbbell 118 5.3 Heat Capacity of a Quantum-Mechanical Gas 120 5.3.1 General Formulas 120 5.3.2 Translation 122 5.3.3 Rotation 124 5.3.4 Vibration 127 5.3.5 Comparison with Classical Models 128 5.4 Distribution of Rotational Energy Levels 129 5.5 Conformations of a Molecule 130 Problems 132 6 Indistinguishable Particles 135 6.1 Distinguishable Particles and Indistinguishable Particles 135 6.2 Partition Function of Indistinguishable Particles 137 6.2.1 System of Distinguishable Particles 137 6.2.2 System of Indistinguishable Particles 137 6.3 Condition of Nondegeneracy 142 6.4 Significance of Division by N! 144 6.4.1 Gas in a Two-Part Box 144 6.4.2 Chemical Potential 145 6.4.3 Mixture of Two Gases 146 6.5 Indistinguishability and Center-of-Mass Movement 147 6.6 Open System of Gas 147 Problems 149 7 Imperfect Gas 153 7.1 Virial Expansion 153 7.2 Molecular Expression of Interaction in the Canonical Ensemble 157 7.3 Second Virial Coefficients in Different Models 164 7.3.1 Hard-Core Repulsion Only 164 7.3.2 Square-well Potential 165 7.3.3 Lennard-Jones Potential 167 7.4 Joule–Thomson Effect 167 Problems 171 8 Rubber Elasticity 175 8.1 Rubber 175 8.2 Polymer Chain in One Dimension 176 8.3 Polymer Chain in Three Dimensions 180 8.4 Network of Springs 184 Problems 185 9 Law of Mass Action 189 9.1 Reaction of Two Monatomic Molecules 190 9.2 Decomposition of Homonuclear Diatomic Molecules 193 9.3 Isomerization 195 9.4 Method of the Steepest Descent 197 Problems 198 10 Adsorption 201 10.1 Adsorption Phenomena 201 10.2 Langmuir Isotherm 202 10.3 BET Isotherm 206 10.4 Dissociative Adsorption 211 10.5 Interaction Between Adsorbed Molecules 213 Problems 213 11 Ising Model 217 11.1 Model 217 11.2 Partition Function 220 11.2.1 One-Dimensional Ising Model 220 11.2.2 Calculating Statistical Averages 221 11.2.2.1 Average Number of Up Spins 222 11.2.2.2 Average of the Number of Spin Alterations (Number of Domains – 1) 222 11.2.2.3 Domain Size 223 11.2.2.4 Size of a Domain of Uniform Spins 223 11.2.3 A Few Examples of 1D Ising Model 223 11.2.3.1 Linear Ising Model, N = 3 223 11.2.3.2 Ring Ising Model, N = 3 225 11.2.3.3 Ring Ising Model, N = 4 225 11.3 Mean-FieldTheories 226 11.3.1 Bragg–Williams (B–W) Approximation 227 11.3.2 Flory–Huggins (F–H) Approximation 231 11.3.3 Approximation by a Mean-Field (MF) Theory 235 11.4 Exact Solution of 1D Ising Model 236 11.4.1 General Formula 236 11.4.2 Large-N Approximation 239 11.4.3 Exact Partition Function for Arbitrary N 241 11.4.4 Ring Ising Model, Arbitrary N 244 11.4.5 Comparison of the Exact Results with Those of Mean-Field Approximations 245 11.5 Variations of the Ising Model 247 11.5.1 System of Uniform Spins 247 11.5.2 Random Local Fields of Opposite Directions 249 11.5.3 Dilute Local Fields 252 Problems 254 12 Helical Polymer 263 12.1 Helix-Forming Polymer 263 12.2 Optical Rotation and Circular Dichroism 266 12.3 Pristine Poly(n-hexyl isocyanate) 267 12.4 Variations to the Helical Polymer 271 12.4.1 Copolymer of Chiral and Achiral Isocyanate Monomers 272 12.4.2 Copolymer of R- and S-Enantiomers of Isocyanate 274 Problems 274 13 Helix–Coil Transition 277 13.1 Historical Background 277 13.2 Polypeptides 281 13.3 Zimm–Bragg Model 283 Problems 289 14 Regular Solutions 291 14.1 Binary Mixture of Equal-Size Molecules 291 14.1.1 Free Energy of Mixing 291 14.1.2 Derivatives of the Free Energy of Mixing 296 14.1.3 Phase Separation 300 14.2 Binary Mixture of Molecules of Different Sizes 304 Problems 312 Appendix A Mathematics 315 A.1 Hyperbolic Functions 315 A.2 Series 317 A.3 Binomial Theorem and Trinomial Theorem 317 A.4 Stirling’s formula 318 A.5 Integrals 318 A.6 Error Functions 318 A.7 Gamma Functions 319 References 321 Index 325

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