Mathematics Books
Basic Books The Model Thinker
Book SynopsisData, data, data: It''s all one ever hears about these days. Science is all about big data. Our bosses call out for analytics, whatever those might be. And everyone wants to predict what will happen next. Can we accurately predict if a company''s stock will rise, whether or not a disease will spread, or who will become the next President of the United States? As anyone who has ever opened up a spreadsheet groaning with weeks, months, or years of data knows, numbers aren''t enough: we have to know how to make them talk.Enter Scott Page and The Model Thinker. A leading professor of quantitative social science at the University of Michigan, he has taken his expertise as both a teacher and researcher and distilled it into the one book anyone will need to master data and turn it to professional use. This is no armchair exercise in imagined understanding, like The Signal and the Noise or The Black Swan or a legion of books on networks, the purposes of which ar
£22.50
John Wiley & Sons Inc A First Course in Finite Elements
Book SynopsisThe text material evolved from over 50 years of combined teaching experience it deals with a formulation and application of the finite element method. A meaningful course can be constructed from a subset of the chapters in this book for a quarter course; instructions for such use are given in the preface.Trade Review"Recommended for upper division undergraduates and above." (CHOICE, February 2008)Table of ContentsPreface xi 1 Introduction 1 1.1 Background 1 1.2 Applications of Finite elements 7 References 9 2 Direct Approach for Discrete Systems 11 2.1 Describing the Behavior of a Single Bar Element 11 2.2 Equations for a System 15 2.2.1 Equations for Assembly 18 2.2.2 Boundary Conditions and System Solution 20 2.3 Applications to Other Linear Systems 24 2.4 Two-Dimensional Truss Systems 27 2.5 Transformation Law 30 2.6 Three-Dimensional Truss Systems 35 References 36 Problems 37 3 Strong andWeak Forms for One-Dimensional Problems 41 3.1 The Strong Form in One-Dimensional Problems 42 3.1.1 The Strong Form for an Axially Loaded Elastic Bar 42 3.1.2 The Strong Form for Heat Conduction in One Dimension 44 3.1.3 Diffusion in One Dimension 46 3.2 TheWeak Form in One Dimension 47 3.3 Continuity 50 3.4 The Equivalence Between theWeak and Strong Forms 51 3.5 One-Dimensional Stress Analysis with Arbitrary Boundary Conditions 58 3.5.1 Strong Form for One-Dimensional Stress Analysis 58 3.5.2 Weak Form for One-Dimensional Stress Analysis 59 3.6 One-Dimensional Heat Conduction with Arbitrary Boundary Conditions 60 3.6.1 Strong Form for Heat Conduction in One Dimension with Arbitrary Boundary Conditions 60 3.6.2 Weak Form for Heat Conduction in One Dimension with Arbitrary Boundary Conditions 61 3.7 Two-Point Boundary Value Problem with Generalized Boundary Conditions 62 3.7.1 Strong Form for Two-Point Boundary Value Problems with Generalized Boundary Conditions 62 3.7.2 Weak Form for Two-Point Boundary Value Problems with Generalized Boundary Conditions 63 3.8 Advection–Diffusion 64 3.8.1 Strong Form of Advection–Diffusion Equation 65 3.8.2 Weak Form of Advection–Diffusion Equation 66 3.9 Minimum Potential Energy 67 3.10 Integrability 71 References 72 Problems 72 4 Approximation of Trial Solutions,Weight Functions and Gauss Quadrature for One-Dimensional Problems 77 4.1 Two-Node Linear Element 79 4.2 Quadratic One-Dimensional Element 81 4.3 Direct Construction of Shape Functions in One Dimension 82 4.4 Approximation of theWeight Functions 84 4.5 Global Approximation and Continuity 84 4.6 Gauss Quadrature 85 Reference 90 Problems 90 5 Finite Element Formulation for One-Dimensional Problems 93 5.1 Development of Discrete Equation: Simple Case 93 5.2 Element Matrices for Two-Node Element 97 5.3 Application to Heat Conduction and Diffusion Problems 99 5.4 Development of Discrete Equations for Arbitrary Boundary Conditions 105 5.5 Two-Point Boundary Value Problem with Generalized Boundary Conditions 111 5.6 Convergence of the FEM 113 5.6.1 Convergence by Numerical Experiments 115 5.6.2 Convergence by Analysis 118 5.7 FEM for Advection–Diffusion Equation 120 References 122 Problems 123 6 Strong andWeak Forms for Multidimensional Scalar Field Problems 131 6.1 Divergence Theorem and Green’s Formula 133 6.2 Strong Form 139 6.3 Weak Form 142 6.4 The Equivalence BetweenWeak and Strong Forms 144 6.5 Generalization to Three-Dimensional Problems 145 6.6 Strong andWeak Forms of Scalar Steady-State Advection–Diffusion in Two Dimensions 146 References 148 Problems 148 7 Approximations of Trial Solutions,Weight Functions and Gauss Quadrature for Multidimensional Problems 151 7.1 Completeness and Continuity 152 7.2 Three-Node Triangular Element 154 7.2.1 Global Approximation and Continuity 157 7.2.2 Higher Order Triangular Elements 159 7.2.3 Derivatives of Shape Functions for the Three-Node Triangular Element 160 7.3 Four-Node Rectangular Elements 161 7.4 Four-Node Quadrilateral Element 164 7.4.1 Continuity of Isoparametric Elements 166 7.4.2 Derivatives of Isoparametric Shape Functions 166 7.5 Higher Order Quadrilateral Elements 168 7.6 Triangular Coordinates 172 7.6.1 Linear Triangular Element 172 7.6.2 Isoparametric Triangular Elements 174 7.6.3 Cubic Element 175 7.6.4 Triangular Elements by Collapsing Quadrilateral Elements 176 7.7 Completeness of Isoparametric Elements 177 7.8 Gauss Quadrature in Two Dimensions 178 7.8.1 Integration Over Quadrilateral Elements 179 7.8.2 Integration Over Triangular Elements 180 7.9 Three-Dimensional Elements 181 7.9.1 Hexahedral Elements 181 7.9.2 Tetrahedral Elements 183 References 185 Problems 186 8 Finite Element Formulation for Multidimensional Scalar Field Problems 189 8.1 Finite Element Formulation for Two-Dimensional Heat Conduction Problems 189 8.2 Verification and Validation 201 8.3 Advection–Diffusion Equation 207 References 209 Problems 209 9 Finite Element Formulation for Vector Field Problems – Linear Elasticity 215 9.1 Linear Elasticity 215 9.1.1 Kinematics 217 9.1.2 Stress and Traction 219 9.1.3 Equilibrium 220 9.1.4 Constitutive Equation 222 9.2 Strong andWeak Forms 223 9.3 Finite Element Discretization 225 9.4 Three-Node Triangular Element 228 9.4.1 Element Body Force Matrix 229 9.4.2 Boundary Force Matrix 230 9.5 Generalization of Boundary Conditions 231 9.6 Discussion 239 9.7 Linear Elasticity Equations in Three Dimensions 240 Problems 241 10 Finite Element Formulation for Beams 249 10.1 Governing Equations of the Beam 249 10.1.1 Kinematics of Beam 249 10.1.2 Stress–Strain Law 252 10.1.3 Equilibrium 253 10.1.4 Boundary Conditions 254 10.2 Strong Form toWeak Form 255 10.2.1 Weak Form to Strong Form 257 10.3 Finite Element Discretization 258 10.3.1 Trial Solution andWeight Function Approximations 258 10.3.2 Discrete Equations 260 10.4 Theorem of Minimum Potential Energy 261 10.5 Remarks on Shell Elements 265 Reference 269 Problems 269 11 Commercial Finite Element Program ABAQUS Tutorials 275 11.1 Introduction 275 11.1.1 Steady-State Heat Flow Example 275 11.2 Preliminaries 275 11.3 Creating a Part 276 11.4 Creating a Material Definition 278 11.5 Defining and Assigning Section Properties 279 11.6 Assembling the Model 280 11.7 Configuring the Analysis 280 11.8 Applying a Boundary Condition and a Load to the Model 280 11.9 Meshing the Model 282 11.10 Creating and Submitting an Analysis Job 284 11.11 Viewing the Analysis Results 284 11.12 Solving the Problem Using Quadrilaterals 284 11.13 Refining the Mesh 285 11.13.1 Bending of a Short Cantilever Beam 287 11.14 Copying the Model 287 11.15 Modifying the Material Definition 287 11.16 Configuring the Analysis 287 11.17 Applying a Boundary Condition and a Load to the Model 288 11.18 Meshing the Model 289 11.19 Creating and Submitting an Analysis Job 290 11.20 Viewing the Analysis Results 290 11.20.1 Plate with a Hole in Tension 290 11.21 Creating a New Model 292 11.22 Creating a Part 292 11.23 Creating a Material Definition 293 11.24 Defining and Assigning Section Properties 294 11.25 Assembling the Model 295 11.26 Configuring the Analysis 295 11.27 Applying a Boundary Condition and a Load to the Model 295 11.28 Meshing the Model 297 11.29 Creating and Submitting an Analysis Job 298 11.30 Viewing the Analysis Results 299 11.31 Refining the Mesh 299 Appendix 303 A.1 Rotation of Coordinate System in Three Dimensions 303 A.2 Scalar Product Theorem 304 A.3 Taylor’s Formula with Remainder and the Mean Value Theorem 304 A.4 Green’s Theorem 305 A.5 Point Force (Source) 307 A.6 Static Condensation 308 A.7 Solution Methods 309 Direct Solvers 310 Iterative Solvers 310 Conditioning 311 References 312 Problem 312 Index 313
£50.30
John Wiley & Sons Inc Analysis of Financial Time Series
Book SynopsisAnalysis of Financial Time Series, Third Edition provides a broad, mature, and systematic introduction to current financial econometric models and their applications to modeling and prediction of financial time series data. It utilizes real-world examples and real financial data throughout the book to apply the models and methods described.Trade Review"Analysis of financial time series, third edition, is an ideal book for introductory courses on time series at the graduate level and a valuable supplement for statistics courses in time series at the upper-undergraduate level." (Mathematical Reviews, 2011) "Nevertheless, all in all the book can be a very useful reference for students as well as for professionals." (Zentralblatt MATH, 2011) "Factor models, an important technique used in quantitative finance, are given a full treatment with macroeconomic factor models and fundamental factor models. The coverage of the book is comprehensive. It starts from basic time series techniques and finishes with advanced concepts such as state space models and MCMC methods. There is a balance between the theoretical background necessary to appreciate the nuances and the practical aspect of implementation. More importantly it gives insights about what time series models can't address. The book has an excellent supporting website which has all the programs and data sets which helps to internalize the concepts. Finally, teaching professionals should find the solutions manual as a valuable tool to explain concepts and to ensure understanding." (BookPleasures.com, January 2011) "This book provides a broad, mature, and systematic introduction to current financial econometric models and their applications to modeling and prediction of financial time series data. It utilizes real-world examples and real financial data throughout the book to apply the models and methods described." (Insurance News Net, 8 December 2010)Table of ContentsPreface xvii Preface to the Second Edition xix Preface to the First Edition xxi 1 Financial Time Series and Their Characteristics 1 1.1 Asset Returns, 2 1.2 Distributional Properties of Returns, 7 1.3 Processes Considered, 22 2 Linear Time Series Analysis and Its Applications 29 2.1 Stationarity, 30 2.2 Correlation and Autocorrelation Function, 30 2.3 White Noise and Linear Time Series, 36 2.4 Simple AR Models, 37 2.5 Simple MA Models, 57 2.6 Simple ARMA Models, 64 2.7 Unit-Root Nonstationarity, 71 2.8 Seasonal Models, 81 2.9 Regression Models with Time Series Errors, 90 2.10 Consistent Covariance Matrix Estimation, 97 2.11 Long-Memory Models, 101 3 Conditional Heteroscedastic Models 109 3.1 Characteristics of Volatility, 110 3.2 Structure of a Model, 111 3.3 Model Building, 113 3.4 The ARCH Model, 115 3.5 The GARCH Model, 131 3.6 The Integrated GARCH Model, 140 3.7 The GARCH-M Model, 142 3.8 The Exponential GARCH Model, 143 3.9 The Threshold GARCH Model, 149 3.10 The CHARMA Model, 150 3.11 Random Coefficient Autoregressive Models, 152 3.12 Stochastic Volatility Model, 153 3.13 Long-Memory Stochastic Volatility Model, 154 3.14 Application, 155 3.15 Alternative Approaches, 159 3.16 Kurtosis of GARCH Models, 165 4 Nonlinear Models and Their Applications 175 4.1 Nonlinear Models, 177 4.2 Nonlinearity Tests, 205 4.3 Modeling, 214 4.4 Forecasting, 215 4.5 Application, 218 5 High-Frequency Data Analysis and Market Microstructure 231 5.1 Nonsynchronous Trading, 232 5.2 Bid–Ask Spread, 235 5.3 Empirical Characteristics of Transactions Data, 237 5.4 Models for Price Changes, 244 5.5 Duration Models, 253 5.6 Nonlinear Duration Models, 264 5.7 Bivariate Models for Price Change and Duration, 265 5.8 Application, 270 6 Continuous-Time Models and Their Applications 287 6.1 Options, 288 6.2 Some Continuous-Time Stochastic Processes, 288 6.3 Ito's Lemma, 292 6.4 Distributions of Stock Prices and Log Returns, 297 6.5 Derivation of Black–Scholes Differential Equation, 298 6.6 Black–Scholes Pricing Formulas, 300 6.7 Extension of Ito's Lemma, 309 6.8 Stochastic Integral, 310 6.9 Jump Diffusion Models, 311 6.10 Estimation of Continuous-Time Models, 318 7 Extreme Values, Quantiles, and Value at Risk 325 7.1 Value at Risk, 326 7.2 RiskMetrics, 328 7.3 Econometric Approach to VaR Calculation, 333 7.4 Quantile Estimation, 338 7.5 Extreme Value Theory, 342 7.6 Extreme Value Approach to VaR, 353 7.7 New Approach Based on the Extreme Value Theory, 359 7.8 The Extremal Index, 377 8 Multivariate Time Series Analysis and Its Applications 389 8.1 Weak Stationarity and Cross-Correlation Matrices, 390 8.2 Vector Autoregressive Models, 399 8.3 Vector Moving-Average Models, 417 8.4 Vector ARMA Models, 422 8.5 Unit-Root Nonstationarity and Cointegration, 428 8.6 Cointegrated VAR Models, 432 8.7 Threshold Cointegration and Arbitrage, 442 8.8 Pairs Trading, 446 9 Principal Component Analysis and Factor Models 467 9.1 A Factor Model, 468 9.2 Macroeconometric Factor Models, 470 9.3 Fundamental Factor Models, 476 9.4 Principal Component Analysis, 483 9.5 Statistical Factor Analysis, 489 9.6 Asymptotic Principal Component Analysis, 498 10 Multivariate Volatility Models and Their Applications 505 10.1 Exponentially Weighted Estimate, 506 10.2 Some Multivariate GARCH Models, 510 10.3 Reparameterization, 516 10.4 GARCH Models for Bivariate Returns, 521 10.5 Higher Dimensional Volatility Models, 537 10.6 Factor–Volatility Models, 543 10.7 Application, 546 10.8 Multivariate t Distribution, 548 11 State-Space Models and Kalman Filter 557 11.1 Local Trend Model, 558 11.2 Linear State-Space Models, 576 11.3 Model Transformation, 577 11.4 Kalman Filter and Smoothing, 591 11.5 Missing Values, 600 11.6 Forecasting, 601 11.7 Application, 602 12 Markov Chain Monte Carlo Methods with Applications 613 12.1 Markov Chain Simulation, 614 12.2 Gibbs Sampling, 615 12.3 Bayesian Inference, 617 12.4 Alternative Algorithms, 622 12.5 Linear Regression with Time Series Errors, 624 12.6 Missing Values and Outliers, 628 12.7 Stochastic Volatility Models, 636 12.8 New Approach to SV Estimation, 649 12.9 Markov Switching Models, 660 12.10 Forecasting, 666 12.11 Other Applications, 669 Exercises, 670 References, 671 Index 673
£112.46
John Wiley & Sons Inc Math for the Professional Kitchen
Book SynopsisA good chef needs a firm grasp of basic math skills in order to cook well and achieve financial success. Ideal for students and working professionals, this book explains all the essential mathematical skills needed to run a successful, profitable food-industry operation.Table of ContentsAcknowledgments vi Foreword vii Introduction viii 1 Units of Measure and Unit Conversions 1 1.1 Measurements Used in the Professional Kitchen 2 1.2 Converting Units of Measure Within Weight or Within Volume 8 1.3 Converting Between Weight and Volume 21 2 Recipe Scaling 35 2.1 Calculating a Scaling Factor 36 2.2 Scaling Recipes Based on a Desired Yield 46 2.3 Scaling Recipes Based on a Constraining Ingredient 56 2.4 Standardizing Recipes 63 3 Yield Percent 73 3.1 What is Yield Percent? 74 3.2 Calculating EP Quantities and AP Quantities 82 3.3 Quantities That Compensate for Waste 91 4 Purchasing and Portioning 95 4.1 Calculating Portion Size or Number of Portions 96 4.2 Calculating AP Quantities Using Portion Sizes or Recipe Quantities 104 4.3 Calculating AP Quantities for a Recipe 112 4.4 Creating a Grocery List 119 5 Recipe Costing 131 5.1 Calculating AP Cost per Unit 132 5.2 Recipe Costing 139 5.3 Food Cost Percent 154 5.4 The 2-in-1 Recipe Costing Form 166 5.5 The 2-in-1 Recipe Costing Form: The Excel Version 192 5.6 Comparative Costing 200 6 Kitchen Ratios 213 6.1 What is a Ratio? 214 6.2 Using a Ratio When One Ingredient Quantity is Known 222 6.3 Using a Ratio When the Desired Yield is Known 231 6.4 Working with Ratios Using Percents 241 6.5 The Baker’s Percent 248 Appendix I Additional Information on Units of Measure 259 Appendix II Volume Unit Equivalent Visual Memorization Aids 261 Appendix III Changing Between Fractions, Decimals, and Percents 263 Appendix IV The Butcher’s Yield 267 Appendix V Information from The Book of Yields 269 Answers to Practice Problems 277 Glossary of Terms 301 References 303 Index 305
£31.35
John Wiley & Sons Inc Technical Math For Dummies
Book SynopsisTechnical Math For Dummies features easy-to-follow, plain-English guidance on mathematical formulas and methods that professionals use every day in the automotive, health, construction, maintenance and other trades. It shows how to apply concepts of mathematics and formulas related to occupational areas of study.Table of ContentsIntroduction. Part I: Basic Math, Basic Tools. Chapter 1: Math that Works as Hard as You Do. Chapter 2: Discovering Technical Math and the Tools of the Trades. Chapter 3: Zero to One and Beyond. Chapter 4: Easy Come, Easy Go: Addition and Subtraction. Chapter 5: Multiplication and Division: Everybody Needs Them. Chapter 6: Measurement and Conversion. Chapter 7: Slaying the Story Problem Dragon. Part II: Making Non-Basic Math Simple and Easy. Chapter 8: Fun with Fractions. Chapter 9: Decimals: They Have Their Place. Chapter 10: Playing with Percentages. Chapter 11: Tackling Exponents and Square Roots. Part III: Basic Algebra, Geometry, and Trigonometry. Chapter 12: Algebra and the Mystery of X. Chapter 13: Formulas (Secret and Otherwise). Chapter 14: Quick-and-Easy Geometry: The Compressed Version. Chapter 15: Calculating Areas, Perimeters, and Volumes. Chapter 16: Trigonometry, the "Mystery Math". Part IV: Math for the Business of Your Work. Chapter 17: Graphs are Novel and Charts Are Off the Chart. Chapter 18: Hold on a Second: Time Math. Chapter 19: Math for Computer Techs and Users. Part V: The Part of Tens. Chapter 20: Ten Tips for Solving Any Math Problem. Chapter 21: Ten Formulas You’ll Use Most Often. Chapter 22: Ten Ways to Avoid Everyday Math Stress. Glossary. Index.
£17.09
John Wiley & Sons Inc Engineering Statistics SI Version
Book Synopsis* Montgomery, Runger, and Hubele provide modern coverage of engineering statistics, focusing on how statistical tools are integrated into the engineering problem-solving process.Table of ContentsChapter 1 The Role of Statistics in Engineering 1 1-1 The Engineering Method and Statistical Thinking 2 1-2 Collecting Engineering Data 6 1-2.1 Retrospective Study 7 1-2.2 Observational Study 8 1-2.3 Designed Experiments 9 1-2.4 Random Samples 12 1-3 Mechanistic and Empirical Models 15 1-4 Observing Processes Over Time 17 Chapter 2 Data Summary and Presentation 23 2-1 Data Summary and Display 24 2-2 Stem-and-Leaf Diagram 29 2-3 Histograms 34 2-4 Box Plot 39 2-5 Time Series Plots 41 2-6 Multivariate Data 46 Chapter 3 Random Variables and Probability Distributions 57 3-1 Introduction 58 3-2 Random Variables 60 3-3 Probability 62 3-4 Continuous Random Variables 66 3-4.1 Probability Density Function 66 3-4.2 Cumulative Distribution Function 68 3-4.3 Mean and Variance 70 3-5 Important Continuous Distributions 74 3-5.1 Normal Distribution 74 3-5.2 Lognormal Distribution 84 3-5.3 Gamma Distribution 86 3-5.4 Weibull Distribution 86 3-5.5 Beta Distribution 88 3-6 Probability Plots 92 3-6.1 Normal Probability Plots 92 3-6.2 Other Probability Plots 94 3-7 Discrete Random Variables 97 3-7.1 Probability Mass Function 97 3-7.2 Cumulative Distribution Function 98 3-7.3 Mean and Variance 99 3-8 Binomial Distribution 102 3-9 Poisson Process 109 3-9.1 Poisson Distribution 109 3-9.2 Exponential Distribution 113 3-10 Normal Approximation to the Binomial and Poisson Distributions 119 3-11 More than One Random Variable and Independence 123 3-11.1 Joint Distributions 123 3-11.2 Independence 124 3-12 Functions of Random Variables 129 3-12.1 Linear Functions of Independent Random Variables 130 3-12.2 Linear Functions of Random Variables That are Not Independent 131 3-12.3 Nonlinear Functions of Independent Random Variables 133 3-13 Random Samples, Statistics, and the Central Limit Theorem 136 Chapter 4 Decision Making for a Single Sample 148 4-1 Statistical Inference 149 4-2 Point Estimation 150 4-3 Hypothesis Testing 156 4-3.1 Statistical Hypotheses 156 4-3.2 Testing Statistical Hypotheses 158 4-3.3 P-Values in Hypothesis Testing 164 4-3.4 One-Sided and Two-Sided Hypotheses 166 4-3.5 General Procedure for Hypothesis Testing 167 4-4 Inference on the Mean of a Population, Variance Known 169 4-4.1 Hypothesis Testing on the Mean 169 4-4.2 Type II Error and Choice of Sample Size 173 4-4.3 Large-Sample Test 177 4-4.4 Some Practical Comments on Hypothesis Testing 177 4-4.5 Confidence Interval on the Mean 178 4-4.6 General Method for Deriving a Confidence Interval 184 4-5 Inference on the Mean of a Population, Variance Unknown 186 4-5.1 Hypothesis Testing on the Mean 187 4-5.2 Type II Error and Choice of Sample Size 193 4-5.3 Confidence Interval on the Mean 195 4-6 Inference on the Variance of a Normal Population 199 4-6.1 Hypothesis Testing on the Variance of a Normal Population 199 4-6.2 Confidence Interval on the Variance of a Normal Population 203 4-7 Inference on a Population Proportion 205 4-7.1 Hypothesis Testing on a Binomial Proportion 205 4-7.2 Type II Error and Choice of Sample Size 208 4-7.3 Confidence Interval on a Binomial Proportion 210 4-8 Other Interval Estimates for a Single Sample 216 4-8.1 Prediction Interval 216 4-8.2 Tolerance Intervals for a Normal Distribution 217 4-9 Summary Tables of Inference Procedures for a Single Sample 219 4-10 Testing for Goodness of Fit 219 Chapter 5 Decision Making for Two Samples 230 5-1 Introduction 231 5-2 Inference on the Means of Two Populations, Variances Known 232 5-2.1 Hypothesis Testing on the Difference in Means, Variances Known 233 5-2.2 Type II Error and Choice of Sample Size 234 5-2.3 Confidence Interval on the Difference in Means, Variances Known 235 5-3 Inference on the Means of Two Populations, Variances Unknown 239 5-3.1 Hypothesis Testing on the Difference in Means 239 5-3.2 Type II Error and Choice of Sample Size 246 5-3.3 Confidence Interval on the Difference in Means 247 5-4 The Paired t-Test 252 5-5 Inference on the Ratio of Variances of Two Normal Populations 259 5-5.1 Hypothesis Testing on the Ratio of Two Variances 259 5-5.2 Confidence Interval on the Ratio of Two Variances 263 5-6 Inference on Two Population Proportions 265 5-6.1 Hypothesis Testing on the Equality of Two Binomial Proportions 265 5-6.2 Type II Error and Choice of Sample Size 268 5-6.3 Confidence Interval on the Difference in Binomial Proportions 269 5-7 Summary Tables for Inference Procedures for Two Samples 271 5-8 What if We Have More than Two Samples? 272 5-8.1 Completely Randomized Experiment and Analysis of Variance 272 5-8.2 Randomized Complete Block Experiment 281 Chapter 6 Building Empirical Models 298 6-1 Introduction to Empirical Models 299 6-2 Simple Linear Regression 304 6-2.1 Least Squares Estimation 304 6-2.2 Testing Hypotheses in Simple Linear Regression 312 6-2.3 Confidence Intervals in Simple Linear Regression 315 6-2.4 Prediction of a Future Observation 318 6-2.5 Checking Model Adequacy 319 6-2.6 Correlation and Regression 322 6-3 Multiple Regression 326 6-3.1 Estimation of Parameters in Multiple Regression 326 6-3.2 Inferences in Multiple Regression 331 6-3.3 Checking Model Adequacy 336 6-4 Other Aspects of Regression 344 6-4.1 Polynomial Models 344 6-4.2 Categorical Regressors 346 6-4.3 Variable Selection Techniques 348 Chapter 7 Design of Engineering Experiments 360 7-1 The Strategy of Experimentation 361 7-2 Factorial Experiments 362 7-3 2k Factorial Design 365 7-3.1 22 Design 366 7-3.2 Statistical Analysis 368 7-3.3 Residual Analysis and Model Checking 374 7-3.4 2k Design for k ≥ 3 Factors 376 7-3.5 Single Replicate of a 2k Design 382 7-4 Center Points and Blocking in 2k Designs 390 7-4.1 Addition of Center Points 390 7-4.2 Blocking and Confounding 393 7-5 Fractional Replication of a 2k Design 398 7-5.1 One-Half Fraction of a 2k Design 398 7-5.2 Smaller Fractions: 2k-pFractional Factorial Designs 404 7-6 Response Surface Methods and Designs 414 7-6.1 Method of Steepest Ascent 416 7-6.2 Analysis of a Second-Order Response Surface 418 7-7 Factorial Experiments With More Than Two Levels 424 Chapter 8 Statistical Process Control 438 8-1 Quality Improvement and Statistical Process Control 439 8-2 Introduction to Control Charts 440 8-2.1 Basic Principles 440 8-2.2 Design of a Control Chart 444 8-2.3 Rational Subgroups 446 8-2.4 Analysis of Patterns on Control Charts 447 8-3 X̄ and R Control Charts 449 8-4 Control Charts For Individual Measurements 456 8-5 Process Capability 461 8-6 Attribute Control Charts 465 8-6.1 P Chart (Control Chart for Proportions) and nP Chart 465 8-6.2 U Chart (Control Chart for Average Number of Defects per Unit) and C Chart 467 8-7 Control Chart Performance 470 8-8 Measurement Systems Capability 473 Appendices 483 Appendix A Statistical Tables and Charts 485 Appendix B Bibliography 500 Appendix C* Answers to Selected Exercises 502 Index 511
£45.59
John Wiley & Sons Inc Mathematics for Physicists
Book SynopsisMathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses.Table of ContentsEditors’ preface to the Manchester Physics Series xi Authors’ preface xiii Notes and website information xv 1 Real numbers, variables and functions 1 1.1 Real numbers 1 1.1.1 Rules of arithmetic: rational and irrational numbers 1 1.1.2 Factors, powers and rationalisation 4 1.1.3 Number systems 6 1.2 Real variables 9 1.2.1 Rules of elementary algebra 9 1.2.2 Proof of the irrationality of 2 11 1.2.3 Formulas, identities and equations 11 1.2.4 The binomial theorem 13 1.2.5 Absolute values and inequalities 17 1.3 Functions, graphs and co-ordinates 20 1.3.1 Functions 20 1.3.2 Cartesian co-ordinates 23 Problems 1 28 2 Some basic functions and equations 31 2.1 Algebraic functions 31 2.1.1 Polynomials 31 2.1.2 Rational functions and partial fractions 37 2.1.3 Algebraic and transcendental functions 41 2.2 Trigonometric functions 41 2.2.1 Angles and polar co-ordinates 41 2.2.2 Sine and cosine 44 2.2.3 More trigonometric functions 46 2.2.4 Trigonometric identities and equations 48 2.2.5 Sine and cosine rules 51 2.3 Logarithms and exponentials 53 2.3.1 The laws of logarithms 54 2.3.2 Exponential function 56 2.3.3 Hyperbolic functions 60 2.4 Conic sections 63 Problems 2 68 3 Differential calculus 71 3.1 Limits and continuity 71 3.1.1 Limits 71 3.1.2 Continuity 75 3.2 Differentiation 77 3.2.1 Differentiability 78 3.2.2 Some standard derivatives 80 3.3 General methods 82 3.3.1 Product rule 83 3.3.2 Quotient rule 83 3.3.3 Reciprocal relation 84 3.3.4 Chain rule 86 3.3.5 More standard derivatives 87 3.3.6 Implicit functions 89 3.4 Higher derivatives and stationary points 90 3.4.1 Stationary points 92 3.5 Curve sketching 95 Problems 3 98 4 Integral calculus 101 4.1 Indefinite integrals 101 4.2 Definite integrals 104 4.2.1 Integrals and areas 105 4.2.2 Riemann integration 108 4.3 Change of variables and substitutions 111 4.3.1 Change of variables 111 4.3.2 Products of sines and cosines 113 4.3.3 Logarithmic integration 115 4.3.4 Partial fractions 116 4.3.5 More standard integrals 117 4.3.6 Tangent substitutions 118 4.3.7 Symmetric and antisymmetric integrals 119 4.4 Integration by parts 120 4.5 Numerical integration 123 4.6 Improper integrals 126 4.6.1 Infinite integrals 126 4.6.2 Singular integrals 129 4.7 Applications of integration 132 4.7.1 Work done by a varying force 132 4.7.2 The length of a curve 133 4.7.3 Surfaces and volumes of revolution 134 4.7.4 Moments of inertia 136 Problems 4 137 5 Series and expansions 143 5.1 Series 143 5.2 Convergence of infinite series 146 5.3 Taylor’s theorem and its applications 149 5.3.1 Taylor’s theorem 149 5.3.2 Small changes and l’Hˆopital’s rule 150 5.3.3 Newton’s method 152 5.3.4 Approximation errors: Euler’s number 153 5.4 Series expansions 153 5.4.1 Taylor and Maclaurin series 154 5.4.2 Operations with series 157 5.5 Proof of d’Alembert’s ratio test 161 5.5.1 Positive series 161 5.5.2 General series 162 5.6 Alternating and other series 163 Problems 5 165 6 Complex numbers and variables 169 6.1 Complex numbers 169 6.2 Complex plane: Argand diagrams 172 6.3 Complex variables and series 176 6.3.1 Proof of the ratio test for complex series 179 6.4 Euler’s formula 180 6.4.1 Powers and roots 182 6.4.2 Exponentials and logarithms 184 6.4.3 De Moivre’s theorem 185 6.4.4 Summation of series and evaluation of integrals 187 Problems 6 189 7 Partial differentiation 191 7.1 Partial derivatives 191 7.2 Differentials 193 7.2.1 Two standard results 195 7.2.2 Exact differentials 197 7.2.3 The chain rule 198 7.2.4 Homogeneous functions and Euler’s theorem 199 7.3 Change of variables 200 7.4 Taylor series 203 7.5 Stationary points 206 *7.6 Lagrange multipliers 209 7.7 Differentiation of integrals 211 Problems 7 214 8 Vectors 219 8.1 Scalars and vectors 219 8.1.1 Vector algebra 220 8.1.2 Components of vectors: Cartesian co-ordinates 221 8.2 Products of vectors 225 8.2.1 Scalar product 225 8.2.2 Vector product 228 8.2.3 Triple products 231 8.2.4 Reciprocal vectors 236 8.3 Applications to geometry 238 8.3.1 Straight lines 238 8.3.2 Planes 241 8.4 Differentiation and integration 243 Problems 8 246 9 Determinants, Vectors and Matrices 249 9.1 Determinants 249 9.1.1 General properties of determinants 253 9.1.2 Homogeneous linear equations 257 9.2 Vectors in n Dimensions 260 9.2.1 Basis vectors 261 9.2.2 Scalar products 263 9.3 Matrices and linear transformations 265 9.3.1 Matrices 265 9.3.2 Linear transformations 270 9.3.3 Transpose, complex, and Hermitian conjugates 273 9.4 Square Matrices 274 9.4.1 Some special square matrices 274 9.4.2 The determinant of a matrix 276 9.4.3 Matrix inversion 278 9.4.4 Inhomogeneous simultaneous linear equations 282 Problems 9 284 10 Eigenvalues and eigenvectors 291 10.1 The eigenvalue equation 291 10.1.1 Properties of eigenvalues 293 10.1.2 Properties of eigenvectors 296 10.1.3 Hermitian matrices 299 10.2 Diagonalisation of matrices 302 10.2.1 Normal modes of oscillation 305 10.2.2 Quadratic forms 308 Problems 10 312 11 Line and multiple integrals 315 11.1 Line integrals 315 11.1.1 Line integrals in a plane 315 11.1.2 Integrals around closed contours and along arcs 319 11.1.3 Line integrals in three dimensions 321 11.2 Double integrals 323 11.2.1 Green’s theorem in the plane and perfect differentials 326 11.2.2 Other co-ordinate systems and change of variables 330 11.3 Curvilinear co-ordinates in three dimensions 333 11.3.1 Cylindrical and spherical polar co-ordinates 334 11.4 Triple or volume integrals 337 11.4.1 Change of variables 338 Problems 11 340 12 Vector calculus 345 12.1 Scalar and vector fields 345 12.1.1 Gradient of a scalar field 346 12.1.2 Div, grad and curl 349 12.1.3 Orthogonal curvilinear co-ordinates 352 12.2 Line, surface, and volume integrals 355 12.2.1 Line integrals 355 12.2.2 Conservative fields and potentials 359 12.2.3 Surface integrals 362 12.2.4 Volume integrals: moments of inertia 367 12.3 The divergence theorem 368 12.3.1 Proof of the divergence theorem and Green’s identities 369 12.3.2 Divergence in orthogonal curvilinear co-ordinates 372 12.3.3 Poisson’s equation and Gauss’ theorem 373 12.3.4 The continuity equation 376 12.4 Stokes’ theorem 377 12.4.1 Proof of Stokes’ theorem 378 12.4.2 Curl in curvilinear co-ordinates 380 12.4.3 Applications to electromagnetic fields 381 Problems 12 384 13 Fourier analysis 389 13.1 Fourier series 389 13.1.1 Fourier coefficients 390 13.1.2 Convergence 394 13.1.3 Change of period 398 13.1.4 Non-periodic functions 399 13.1.5 Integration and differentiation of Fourier series 401 13.1.6 Mean values and Parseval’s theorem 405 13.2 Complex Fourier series 407 13.2.1 Fourier expansions and vector spaces 409 13.3 Fourier transforms 410 13.3.1 Properties of Fourier transforms 414 13.3.2 The Dirac delta function 419 13.3.3 The convolution theorem 423 Problems 13 426 14 Ordinary differential equations 431 14.1 First-order equations 433 14.1.1 Direct integration 433 14.1.2 Separation of variables 434 14.1.3 Homogeneous equations 435 14.1.4 Exact equations 438 14.1.5 First-order linear equations 440 14.2 Linear ODEs with constant coefficients 441 14.2.1 Complementary functions 442 14.2.2 Particular integrals: method of undetermined coefficients 446 14.2.3 Particular integrals: the D-operator method 448 14.2.4 Laplace transforms 453 14.3 Euler’s equation 459 Problems 14 461 15 Series solutions of ordinary differential equations 465 15.1 Series solutions 465 15.1.1 Series solutions about a regular point 467 15.1.2 Series solutions about a regular singularity: Frobenius method 469 15.1.3 Polynomial solutions 475 15.2 Eigenvalue equations 478 15.3 Legendre’s equation 481 15.3.1 Legendre functions and Legendre polynomials 482 15.3.2 The generating function 487 15.3.3 Associated Legendre equation 490 15.3.4 Rodrigues’ formula 492 15.4 Bessel’s equation 494 15.4.1 Bessel functions 495 15.4.2 Properties of non-singular Bessel functions Jν (x) 499 Problems 15 502 16 Partial differential equations 507 16.1 Some important PDEs in physics 510 16.2 Separation of variables: Cartesian co-ordinates 511 16.2.1 The wave equation in one spatial dimension 512 16.2.2 The wave equation in three spatial dimensions 515 16.2.3 The diffusion equation in one spatial dimension 518 16.3 Separation of variables: polar co-ordinates 520 16.3.1 Plane-polar co-ordinates 520 16.3.2 Spherical polar co-ordinates 524 16.3.3 Cylindrical polar co-ordinates 529 16.4 The wave equation: d’Alembert’s solution 532 16.5 Euler equations 535 16.6 Boundary conditions and uniqueness 538 16.6.1 Laplace transforms 540 Problems 16 544 Answers to selected problems 549 Index 559
£42.70
John Wiley & Sons Inc Reinsurance
Book SynopsisWhile the literature on reinsurance is vast, there is currently no comprehensive treatment of the major actuarial and financial aspects of the subject. Many publications deal with specific aspects of the theory without putting them into a proper perspective. Reinsurance: Actuarial and Statistical Aspects treats the topic differently.Table of ContentsPreface ix 1 Introduction 1 1.1 What is Reinsurance? 1 1.2 Why Reinsurance? 2 1.3 Reinsurance Data 4 1.3.1 Case Study I: Motor Liability Data 5 1.3.2 Case Study II: Dutch Fire Insurance Data 10 1.3.3 Case Study III: Austrian Storm Claim Data 10 1.3.4 Case Study IV: European Flood Risk Data 11 1.3.5 Case Study V: Groningen Earthquakes 12 1.3.6 Case Study VI: Danish Fire Insurance Data 12 1.4 Notes and Bibliography 16 2 Reinsurance Forms and their Properties 19 2.1 Quota-share Reinsurance 19 2.1.1 Some Practical Considerations 20 2.2 Surplus Reinsurance 21 2.3 Excess-of-loss Reinsurance 24 2.3.1 Moment Calculations 25 2.3.2 Reinstatements 27 2.3.3 Further Practical Considerations 29 2.4 Stop-loss Reinsurance 30 2.5 Large Claim Reinsurance 31 2.6 Combinations of Reinsurance Forms and Global Protections 32 2.7 Facultative Contracts 33 2.8 Notes and Bibliography 33 3 Models for Claim Sizes 35 3.1 Tails of Distributions 35 3.2 Large Claims 36 3.3 Common Claim Size Distributions 40 3.3.1 Light-tailed Models 41 3.3.2 Heavy-tailed Models 44 3.4 Mean Excess Analysis 49 3.5 Full Models: Splicing 50 3.6 Multivariate Modelling of Large Claims 52 4 Statistics for Claim Sizes 59 4.1 Heavy or Light Tails: QQ- and Derivative Plots 60 4.2 Large Claims Modelling through Extreme Value Analysis EVA for Pareto-type Tails 63 4.2.1 EVA for Pareto-type Tails 63 4.2.2 General Tail Modelling using EVA 82 4.2.3 EVA under Upper-truncation 91 4.3 Global Fits: Splicing, Upper-truncation and Interval Censoring 97 4.3.1 Tail-mixed Erlang Splicing 97 4.3.2 Tail-mixed Erlang Splicing under Censoring and Upper-truncation 99 4.4 Incorporating Covariate Information 114 4.4.1 Pareto-type Modelling 114 4.4.2 Generalized Pareto Modelling 116 4.4.3 Regression Extremes with Censored Data 119 4.5 Multivariate Analysis of Claim Distributions 123 4.5.1 The Multivariate POT Approach 124 4.5.2 Multivariate Mixtures of Erlangs 125 4.6 Estimation of Other Tail Characteristics 128 4.7 Further Case Studies 132 4.8 Notes and Bibliography 137 5 Models for Claim Counts 139 5.1 General Treatment 139 5.1.1 Main Properties of the Claim Number Process 140 5.2 The Poisson Process and its Extensions 141 5.2.1 The Homogeneous Poisson Process 141 5.2.2 Inhomogeneous Poisson Processes 143 5.2.3 Mixed Poisson Processes 144 5.2.4 Doubly Stochastic Poisson Processes 149 5.3 Other Claim Number Processes 157 5.3.1 The Nearly Mixed Poisson Model 157 5.3.2 Infinitely Divisible Processes 158 5.3.3 The Renewal Model 160 5.3.4 Markov Models 161 5.4 Discrete Claim Counts 161 5.5 Statistics of Claim Counts 164 5.5.1 Modelling Yearly Claim Counts 164 5.5.2 Modelling the Claim Arrival Process 172 5.6 Claim Numbers under Reinsurance 183 5.6.1 Number of Claims under Excess-loss Reinsurance 183 5.7Notes and Bibliography 187 6 Total Claim Amount 189 6.1 General Formulas for Aggregating Independent Risks 189 6.2 Classical Approximations for the Total Claim Size 191 6.2.1 Approximations based on the First Few Moments 191 6.2.2 Asymptotic Approximations for Light-tailed Claims 193 6.2.3 Asymptotic Approximations for Heavy-tailed Claims 198 6.3 Panjer Recursion 199 6.4 Fast Fourier Transform 200 6.5 Total Claim Amount under Reinsurance 201 6.5.1 Proportional Reinsurance 201 6.5.2 Excess-loss Reinsurance 202 6.5.3 Stop-loss Reinsurance 204 6.6 Numerical Illustrations 206 6.7 Aggregation for Dependent Risks 208 6.8 Notes and Bibliography 212 7 Reinsurance Pricing 217 7.1 Classical Principles of Premium Calculation 219 7.2 Solvency Considerations 219 7.2.1 The Ruin Probability 223 7.2.2 One-year Time Horizon and Cost of Capital 226 7.3 Pricing Proportional Reinsurance 228 7.4 Pricing Non-proportional Reinsurance 229 7.4.1 Exposure Rating 229 7.4.2 Experience Rating 232 7.4.3 Aggregate Pure Premium 234 7.5 The Aggregate Risk Margin 235 7.6 Leading and Following Reinsurers 237 7.7 Notes and Bibliography 238 8 Choice of Reinsurance 241 8.1 Decision Criteria 243 8.2 Classical Optimality Results 245 8.2.1 Pareto-optimal Risk Sharing 245 8.2.2 Stochastic Ordering 247 8.2.3 Minimizing Retained Variance 248 8.2.4 Maximizing Expected Utility 251 8.2.5 Minimizing the Ruin Probability 253 8.2.6 Combining Reinsurance Treaties over Subportfolios 8.3 Solvency Constraints and Cost of Capital 259 8.4 Minimizing Other Risk Measures 261 8.5 Combining Reinsurance Treaties 262 8.6 Reinsurance Chains 263 8.7 Dynamic Reinsurance 264 8.8 Beyond Piecewise Linear Contracts 266 8.9 Notes and Bibliography 268 9 Simulation 273 9.1 The Monte Carlo Method 273 9.2 Variance Reduction Techniques 276 9.2.1 Conditional Monte Carlo 277 9.2.2 Importance Sampling 277 9.3 Quasi-Monte Carlo Techniques 283 9.4 Notes and Bibliography 288 10 Further Topics 291 10.1 More on Large Claim Reinsurance 291 10.1.1 The Ordered Claims 291 10.1.2 Large Claim Reinsurance 296 10.1.3 ECOMOR 298 10.2 Alternative Risk Transfer 300 10.2.1 Notes and Bibliography 304 10.3 Reinsurance and Finance 305 10.4 Catastrophic Risk 306 References 309 Index 347
£63.86
John Wiley & Sons Inc More Rapid Math Tricks and Tips
Book SynopsisMath skills you can count on! In this eagerly awaited sequel to the popular Rapid Math Tricks and Tips, Professor Ed Julius shows you how to master difficult problems in addition, subtraction, multiplication, and division quickly, easily?and without a calculator.Table of ContentsPartial table of contents: MORE BASIC RAPID MATH TRICKS. Multiplying with Little or No Carrying. Subtracting Without Borrowing. Adding Pluses and Minuses. Multiplying with Factors. Multiplying by 6. Adding by Multiplying. MORE INTERMEDIATE RAPID MATH TRICKS. Dividing by Showing Little or No Work. Dividing by Regrouping I. Multiplying by 12. Subtracting by Oversubtracting. MORE ADVANCED RAPID MATH TRICKS. Multiplying with Numbers 11 Through 19. Squaring Any Number Ending in 2 or 8. Squaring Any Number Ending in 6. Squaring Numbers Between 90 and 100. MORE UNUSUAL RAPID MATH TRICKS. Multiplying Consecutive Numbers Ending in 5. Multiplying by Fractions. Multiplying by 999. Checking Addition and Subtraction. Conclusion. Appendices. Solutions. Summary of the 54 Number-Mastery Tricks for Handy Reference.
£14.39
John Wiley & Sons Inc A First Course in Stochastic Models
Book SynopsisAn integrated presentation of theory, applications and algorithms that demonstrates how useful simple stochastic (random) models can be for gaining insight into the behaviour of complex stochastic systems. The methods described can be used to obtain solutions to problems in statistics, operations research, finance, economics and engineering.Trade Review"…successfully combined theory and real world examples into a systematic introduction...an excellent reference for the applied statistician who deals in various queuing models." (Technometrics, August 2005) “…clear and straightforward…plenty of worked (or orientated) examples as well as a substantial set of exercises…” (Short Book Reviews, August 2004)Table of ContentsPreface ix 1 The Poisson Process and Related Processes 1 1.0 Introduction 1 1.1 The Poisson Process 1 1.1.1 The Memoryless Property 2 1.1.2 Merging and Splitting of Poisson Processes 6 1.1.3 The M/G/∞ Queue 9 1.1.4 The Poisson Process and the Uniform Distribution 15 1.2 Compound Poisson Processes 18 1.3 Non-Stationary Poisson Processes 22 1.4 Markov Modulated Batch Poisson Processes 24 Exercises 28 Bibliographic Notes 32 References 32 2 Renewal-Reward Processes 33 2.0 Introduction 33 2.1 Renewal Theory 34 2.1.1 The Renewal Function 35 2.1.2 The Excess Variable 37 2.2 Renewal-Reward Processes 39 2.3 The Formula of Little 50 2.4 Poisson Arrivals See Time Averages 53 2.5 The Pollaczek–Khintchine Formula 58 2.6 A Controlled Queue with Removable Server 66 2.7 An Up- And Downcrossing Technique 69 Exercises 71 Bibliographic Notes 78 References 78 3 Discrete-Time Markov Chains 81 3.0 Introduction 81 3.1 The Model 82 3.2 Transient Analysis 87 3.2.1 Absorbing States 89 3.2.2 Mean First-Passage Times 92 3.2.3 Transient and Recurrent States 93 3.3 The Equilibrium Probabilities 96 3.3.1 Preliminaries 96 3.3.2 The Equilibrium Equations 98 3.3.3 The Long-run Average Reward per Time Unit 103 3.4 Computation of the Equilibrium Probabilities 106 3.4.1 Methods for a Finite-State Markov Chain 107 3.4.2 Geometric Tail Approach for an Infinite State Space 111 3.4.3 Metropolis—Hastings Algorithm 116 3.5 Theoretical Considerations 119 3.5.1 State Classification 119 3.5.2 Ergodic Theorems 126 Exercises 134 Bibliographic Notes 139 References 139 4 Continuous-Time Markov Chains 141 4.0 Introduction 141 4.1 The Model 142 4.2 The Flow Rate Equation Method 147 4.3 Ergodic Theorems 154 4.4 Markov Processes on a Semi-Infinite Strip 157 4.5 Transient State Probabilities 162 4.5.1 The Method of Linear Differential Equations 163 4.5.2 The Uniformization Method 166 4.5.3 First Passage Time Probabilities 170 4.6 Transient Distribution of Cumulative Rewards 172 4.6.1 Transient Distribution of Cumulative Sojourn Times 173 4.6.2 Transient Reward Distribution for the General Case 176 Exercises 179 Bibliographic Notes 185 References 185 5 Markov Chains and Queues 187 5.0 Introduction 187 5.1 The Erlang Delay Model 187 5.1.1 The M/M/1 Queue 188 5.1.2 The M/M/c Queue 190 5.1.3 The Output Process and Time Reversibility 192 5.2 Loss Models 194 5.2.1 The Erlang Loss Model 194 5.2.2 The Engset Model 196 5.3 Service-System Design 198 5.4 Insensitivity 202 5.4.1 A Closed Two-node Network with Blocking 203 5.4.2 The M/G/1 Queue with Processor Sharing 208 5.5 A Phase Method 209 5.6 Queueing Networks 214 5.6.1 Open Network Model 215 5.6.2 Closed Network Model 219 Exercises 224 Bibliographic Notes 230 References 231 6 Discrete-Time Markov Decision Processes 233 6.0 Introduction 233 6.1 The Model 234 6.2 The Policy-Improvement Idea 237 6.3 The Relative Value Function 243 6.4 Policy-Iteration Algorithm 247 6.5 Linear Programming Approach 252 6.6 Value-Iteration Algorithm 259 6.7 Convergence Proofs 267 Exercises 272 Bibliographic Notes 275 References 276 7 Semi-Markov Decision Processes 279 7.0 Introduction 279 7.1 The Semi-Markov Decision Model 280 7.2 Algorithms for an Optimal Policy 284 7.3 Value Iteration and Fictitious Decisions 287 7.4 Optimization of Queues 290 7.5 One-Step Policy Improvement 295 Exercises 300 Bibliographic Notes 304 References 305 8 Advanced Renewal Theory 307 8.0 Introduction 307 8.1 The Renewal Function 307 8.1.1 The Renewal Equation 308 8.1.2 Computation of the Renewal Function 310 8.2 Asymptotic Expansions 313 8.3 Alternating Renewal Processes 321 8.4 Ruin Probabilities 326 Exercises 334 Bibliographic Notes 337 References 338 9 Algorithmic Analysis of Queueing Models 339 9.0 Introduction 339 9.1 Basic Concepts 341 9.2 The M/G/1 Queue 345 9.2.1 The State Probabilities 346 9.2.2 The Waiting-Time Probabilities 349 9.2.3 Busy Period Analysis 353 9.2.4 Work in System 358 9.3 The MX/G/1 Queue 360 9.3.1 The State Probabilities 361 9.3.2 The Waiting-Time Probabilities 363 9.4 M/G/1 Queues with Bounded Waiting Times 366 9.4.1 The Finite-Buffer M/G/1 Queue 366 9.4.2 An M/G/1 Queue with Impatient Customers 369 9.5 The GI/G/1 Queue 371 9.5.1 Generalized Erlangian Services 371 9.5.2 Coxian-2 Services 372 9.5.3 The GI /P h/1 Queue 373 9.5.4 The Ph/G/1 Queue 374 9.5.5 Two-moment Approximations 375 9.6 Multi-Server Queues with Poisson Input 377 9.6.1 The M/D/c Queue 378 9.6.2 The M/G/c Queue 384 9.6.3 The MX/G/c Queue 392 9.7 The GI/G/c Queue 398 9.7.1 The GI/M/c Queue 400 9.7.2 The GI/D/c Queue 406 9.8 Finite-Capacity Queues 408 9.8.1 The M/G/c/c + N Queue 408 9.8.2 A Basic Relation for the Rejection Probability 410 9.8.3 The MX/G/c/c + N Queue with Batch Arrivals 413 9.8.4 Discrete-Time Queueing Systems 417 Exercises 420 Bibliographic Notes 428 References 428 Appendices 431 Appendix A. Useful Tools in Applied Probability 431 Appendix B. Useful Probability Distributions 440 Appendix C. Generating Functions 449 Appendix D. The Discrete Fast Fourier Transform 455 Appendix E. Laplace Transform Theory 458 Appendix F. Numerical Laplace Inversion 462 Appendix G. The Root-Finding Problem 470 References 474 Index 475
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John Wiley & Sons Inc Rapid Math Tricks Tips
Book SynopsisDemonstrates a slew of time-saving tips and tricks for performing common math calculations. Contains sample problems for each trick, leading the reader through step-by-step. Features two mid-terms and a final exam to test your progress plus hundreds of exercise problems ranging from simple to more sophisticated.Table of ContentsIntroduction 1 Week 1: Multiplication and Division I 13 Week 2: Multiplication and Division II 55 Week 3: Addition and Subtraction 99 Week 4: Conversion Tricks and Estimation 141 Days 29 and 30: Grand Finale 183 Pre-Test Revisited 192 Final Exam 192 In Conclusion 195 Solutions 197 Summary of the 60 Number-Power Tricks for Handy Reference 227
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John Wiley & Sons Inc Markov Decision Processes
Book SynopsisThis book is an up-to-date, unified and rigorous treatment of theoretical, computational and applied research on Markov decision process models. The concentration of the book is on infinite-horizon discrete-time models, and it also discusses arbitrary state spaces, finite-horizon and continuous-time discrete-state models.Table of ContentsPreface. 1. Introduction. 2. Model Formulation. 3. Examples. 4. Finite-Horizon Markov Decision Processes. 5. Infinite-Horizon Models: Foundations. 6. Discounted Markov Decision Problems. 7. The Expected Total-Reward. Criterion. 8. Average Reward and Related Criteria. 9. The Average Reward Criterion-Multichain and Communicating Models. 10. Sensitive Discount Optimality. 11. Continuous-Time Models. Afterword. Notation. Appendix A. Markov Chains. Appendix B. Semicontinuous Functions. Appendix C. Normed Linear Spaces. Appendix D. Linear Programming. Bibliography. Index.
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John Wiley & Sons Inc Linear Algebra and Its Applications
Book SynopsisThis set featuresLinear Algebra and Its Applications, Second Edition (978-0-471-75156-4)Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book''s accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems.Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces.Further updates and revisions have been iTrade Review"...an informative and useful book, distinguished by its blend of theory and applications, which fulfills its goals admirably." (MAA Review March 2008)Table of ContentsPreface. Preface to the First Edition. 1. Fundamentals. 2. Duality. 3. Linear Mappings. 4. Matrices. 5. Determinant and Trace. 6. Spectral Theory. 7. Euclidean Structure. 8. Spectral Theory of Self-Adjoint Mappings. 9. Calculus of Vector- and Matrix-Valued Functions. 10. Matrix Inequalities. 11. Kinematics and Dynamics. 12. Convexity. 13. The Duality Theorem. 14. Normed Linear Spaces. 15. Linear Mappings Between Normed Linear Spaces. 16. Positive Matrices. 17. How to Solve Systems of Linear Equations. 18. How to Calculate the Eigenvalues of Self-Adjoint Matrices. 19. Solutions. Bibliography. Appendix 1. Special Determinants. Appendix 2. The Pfaffian. Appendix 3. Symplectic Matrices. Appendix 4. Tensor Product. Appendix 5. Lattices. Appendix 6. Fast Matrix Multiplication. Appendix 7. Gershgorin's Theorem. Appendix 8. The Multiplicity of Eigenvalues. Appendix 9. The Fast Fourier Transform. Appendix 10. The Spectral Radius. Appendix 11. The Lorentz Group. Appendix 12. Compactness of the Unit Ball. Appendix 13. A Characterization of Commutators. Appendix 14. Liapunov's Theorem. Appendix 15. The Jordan Canonical Form. Appendix 16. Numerical Range. Index.
£75.56
Dover Publications Inc. Geometry Relativity and the Fourth Dimension
Book SynopsisExposition of 4th dimension, concepts of relativity as Flatland characters continue adventures. Popular, easily followed yet accurate, profound. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Accessible to lay readers but also of interest to specialists. Includes 141 illustrations.
£9.49
Dover Publications Inc. Famous Problems in Geometry and How to Solve Them
Book SynopsisDelve into the development of modern mathematics and match wits with Euclid, Newton, Descartes, and others. Each chapter explores an individual type of challenge, with commentary and practice problems. Solutions.
£10.44
Dover Publications Inc. Williams J Compleat Strategyst
Book SynopsisThis entertaining text is essential for anyone interested in game theory. Only a basic understanding of arithmetic is needed to grasp the necessary aspects of strategy games for two, three, four, and more players that feature two or more sets of inimical interests and a limitless array of zero-sum payoffs.
£13.49
Dover Publications Inc. The Works of Archimedes
Book SynopsisComplete works of ancient geometer in highly accessible translation by distinguished scholar. Topics include the famous problems of the ratio of the areas of a cylinder and an inscribed sphere; the measurement of a circle; the properties of conoids, spheroids, and spirals; and the quadrature of the parabola. Informative introduction and 52-page supplement.
£23.59
Dover Publications Inc. Functions and Graphs
Book SynopsisThe second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book''s margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple functions to analyze the fundamental methods of constructing graphs. The second half deals with more complicated and refined questions concerning linear functions, quadratic trinomials, linear fractional functions, power functions, and rational functions.
£10.77
Dover Publications Inc. Counterexamples in Analysis
Book SynopsisThese counterexamples deal mostly with the part of analysis known as real variables. The 1st half of the book discusses the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, more. The 2nd half examines functions of 2 variables, plane sets, area, metric and topological spaces, and function spaces. 1962 edition. Includes 12 figures.
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Dover Publications Inc. Elementary Number Theory
Book SynopsisMinimal prerequisites make this text ideal for a first course in number theory. Written in a lively, engaging style by the author of popular mathematics books, it features nearly 1,000 imaginative exercises and problems. Solutions to many of the problems are included, and a teacher''s guide is available. 1978 edition.
£13.04
Dover Publications Inc. An Introduction to Mathematical Logic
Book SynopsisComprehensive overview, suitable for advanced undergraduates and graduate students, covers propositional logic; first-order languages and logic; incompleteness, undecidability, and indefinability; recursive functions; computability; and Hilbert's Tenth Problem. 1995 edition.
£30.39
Dover Publications Inc. Introduction to NonEuclidean Geometry
Book SynopsisOne of the first college-level texts for elementary courses in non-Euclidean geometry, this volumeis geared toward students familiar with calculus. Topics include the fifth postulate, hyperbolicplane geometry and trigonometry, and elliptic plane geometry and trigonometry. Extensiveappendixes offer background information on Euclidean geometry, and numerous exercisesappear throughout the text.Reprint of the Holt, Rinehart & Winston, Inc., New York, 1945 edition
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Dover Publications Inc. Partial Differential Equations for Scientists and
Book SynopsisThis highly useful text for students and professionals working in the applied sciences shows how to formulate and solve partial differential equations. Realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems and numerical and approximate methods. Suggestions for further reading. Solution guide available upon request. 1982 edition.
£15.19
Dover Publications Inc. Croom F Principles of Topology
Book SynopsisDesigned for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students who have studied multivariate calculus. Topics include metric spaces, general topological spaces, continuity, topological equivalence, basis and subbasis, connectedness and compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces.
£18.69
Cengage Learning, Inc Student Solutions Manual for
Book SynopsisPrepare for exams and succeed in your mathematics course with this comprehensive solutions manual! Featuring worked out-solutions to the problems in MATHEMATICAL STATISTICS WITH APPLICATIONS, 7th Edition, this manual shows you how to approach and solve problems using the same step-by-step explanations found in your textbook examples.
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Cambridge University Press Results and Problems in Combinatorial Geometry
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Cambridge University Press Statistical Prediction Analysis
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Cambridge University Press Probability with Martingales Cambridge
Book SynopsisThis key book is a rigorous account which has Doob's theory of martingales in discrete time as its main theme. A distinguishing feature of this study is its determination to keep the probability flowing at a nice tempo. It achieves this by being selective rather than encyclopaedic, presenting only what is essential to understand the fundamentals.Trade Review'… one of the best introductions to Martingale theory.' Monatshefte für MathematikTable of Contents1. A branching-process example; Part I. Foundations: 2. Measure spaces; 3. Events; 4. Random variables; 5. Independence; 6. Integration; 7. Expectation; 8. An easy strong law: product measure; Part II. Martingale Theory: 9. Conditional expectation; 10. Martingales; 11. The convergence theorem; 12. Martingales bounded in L2; 13. Uniform integrability; 14. UI martingales; 15. Applications; Part III. Characteristic Functions: 16. Basic properties of CFs; 17. Weak convergence; 18. The central limit theorem; Appendices; Exercises.
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Cambridge University Press Geometry and Topology
Book SynopsisGeometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the MÃbius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups,having applications to relativity theory and quantum mechTrade ReviewA welcome addition to the undergraduate library. Highly recommended. --ChoiceTable of ContentsIntroduction; 1. Euclidean geometry; 2. Composing maps; 3. Non-Euclidean; 4. Affine geometry; 5. Projective geometry; 6. Geometry and group theory; 7. Topology; 8. Geometry of transformation groups; 9. Concluding remarks; A. Metrics; B. Linear algebra; References; Index.
£49.39
Cambridge University Press Intro Mathemat Physiology Biol 2ed 16 Cambridge Studies in Mathematical Biology Series Number 16
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£42.74
Cambridge University Press An Introduction to KTheory for CAlgebras 49
Book SynopsisOver the last 25 years K-theory has become an integrated part of the study of C*-algebras. This book gives an elementary introduction to this interesting and rapidly growing area of mathematics. Fundamental to K-theory is the association of a pair of Abelian groups, K0(A) and K1(A), to each C*-algebra A. These groups reflect the properties of A in many ways. This book covers the basic properties of the functors K0 and K1 and their interrelationship. Applications of the theory include Elliott's classification theorem for AF-algebras, and it is shown that each pair of countable Abelian groups arises as the K-groups of some C*-algebra. The theory is well illustrated with 120 exercises and examples, making the book ideal for beginning graduate students working in functional analysis, especially operator algebras, and for researchers from other areas of mathematics who want to learn about this subject.Trade Review'The textbook is a nice introduction to the subject preparing the ground for the study of more advanced texts.' H. Schröder, Zentralblatt für MathematikTable of ContentsPreface; 1. C*-algebra theory; 2. Projections and unitary elements; 3. The K0-group of a unital C*-algebra; 4. The functor K0; 5. The ordered Abelian group K0(A); 6. Inductive limit C*-algebras; 7. Classification of AF-algebras; 8. The functor K1; 9. The index map; 10. The higher K-functors; 11. Bott periodicity; 12. The six-term exact sequence; 13. Inductive limits of dimension drop algebras; References; Table of K-groups; Index of symbols; General index.
£41.79
Cambridge University Press Automorphic Forms and LFunctions for the Group GLnR 99 Cambridge Studies in Advanced Mathematics Series Number 99
Book SynopsisL-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.Trade Review'… a gentle introduction to this fascinating new subject. The presentation is very explicit and many examples are worked out with great detail … This book should be of great interest to students beginning with the theory of modular forms or for more advanced readers wanting to know about general L-functions.' Emmanuel P. Royer, Mathematical Reviews'This book, whose clear and sometimes simplified proofs make the basic theory of automorphic forms on GL(n) accessible to a wide audience, will be valuable for students. It nicely complements D. Bump's book (Automorphic Forms and Representations, Cambridge, 1997), which offers a greater emphasis on representation theory and a different selection of topics.' Zentralblatt MATH'Unfortunately, when n > 2 the GL(n) theory is not very accessible to the student of analytic number theory, yet it is increasing in importance. [This book] addresses this problem by developing a large part of the theory in a way that is carefully designed to make the field accessible … much of the literature is written in the adele language, and seeing how it translates into classical terms is both useful and enlightening … This is a unique and very welcome book, one that the student of automorphic forms will want to study, and also useful to experts.' Daniel Bump, SIAM ReviewTable of ContentsIntroduction; 1. Discrete group actions; 2. Invariant differential operators; 3. Automorphic forms and L-functions for SL(2,Z); 4. Existence of Maass forms; 5. Maass forms and Whittaker functions for SL(n,Z); 6. Automorphic forms and L-functions for SL(3,Z); 7. The Gelbert–Jacquet lift; 8. Bounds for L-functions and Siegel zeros; 9. The Godement–Jacquet L-function; 10. Langlands Eisenstein series; 11. Poincaré series and Kloosterman sums; 12. Rankin–Selberg convolutions; 13. Langlands conjectures; Appendix. The GL(n)pack manual; References.
£99.75
Cambridge University Press Numerical Recipes
Book SynopsisThe essential text and reference for modern scientific computing now also covers computational geometry, classification and inference, and much more.Trade Review'This monumental and classic work is beautifully produced and of literary as well as mathematical quality. It is an essential component of any serious scientific or engineering library.' Computing Reviews'… an instant 'classic,' a book that should be purchased and read by anyone who uses numerical methods …' American Journal of Physics'… replete with the standard spectrum of mathematically pretreated and coded/numerical routines for linear equations, matrices and arrays, curves, splines, polynomials, functions, roots, series, integrals, eigenvectors, FFT and other transforms, distributions, statistics, and on to ODE's and PDE's … delightful.' Physics in Canada'… if you were to have only a single book on numerical methods, this is the one I would recommend.' EEE Computational Science & Engineering'This encyclopedic book should be read (or at least owned) not only by those who must roll their own numerical methods, but by all who must use prepackaged programs.' New Scientist'These books are a must for anyone doing scientific computing.' Journal of the American Chemical Society'The authors are to be congratulated for providing the scientific community with a valuable resource.' The Scientist'I think this is an incredibly valuable book for both learning and reference and I recommend it for any scientists or student in a numerate discipline who need to understand and/or program numerical algorithms.' International Association for Pattern Recognition'The attractive style of the text and the availability of the codes ensured the popularity of the previous editions and also recommended this recent volume to different categories of readers, more or less experienced in numerical computation.' Octavian Pastravanu, Zentralblatt MATHTable of Contents1. Preliminaries; 2. Solution of linear algebraic equations; 3. Interpolation and extrapolation; 4. Integration of functions; 5. Evaluation of functions; 6. Special functions; 7. Random numbers; 8. Sorting and selection; 9. Root finding and nonlinear sets of equations; 10. Minimization or maximization of functions; 11. Eigensystems; 12. Fast Fourier transform; 13. Fourier and spectral applications; 14. Statistical description of data; 15. Modeling of data; 16. Classification and inference; 17. Integration of ordinary differential equations; 18. Two point boundary value problems; 19. Integral equations and inverse theory; 20. Partial differential equations; 21. Computational geometry; 22. Less-numerical algorithms; References.
£94.99
Cambridge University Press Trigonometric Series Volumes I II Combines 12 Cambridge Mathematical Library
Book SynopsisProfessor Zygmund's Trigonometric Series, first published in Warsaw in 1935, established itself as a classic. It presented a concise account of the main results then known, but was on a scale which limited the amount of detailed discussion possible. A greatly enlarged second edition published by Cambridge in two volumes in 1959 took full account of developments in trigonometric series, Fourier series and related branches of pure mathematics since the publication of the original edition. The two volumes are here bound together with a foreword from Robert Fefferman outlining the significance of this text. Volume I, containing the completely rewritten material of the original work, deals with trigonometric series and Fourier series. Volume II provides much material previously unpublished in book form.Trade Review'... much material previously unpublished in book form.' Zentralblatt MATHTable of ContentsPart I: 1. Trigonometric series and Fourier series, auxilliary results; 2. Fourier coefficients, elementary theorems on the convergence of S[f] and \tilde{S}[f]; 3. Summability of Fourier series; 4. Classes of functions and Fourier series; 5. Special trigonometric series; 6. The absolute convergence of trigonometric series; 7. Complex methods in Fourier series; 8. Divergence of Fourier series; 9. Riemann's theory of trigonometric series; Part II: 10. Trigonometric interpolation; 11. Differentiation of series, generalised derivatives; 12. Interpolation of linear operations, more about Fourier coefficients; 13. Convergence and summability almost everywhere; 14. More about complex methods; 15. Applications of the Littlewood-Paley function to Fourier series; 16. Fourier integrals; 17. A topic in multiple Fourier series.
£89.29
Princeton University Press The Princeton Companion to Mathematics
Book SynopsisPresents two hundred entries that introduce basic mathematical tools and vocabulary. This title traces the development of modern mathematics. It explains essential terms and concepts; examines core ideas in major areas of mathematics; and describes the achievements of scores of famous mathematicians.Trade ReviewWinner of the 2011 Euler Book Prize, Mathematical Association of America Honorable Mention for the 2008 PROSE Award for Single Volume Reference/Science, Association of American Publishers One of Choice's Outstanding Academic Titles for 2009 "The Princeton Companion to Mathematics makes a heroic attempt to keep [abstract concepts] to a minimum ... and conveys the breadth, depth and diversity of mathematics. It is impressive and well written and it's good value for [the] money."--Ian Stewart, The Times "This is a panoramic view of modern mathematics. It is tough going in some places, but much of it is surprisingly accessible. A must for budding number-crunchers."--The Economist (Best Books of 2008) "Although the editors' original goal of text that could be understood by anyone with a good background in high school mathematics provided short-lived, this wide-ranging account should reward undergraduate and graduate students and anyone curious about math as well as help research mathematicians understand the work of their colleagues in other specialties. The editors note some advantages a carefully organized printed reference may enjoy over a collection of Web pages, and this impressive volume supports their claim."--Science "This impressive book represents an extremely ambitious and, I might add, highly successful attempt by Timothy Gowers and his coeditors, June Barrow-Green and Imre Leader, to give a current account of the subject of mathematics. It has something for nearly everyone, from beginning students of mathematics who would like to get some sense of what the subject is all about, all the way to professional mathematicians who would like to get a better idea of what their colleagues are doing... If I had to choose just one book in the world to give an interested reader some idea of the scope, goals and achievements of modern mathematics, without a doubt this would be the one. So try it. I guarantee you'll like it!"--American Scientist "Accessible, technically precise and thorough account of all math's major aspects. Students of math will find this book a helpful reference for understanding their classes; students of everything else will find helpful guides to understanding how math describes it all."--Tom Siegfried, Science News "Once in a while a book comes along that should be on every mathematician's bookshelf. This is such a book. Described as a 'companion', this 1000-page tome is an authoritative and informative reference work that is also highly pleasurable to dip into. Much of it can be read with benefit by undergraduate mathematicians, while there is a great deal to engage professional mathematicians of all persuasions."--Robin Wilson, London Mathematical Society "Imagine taking an overview of elementary and advanced mathematics, a history of mathematics and mathematicians, and a mathematical encyclopedia and combining them all into one comprehensive reference book. That is what Timothy Gowers, the 1998 Fields Medal laureate, has successfully accomplished in compiling and editing The Princeton Companion to Mathematics. At more than 1,000 pages and with nearly 200 entries written by some of the leading mathematicians of our time and specialists in their fields, this book is a one-of-a-kind reference for all things mathematics."--Mathematics Teacher "Overall [The Princeton Companion to Mathematics] is an enormous achievement for which the authors deserve to be thanked. It contains a wealth of material, much of a kind one would not find elsewhere, and can be enjoyed by readers with man different backgrounds."--Simon Donaldson, Notices of the American Mathematical Society "This is an enormously ambitious book, full of beautiful things; I would wish to keep it on my bedside table, but that could only be possible relays, since of course it is far too large... To sum up, [The Princeton Companion to Mathematics] is really excellent. I know of no book that will give a young student a better idea of what mathematics is about. I am certain that this is the only single book that is likely to tell me what my colleagues are doing."--Bryan Birch, Notices of the American Mathematical Society "The book is so rich and yet it is well done. A rare achievement indeed!"--Gil Kalai, Notices of the American Mathematical Society "My advice to you, reader is to buy the book, open it to a random page, read, enjoy, and be enlightened."--Richard Kenyon, Notices of the American Mathematical Society "Massive ... endlessly fascinating."--Gregory McNamee, Bloomsbury Review "This volume is an enormous, far-reaching effort to survey the current landscape of (pure) mathematics. Chief editor Gowers and associate editors Barrow-Green and Leader have enlisted scores of leading mathematicians worldwide to produce a gorgeous volume of longer essays and short, specific articles that convey some of the dense fabric of ideas and techniques of modern mathematics... This volume should be on the shelf of every university and public library, and of every mathematician--professional and amateur alike."--S.J. Colley, Choice "The Princeton Companion to Mathematics is a friendly, informative reference book that attempts to explain what mathematics is about and what mathematicians do. Over 200 entries by a panel of experts span such topics as: the origins of modern mathematics; mathematical concepts; branches of mathematics; mathematicians that contributed to the present state of the discipline; theorems and problems; the influences of mathematics and some perspectives. Its presentations are selective, satisfying, and complete within themselves but not overbearingly comprehensive. Any reader from a curious high school student to an experienced mathematician seeking information on a particular mathematical subject outside his or her field will find this book useful. The writing is clear and the examples and illustrations beneficial."--Frank Swetz, Convergence "Every research mathematician, every university student of mathematics, and every serious amateur of mathematical science should own a least one copy of The Companion. Indeed, the sheer weight of the volume suggests that it is advisable to own two: one for work and one at home... Even an academic sourpuss should be pleased with the attention to detail of The Companion's publishers, editors, and authors and with many judicious decisions about the level of exposition, level of detail, what to include and what to omit, and much more--which have led to a well-integrated and highly readable volume."--Jonathan M. Borwein, SIAM Review "Edited by Gowers, a recipient of the Fields Medal, this volume contains almost 200 entries, commissioned especially for this book from the world's leading mathematicians. It introduces basic mathematical tools and vocabulary, traces the development of modern mathematics, defines essential terms and concepts, and puts them in context... Packed with information presented in an accessible style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties."--Library Journal "The book I'm talking about is The Princeton Companion to Mathematics. If you are in an absolute rush, the short version of my post today is, buy this book. You don't have to click on the link with my referral if you don't want to, seriously just pick up a copy of this book, I can guarantee you that it will be love at first sight... The Princeton Companion to Mathematics is not only a beautiful book from an aesthetic standpoint, with its heavy, high quality pages and sturdy binding, but above all it's a monumental piece of work. I have never seen a book like this before... [T]he bible of mathematics... I believe this is the kind of book that will still be in use a hundred years from now."--Antonio Cangiano, Math-Blog.com "I'm completely charmed. This is one of those books that makes you wish you had a desert island to be marooned on."--Brian Hayes, bit-player.org "This has been a long time coming, but the wait was worth it! After many years of slogging through textbooks that presented too many proofs and demonstrations that were left to the student or lacking numerous intermediate steps, after encountering numerous 'introductions' that were obtuse and highly theoretical and after digesting far too many explanations with maximal equations and minimal verbiage, we arrive at the happy medium. This book is a companion in every sense of the word and a very friendly one at that... For a comprehensive overview of many areas of mathematics in a readable format, there has never been anything quite like this. I would urge a trip to the local library to have a look."--John A. Wass, Scientific Computing "This book is supremely accessible. Many in the sugar industry with a fairly good grasp of mathematics will probably not struggle with it, and will invariably marvel at its richness and diversity. [A] great companion."--International Sugar Journal "The book contains some valuable surveys of the main branches of mathematics that are written in an accessible style. Hence, it is recommended both to students of mathematics and researchers seeking to understand areas outside their specialties."--European Mathematical Society NewsletterTable of ContentsPreface ix Contributors xvii Part I Introduction I.1 What Is Mathematics About? 1 I.2 The Language and Grammar of Mathematics 8 I.3 Some Fundamental Mathematical Definitions 16 I.4 The General Goals of Mathematical Research 48 Part II The Origins of Modern Mathematics II.1 From Numbers to Number Systems 77 II.2 Geometry 83 II.3 The Development of Abstract Algebra 95 II.4 Algorithms 106 II.5 The Development of Rigor in Mathematical Analysis 117 II.6 The Development of the Idea of Proof 129 II.7 The Crisis in the Foundations of Mathematics 142 Part III Mathematical Concepts III.1 The Axiom of Choice 157 III.2 The Axiom of Determinacy 159 III.3 Bayesian Analysis 159 III.4 Braid Groups 160 III.5 Buildings 161 III.6 Calabi-Yau Manifolds 163 III.7 Cardinals 165 III.8 Categories 165 III.9 Compactness and Compactification 167 III.10 Computational Complexity Classes 169 III.11 Countable and Uncountable Sets 170 III.12 C*-Algebras 172 III.13 Curvature 172 III.14 Designs 172 III.15 Determinants 174 III.16 Differential Forms and Integration 175 III.17 Dimension 180 III.18 Distributions 184 III.19 Duality 187 III.20 Dynamical Systems and Chaos 190 III.21 Elliptic Curves 190 III.22 The Euclidean Algorithm and Continued Fractions 191 III.23 The Euler and Navier-Stokes Equations 193 III.24 Expanders 196 III.25 The Exponential and Logarithmic Functions 199 III.26 The Fast Fourier Transform 202 III.27 The Fourier Transform 204 III.28 Fuchsian Groups 208 III.29 Function Spaces 210 III.30 Galois Groups 213 III.31 The Gamma Function 213 III.32 Generating Functions 214 III.33 Genus 215 III.34 Graphs 215 III.35 Hamiltonians 215 III.36 The Heat Equation 216 III.37 Hilbert Spaces 219 III.38 Homology and Cohomology 221 III.39 Homotopy Groups 221 III.40 The Ideal Class Group 221 III.41 Irrational and Transcendental Numbers 222 III.42 The Ising Model 223 III.43 Jordan Normal Form 223 III.44 Knot Polynomials 225 III.45 K-Theory 227 III.46 The Leech Lattice 227 III.47 L-Functions 228 III.48 Lie Theory 229 III.49 Linear and Nonlinear Waves and Solitons 234 III.50 Linear Operators and Their Properties 239 III.51 Local and Global in Number Theory 241 III.52 The Mandelbrot Set 244 III.53 Manifolds 244 III.54 Matroids 244 III.55 Measures 246 III.56 Metric Spaces 247 III.57 Models of Set Theory 248 III.58 Modular Arithmetic 249 III.59 Modular Forms 250 III.60 Moduli Spaces 252 III.61 The Monster Group 252 III.62 Normed Spaces and Banach Spaces 252 III.63 Number Fields 254 III.64 Optimization and Lagrange Multipliers 255 III.65 Orbifolds 257 III.66 Ordinals 258 III.67 The Peano Axioms 258 III.68 Permutation Groups 259 III.69 Phase Transitions 261 III.70 p 261 III.71 Probability Distributions 263 III.72 Projective Space 267 III.73 Quadratic Forms 267 III.74 Quantum Computation 269 III.75 Quantum Groups 272 III.76 Quaternions, Octonions, and Normed Division Algebras 275 III.77 Representations 279 III.78 Ricci Flow 279 III.79 Riemann Surfaces 282 III.80 The Riemann Zeta Function 283 III.81 Rings, Ideals, and Modules 284 III.82 Schemes 285 III.83 The Schrodinger Equation 285 III.84 The Simplex Algorithm 288 III.85 Special Functions 290 III.86 The Spectrum 294 III.87 Spherical Harmonics 295 III.88 Symplectic Manifolds 297 III.89 Tensor Products 301 III.90 Topological Spaces 301 III.91 Transforms 303 III.92 Trigonometric Functions 307 III.93 Universal Covers 309 III.94 Variational Methods 310 III.95 Varieties 313 III.96 Vector Bundles 313 III.97 Von Neumann Algebras 313 III.98 Wavelets 313 III.99 The Zermelo-Fraenkel Axioms 314 Part IV Branches of Mathematics IV.1 Algebraic Numbers 315 IV.2 Analytic Number Theory 332 IV.3 Computational Number Theory 348 IV.4 Algebraic Geometry 363 IV.5 Arithmetic Geometry 372 IV.6 Algebraic Topology 383 IV.7 Differential Topology 396 IV.8 Moduli Spaces 408 IV.9 Representation Theory 419 IV.10 Geometric and Combinatorial Group Theory 431 IV.11 Harmonic Analysis 448 IV.12 Partial Differential Equations 455 IV.13 General Relativity and the Einstein Equations 483 IV.14 Dynamics 493 IV.15 Operator Algebras 510 IV.16 Mirror Symmetry 523 IV.17 Vertex Operator Algebras 539 IV.18 Enumerative and Algebraic Combinatorics 550 IV.19 Extremal and Probabilistic Combinatorics 562 IV.20 Computational Complexity 575 IV.21 Numerical Analysis 604 IV.22 Set Theory 615 IV.23 Logic and Model Theory 635 IV.24 Stochastic Processes 647 IV.25 Probabilistic Models of Critical Phenomena 657 IV.26 High-Dimensional Geometry and Its Probabilistic Analogues 670 Part V Theorems and Problems V.1 The ABC Conjecture 681 V.2 The Atiyah-Singer Index Theorem 681 V.3 The Banach-Tarski Paradox 684 V.4 The Birch-Swinnerton-Dyer Conjecture 685 V.5 Carleson's Theorem 686 V.6 The Central Limit Theorem 687 V.7 The Classification of Finite Simple Groups 687 V.8 Dirichlet's Theorem 689 V.9 Ergodic Theorems 689 V.10 Fermat's Last Theorem 691 V.11 Fixed Point Theorems 693 V.12 The Four-Color Theorem 696 V.13 The Fundamental Theorem of Algebra 698 V.14 The Fundamental Theorem of Arithmetic 699 V.15 Godel's Theorem 700 V.16 Gromov's Polynomial-Growth Theorem 702 V.17 Hilbert's Nullstellensatz 703 V.18 The Independence of the Continuum Hypothesis 703 V.19 Inequalities 703 V.20 The Insolubility of the Halting Problem 706 V.21 The Insolubility of the Quintic 708 V.22 Liouville's Theorem and Roth's Theorem 710 V.23 Mostow's Strong Rigidity Theorem 711 V.24 The P versus NP Problem 713 V.25 The Poincare Conjecture 714 V.26 The Prime Number Theorem and the Riemann Hypothesis 714 V.27 Problems and Results in Additive Number Theory 715 V.28 From Quadratic Reciprocity to Class Field Theory 718 V.29 Rational Points on Curves and the Mordell Conjecture 720 V.30 The Resolution of Singularities 722 V.31 The Riemann-Roch Theorem 723 V.32 The Robertson-Seymour Theorem 725 V.33 The Three-Body Problem 726 V.34 The Uniformization Theorem 728 V.35 The Weil Conjectures 729 Part VI Mathematicians VI.1 Pythagoras (ca. 569 B.C.E.-ca. 494 B.C.E.) 733 VI.2 Euclid (ca. 325 B.C.E.-ca. 265 B.C.E.) 734 VI.3 Archimedes (ca. 287 B.C.E.-212 B.C.E.) 734 VI.4 Apollonius (ca. 262 B.C.E.-ca. 190 B.C.E.) 735 VI.5 Abu Ja'far Muhammad ibn Musa al-Khwarizmi (800-847) 736 VI.6 Leonardo of Pisa (known as Fibonacci) (ca. 1170-ca. 1250) 737 VI.7 Girolamo Cardano (1501-1576) 737 VI.8 Rafael Bombelli (1526-after 1572) 737 VI.9 Francois Viete (1540-1603) 737 VI.10 Simon Stevin (1548-1620) 738 VI.11 Rene Descartes (1596-1650) 739 VI.12 Pierre Fermat (160?-1665) 740 VI.13 Blaise Pascal (1623-1662) 741 VI.14 Isaac Newton (1642-1727) 742 VI.15 Gottfried Wilhelm Leibniz (1646-1716) 743 VI.16 Brook Taylor (1685-1731) 745 VI.17 Christian Goldbach (1690-1764) 745 VI.18 The Bernoullis (fl. 18th century) 745 VI.19 Leonhard Euler (1707-1783) 747 VI.20 Jean Le Rond d'Alembert (1717-1783) 749 VI.21 Edward Waring (ca. 1735-1798) 750 VI.22 Joseph Louis Lagrange (1736-1813) 751 VI.23 Pierre-Simon Laplace (1749-1827) 752 VI.24 Adrien-Marie Legendre (1752-1833) 754 VI.25 Jean-Baptiste Joseph Fourier (1768-1830) 755 VI.26 Carl Friedrich Gauss (1777-1855) 755 VI.27 Simeon-Denis Poisson (1781-1840) 757 VI.28 Bernard Bolzano (1781-1848) 757 VI.29 Augustin-Louis Cauchy (1789-1857) 758 VI.30 August Ferdinand Mobius (1790-1868) 759 VI.31 Nicolai Ivanovich Lobachevskii (1792-1856) 759 VI.32 George Green (1793-1841) 760 VI.33 Niels Henrik Abel (1802-1829) 760 VI.34 Janos Bolyai (1802-1860) 762 VI.35 Carl Gustav Jacob Jacobi (1804-1851) 762 VI.36 Peter Gustav Lejeune Dirichlet (1805-1859) 764 VI.37 William Rowan Hamilton (1805-1865) 765 VI.38 Augustus De Morgan (1806-1871) 765 VI.39 Joseph Liouville (1809-1882) 766 VI.40 Eduard Kummer (1810-1893) 767 VI.41 Evariste Galois (1811-1832) 767 VI.42 James Joseph Sylvester (1814-1897) 768 VI.43 George Boole (1815-1864) 769 VI.44 Karl Weierstrass (1815-1897) 770 VI.45 Pafnuty Chebyshev (1821-1894) 771 VI.46 Arthur Cayley (1821-1895) 772 VI.47 Charles Hermite (1822-1901) 773 VI.48 Leopold Kronecker (1823-1891) 773 VI.49 Georg Friedrich Bernhard Riemann (1826-1866) 774 VI.50 Julius Wilhelm Richard Dedekind (1831-1916) 776 VI.51 Emile Leonard Mathieu (1835-1890) 776 VI.52 Camille Jordan (1838-1922) 777 VI.53 Sophus Lie (1842-1899) 777 VI.54 Georg Cantor (1845-1918) 778 VI.55 William Kingdon Clifford (1845-1879) 780 VI.56 Gottlob Frege (1848-1925) 780 VI.57 Christian Felix Klein (1849-1925) 782 VI.58 Ferdinand Georg Frobenius (1849-1917) 783 VI.59 Sofya (Sonya) Kovalevskaya (1850-1891) 784 VI.60 William Burnside (1852-1927) 785 VI.61 Jules Henri Poincare (1854-1912) 785 [Illustration credit: Portrait courtesy of Henri Poincare Archives (CNRS,UMR 7117, Nancy)] VI.62 Giuseppe Peano (1858-1932) 787 VI.63 David Hilbert (1862-1943) 788 VI.64 Hermann Minkowski (1864-1909) 789 VI.65 Jacques Hadamard (1865-1963) 790 VI.66 Ivar Fredholm (1866-1927) 791 VI.67 Charles-Jean de la Vallee Poussin (1866-1962) 792 VI.68 Felix Hausdorff (1868-1942) 792 VI.69 Elie Joseph Cartan (1869-1951) 794 VI.70 Emile Borel (1871-1956) 795 VI.71 Bertrand Arthur William Russell (1872-1970) 795 VI.72 Henri Lebesgue (1875-1941) 796 VI.73 Godfrey Harold Hardy (1877-1947) 797 VI.74 Frigyes (Frederic) Riesz (1880-1956) 798 VI.75 Luitzen Egbertus Jan Brouwer (1881-1966) 799 VI.76 Emmy Noether (1882-1935) 800 VI.77 Wac?aw Sierpinski (1882-1969) 801 VI.78 George Birkhoff (1884-1944) 802 VI.79 John Edensor Littlewood (1885-1977) 803 VI.80 Hermann Weyl (1885-1955) 805 VI.81 Thoralf Skolem (1887-1963) 806 VI.82 Srinivasa Ramanujan (1887-1920) 807 VI.83 Richard Courant (1888-1972) 808 VI.84 Stefan Banach (1892-1945) 809 VI.85 Norbert Wiener (1894-1964) 811 VI.86 Emil Artin (1898-1962) 812 VI.87 Alfred Tarski (1901-1983) 813 VI.88 Andrei Nikolaevich Kolmogorov (1903-1987) 814 VI.89 Alonzo Church (1903-1995) 816 VI.90 William Vallance Douglas Hodge (1903-1975) 816 VI.91 John von Neumann (1903-1957) 817 VI.92 Kurt Godel (1906-1978) 819 VI.93 Andre Weil (1906-1998) 819 VI.94 Alan Turing (1912-1954) 821 VI.95 Abraham Robinson (1918-1974) 822 VI.96 Nicolas Bourbaki (1935-) 823 Part VII The Influence of Mathematics VII.1 Mathematics and Chemistry 827 VII.2 Mathematical Biology 837 VII.3 Wavelets and Applications 848 VII.4 The Mathematics of Traffic in Networks 862 VII.5 The Mathematics of Algorithm Design 871 VII.6 Reliable Transmission of Information 878 VII.7 Mathematics and Cryptography 887 VII.8 Mathematics and Economic Reasoning 895 VII.9 The Mathematics of Money 910 VII.10 Mathematical Statistics 916 VII.11 Mathematics and Medical Statistics 921 VII.12 Analysis, Mathematical and Philosophical 928 VII.13 Mathematics and Music 935 VII.14 Mathematics and Art 944 Part VIII Final Perspectives VIII.1 The Art of Problem Solving 955 VIII.2 "Why Mathematics?" You Might Ask 966 VIII.3 The Ubiquity of Mathematics 977 VIII.4 Numeracy 983 VIII.5 Mathematics: An Experimental Science 991 VIII.6 Advice to a Young Mathematician 1000 VIII.7 A Chronology of Mathematical Events 1010 Index 1015
£79.20
Schofield & Sims Ltd Mental Arithmetic Book 1 Answers Year 3 Ages 78
Book SynopsisMental Arithmetic provides rich and varied practice to develop pupils' essential maths skills at Key Stage 2 and beyond. Mental Arithmetic 1 Answers contains answers to all the questions included in the Mental Arithmetic 1 pupil book.
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Schofield & Sims Ltd Mental Arithmetic Book 3 Answers Years 45 Ages
Book SynopsisMental Arithmetic provides rich and varied practice to develop pupils' essential maths skills at Key Stage 2 and beyond. Mental Arithmetic 3 Answers contains answers to all the questions included in the Mental Arithmetic 3 pupil book.
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Schofield & Sims Ltd Mental Arithmetic Introductory Book Answers Years
Book SynopsisMental Arithmetic provides rich and varied practice to develop pupils' essential maths skills at Key Stage 2 and beyond. Mental Arithmetic Introductory Book Answers contains answers to all the questions included in the Mental Arithmetic Introductory Book, as well as additional diagnostic notes and guidance.
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CRC Press Geometry Topology and Physics
Book SynopsisDifferential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields.The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, generaTrade Review"…a very impressive book." -Australian and New Zealand Physicists "The clarity of the presentation is enhanced by explicit calculations and diagrams; the proof of a theorem is given only when it is instructive and not very technical. There is also a large number of exercises and problems, and last but not least, an index … superb layout…" - Zentralblatt fur Mathematick un ihre Grenzgebiete "I believe that the book will not only boost modernization of the traditional courses of theoretical physics but will prompt the specialist in topology and differential geometry to have a closer look at the applications. So I welcome this second edition." -Christopher GilmourTable of ContentsQuantum Physics. Mathematical Preliminaries. Homology Groups. Homotopy Groups. Manifolds. DeRham Cohomology Groups. Riemannian Geometry. Complex Manifolds. Fibre Bundles. Connections on Fibre Bundles. Characteristic Classes. Index Theorems. Anomalies in Gauge Field Theories. Bosonic String Theory. References. Index.
£80.74
Institute of Physics Publishing Computational Physics with R
a huge range and FREE tracked UK delivery on ALL orders.
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Workman Publishing The Book of Perfectly Perilous Math
Book SynopsisMath rocks! At least it does in the gifted hands of Sean Connolly, who blends middle school math with fantasy to create an exciting adventure in problem-solving. These word problems are perilous, do-or-die scenarios of blood-sucking vampires (How many months would it take a single vampire to completely take over a town of 500,000 people?), or a rowboat of 5 shipwrecked sailors with a single barrel of freshwater (How much can they drink, and for how long, before they go mad from thirst???). Each problem requires readers to dig deep into the tools they’re learning in school to figure out how to survive.Kids will love solving these problems. Sean Connolly knows how to make tough subjects exciting and he brings that same intuitive understanding of what inspires and challenges kids’ curiosity to the 24 problems in The Book of Perfectly Perilous Math. These problems are as fun to read as they are challenging to solve. They test readers on fractions, algebra, geometry, probability, expressions and equations, and more.Use geometry to fill in for the ship’s navigator and make it safely to the New World. Escape an evil Duke’s executioner by picking the right door—probability will save your neck.
£11.12
Taylor & Francis Inc Mathematics for Biological Scientists
Book SynopsisMathematics for Biological Scientists is a new undergraduate textbook which covers the mathematics necessary for biology students to understand, interpret and discuss biological questions.The book's twelve chapters are organized into four themes. The first theme covers the basic concepts of mathematics in biology, discussing the mathematics used in biological quantities, processes and structures. The second theme, calculus, extends the language of mathematics to describe change. The third theme is probability and statistics, where the uncertainty and variation encountered in real biological data is described. The fourth theme is explored briefly in the final chapter of the book, which is to show how the 'tools' developed in the first few chapters are used within biology to develop models of biological processes.Mathematics for Biological Scientists fully integrates mathematics and biology with the use of colour illustrations and photographs to provide an engaging and informative approach to the subject of mathematics and statistics within biological science.Trade Review"This book should help remind students that there can be concrete applications for mathematics." - The Quarterly Review of Biology, Volume 85, December 2010 "...pitched at a good level ... enough detail to interest the more able/interested student, while the basic mathematics was introduced in an intuitive and engaging manner that would enable understanding for students with less mathematical background. The use of the text boxes and highlight boxes was extremely useful, presenting critical information in a manner that was easy to follow. Moreover, these gave the book the 'feel' of a biological textbook, rather than a more traditional mathematical textbook." - Kevin Painter, Heriot-Watt UniversityThis book should help remind students that there can be concrete applications for mathematics.—The Quarterly Review of Biology, Volume 85, December 2010...pitched at a good level ... enough detail to interest the more able/interested student, while the basic mathematics was introduced in an intuitive and engaging manner that would enable understanding for students with less mathematical background. The use of the text boxes and highlight boxes was extremely useful, presenting critical information in a manner that was easy to follow. Moreover, these gave the book the 'feel' of a biological textbook, rather than a more traditional mathematical textbook.—Kevin Painter, Heriot-Watt UniversityTable of Contents1. Quantities and Units 2. Numbers and Equations 3. Tables, Graphs and Functions 4. Shapes, Waves and Trigonometry 5. Differentiation 6. Integration 7. Calculus: Expanding the Toolkit 8. The Calculus of Growth and Decay Processes 9. Descriptive Statistics and Data Display 10. Probability 11. Statistical Inference 12. Biological Modeling Presenting Your WorkEnd of Chapter QuestionsAnswers to End of Chapter Questions
£51.29
Birkhauser Boston Inc Algebra
Book SynopsisThis book is about algebra. This is a very old science and its gems have lost their charm for us through everyday use. We have tried in this book to refresh them for you. The main part of the book is made up of problems. The best way to deal with them is: Solve the problem by yourself - compare your solution with the solution in the book (if it exists) - go to the next problem. However, if you have difficulties solving a problem (and some of them are quite difficult), you may read the hint or start to read the solution. If there is no solution in the book for some problem, you may skip it (it is not heavily used in the sequel) and return to it later. The book is divided into sections devoted to different topics. Some of them are very short, others are rather long. Of course, you know arithmetic pretty well. However, we shall go through it once more, starting with easy things. 2 ETrade Review“The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy lies behind the current text by Gelfand and Shen. There are specific ‘practical’ problems but there is much more development of the ideas … [The authors] have shown how to write a serious yet lively look at algebra.” —The American Mathematics Monthly“Were ‘Algebra’ to be used solely for supplementary reading, it could be wholeheartedly recommended to any high school student of any teacher … In fact, given the long tradition of mistreating algebra as a disjointed collection of techniques in the schools, there should be some urgency in making this book compulsory reading for anyone interested in learning mathematics.” —The Mathematical IntelligencerTable of Contents1 Introduction.- 2 Exchange of terms in addition.- 3 Exchange of terms in multiplication.- 4 Addition in the decimal number system.- 5 The multiplication table and the multiplication algorithm.- 6 The division algorithm.- 7 The binary system.- 8 The commutative law.- 9 The associative law.- 10 The use of parentheses.- 11 The distributive law.- 12 Letters in algebra.- 13 The addition of negative numbers.- 14 The multiplication of negative numbers.- 15 Dealing with fractions.- 16 Powers.- 17 Big numbers around us.- 18 Negative powers.- 19 Small numbers around us.- 20 How to multiply am by an, or why our definition is convenient.- 21 The rule of multiplication for powers.- 22 Formula for short multiplication: The square of a sum.- 23 How to explain the square of the sum formula to our younger brother or sister.- 24 The difference of squares.- 25 The cube of the sum formula.- 26 The formula for (a + b)4.- 27 Formulas for (a + b)5, (a + b)6,... and Pascal’s triangle.- 28 Polynomials.- 29 A digression: When are polynomials equal?.- 30 How many monomials do we get?.- 31 Coefficients and values.- 32 Factoring.- 33 Rational expressions.- 34 Converting a rational expression into the quotient of two polynomials.- 35 Polynomial and rational fractions in one variable.- 36 Division of polynomials in one variable; the remainder.- 37 The remainder when dividing by x - a.- 38 Values of polynomials, and interpolation.- 39 Arithmetic progressions.- 40 The sum of an arithmetic progression.- 41 Geometric progressions.- 42 The sum of a geometric progression.- 43 Different problems about progressions.- 44 The well-tempered clavier.- 45 The sum of an infinite geometric progression.- 46 Equations.- 47 A short glossary.- 48 Quadratic equations.- 49 The case p =. Square roots.- 50 Rules for square roots.- 51 The equation x2 + px + q =.- 52 Vieta’s theorem.- 53 Factoring ax2 + bx + c.- 54 A formula for ax2 + bx + c = (where a ? 0).- 55 One more formula concerning quadratic equations.- 56 A quadratic equation becomes linear.- 57 The graph of the quadratic polynomial.- 58 Quadratic inequalities.- 59 Maximum and minimum values of a qua ratic polynomial.- 60 Biquadratic equations.- 61 Symmetric equations.- 62 How to confuse students on an exam.- 63 Roots.- 64 Non-integer powers.- 65 Proving inequalities.- 66 Arithmetic and geometric means.- 67 The geometric mean does not exceed the arithmetic mean.- 68 Problems about maximum and minimum.- 69 Geometric illustrations.- 70 The arithmetic and geometric means of everal numbers.- 71 The quadratic mean.- 72 The harmonic mean.
£49.49
Royal Society of Chemistry Practical Statistics for the Analytical Scientist
Book SynopsisAnalytical chemists must use a range of statistical tools in their treatment of experimental data to obtain reliable results. Practical Statistics for the Analytical Scientist is a manual designed to help them negotiate the daunting specialist terminology and symbols. Prepared in conjunction with the Department of Trade and Industry''s Valid Analytical Measurement (VAM) programme, this volume covers the basic statistics needed in the laboratory. It describes the statistical procedures that are most likely to be required including summary and descriptive statistics, calibration, outlier testing, analysis of variance and basic quality control procedures. To improve understanding, many examples provide the user with material for consolidation and practice. The fully worked answers are given both to check the correct application of the procedures and to provide a template for future problems. Practical Statistics for the Analytical Scientist will be welcomed by practising analytical chemisTable of ContentsIntroduction: Choosing the Correct Statistics; Descriptive Statistics; Distribution Descriptives; Probability Distributions; Confidence Limits; Accuracy and Precision; Significance Testing; Outlier Tests; The ANalysis Of VAriance; Linear Regression; Polynomial Regression; Repeatability Standard Deviation; Reproducibility Standard Deviation; Analytical Quality Control; Statistical Sampling; Appendices; Subject Index
£28.45
John Wiley and Sons Ltd Essential Medical Statistics
Book SynopsisBlackwell Publishing is delighted to announce that this book has been Highly Commended in the 2004 BMA Medical Book Competition. Here is the judges' summary of this book: "This is a technical book on a technical subject but presented in a delightful way.Trade Review"This book is the statistics book of choice for anyone wanting a proper appreciation of the use and application of statistics in health care. I highly recommend this book." (Journal of Renal Nursing, 6 November 2011) the breadth of coverage of the book is excellent ... a rather different approach to teaching medical statistics." Statistics in Medicine "The most readable book that I have yet discovered in the topic" Community Health Studies "This book is statistically correct. That is enough to distinguish it from most of its competitors." British Medical Journal Published Reviews of the 2th Edition "One word which definitely describes this book is "comprehensive". Anything you ever wanted to know about medical statistics is covered in immense detail." 4th Year Medical Student Liverpool Medical School Sphincter, December 2003 "This is a comprehensive book that includes an impressive range of topics often omitted from books aimed at non-statisticians. ...a resource that makes it easy for a beginner to comprehend a wide range of statistical concepts and tools. Essential Medical Statistics fills an important niche by providing practical information on a comprehensive scope of modern statistical methods and, at the same time, communicating on the same wavelengths as physicians and other nonstatisticians." Teaching of Statistics in the Health Sciences, Section of the American Statistical Association, Spring 2004 "The book is laid out in a logical fashion and includes all of the tables you need to find p-values once you have performed a test. It covers simple statistical methods, such as how to calculate the mean and standard deviation, progressing to linear and multiple regression, Poisson regression and measures of impact and association. ...I would recommend using it to anyone who is still struggling with statistics." North Wing, Sheffield Medics Magazine, Winter 2004 "The book is generally well laid out, the indexing is well structured and a comprehensive bibliography is provided. The topics are easy to locate and include practical examples. These attributes make it a useful text for both consulting and teaching purposes." Statistics in Medicine, Vol 24, Number 5, March 2005Table of ContentsPart A. Basics. 1. Using this book. 2. Defining the data. 3. Displaying the data. Part B. Analysis of numerical outcomes. 4. Means, Standard Deviations and Standard Errors. 5. The Normal Distribution. 6. Confidence Interval for a Mean. 7. Comparison of two means: confidence intervals, hypothesis tests and P-values. 8. Using P-values and confidence intervals to interpret the results of statistical analyses. 9. Comparison of means from several groups: analysis of variance. 10. Linear Regression and Correlation. 11. Multiple Regression. 12. Goodness of fit and regression diagnostics. 13. Transformations. Part C. Analysis of binary outcomes. 14. Probability, risks and odds (of disease). 15. Proportions and the binomial distribution. 16. Comparing two proportions. 17. Chi-squared tests for 2 × 2 and larger contingency tables. 18. Controlling for confounding: stratification. 19. Logistic regression: comparing two or more exposure groups. 20. Logisitic regression: controlling for confounding and other extensions. 21. Matched studies. Part D. Longitudinal studies: Analysis of rates and survival times. 22. Longitudinal studies, rates and the Poisson distribution. 23. Comparing rates. 24. Poisson regression. 25. Standardisation. 26. Survival analysis: displaying and comparing survival patterns. 27. Regression analysis of survival data. Part E. Statistical modelling. 28. Likelihood. 29. Regression modelling. 30. Relaxing model assumptions. 31. Analysis of clustered data. 32. Systematic reviews and meta-analysis. 33. Bayesian statistics. Part F. Study design, analysis and interpretation. 34. Linking analysis to study design: summary of methods. 35. Calculation of Required Sample Size. 36. Measurement error: assessment and implications. 37. Measures of association and impact. 38. Strategies for analysis. APPENDIX: Statistical Tables. Bibliography
£44.60
Cambridge University Press Why Does Math Work ... If Its Not Real
Book SynopsisAccording to G. H. Hardy, the ''real'' mathematics of the greats like Fermat and Euler is ''useless,'' and thus the work of mathematicians should not be judged on its applicability to real-world problems. Yet, mysteriously, much of mathematics used in modern science and technology was derived from this ''useless'' mathematics. Mobile phone technology is based on trig functions, which were invented centuries ago. Newton observed that the Earth''s orbit is an ellipse, a curve discovered by ancient Greeks in their futile attempt to double the cube. It is like some magic hand had guided the ancient mathematicians so their formulas were perfectly fitted for the sophisticated technology of today. Using anecdotes and witty storytelling, this book explores that mystery. Through a series of fascinating stories of mathematical effectiveness, including Planck''s discovery of quanta, mathematically curious readers will get a sense of how mathematicians develop their concepts.Table of ContentsPreface; Acknowledgements; Part I. Rare Axioms; 1. Introducing the Mystery; 2. On Classical Mathematics; 3. On Modern Physics; Intermezzo: What Have We Learned?; 4. On Computer Games; 5. On Mathematical Logic; 6. On Postulates and Axioms; Part II. The Oracle; 7. Introducing the Oracle; 8. On Probability; 9. The Oracle, Its Majesty; Epilogue: The Eternal Blueprint; Post Scriptum: On Mathematical Grand Design; Appendix; Recommended Reading; Index.
£15.99
Cambridge University Press PopUp Geometry
Book SynopsisAnyone browsing at the stationery store will see an incredible array of pop-up cards available for any occasion. The workings of pop-up cards and pop-up books can be remarkably intricate. Behind such designs lies beautiful geometry involving the intersection of circles, cones, and spheres, the movements of linkages, and other constructions. The geometry can be modelled by algebraic equations, whose solutions explain the dynamics. For example, several pop-up motions rely on the intersection of three spheres, a computation made every second for GPS location. Connecting the motions of the card structures with the algebra and geometry reveals abstract mathematics performing tangible calculations. Beginning with the nephroid in the 19th-century, the mathematics of pop-up design is now at the frontiers of rigid origami and algorithmic computational complexity. All topics are accessible to those familiar with high-school mathematics; no calculus required. Explanations are supplemented by 140+Trade Review'What a delight! Finally, a book that explains the geometry behind pop-up cards in a simple and straight-forward way with loads of illustrations and web animations to help. I look forward to sharing this gem with my own students.' Thomas Hull, Western New England University'Pop-Up Geometry is a beautifully written book. This book focuses on the aspect of pop-up structures of computational origami, a recent trend in computational geometry. Once you flip the pages, you will find various colorful figures. These figures nicely give you inspirations of paper art and ideas of the mathematical background of pop-up paper sculptures.' Ryuhei Uehara, Japan Advanced Institute of Science and Technology'There are many books about pop-ups, but only one about the mathematics of how they work. From analyzing standard pop-up mechanisms to advanced computational design, geometry master O'Rourke gives an excellent tour of this wonderful world.' Erik Demaine, Massachusetts Institute of Technology'This text can readily be used as a supplement to a geometry course. I also see this book serving as a foundation for a multi-disciplined extracurricular activity called 'Pop-Up Card Design'. This activity would encourage students interested in enhancing their skills in English, Mathematics, and Art as they work together in a cooperative effort to produce Pop-Up cards or Pop-Up books.' Tom French, MAA Reviews'Complete with vibrantly colored graphics, companion animations that depict the motion described in the book, and templates for the reader to make the pop-up creations the book is analyzing, this book makes it easy for the reader to engage with the material they are learning.' Katelynn Kochalski, Notices of the American Mathematical SocietyTable of ContentsPreface; 1. Parallel Folds; 2. V-Folds and Rotary Motion; 3. The Knight's Visor; 4. Pop-up Spinner; 5. Polyhedra: Rigid Origami and Flattening; 6. Algorithms for Pop-Up Design; 7. Pop-Up Design is Hard; 8. Solutions to Exercises.
£19.94
Cambridge University Press Introduction to Proofs and Proof Strategies
Book SynopsisEmphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof as they transition to advanced mathematics. Using several strategies, students will develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow.Trade Review'Every student in the sciences should be exposed to the basic language of modern mathematics, and standard courses such as calculus or linear algebra do not play this role. The ideal textbook for such a course should not attempt to be encyclopedic and should not assume special prerequisites. It should cover a carefully chosen selection of topics efficiently, engagingly, thoroughly, without being overbearing. Fuchs' text fits this description admirably. The level is right, the math is rock solid, the writing is very pleasant. The book talks to the reader, without ever sounding patronizing. A vast selection of problems, many including solutions, will be splendidly helpful both in a classroom setting and for self-study.' Paolo Aluffi, Florida State University'This well-written text strikes a good balance between conciseness and clarity. Students are led from looking more deeply into familiar topics, such as the quadratic formula, to an understanding of the nature, structure, and methods of proof. The examples and problems are a strong point. I look forward to teaching from it.' Eric Gottlieb, Rhodes College'Fuchs' text is an excellent addition to the 'transitions to proof' literature. I will use it when I next teach such a course. Except for the excellent 'Additional Topics' sections, the content is standard, but the spiraling presentation and helpful narrative around proofs are what truly elevate this text. Fuchs has made every attempt to connect the structure and rigor of mathematics with the intuition of the student. For example, the notion of function arises in three different chapters, with two increasingly rigorous 'provisional definitions,' before a complete definition is given within a wider discussion of relations. I anticipate this approach resonating with students. Fuchs' Chapter 3, which introduces logic and proof strategies, is the most usable presentation of the material I have seen or used. The practice of mathematics and mathematical thinking is communicated well, while opportunities for confusion and obfuscation via a blizzard of symbols are minimized.' Ryan Grady, Montana State University'This book is a must-have resource for an undergraduate mathematics student or interested reader to learn the fundamental topics in how to prove things. The text is thorough and of top quality, yet it is conversational and easy to absorb. Maybe the most important quality, it offers advice about how to approach problems, making it perfect for an introduction to proofs class.' Andrew McEachern, York University, Canada'This is a great choice of textbook for any course introducing undergraduates to mathematical proofs. What makes this book stand out are the early chapters, as well as the 'Additional Topics,' both with accompanying exercises. The book begins by gently introducing proof-based thinking by posing well-motivated prompts and exercises concerning familiar arithmetic of real numbers and the integers. It then introduces fields as a playground to practice working with axioms and drawing (sometimes surprising) conclusions from them. The book proceeds with introducing formal logic, mathematical induction, set theory, and relations on sets. The book's design nicely enables framing classes around a choice sampling among the abundant exercises. The book's 'Additional Topics' can serve to engage those students with a brimming imagination and who are already familiar with basic notions of proofs.' David Ayala, Montana State University'Fuchs' Introduction to Proofs and Proof Strategies is an excellent textbook choice for an undergraduate proof-writing course. The author takes a friendly and conversational approach, giving many worked examples throughout each section. Furthermore, each section is replete with exercises for the reader, along with fully worked solutions at chapter's end. This is exactly the 'get your hands dirty' approach students and readers will benefit greatly from!' Frank Patane, Samford University'The book Introduction to Proofs and Proof Strategies by Shay Fuchs takes the problem-solving approach to the forefront by accompanying the reader in the construction and deconstruction of proofs through numerous examples and challenging exercises. The fundamental principles of mathematics are introduced in a creative and innovative way, making learning an enjoyable journey.' Roberto Bruni, Università di Pisa'This textbook is easy to read and designed to enhance students' problem-solving skills in their first year of university. The book really stands out due to the variety and quality of exercises at the end of each chapter. The latter chapters dive into more advanced topics for interested students.' Marina Tvalavadze, University of Toronto MississaugaTable of ContentsContents; Preface; Part I. Core Material; 1. Numbers, Quadratics and Inequalities; 2. Sets, Functions and the Field Axioms; 3. Informal Logic and Proof Strategies; 4. Mathematical Induction; 5. Bijections and Cardinality; 6. Integers and Divisibility; 7. Relations; Part II. Additional Topics; 8. Elementary Combinatorics; 9. Preview of Real Analysis – Limits and Continuity; 10. Complex Numbers; 11. Preview of Linear Algebra; Notes; References; Index.
£33.24
