Mathematics Books

Book SynopsisAlgebra I For Dummies, 2nd Edition (9781119293576) was previously published as Algebra I For Dummies, 2nd Edition (9780470559642). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Factor fearlessly, conquer the quadratic formula, and solve linear equations There''s no doubt that algebra can be easy to some while extremely challenging to others. If you''re vexed by variables,Algebra I For Dummies, 2nd Edition provides the plain-English, easy-to-follow guidance you need to get the right solution every time! Now with 25% new and revised content, this easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems with confidence. You''ll understand how to factor fearlessly, conquer the quadratic formula, and solve linear equations. Table of ContentsIntroduction 1 About This Book 1 Conventions Used in This Book 2 What You’re Not to Read 2 Foolish Assumptions 3 How This Book Is Organized 3 Part 1: Starting Off with the Basics 3 Part 2: Figuring Out Factoring 4 Part 3: Working Equations 4 Part 4: Applying Algebra 4 Part 5: The Part of Tens 5 Icons Used in This Book 5 Where to Go from Here 6 Part 1: Starting off with the Basics 7 Chapter 1: Assembling Your Tools 9 Beginning with the Basics: Numbers 10 Really real numbers 10 Counting on natural numbers 10 Wholly whole numbers 11 Integrating integers 12 Being reasonable: Rational numbers 12 Restraining irrational numbers 12 Picking out primes and composites 13 Speaking in Algebra 13 Taking Aim at Algebra Operations 14 Deciphering the symbols 14 Grouping 15 Defining relationships 16 Taking on algebraic tasks 16 Chapter 2: Assigning Signs: Positive and Negative Numbers 19 Showing Some Signs 20 Picking out positive numbers 20 Making the most of negative numbers 20 Comparing positives and negatives 21 Zeroing in on zero 22 Going In for Operations 22 Breaking into binary operations 22 Introducing non-binary operations 23 Operating with Signed Numbers 25 Adding like to like: Same-signed numbers 25 Adding different signs 26 Subtracting signed numbers 27 Multiplying and dividing signed numbers 29 Working with Nothing: Zero and Signed Numbers 31 Associating and Commuting with Expressions 31 Reordering operations: The commutative property 32 Associating expressions: The associative property 33 Chapter 3: Figuring Out Fractions and Dealing with Decimals 35 Pulling Numbers Apart and Piecing Them Back Together 36 Making your bow to proper fractions 36 Getting to know improper fractions 37 Mixing it up with mixed numbers 37 Following the Sterling Low-Fraction Diet 38 Inviting the loneliest number one 39 Figuring out equivalent fractions 40 Realizing why smaller or fewer is better 41 Preparing Fractions for Interactions 43 Finding common denominators 43 Working with improper fractions 45 Taking Fractions to Task 46 Adding and subtracting fractions 46 Multiplying fractions 47 Dividing fractions 50 Dealing with Decimals 51 Changing fractions to decimals 52 Changing decimals to fractions 53 Chapter 4: Exploring Exponents and Raising Radicals 55 Multiplying the Same Thing Over and Over and Over 55 Powering up exponential notation 56 Comparing with exponents 57 Taking notes on scientific notation 58 Exploring Exponential Expressions 60 Multiplying Exponents 65 Dividing and Conquering 66 Testing the Power of Zero 66 Working with Negative Exponents 67 Powers of Powers 68 Squaring Up to Square Roots 69 Chapter 5: Doing Operations in Order and Checking Your Answers 73 Ordering Operations 74 Gathering Terms with Grouping Symbols 76 Checking Your Answers 78 Making sense or cents or scents 79 Plugging in to get a charge of your answer 79 Curbing a Variable’s Versatility 80 Representing numbers with letters 81 Attaching factors and coefficients 82 Interpreting the operations 82 Doing the Math 83 Adding and subtracting variables 84 Adding and subtracting with powers 85 Multiplying and Dividing Variables 86 Multiplying variables 86 Dividing variables 87 Doing it all 88 Part 2: Figuring Out Factoring 91 Chapter 6: Working with Numbers in Their Prime 93 Beginning with the Basics 94 Composing Composite Numbers 95 Writing Prime Factorizations 96 Dividing while standing on your head 96 Getting to the root of primes with a tree 98 Wrapping your head around the rules of divisibility 99 Getting Down to the Prime Factor 100 Taking primes into account 100 Pulling out factors and leaving the rest 103 Chapter 7: Sharing the Fun: Distribution 107 Giving One to Each 108 Distributing first 109 Adding first 109 Distributing Signs 110 Distributing positives 110 Distributing negatives 111 Reversing the roles in distributing 112 Mixing It Up with Numbers and Variables 113 Negative exponents yielding fractional answers 115 Working with fractional powers 115 Distributing More Than One Term 117 Distributing binomials 117 Distributing trinomials 118 Multiplying a polynomial times another polynomial 119 Making Special Distributions 120 Recognizing the perfectly squared binomial 120 Spotting the sum and difference of the same two terms 121 Working out the difference and sum of two cubes 123 Chapter 8: Getting to First Base with Factoring 127 Factoring 127 Factoring out numbers 128 Factoring out variables 130 Unlocking combinations of numbers and variables 131 Changing factoring into a division problem 133 Grouping Terms 134 Chapter 9: Getting the Second Degree 139 The Standard Quadratic Expression 140 Reining in Big and Tiny Numbers 141 FOILing 142 FOILing basics 142 FOILed again, and again 143 Applying FOIL to a special product 146 UnFOILing 147 Unwrapping the FOILing package 148 Coming to the end of the FOIL roll 151 Making Factoring Choices 152 Combining unFOIL and the greatest common factor 153 Grouping and unFOILing in the same package 154 Chapter 10: Factoring Special Cases 157 Befitting Binomials 157 Factoring the difference of two perfect squares 158 Factoring the difference of perfect cubes 159 Factoring the sum of perfect cubes 162 Tinkering with Multiple Factoring Methods 163 Starting with binomials 163 Ending with binomials 164 Knowing When to Quit 165 Incorporating the Remainder Theorem 166 Synthesizing with synthetic division 166 Choosing numbers for synthetic division 167 Part 3: Working Equations 169 Chapter 11: Establishing Ground Rules for Solving Equations 171 Creating the Correct Setup for Solving Equations 172 Keeping Equations Balanced 172 Balancing with binary operations 173 Squaring both sides and suffering the consequences 174 Taking a root of both sides 175 Undoing an operation with its opposite 176 Solving with Reciprocals 176 Making a List and Checking It Twice 179 Doing a reality check 179 Thinking like a car mechanic when checking your work 180 Finding a Purpose 181 Chapter 12: Solving Linear Equations 183 Playing by the Rules 184 Solving Equations with Two Terms 184 Devising a method using division 185 Making the most of multiplication 186 Reciprocating the invitation 188 Extending the Number of Terms to Three 189 Eliminating the extra constant term 189 Vanquishing the extra variable term 190 Simplifying to Keep It Simple 191 Nesting isn’t for the birds 192 Distributing first 192 Multiplying or dividing before distributing 194 Featuring Fractions 196 Promoting practical proportions 196 Transforming fractional equations into proportions 198 Solving for Variables in Formulas 199 Chapter 13: Taking a Crack at Quadratic Equations 203 Squaring Up to Quadratics 204 Rooting Out Results from Quadratic Equations 206 Factoring for a Solution 208 Zeroing in on the multiplication property of zero 209 Assigning the greatest common factor and multiplication property of zero to solving quadratics 210 Solving Quadratics with Three Terms 211 Applying Quadratic Solutions 217 Figuring Out the Quadratic Formula 219 Imagining the Worst with Imaginary Numbers 221 Chapter 14: Distinguishing Equations with Distinctive Powers 223 Queuing Up to Cubic Equations 224 Solving perfectly cubed equations 224 Working with the not-so-perfectly cubed 225 Going for the greatest common factor 226 Grouping cubes 228 Solving cubics with integers 228 Working Quadratic-Like Equations 230 Rooting Out Radicals 234 Powering up both sides 235 Squaring both sides twice 237 Solving Synthetically 239 Chapter 15: Rectifying Inequalities 243 Translating between Inequality and Interval Notation 244 Intervening with interval notation 244 Grappling with graphing inequalities 246 Operating on Inequalities 247 Adding and subtracting inequalities 247 Multiplying and dividing inequalities 248 Solving Linear Inequalities 249 Working with More Than Two Expressions 250 Solving Quadratic and Rational Inequalities 252 Working without zeros 255 Dealing with more than two factors 255 Figuring out fractional inequalities 256 Working with Absolute-Value Inequalities 258 Working absolute-value equations 258 Working absolute-value inequalities 260 Part 4: Applying Algebra 263 Chapter 16: Taking Measure with Formulas 265 Measuring Up 265 Finding out how long: Units of length 266 Putting the Pythagorean theorem to work 267 Working around the perimeter 269 Spreading Out: Area Formulas 273 Laying out rectangles and squares 273 Tuning in triangles 274 Going around in circles 276 Pumping Up with Volume Formulas 276 Prying into prisms and boxes 277 Cycling cylinders 277 Scaling a pyramid 278 Pointing to cones 279 Rolling along with spheres 279 Chapter 17: Formulating for Profit and Pleasure 281 Going the Distance with Distance Formulas 282 Calculating Interest and Percent 283 Compounding interest formulas 284 Gauging taxes and discounts 286 Working Out the Combinations and Permutations 287 Counting down to factorials 288 Counting on combinations 288 Ordering up permutations 290 Chapter 18: Sorting Out Story Problems 291 Setting Up to Solve Story Problems 292 Working around Perimeter, Area, and Volume 294 Parading out perimeter and arranging area 294 Adjusting the area 295 Pumping up the volume 297 Making Up Mixtures 300 Mixing up solutions 301 Tossing in some solid mixtures 302 Investigating investments and interest 302 Going for the green: Money 304 Going the Distance 305 Figuring distance plus distance 306 Figuring distance and fuel 307 Going ’Round in Circles 307 Chapter 19: Going Visual: Graphing 311 Graphing Is Good 312 Grappling with Graphs 313 Making a point 314 Ordering pairs, or coordinating coordinates 315 Actually Graphing Points 316 Graphing Formulas and Equations 317 Lining up a linear equation 317 Going around in circles with a circular graph 318 Throwing an object into the air 319 Curling Up with Parabolas 321 Trying out the basic parabola 321 Putting the vertex on an axis 322 Sliding and multiplying 324 Chapter 20: Lining Up Graphs of Lines 327 Graphing a Line 327 Graphing the equation of a line 329 Investigating Intercepts 332 Sighting the Slope 333 Formulating slope 335 Combining slope and intercept 337 Getting to the slope-intercept form 337 Graphing with slope-intercept 338 Marking Parallel and Perpendicular Lines 339 Intersecting Lines 341 Graphing for intersections 341 Substituting to find intersections 342 Part 5: The Part of Tens 345 Chapter 21: The Ten Best Ways to Avoid Pitfalls 347 Keeping Track of the Middle Term 348 Distributing: One for You and One for Me 348 Breaking Up Fractions (Breaking Up Is Hard to Do) 348 Renovating Radicals 349 Order of Operations 349 Fractional Exponents 349 Multiplying Bases Together 350 A Power to a Power 350 Reducing for a Better Fit 351 Negative Exponents 351 Chapter 22: The Ten Most Famous Equations 353 Albert Einstein’s Theory of Relativity 353 The Pythagorean Theorem 354 The Value of e 354 Diameter and Circumference Related with Pi 354 Isaac Newton’s Formula for the Force of Gravity 355 Euler’s Identity 355 Fermat’s Last Theorem 356 Monthly Loan Payments 356 The Absolute-Value Inequality 356 The Quadratic Formula 357 Index 359

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Book SynopsisMaster the fundamentals first for a smoother ride through math Basic Math & Pre-Algebra Workbook For Dummies is your ticket to finally getting a handle on math! Designed to help you strengthen your weak spots and pinpoint problem areas, this book provides hundreds of practice problems to help you get over the hump. Each section includes a brief review of key concepts and full explanations for every practice problem, so you''ll always know exactly where you went wrong. The companion website gives you access to quizzes for each chapter, so you can test your understanding and identify your sticking points before moving on to the next topic. You''ll brush up on the rules of basic operations, and then learn what to do when the numbers just won''t behavenegative numbers, inequalities, algebraic expressions, scientific notation, and other tricky situations will become second nature as you refresh what you know and learn what you missed. Each math class you taTable of ContentsIntroduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 2 Beyond the Book 3 Where to Go from Here 3 Part 1: Getting Started with Basic Math and Pre-algebra 5 Chapter 1: We’ve Got Your Numbers 7 Getting in Place with Numbers and Digits 8 Rollover: Rounding Numbers Up and Down 10 Using the Number Line with the Big Four 12 The Column Lineup: Adding and Subtracting 14 Multiplying Multiple Digits 15 Cycling through Long Division 16 Solutions to We’ve Got Your Numbers 19 Chapter 2: Smooth Operators: Working with the Big Four Operations 23 Switching Things Up with Inverse Operations and the Commutative Property 24 Getting with the In-Group: Parentheses and the Associative Property 27 Becoming Unbalanced: Inequalities 29 Special Times: Powers and Square Roots 31 Answers to Problems in Smooth Operators 34 Chapter 3: Getting Down with Negative Numbers 37 Understanding Where Negative Numbers Come From 37 Sign-Switching: Understanding Negation and Absolute Value 39 Adding with Negative Numbers 40 Subtracting with Negative Numbers 42 Knowing Signs of the Times (And Division) for Negative Numbers 43 Answers to Problems in Getting Down with Negative Numbers 45 Chapter 4: It’s Just an Expression 49 Evaluating Expressions with Addition and Subtraction 50 Evaluating Expressions with Multiplication and Division 51 Making Sense of Mixed-Operator Expressions 52 Handling Powers Responsibly 53 Prioritizing Parentheses 55 Pulling Apart Parentheses and Powers 56 Figuring Out Nested Parentheses 58 Bringing It All Together: The Order of Operations 59 Solutions to It’s Just an Expression 61 Chapter 5: Dividing Attention: Divisibility, Factors, and Multiples 69 Checking for Leftovers: Divisibility Tests 70 Understanding Factors and Multiples 72 One Number, Indivisible: Identifying Prime (And Composite) Numbers 73 Generating a Number’s Factors 75 Decomposing a Number into Its Prime Factors 77 Finding the Greatest Common Factor 78 Generating the Multiples of a Number 80 Finding the Least Common Multiple 81 Solutions to Divisibility, Factors, and Multiples 83 Part 2: Slicing Things Up: Fractions, Decimals, and Percents 89 Chapter 6: Fractions Are a Piece of Cake 91 Getting Down the Basic Fraction Stuff 91 In Mixed Company: Converting between Mixed Numbers and Improper Fractions 94 Increasing and Reducing the Terms of Fractions 96 Comparing Fractions with Cross-Multiplication 99 Working with Ratios and Proportions 101 Solutions to Fractions Are a Piece of Cake 103 Chapter 7: Fractions and the Big Four 109 Multiplying Fractions: A Straight Shot 109 Flipping for Fraction Division 111 Reaching the Common Denominator: Adding Fractions 113 The Other Common Denominator: Subtracting Fractions 116 Multiplying and Dividing Mixed Numbers 118 Carried Away: Adding Mixed Numbers 120 Borrowing from the Whole: Subtracting Mixed Numbers 123 Solutions to Fractions and the Big Four 126 Chapter 8: Getting to the Point with Decimals 143 Getting in Place: Basic Decimal Stuff 143 Simple Decimal-Fraction Conversions 146 New Lineup: Adding and Subtracting Decimals 148 Counting Decimal Places: Multiplying Decimals 150 Points on the Move: Dividing Decimals 151 Decimals to Fractions 153 Fractions to Decimals 155 Solutions to Getting to the Point with Decimals 157 Chapter 9: Playing the Percentages 165 Converting Percents to Decimals 165 Changing Decimals to Percents 167 Switching from Percents to Fractions 168 Converting Fractions to Percents 169 Solving a Variety of Percent Problems Using Word Equations 171 Solutions to Playing the Percentages 173 Part 3: a Giant Step Forward: Intermediate Topics 177 Chapter 10: Seeking a Higher Power through Scientific Notation 179 On the Count of Zero: Understanding Powers of Ten 180 Exponential Arithmetic: Multiplying and Dividing Powers of Ten 182 Representing Numbers in Scientific Notation 183 Multiplying and Dividing with Scientific Notation 184 Answers to Problems in Seeking a Higher Power through Scientific Notation 186 Chapter 11: Weighty Questions on Weights and Measures 189 The Basics of the English System 190 Going International with the Metric System 192 Converting Between English and Metric Units 194 Answers to Problems in Weighty Questions on Weights and Measures 198 Chapter 12: Shaping Up with Geometry 203 Getting in Shape: Polygon (And Non-Polygon) Basics 204 Squaring Off with Quadrilaterals 204 Making a Triple Play with Triangles 208 Getting Around with Circle Measurements 212 Building Solid Measurement Skills 214 Answers to Problems in Shaping Up with Geometry 218 Chapter 13: Getting Graphic: Xy-Graphs 223 Getting the Point of the Xy-Graph 223 Drawing the Line on the Xy-Graph 227 Answers to Problems in Getting Graphic: Xy-Graphs 230 Part 4: the X Factor: Introducing Algebra 235 Chapter 14: Expressing Yourself with Algebraic Expressions 237 Plug It In: Evaluating Algebraic Expressions 238 Knowing the Terms of Separation 240 Adding and Subtracting Like Terms 242 Multiplying and Dividing Terms 243 Simplifying Expressions by Combining Like Terms 245 Simplifying Expressions with Parentheses 247 FOILing: Dealing with Two Sets of Parentheses 249 Answers to Problems in Expressing Yourself with Algebraic Expressions 251 Chapter 15: Finding the Right Balance: Solving Algebraic Equations 259 Solving Simple Algebraic Equations 259 Equality for All: Using the Balance Scale to Isolate X 262 Switching Sides: Rearranging Equations to Isolate X 264 Barring Fractions: Cross-Multiplying to Simplify Equations 266 Answers to Problems in Finding the Right Balance: Solving Algebraic Equations 268 Part 5: the Part of Tens 277 Chapter 16: Ten Alternative Numeral and Number Systems 279 Tally Marks 279 Bundled Tally Marks 280 Egyptian Numerals 280 Babylonian Numerals 281 Ancient Greek Numerals 281 Roman Numerals 282 Mayan Numerals 282 Base-2 (Binary) Numbers 283 Base-16 (Hexadecimal) Numbers 284 Prime-Based Numbers 285 Chapter 17: Ten Curious Types of Numbers 287 Square Numbers 287 Triangular Numbers 288 Cubic Numbers 289 Factorial Numbers 289 Powers of Two 290 Perfect Numbers 290 Amicable Numbers 291 Prime Numbers 291 Mersenne Primes 291 Fermat Primes 292 Index 293

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Book SynopsisA valuable new edition of a standard reference The use of statistical methods for categorical data has increased dramatically, particularly for applications in the biomedical and social sciences. An Introduction to Categorical Data Analysis, Third Edition summarizes these methods and shows readers how to use them using software. Readers will find a unified generalized linear models approach that connects logistic regression and loglinear models for discrete data with normal regression for continuous data. Adding to the value in the new edition is: Illustrations of the use of R software to perform all the analyses in the book A new chapter on alternative methods for categorical data, including smoothing and regularization methods (such as the lasso), classification methods such as linear discriminant analysis and classification trees, and cluster analysis New sections in many chapters introducing the Bayesian approach for the methodTable of ContentsPreface ix About the Companion Website xiii 1 Introduction 1 1.1 Categorical Response Data 1 1.2 Probability Distributions for Categorical Data 3 1.3 Statistical Inference for a Proportion 5 1.4 Statistical Inference for Discrete Data 10 1.5 Bayesian Inference for Proportions * 13 1.6 Using R Software for Statistical Inference about Proportions * 17 Exercises 21 2 Analyzing Contingency Tables 25 2.1 Probability Structure for Contingency Tables 26 2.2 Comparing Proportions in 2 × 2 Contingency Tables 29 2.3 The Odds Ratio 31 2.4 Chi-Squared Tests of Independence 36 2.5 Testing Independence for Ordinal Variables 42 2.6 Exact Frequentist and Bayesian Inference * 46 2.7 Association in Three-Way Tables 52 Exercises 56 3 Generalized Linear Models 65 3.1 Components of a Generalized Linear Model 66 3.2 Generalized Linear Models for Binary Data 68 3.3 Generalized Linear Models for Counts and Rates 72 3.4 Statistical Inference and Model Checking 76 3.5 Fitting Generalized Linear Models 82 Exercises 84 4 Logistic Regression 89 4.1 The Logistic Regression Model 89 4.2 Statistical Inference for Logistic Regression 94 4.3 Logistic Regression with Categorical Predictors 98 4.4 Multiple Logistic Regression 102 4.5 Summarizing Effects in Logistic Regression 107 4.6 Summarizing Predictive Power: Classification Tables, ROC Curves, and Multiple Correlation 110 Exercises 113 5 Building and Applying Logistic Regression Models 123 5.1 Strategies in Model Selection 123 5.2 Model Checking 130 5.3 Infinite Estimates in Logistic Regression 136 5.4 Bayesian Inference, Penalized Likelihood, and Conditional Likelihood for Logistic Regression * 140 5.5 Alternative Link Functions: Linear Probability and Probit Models * 145 5.6 Sample Size and Power for Logistic Regression * 150 Exercises 151 6 Multicategory Logit Models 159 6.1 Baseline-Category Logit Models for Nominal Responses 159 6.2 Cumulative Logit Models for Ordinal Responses 167 6.3 Cumulative Link Models: Model Checking and Extensions * 176 6.4 Paired-Category Logit Modeling of Ordinal Responses * 184 Exercises 187 7 Loglinear Models for Contingency Tables and Counts 193 7.1 Loglinear Models for Counts in Contingency Tables 194 7.2 Statistical Inference for Loglinear Models 200 7.3 The Loglinear – Logistic Model Connection 207 7.4 Independence Graphs and Collapsibility 210 7.5 Modeling Ordinal Associations in Contingency Tables 214 7.6 Loglinear Modeling of Count Response Variables * 217 Exercises 221 8 Models for Matched Pairs 227 8.1 Comparing Dependent Proportions for Binary Matched Pairs 228 8.2 Marginal Models and Subject-Specific Models for Matched Pairs 230 8.3 Comparing Proportions for Nominal Matched-Pairs Responses 235 8.4 Comparing Proportions for Ordinal Matched-Pairs Responses 239 8.5 Analyzing Rater Agreement * 243 8.6 Bradley–Terry Model for Paired Preferences * 247 Exercises 249 9 Marginal Modeling of Correlated, Clustered Responses 253 9.1 Marginal Models Versus Subject-Specific Models 254 9.2 Marginal Modeling: The Generalized Estimating Equations (GEE) Approach 255 9.3 Marginal Modeling for Clustered Multinomial Responses 260 9.4 Transitional Modeling, Given the Past 263 9.5 Dealing with Missing Data * 266 Exercises 268 10 Random Effects: Generalized Linear Mixed Models 273 10.1 Random Effects Modeling of Clustered Categorical Data 273 10.2 Examples: Random Effects Models for Binary Data 278 10.3 Extensions to Multinomial Responses and Multiple Random Effect Terms 284 10.4 Multilevel (Hierarchical) Models 288 10.5 Latent Class Models * 291 Exercises 295 11 Classification and Smoothing * 299 11.1 Classification: Linear Discriminant Analysis 300 11.2 Classification: Tree-Based Prediction 302 11.3 Cluster Analysis for Categorical Responses 306 11.4 Smoothing: Generalized Additive Models 310 11.5 Regularization for High-Dimensional Categorical Data (Large p) 313 Exercises 321 12 A Historical Tour of Categorical Data Analysis * 325 Appendix: Software for Categorical Data Analysis 331 A.1 R for Categorical Data Analysis 331 A.2 SAS for Categorical Data Analysis 332 A.3 Stata for Categorical Data Analysis 342 A.4 SPSS for Categorical Data Analysis 346 Brief Solutions to Odd-Numbered Exercises 349 Bibliography 363 Examples Index 365 Subject Index 369

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Book SynopsisTable of ContentsTABLE OF CONTENTS 1 INTRODUCTION TO STATISTICS 1 1 The Subject and Scope of Statistics 2 2 Statistics in Aid of Scientific Inquiry 4 3 Two Basic Concepts—Population and Sample 6 4 The Purposeful Collection of Data 11 Case Study: Statistics in Context 12 5 Objectives of Statistics 14 2 ORGANIZATION AND DESCRIPTION OF DATA 17 1 Main Types of Data 18 2 Describing Data by Tables and Graphs 19 3 Measures of Center 31 4 Measures of Variation 37 5 Checking the Stability of the Observations over Time 47 6 More on Graphics 50 Case Study: Statistics in Context 52 3 DESCRIPTIVE STUDY OF BIVARIATE DATA 64 1 Summarization of Bivariate Categorical Data 65 2 A Designed Experiment for Making a Comparison 69 3 Scatter Diagram of Bivariate Measurement Data 70 4 The Correlation Coefficient—A Measure of Linear Relation 73 5 Prediction of One Variable from another (Linear Regression) 82 4 PROBABILITY 91 1 Probability of an Event 92 2 Methods of Assigning Probability 97 3 Event Operations and Two Laws of Probability 102 4 Conditional Probability and Independence 109 5 Bayes’ Theorem 117 6 Random Sampling from a Finite Population 121 Case Study: Statistics in Context 126 5 PROBABILITY DISTRIBUTIONS 134 1 Random Variables 135 2 Probability Distribution of a Discrete Random Variable 138 3 Mean (Expected Value) and Standard Deviation of a Probability Distribution 144 4 Successes and Failures—Bernoulli Trials 150 5 The Binomial Distribution 154 6 The Poisson Distribution and Rare Events 165 6 THE NORMAL DISTRIBUTION 178 1 Probability Model for a Continuous Random Variable 179 2 The Normal Distribution—Its General Features 184 3 The Standard Normal Distribution 186 4 Probability Calculations with Normal Distributions 191 5 The Normal Approximation to the Binomial 194 6 Checking the Plausibility of a Normal Model 199 7 Transforming Observations to Attain Near Normality 202 7 VARIATION IN REPEATED SAMPLES—SAMPLING DISTRIBUTIONS 210 1 The Sampling Distribution of a Statistic 212 2 Distribution of the Sample Mean and the Central Limit Theorem 218 Case Study: Statistics in Context 228 8 DRAWING INFERENCES FROM LARGE SAMPLES 235 1 Two Types of Statistical Inference: Estimation and Testing 236 2 Point Estimation of a Population Mean 238 3 Confidence Interval Estimation of a Population Mean 242 4 Testing Hypotheses about a Population Mean 250 5 Inferences about a Population Proportion 261 9 SMALL SAMPLE INFERENCES FOR NORMAL POPULATIONS 278 1 Student’s t Distribution 279 2 Inferences about 𝜇—Small Sample Size 282 3 Relationship between Tests and Confidence Intervals 289 4 Inferences about the Standard Deviation 𝜎 (The Chi-Square Distribution) 291 5 Robustness of Inference Procedures 296 10 COMPARING TWO TREATMENTS 303 1 Two Designs: Independent Samples and Matched Pairs Sample 305 2 Inferences about the Difference of Means—Independent Large Samples 307 3 Inferences about the Difference of Means—Independent Small Samples from Normal Populations 314 4 Randomization and Its Role in Inference 323 5 Matched Pairs Comparisons 325 6 Choosing Between Independent Samples and a Matched Pairs Sample 332 7 Comparing Two Population Proportions 333 11 REGRESSION ANALYSIS I Simple Linear Regression 349 1 Regression with a Single Predictor 350 2 A Straight Line Regression Model 353 3 The Method of Least Squares 355 4 The Sampling Variability of the Least Squares Estimators—Tools for Inference 362 5 Important Inference Problems 363 6 The Strength of a Linear Relation 373 7 Remarks about the Straight Line Model Assumptions 377 12 REGRESSION ANALYSIS II Multiple Linear Regression and Other Topics 384 1 Nonlinear Relations and Linearizing Transformations 385 2 Multiple Linear Regression 390 3 Residual Plots to Check the Adequacy of a Statistical Model 398 13 ANALYSIS OF CATEGORICAL DATA 408 1 Formulating Testing Problems Concerning Categorical Data 409 2 Pearson’s χ2 Test for Goodness of Fit 411 3 Contingency Table with One Margin Fixed (Test of Homogeneity) 415 4 Contingency Table with Neither Margin Fixed (Test of Independence) 422 14 ANALYSIS OF VARIANCE (ANOVA) 432 1 Comparison of Several Treatments—One-Way Analysis of Variance 433 2 Population Model and Inferences for a One-Way Analysis of Variance 439 3 Simultaneous Confidence Intervals 443 4 Graphical Diagnostics and Displays to Supplement ANOVA 446 5 Randomized Block Experiments for Comparing k Treatments 448 15 NONPARAMETRIC INFERENCE 460 1 The Wilcoxon Rank-Sum Test for Comparing Two Treatments 461 2 Matched Pairs Comparisons 469 3 Measure of Correlation Based on Ranks 475 4 Concluding Remarks 478 APPENDIX A1 SUMMATION NOTATION 483 APPENDIX A2 RULES FOR COUNTING 488 APPENDIX A3 EXPECTATION AND STANDARD DEVIATION—PROPERTIES 490 APPENDIX A4 THE EXPECTED VALUE AND STANDARD DEVIATION OF X 496 APPENDIX B TABLES 498 Table 1 Random Digits 498 Table 2 Cumulative Binomial Probabilities 501 Table 3 Cumulative Poisson Probabilities 507 Table 4 Standard Normal Probabilities 509 Table 5 Percentage Points t𝛼 of t Distributions 511 Table 6 Percentage Points χ2𝛼 of χ2 Distributions 512 Table 7 Percentage Points of F( v1, v2 ) Distributions 513 Table 8 Selected Tail Probabilities for the Null Distribution of Wilcoxon’s Rank-Sum Statistic 515 Table 9 Selected Tail Probabilities for the Null Distribution of Wilcoxon’s Signed-Rank Statistic 520 Table F1 General Formulas for Inferences about a Mean (𝜇), Difference of Two Means ( 𝜇1 − 𝜇2 ) 522 Table F2 Inference about Proportions 523 Summary of Formulas Useful for Exams 524 DATA BANK 530 ANSWERS TO SELECTED ODD-NUMBERED EXERCISES 544 INDEX 557

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Book SynopsisStatistics Essentials For Dummies(9781119590309) was previously published asStatistics Essentials For Dummies (9780470618394). While this version features a newDummiescover and design, the content is the same as the prior release and should not be considered a new or updated product. Statistics Essentials For Dummiesnot only provides students enrolled in Statistics I with an excellent high-level overview of key concepts, but it also serves as a reference or refresher for students in upper-level statistics courses. Free of review and ramp-up material,Statistics Essentials For Dummiessticks to the point, with content focused on key course topics only. It provides discrete explanations of essential concepts taught in a typical first semester college-level statistics course, from odds and error margins to confidence intervals and conclusions. This guide is also a perfect reference for parents who need to review critical statistics concepts as they help high school students with homeworkTable of ContentsIntroduction 1 Chapter 1: Statistics in a Nutshell 5 Chapter 2: Descriptive Statistics 13 Chapter 3: Charts and Graphs 23 Chapter 4: The Binomial Distribution 35 Chapter 5: The Normal Distribution 45 Chapter 6: Sampling Distributions and the Central Limit Theorem 55 Chapter 7: Confidence Intervals 69 Chapter 8: Hypothesis Tests 87 Chapter 9: The t-Distribution 107 Chapter 10: Correlation and Regression 113 Chapter 11: Two-Way Tables 127 Chapter 12: A Checklist for Samples and Surveys 137 Chapter 13: A Checklist for Judging Experiments 147 Chapter 14: Ten Common Statistical Mistakes 155 Appendix: Tables for Reference 163 Index 171

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Book SynopsisAlgebra II Essentials For Dummies (9781119590873) was previously published as Algebra II Essentials For Dummies (9780470618400). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Passing grades in two years of algebra courses are required for high school graduation. Algebra II Essentials For Dummies covers key ideas from typical second-year Algebra coursework to help students get up to speed. Free of ramp-up material, Algebra II Essentials For Dummies sticks to the point, with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical Algebra II course, from polynomials, conics, and systems of equations to rational, exponential, and logarithmic functions. This guide is also a perfect reference for parents who need to review critical algebra concepts as they help students with homework assignments, as well as for adult learnTable of ContentsIntroduction 1 About This Book 1 Conventions Used in This Book 2 Foolish Assumptions 2 Icons Used in This Book 2 Where to Go from Here 3 Chapter 1: Making Advances in Algebra 5 Bringing Out the Best in Algebraic Properties 5 Making short work of the basic properties 6 Organizing your operations 7 Enumerating Exponential Rules 8 Multiplying and dividing exponents 8 Rooting out exponents 9 Powering up exponents 10 Working with negative exponents 10 Assigning Factoring Techniques 10 Making two terms factor 11 Factoring three terms 12 Factoring four or more terms by grouping 13 Chapter 2: Lining Up Linear Equations 15 Getting the First Degree: Linear Equations 15 Solving basic linear equations 16 Eliminating fractions 16 Lining Up Linear Inequalities 17 Solving basic inequalities 18 Introducing interval notation 19 Absolute Value: Keeping Everything in Line 20 Solving absolute value equations 20 Seeing through absolute value inequality 21 Chapter 3: Making Quick Work of Quadratic Equations 23 Using the Square Root Rule When Possible 24 Solving Quadratic Equations by Factoring 24 Factoring quadratic binomials 25 Factoring quadratic trinomials 26 The Quadratic Formula to the Rescue 27 Realizing rational solutions 27 Investigating irrational solutions 27 Promoting Quadratic-like Equations 28 Solving Quadratic Inequalities 29 Keeping it strictly quadratic 30 Signing up for fractions 31 Increasing the number of factors 33 Chapter 4: Rolling Along with Rational and Radical Equations 35 Rounding Up Rational Equations and Eliminating Fractions 35 Making your least common denominator work for you 36 Proposing proportions for solving rational equations 38 Reasoning with Radicals 39 Squaring both sides of the equation 39 Taking on two radicals 40 Dealing with Negative Exponents 42 Factoring out a negative exponent as a greatest common factor 42 Solving quadratic-like trinomials 43 Fiddling with Fractional Exponents 44 Solving equations by factoring fractional exponents 44 Promoting techniques for working with fractional exponents 44 Chapter 5: Forging Function Facts 47 Describing Function Characteristics 47 Denoting function notation 48 Using function notation to evaluate functions 48 Determining Domain and Range 49 Delving into domain 49 Wrangling with range 50 Counting on Even and Odd Functions 51 Determining whether even or odd 52 Using even and odd functions in graphs 53 Taking on Functions One-to-One 53 Defining which functions are one-to-one 54 Testing for one-to-one functions 54 Composing Functions 55 Composing yourself with functions 55 Composing with the difference quotient 56 Getting into Inverse Functions 57 Finding which functions are inverses 58 Finding an inverse of a function 59 Chapter 6: Graphing Linear and Quadratic Functions 61 Identifying Some Graphing Techniques 61 Finding x- and y-intercepts 62 Reflecting on a graph’s symmetry 62 Mastering the Graphs of Lines 64 Determining the slope of a line 64 Describing two line equations 65 Identifying parallel and perpendicular lines 67 Coming to Terms with the Standard Form of a Quadratic 67 Starting with “a” in the standard form 68 Following “a” with “b” and “c” 69 Eyeing a Quadratic’s Intercepts 69 Finding the one and only y-intercept 69 Getting at the x-intercepts 70 Finding the Vertex of a Parabola 71 Computing vertex coordinates 71 Linking up with the axis of symmetry 72 Sketching a Graph from the Available Information 72 Chapter 7: Pondering Polynomials 75 Sizing Up a Polynomial Equation 75 Identifying Intercepts and Turning Points 76 Interpreting relative value and absolute value 76 Dealing with intercepts and turning points 77 Solving for y-intercepts and x-intercepts 78 Determining When a Polynomial is Positive or Negative 79 Incorporating a sign line 79 Recognizing a sign change rule 80 Solving Polynomial Equations 81 Factoring for roots 81 Taking sane steps with the rational root theorem 82 Putting Descartes in charge of signs 84 Finding Roots Synthetically 86 Using synthetic division when searching for roots 86 Synthetically dividing by a binomial 88 Chapter 8: Being Respectful of Rational Functions 91 Examining Rational Functions 91 Deliberating on domain 92 Investigating intercepts 92 Assigning Roles to Asymptotes 93 Validating vertical asymptotes 93 Finding equations for horizontal asymptotes 94 Taking vertical and horizontal asymptotes to graphs 94 Getting the scoop on oblique (slant) asymptotes 96 Discounting Removable Discontinuities 97 Finding removable discontinuities by factoring 97 Evaluating the removals 98 Looking at Limits of Rational Functions 99 Determining limits at function discontinuities 100 Finding infinity 102 Looking at infinity 104 Chapter 9: Examining Exponential and Logarithmic Functions 107 Computing Exponentially 107 Getting to the Base of Exponential Functions 108 Classifying bases 108 Introducing the more frequently used bases: 10 and e 110 Exponential Equation Solutions 110 Creating matching bases 111 Quelling quadratic patterns 111 Looking into Logarithmic Functions 113 Presenting the properties of logarithms 113 Doing more with logs than sawing 115 Solving Equations Containing Logs 117 Seeing all logs created equal 117 Solving log equations by changing to exponentials 118 Chapter 10: Getting Creative with Conics 121 Posing with Parabolas 122 Generalizing the form of a parabola’s equation 123 Making short work of a parabola’s sketch 124 Changing a parabola’s equation to the standard form 125 Circling around a Conic 126 Getting Eclipsed by Ellipses 127 Determining the shape 129 Finding the foci 130 Getting Hyped for Hyperbolas 130 Including the asymptotes 131 Graphing hyperbolas 132 Chapter 11: Solving Systems of Equations 135 Looking at Solutions Using the Standard Linear-Systems Form 136 Solving Linear Systems by Graphing 136 Interpreting an intersection 137 Tackling the same line 137 Putting up with parallel lines 137 Using Elimination (Addition) to Solve Systems of Equations 138 Finding Substitution to Be a Satisfactory Substitute 139 Variable substituting made easy 139 Writing solutions for coexisting lines 140 Taking on Systems of Three Linear Equations 141 Finding the solution of a system of three linear equations 141 Generalizing with a system solution 143 Increasing the Number of Equations 144 Intersecting Parabolas and Lines 146 Determining if and where lines and parabolas cross paths 147 Determining that there’s no solution 149 Crossing Parabolas with Circles 150 Finding multiple intersections 150 Sifting through the possibilities for solutions 151 Chapter 12: Taking the Complexity Out of Complex Numbers 155 Simplifying Powers of i 156 Getting More Complex with Complex Numbers 157 Performing complex operations 157 Performing complex division by multiplying by the conjugate 158 Simplifying reluctant radicals 159 Unraveling Complex Solutions in Quadratic Equations 160 Investigating Polynomials with Complex Roots 160 Classifying conjugate pairs 161 Making use of complex zeros 161 Chapter 13: Ten (or So) Special Formulas 163 Using Multiplication to Add 163 Factoring in Factorial 164 Picking Out Permutations 164 Collecting Combinations 164 Adding n Integers 165 Adding n Squared Integers 165 Adding Odd Numbers 165 Going for the Geometric 166 Calculating Compound Interest 166 Index 167

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Book SynopsisA PRACTICAL GUIDE TO OPTIMIZATION PROBLEMS WITH DISCRETE OR INTEGER VARIABLES, REVISED AND UPDATED The revised second edition of Integer Programming explains in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems. The second edition also includes information on the remarkable progress in the development of mixed integer programming solvers in the 22 years since the first edition of the book appeared. The updated text includes information on the most recent developments in the field such as the much improved preprocessing/presolving and the many new ideas for primal heuristics included in the solvers. The result has been a speed-up of several orders of magnitude. The other major change reflected in the text is the widespread use of decomposition algorithms, in particular column generation (branch-(cut)-and-price) and Benders' decompositiTable of ContentsPreface to the Second Edition xii Preface to the First Edition xiii Abbreviations and Notation xvii About the Companion Website xix 1 Formulations 1 1.1 Introduction 1 1.2 What Is an Integer Program? 3 1.3 Formulating IPs and BIPs 5 1.4 The Combinatorial Explosion 8 1.5 Mixed Integer Formulations 9 1.6 Alternative Formulations 12 1.7 Good and Ideal Formulations 15 1.8 Notes 18 1.9 Exercises 19 2 Optimality, Relaxation, and Bounds 25 2.1 Optimality and Relaxation 25 2.2 Linear Programming Relaxations 27 2.3 Combinatorial Relaxations 28 2.4 Lagrangian Relaxation 29 2.5 Duality 30 2.6 Linear Programming and Polyhedra 32 2.7 Primal Bounds: Greedy and Local Search 34 2.8 Notes 38 2.9 Exercises 38 3 Well-Solved Problems 43 3.1 Properties of Easy Problems 43 3.2 IPs with Totally Unimodular Matrices 44 3.3 Minimum Cost Network Flows 46 3.4 Special Minimum Cost Flows 48 3.4.1 Shortest Path 48 3.4.2 Maximum s − t Flow 49 3.5 Optimal Trees 50 3.6 Submodularity and Matroids 54 3.7 Two Harder Network Flow Problems 57 3.8 Notes 59 3.9 Exercises 60 4 Matchings and Assignments 63 4.1 Augmenting Paths and Optimality 63 4.2 Bipartite Maximum Cardinality Matching 65 4.3 The Assignment Problem 67 4.4 Matchings in Nonbipartite Graphs 73 4.5 Notes 74 4.6 Exercises 75 5 Dynamic Programming 79 5.1 Some Motivation: Shortest Paths 79 5.2 Uncapacitated Lot-Sizing 80 5.3 An Optimal Subtree of a Tree 83 5.4 Knapsack Problems 84 5.4.1 0–1 Knapsack Problems 85 5.4.2 Integer Knapsack Problems 86 5.5 The Cutting Stock Problem 89 5.6 Notes 91 5.7 Exercises 92 6 Complexity and Problem Reductions 95 6.1 Complexity 95 6.2 Decision Problems, and Classes NP and P 96 6.3 Polynomial Reduction and the Class NPC 98 6.4 Consequences of P =NP orP ≠NP 103 6.5 Optimization and Separation 104 6.6 The Complexity of Extended Formulations 105 6.7 Worst-Case Analysis of Heuristics 106 6.8 Notes 109 6.9 Exercises 110 7 Branch and Bound 113 7.1 Divide and Conquer 113 7.2 Implicit Enumeration 114 7.3 Branch and Bound: an Example 116 7.4 LP-Based Branch and Bound 120 7.5 Using a Branch-and-Bound/Cut System 123 7.6 Preprocessing or Presolve 129 7.7 Notes 134 7.8 Exercises 135 8 Cutting Plane Algorithms 139 8.1 Introduction 139 8.2 Some Simple Valid Inequalities 140 8.3 Valid Inequalities 143 8.4 A Priori Addition of Constraints 147 8.5 Automatic Reformulation or Cutting Plane Algorithms 149 8.6 Gomory’s Fractional Cutting Plane Algorithm 150 8.7 Mixed Integer Cuts 153 8.7.1 The Basic Mixed Integer Inequality 153 8.7.2 The Mixed Integer Rounding (MIR) Inequality 155 8.7.3 The Gomory Mixed Integer Cut 155 8.7.4 Split Cuts 156 8.8 Disjunctive Inequalities and Lift-and-Project 158 8.9 Notes 161 8.10 Exercises 162 9 Strong Valid Inequalities 167 9.1 Introduction 167 9.2 Strong Inequalities 168 9.3 0–1 Knapsack Inequalities 175 9.3.1 Cover Inequalities 175 9.3.2 Strengthening Cover Inequalities 176 9.3.3 Separation for Cover Inequalities 178 9.4 Mixed 0–1 Inequalities 179 9.4.1 Flow Cover Inequalities 179 9.4.2 Separation for Flow Cover Inequalities 181 9.5 The Optimal Subtour Problem 183 9.5.1 Separation for Generalized Subtour Constraints 183 9.6 Branch-and-Cut 186 9.7 Notes 189 9.8 Exercises 190 10 Lagrangian Duality 195 10.1 Lagrangian Relaxation 195 10.2 The Strength of the Lagrangian Dual 200 10.3 Solving the Lagrangian Dual 202 10.4 Lagrangian Heuristics 205 10.5 Choosing a Lagrangian Dual 207 10.6 Notes 209 10.7 Exercises 210 11 Column (and Row) Generation Algorithms 213 11.1 Introduction 213 11.2 The Dantzig–Wolfe Reformulation of an IP 215 11.3 Solving the LP Master Problem: Column Generation 216 11.4 Solving the Master Problem: Branch-and-Price 219 11.5 Problem Variants 222 11.5.1 Handling Multiple Subproblems 222 11.5.2 Partitioning/Packing Problems with Additional Variables 223 11.5.3 Partitioning/Packing Problems with Identical Subsets 224 11.6 Computational Issues 225 11.7 Branch-Cut-and-Price: An Example 226 11.7.1 A Capacitated Vehicle Routing Problem 226 11.7.2 Solving the Subproblems 229 11.7.3 The Load Formulation 230 11.8 Notes 231 11.9 Exercises 232 12 Benders’ Algorithm 235 12.1 Introduction 235 12.2 Benders’ Reformulation 236 12.3 Benders’ with Multiple Subproblems 240 12.4 Solving the Linear Programming Subproblems 242 12.5 Integer Subproblems: Basic Algorithms 244 12.5.1 Branching in the (x, 𝜂, y)-Space 244 12.5.2 Branching in (x, 𝜂)-Space and “No-Good” Cuts 246 12.6 Notes 247 12.7 Exercises 248 13 Primal Heuristics 251 13.1 Introduction 251 13.2 Greedy and Local Search Revisited 252 13.3 Improved Local Search Heuristics 255 13.3.1 Tabu Search 255 13.3.2 Simulated Annealing 256 13.3.3 Genetic Algorithms 257 13.4 Heuristics Inside MIP Solvers 259 13.4.1 Construction Heuristics 259 13.4.2 Improvement Heuristics 261 13.5 User-Defined MIP heuristics 262 13.6 Notes 265 13.7 Exercises 266 14 From Theory to Solutions 269 14.1 Introduction 269 14.2 Software for Solving Integer Programs 269 14.3 How Do We Find an Improved Formulation? 272 14.4 Multi-item Single Machine Lot-Sizing 277 14.5 A Multiplexer Assignment Problem 282 14.6 Integer Programming and Machine Learning 285 14.7 Notes 287 14.8 Exercises 287 References 291 Index 311

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Book SynopsisTable of Contents1 Limits and Continuity 1 1.1 Limits (An Intuitive Approach) 1 1.2 Computing Limits 13 1.3 Limits at Infinity; End Behavior of a Function 22 1.4 Limits (Discussed More Rigorously) 31 1.5 Continuity 40 1.6 Continuity of Trigonometric Functions 51 2 The Derivative 59 2.1 Tangent Lines and Rates of Change 59 2.2 The Derivative Function 69 2.3 Introduction to Techniques of Differentiation 80 2.4 The Product and Quotient Rules 88 2.5 Derivatives of Trigonometric Functions 93 2.6 The Chain Rule 98 2.7 Implicit Differentiation 105 2.8 Related Rates 112 2.9 Local Linear Approximation; Differentials 119 3 The Derivative in Graphing and Applications 130 3.1 Analysis of Functions I: Increase, Decrease, and Concavity 130 3.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 139 3.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 148 3.4 Absolute Maxima and Minima 157 3.5 Applied Maximum and Minimum Problems 164 3.6 Rectilinear Motion 177 3.7 Newton’s Method 185 3.8 Rolle’s Theorem; Mean-Value Theorem 191 4 Integration 203 4.1 An Overview of the Area Problem 203 4.2 The Indefinite Integral 208 4.3 Integration by Substitution 217 4.4 The Definition of Area as a Limit; Sigma Notation 223 4.5 The Definite Integral 233 4.6 The Fundamental Theorem of Calculus 242 4.7 Rectilinear Motion Revisited Using Integration 253 4.8 Average Value of a Function and its Applications 262 4.9 Evaluating Definite Integrals by Substitution 266 5 Applications of the Definite Integral in Geometry, Science, and Engineering 277 5.1 Area Between Two Curves 277 5.2 Volumes by Slicing; Disks and Washers 284 5.3 Volumes by Cylindrical Shells 294 5.4 Length of a Plane Curve 300 5.5 Area of a Surface of Revolution 306 5.6 Work 311 5.7 Moments, Centers of Gravity, and Centroids 319 5.8 Fluid Pressure and Force 328 6 Exponential, Logarithmic, and Inverse Trigonometric Functions 336 6.1 Exponential and Logarithmic Functions 336 6.2 Derivatives and Integrals Involving Logarithmic Functions 347 6.3 Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions 353 6.4 Graphs and Applications Involving Logarithmic and Exponential Functions 360 6.5 L’Hôpital’s Rule; Indeterminate Forms 367 6.6 Logarithmic and Other Functions Defined by Integrals 376 6.7 Derivatives and Integrals Involving Inverse Trigonometric Functions 387 6.8 Hyperbolic Functions and Hanging Cables 398 7 Principles of Integral Evaluation 412 7.1 An Overview of Integration Methods 412 7.2 Integration by Parts 415 7.3 Integrating Trigonometric Functions 423 7.4 Trigonometric Substitutions 431 7.5 Integrating Rational Functions by Partial Fractions 437 7.6 Using Computer Algebra Systems and Tables of Integrals 445 7.7 Numerical Integration; Simpson’s Rule 454 7.8 Improper Integrals 467 8 Mathematical Modeling with Differential Equations 481 8.1 Modeling with Differential Equations 481 8.2 Separation of Variables 487 8.3 Slope Fields; Euler’s Method 498 8.4 First-Order Differential Equations and Applications 504 9 Infinite Series 514 9.1 Sequences 514 9.2 Monotone Sequences 524 9.3 Infinite Series 531 9.4 Convergence Tests 539 9.5 The Comparison, Ratio, and Root Tests 547 9.6 Alternating Series; Absolute and Conditional Convergence 553 9.7 Maclaurin and Taylor Polynomials 563 9.8 Maclaurin and Taylor Series; Power Series 573 9.9 Convergence of Taylor Series 582 9.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 591 10 Parametric and Polar Curves; Conic Sections 605 10.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 605 10.2 Polar Coordinates 617 10.3 Tangent Lines, Arc Length, and Area for Polar Curves 630 10.4 Conic Sections 639 10.5 Rotation of Axes; Second-Degree Equations 656 10.6 Conic Sections in Polar Coordinates 661 11 Three-Dimensional Space; Vectors 674 11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 674 11.2 Vectors 680 11.3 Dot Product; Projections 691 11.4 Cross Product 700 11.5 Parametric Equations of Lines 710 11.6 Planes in 3-Space 717 11.7 Quadric Surfaces 725 11.8 Cylindrical and Spherical Coordinates 735 12 Vector-Valued Functions 744 12.1 Introduction to Vector-Valued Functions 744 12.2 Calculus of Vector-Valued Functions 750 12.3 Change of Parameter; Arc Length 759 12.4 Unit Tangent, Normal, and Binormal Vectors 768 12.5 Curvature 773 12.6 Motion Along a Curve 781 12.7 Kepler’s Laws of Planetary Motion 794 13 Partial Derivatives 805 13.1 Functions of Two or More Variables 805 13.2 Limits and Continuity 815 13.3 Partial Derivatives 824 13.4 Differentiability, Differentials, and Local Linearity 837 13.5 The Chain Rule 845 13.6 Directional Derivatives and Gradients 855 13.7 Tangent Planes and Normal Vectors 866 13.8 Maxima and Minima of Functions of Two Variables 872 13.9 Lagrange Multipliers 883 14 Multiple Integrals 894 14.1 Double Integrals 894 14.2 Double Integrals over Nonrectangular Regions 902 14.3 Double Integrals in Polar Coordinates 910 14.4 Surface Area; Parametric Surfaces 918 14.5 Triple Integrals 930 14.6 Triple Integrals in Cylindrical and Spherical Coordinates 938 14.7 Change of Variables in Multiple Integrals; Jacobians 947 14.8 Centers of Gravity Using Multiple Integrals 959 15 Topics in Vector Calculus 971 15.1 Vector Fields 971 15.2 Line Integrals 980 15.3 Independence of Path; Conservative Vector Fields 995 15.4 Green’s Theorem 1005 15.5 Surface Integrals 1013 15.6 Applications of Surface Integrals; Flux 1021 15.7 The Divergence Theorem 1030 15.8 Stokes’ Theorem 1039 A Appendices A Trigonometry Review (Summary) A1 B Functions (Summary) A8 C New Functions from Old (Summary) A11 D Families of Functions (Summary) A16 E Inverse Functions (Summary) A23 Answers to Odd-Numbered Exercises A28 Index I-1 Web Appendices (online only) Available for download at www.wiley.com/college/anton or at www.howardanton.com and in WileyPLUS. A Trigonometry Review B Functions C New Functions from Old D Families of Functions E Inverse Functions F Real Numbers, Intervals, and Inequalities G Absolute Value H Coordinate Planes, Lines, And Linear Functions I Distance, Circles, And Quadratic Equations J Solving Polynomial Equations K Graphing Functions Using Calculators and Computer Algebra Systems L Selected Proofs M Early Parametric Equations Option N Mathematical Models O The Discriminant P Second-Order Linear Homogeneous Differential Equations Chapter Web Projects: Expanding the Calculus Horizon (online only) Available for download at www.wiley.com/college/anton or at www.howardanton.com and in WileyPLUS. Robotics – Chapter 2 Railroad Design – Chapter 7 Iteration and Dynamical Systems – Chapter 9 Comet Collision – Chapter 10 Blammo the Human Cannonball – Chapter 12 Hurricane Modeling – Chapter 15

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Book SynopsisTable of ContentsCHAPTER 1 Limits and Continuity 1.1 Limits (An Intuitive Approach) 1.2 Computing Limits 1.3 Limits at Infinity; End Behavior of a Function 1.4 Limits (Discussed More Rigorously) 1.5 Continuity 1.6 Trigonometric Functions 1.7 Inverse Trigonometric Functions 1.8 Exponential and Logarithmic Functions CHAPTER 2 The Derivative 2.1 Tangent Lines and Rates of Change 2.2 The Derivative Function 2.3 Introduction to Techniques of Differentiation 2.4 The Product and Quotient Rules 2.5 Derivatives of Trigonometric Functions 2.6 The Chain Rule CHAPTER 3 Differentiation 3.1 Implicit Differentiation 3.2 Derivatives of Logarithmic Functions 3.3 Derivatives of Exponential and Inverse Trigonometric Functions 3.4 Related Rates 3.5 Local Linear Approximation; Differentials 3.6 L'Hôpital's Rule; Indeterminate Forms CHAPTER 4 The Derivative in Graphing and Applications 4.1 Analysis of Functions I: Increase, Decrease, and Concavity 4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 4.4 Absolute Maxima and Minima 4.5 Applied Maximum and Minimum Problems 4.6 Rectilinear Motion 4.7 Newton's Method 4.8 Rolle's Theorem; Mean-Value Theorem CHAPTER 5 Integration 5.1 An Overview of Area and Speed-Distance Problems 5.2 The Indefinite Integral 5.3 Integration by Substitution 5.4 The Definition of Area as a Limit; Sigma Notation 5.5 The Definite Integral 5.6 The Fundamental Theorem of Calculus 5.7 Rectilinear Motion Revisited Using Integration 5.8 Average Value of a Function and its Applications 5.9 Evaluating Definite Integrals by Substitution 5.10 Logarithmic and Other Functions Defined by Integrals CHAPTER 6 Applications of the Definite Integral 6.1 Area Between Two Curves 6.2 Volumes by Slicing; Disks and Washers 6.3 Volumes by Cylindrical Shells 6.4 Length of a Plane Curve 6.5 Area of a Surface of Revolution 6.6 Work 6.7 Moments, Centers of Gravity, and Centroids 6.8 Fluid Pressure and Force 6.9 Hyperbolic Functions and Hanging Cables CHAPTER 7 Principles of Integral Evaluation 7.1 An Overview of Integration Methods 7.2 Integration by Parts 7.3 Integrating Trigonometric Functions 7.4 Trigonometric Substitutions 7.5 Integrating Rational Functions by Partial Fractions 7.6Using Computer Algebra Systems and Tables of Integrals 7.7 Numerical Integration; Simpson's Rule 7.8 Improper Integrals CHAPTER 8 Mathematical Modeling with Differential Equations 8.1 Modeling with Differential Equations 8.2 Separation of Variables 8.3 Slope Fields; Euler's Method 8.4 First-Order Differential Equations and Applications 8.5 Prey-Predator Model CHAPTER 9 Parametric and Polar Curves; Conic Sections 9.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves 9.2 Polar Coordinates 9.3 Tangent Lines, Arc Length, and Area for Polar Curves 9.4 Conic Sections 9.5 Rotation of Axes; Second-Degree Equations 9.6 Conic Sections in Polar Coordinates CHAPTER 10 Sequence and Infinite Series 10.1 Sequences 10.2 Monotone Sequences 10.3 Infinite Series 10.4 Convergence Tests 10.5 The Comparison, Ratio, and Root Tests 10.6 Alternating Series; Absolute and Conditional Convergence 10.7 Maclaurin and Taylor Polynomials 10.8 Maclaurin and Taylor Series; Power Series 10.9 Convergence of Taylor Series 10.10 Differentiating and Integrating Power Series; Modeling with Taylor Series CHAPTER 11 Three-dimensional Space; Vectors 11.1 Rectangular Coordinates in 3-space; Spheres; Cylindrical Surfaces 11.2 Vectors 11.3 Dot Product; Projections 11.4 Cross Product 11.5 Parametric Equations of Lines 11.6 Planes in 3-space 11.7 Quadric Surfaces 11.8 Cylindrical and Spherical Coordinates CHAPTER 12 Vector-Valued Functions 12.1 Introduction to Vector-Valued Functions 12.2 Calculus of Vector-Valued Functions 12.3 Change of Parameter; Arc Length 12.4 Unit Tangent, Normal, and Binormal Vectors 12.5 Curvature 12.6 Motion Along a Curve 12.7 Kepler's Laws of Planetary Motion CHAPTER 13 Partial Derivatives 13.1 Functions of Two or More Variables 13.2 Limits and Continuity 13.3 Partial Derivatives 13.4 Differentiability, Differentials, and Local Linearity 13.5 The Chain Rule 13.6 Directional Derivatives and Gradients 13.7 Tangent Planes and Normal Vectors 13.8 Maxima and Minima of Functions of Two Variables 13.9 Lagrange Multipliers CHAPTER 14 Multiple Integrals 14.1 Double Integrals 14.2 Double Integrals Over Nonrectangular Regions 14.3 Double Integrals in Polar Coordinates 14.4 Surface Area; Parametric Surfaces 14.5 Triple Integrals 14.6 Triple Integrals in Cylindrical and Spherical Coordinates 14.7 Change of Variables in Multiple Integrals; Jacobians 14.8Centers of Gravity Using Multiple Integrals CHAPTER 15 Vector Calculus 15.1 Vector Fields 15.2 Line Integrals 15.3 Independence of Path; Conservative Vector Fields 15.4 Green's Theorem 15.5 Surface Integrals 15.6 Applications of Surface Integrals; Flux 15.7 The Divergence Theorem 15.8 Stokes' Theorem APPENDICES A TRIGONOMETRY SUMMARY B FUNCTIONS (SUMMARY) C NEW FUNCTIONS FROM OLD (SUMMARY) D FAMILIES OF FUNCTIONS (SUMMARY) E Inverse Functions (Summary READY REFERENCE RR-1 ANSWERS TO ODD-NUMBERED EXERCISES Ans-1 INDEX Ind-1 WEB APPENDICES (online only) Available for download at wwww.wiley.com A TRIGONOMETRY REVIEW B FUNCTIONS C NEW FUNCTIONS FROM OLD D FAMILIES OF FUNCTIONS E INVERSE FUNCTIONS F REAL NUMBERS, INTERVALS, AND INEQUALITIES G ABSOLUTE VALUE H COORDINATE PLANES, LINES, AND LINEAR FUNCTIONS I DISTANCE, CIRCLES, AND QUADRATIC EQUATIONS J SOLVING POLYNOMIAL EQUATIONS K GRAPHING FUNCTIONS USING CALCULATORS AND COMPUTER ALGEBRA SYSTEMS L SELECTED PROOFS M EARLY PARAMETRIC EQUATIONS OPTION N MATHEMATICAL MODELS O THE DISCRIMINANT P SECOND-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS Chapter Web Projects: Expanding the Calculus Horizon (online only) Available for download at www.wiley.com Robotics -- Chapter 2 Railroad Design -- Chapter 7 Iteration and Dynamical Systems -- Chapter 9 Comet Collision -- Chapter 10 Blammo the Human Cannonball -- Chapter 12 Hurricane Modeling -- Chapter 15

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Book SynopsisTable of ContentsIntroduction 1 About This Book 1 Foolish Assumptions 2 Icons Used in This Book 2 Beyond the Book 3 Where to Go from Here 3 Book 1: Starting Out With Numbers and Properties 5 Chapter 1: Assembling Your Tools: Number Systems 7 Identifying Numbers by Name 8 Realizing real numbers 8 Counting on natural numbers 8 Whittling out whole numbers 8 Integrating integers 9 Being reasonable: Rational numbers 9 Restraining irrational numbers 9 Picking out primes and composites 10 Zero: It’s Complicated 10 Imagining imaginary numbers 10 Coping with complex numbers 10 Placing Numbers on the Number Line 12 Speaking in Algebra 13 Being precise with words 13 Describing the size of an expression 15 Relating operations with symbols 15 Taking Aim at Algebra-Speak 17 Herding numbers with grouping symbols 17 Defining relationships 19 Taking on algebraic tasks 20 Practice Questions Answers and Explanations 22 Whaddya Know? Chapter 1 Quiz 23 Answers to Chapter 1 Quiz 25 Chapter 2: Deciphering Signs in Expressions 27 Assigning Numbers Their Place 27 Using the number line 28 Comparing positives and negatives with symbols 29 Zeroing in on Zero 31 Going in for Operations 32 Sorting out types of operations 32 Tackling the Basic Binary Operations 35 Adding signed numbers 35 Making a Difference with Signed Numbers 38 Multiplying Signed Numbers 40 Dividing Signed Numbers 41 Working with Nothing: Zero and Signed Numbers 42 Practice Questions Answers and Explanations 44 Whaddya Know? Chapter 2 Quiz 47 Answers to Chapter 2 Quiz 48 Chapter 3: Incorporating Algebraic Properties 49 Getting a Grip on Grouping Symbols 49 Spreading, Grouping, and Changing the Order 52 Distributing the wealth 52 Making Associations Work 53 Computing by Commuting 55 Relating Inverses and Identities 56 Investigating Inverses 56 Identifying Identities 58 Working with Factorial 59 Applying the Greatest Integer Function 60 Practice Question Answers and Explanations 62 Whaddya Know? Chapter 3 Quiz 66 Answers to Chapter 3 Quiz 67 Chapter 4: Coordinating Fractions and Decimals 69 Converting Improper Fractions and Mixed Numbers 70 Finding Fraction Equivalences 72 Rewriting fractions 72 Determining lowest terms 74 Making Proportional Statements 75 Finding Common Denominators 77 Creating common denominators from multiples of factors 78 Using the box method 80 Applying Fractional Operations 81 Adding and subtracting fractions 81 Multiplying and dividing fractions 83 Simplifying Complex Fractions 86 Performing Operations with Decimals 88 Changing Fractions to Decimals and Vice Versa 89 Making fractions become decimals 90 Rounding decimals 91 Writing decimals as equivalent fractions 91 Practice Question Answers and Explanations 94 Whaddya Know? Chapter 4 Quiz 101 Answers to Chapter 4 Quiz 103 Book 2: Operating On Operations 105 Chapter 5: Taming Rampaging Radicals 107 Simplifying Radical Terms 108 Working through Radical Expressions 109 Recognizing perfect square terms 109 Rewriting radical terms 110 Rationalizing Fractions 113 Managing Radicals as Exponential Terms 114 Using Fractional Exponents 116 Making the switch to fractional exponents 117 Simplifying expressions with exponents 118 Estimating Answers 119 Practice Questions Answers and Explanations 120 Whaddya Know? Chapter 5 Quiz 124 Answers to Chapter 5 Quiz 125 Chapter 6: Exploring Exponents 127 Powering up with Exponential Notation 127 Using Negative Exponents 130 Multiplying and Dividing Exponentials 132 Multiplying the same base 132 Multiplying the same power 133 Dividing with exponents 135 Raising Powers to Powers 137 Testing the Power of Zero 139 Writing Numbers with Scientific Notation 140 Practice Questions Answers and Explanations 143 Whaddya Know? Chapter 6 Quiz 145 Answers to Chapter 6 Quiz 146 Book 3: Making Things Simple by Simplifying 149 Chapter 7: Simplifying Algebraic Expressions 151 Addressing the Order of Operations 152 Adding and Subtracting Like Terms 154 Multiplying and Dividing Algebraically 157 Dealing with factors 157 Diving into dividing 158 Gathering Terms with Grouping Symbols 160 Evaluating Expressions 163 Checking Your Answers 165 Seeing if it makes sense 165 Plugging in values 166 Practice Questions Answers and Explanations 168 Whaddya Know? Chapter 7 Quiz 171 Answers to Chapter 7 Quiz 172 Chapter 8: Working with Numbers in Their Prime 175 Beginning with the Basics 176 Composing Composite Numbers 178 Writing Prime Factorizations 178 Dividing while standing on your head 178 Getting to the root of primes with a tree 180 Wrapping your head around the rules of divisibility 182 Making Use of a Prime Factor 185 Taking primes into account 185 Pulling out factors and leaving the rest 187 Practice Questions Answers and Explanations 190 Whaddya Know? Chapter 8 Quiz 194 Answers to Chapter 8 Quiz 195 Chapter 9: Specializing in Multiplication Matters 197 Distributing One Factor Over Many 198 Distributing Signs 200 Mixing It up with Numbers and Variables 201 Negative exponents yielding fractional answers 203 Working with Fractional Powers 205 Distributing More Than One Term 207 Distributing binomials 207 Distributing trinomials 209 Curses, Foiled Again — Or Not 210 Squaring Binomials 211 Multiplying the Sum and Difference of the Same Two Terms 212 Powering Up Binomials 213 Cubing binomials 213 Raising Binomials to Higher Powers 215 Creating the Sum and Difference of Cubes 217 Multiplying Conjugates 218 Practice Questions Answers and Explanations 220 Whaddya Know? Chapter 9 Quiz 225 Answers to Chapter 9 Quiz 226 Chapter 10: Dividing the Long Way to Simplify Algebraic Expressions 229 Dividing by a Monomial 229 Dividing by a Binomial 231 Dividing by Polynomials with More Terms 233 Simplifying Division Synthetically 235 Practice Questions Answers and Explanations 237 Whaddya Know? Chapter 10 Quiz 240 Answers to Chapter 10 Quiz 241 Book 4: Factoring 243 Chapter 11: Figuring on Factoring 245 Factoring out the Greatest Common Factor 245 Factoring out numbers 246 Factoring out variables 249 Unlocking combinations of numbers and variables 252 Using the Box Method 255 Changing Factoring into a Division Problem 257 Reducing Algebraic Fractions 258 Practice Questions Answers and Explanations 260 Whaddya Know? Chapter 11 Quiz 262 Answers to Chapter 11 Quiz 264 Chapter 12: Taking the Bite out of Binomial Factoring 267 Reining in Big and Tiny Numbers 268 Factoring the Difference of Squares 269 Factoring Differences and Sums of Cubes 271 Making Factoring a Multiple Mission 274 Practice Questions Answers and Explanations 277 Whaddya Know? Chapter 12 Quiz 279 Answers to Chapter 12 Quiz 280 Chapter 13: Factoring Trinomials and Special Polynomials 281 Recognizing the Standard Quadratic Expression 281 Focusing First on the Greatest Common Factor 283 Unwrapping the FOILing Package 284 The opening to unFOIL 284 Coming to the end of the FOIL roll 287 Factoring Quadratic-Like Trinomials 290 Factoring Trinomials Using More Than One Method 291 Factoring by Grouping 293 Putting All the Factoring Together and Making Factoring Choices 297 Combining unFOIL and the GCF 297 Grouping and unFOILing in the same package 298 Incorporating the Remainder Theorem 301 Synthesizing with synthetic division 302 Choosing numbers for synthetic division 303 Practice Questions Answers and Explanations 305 Whaddya Know? Chapter 13 Quiz 310 Answers to Chapter 13 Quiz 311 Book 5: Solving Linear And Polynomial Equations 313 Chapter 14: Establishing Ground Rules for Solving Equations 315 Creating the Correct Setup for Solving Equations 316 Setting up equations for further action 316 Making plans for solving equations 316 Keeping Equations Balanced 318 Balancing with binary operations 318 Squaring both sides and suffering the consequences 320 Taking a root of both sides 322 Solving with Reciprocals 323 Making a List and Checking It Twice 324 Doing a reality check 324 Thinking like a car mechanic when checking your work 325 Practice Problems Answers and Explanations 328 Whaddya Know? Chapter 14 Quiz 330 Answers to Chapter 14 Quiz 331 Chapter 15: Lining Up Linear Equations 333 Playing by the Rules 334 Using the Addition/Subtraction Property 334 Using the Multiplication/Division Property 336 Devising a method using division 336 Making the most of multiplication 337 Reciprocating the invitation 338 Putting Several Operations Together 339 Solving Linear Equations with Grouping Symbols 343 Nesting isn’t for the birds 343 Distributing first 343 Multiplying or dividing before distributing 346 Working with Proportions 349 Using the rules for proportions 349 Transforming fractional equations into proportions 351 Solving for Variables in Formulas 352 Practice Questions Answers and Explanations 355 Whaddya Know? Chapter 15 Quiz 363 Answers to Chapter 15 Quiz 364 Chapter 16: Muscling Up to Quadratic Equations 367 Using the Square-Root Rule 368 Factoring for a Solution 370 Zeroing in on the multiplication property of zero 370 Assigning the greatest common factor and multiplication property of zero to solving quadratics 372 Solving Quadratics with Three Terms 373 Using the Quadratic Formula 379 Completing the Square 383 Imagining the Worst with Imaginary Numbers 384 Practice Problems Answers and Explanations 387 Whaddya Know? Chapter 16 Quiz 392 Answers to Chapter 16 Quiz 393 Book 6: Dealing With Non-Polynomial Equations and Inequalities 395 Chapter 17: Yielding to Higher Powers 397 Queuing Up to Cubic Equations 397 Solving perfectly cubed equations 398 Working with the not-so-perfectly cubed 400 Going for the greatest common factor 401 Grouping cubes 404 Solving cubics with integers 405 Determining How Many Possible Roots 407 Applying the Rational Root Theorem 408 Using the Factor/Root Theorem 410 Solving by Factoring 411 Solving Powers That Are Quadratic-Like 412 Solving Synthetically 416 Practice Questions Answers and Explanations 420 Whaddya Know? Chapter 17 Quiz 426 Answers to Chapter 17 Quiz 427 Chapter 18: Reeling in Radical and Absolute Value Equations 429 Raising Both Sides to Solve Radical Equations 430 Powering up by squaring both sides 430 Raising to higher powers 433 Doubling the Fun with Radical Equations .435 Solving Absolute Value Equations 437 Making linear absolute value equations absolutely wonderful 437 Factoring absolute value equations for solutions 440 Checking for Absolute Value Extraneous Roots 441 Practice Questions Answers and Explanations 443 Whaddya Know? Chapter 18 Quiz 447 Answers to Chapter 18 Quiz 448 Chapter 19: Getting Even with Inequalities 449 Defining the Inequality Notation 450 Pointing in the right direction 450 Grappling with graphing inequalities 450 Using the Rules to Work on Inequality Statements 451 Rewriting Inequalities Using Interval Notation 453 Solving Linear Inequalities 455 Solving Quadratic Inequalities 457 Dealing with Polynomial and Rational Inequalities 460 Solving Absolute-Value Inequalities 463 Solving Complex Inequalities 465 Practice Questions Answers and Explanations 467 Whaddya Know? Chapter 19 Quiz 471 Answers to Chapter 19 Quiz 472 Book 7: Evaluating Formulas and Story Problems 475 Chapter 20: Facing Up to Formulas 477 Working with Formulas 477 Measuring Up 479 Finding out how long: Units of length 479 Putting the Pythagorean Theorem to work 482 Deciphering Perimeter, Area, and Volume 484 Using perimeter formulas to get around 484 Squaring off with area formulas 486 Soaring with Heron’s formula 488 Working with volume formulas 490 Getting Interested in Using Percent 492 Compounding interest formulas 492 Gauging taxes and discounts 495 Working out the Combinations and Permutations 497 Counting down to factorials 498 Counting on combinations 498 Ordering up permutations 500 Practice Questions Answers and Explanations 502 Whaddya Know? Chapter 20 Quiz 505 Answers to Chapter 20 Quiz 507 Chapter 21: Making Formulas Work in Basic Story Problems 509 Setting Up to Solve Story Problems 509 Applying the Pythagorean Theorem 511 Using Geometry to Solve Story Problems 513 Working around Perimeter, Area, and Volume 515 Parading out perimeter and arranging area 515 Adjusting the area 517 Pumping up the volume 519 Going ’Round in Circles 523 Putting Distance, Rate, and Time in a Formula 525 Going the distance with the distance-rate-time formula 525 Figuring distance plus distance 527 Equating distances 528 Figuring distance and fuel 529 Counting on Interest and Percent 530 Practice Questions Answers and Explanations 532 Whaddya Know? Chapter 21 Quiz 537 Answers to Chapter 21 Quiz 539 Chapter 22: Relating Values in Story Problems 541 Tackling Age Problems 542 Tackling Consecutive Integer Problems 543 Working Together on Work Problems 545 Throwing an Object into the Air 547 Practice Questions Answers and Explanations 550 Whaddya Know? Chapter 22 Quiz 553 Answers to Chapter 22 Quiz 554 Chapter 23: Measuring Up with Quality and Quantity Story Problems 555 Achieving the Right Blend with Mixture Problems 556 Concocting the Correct Solution 100% of the Time 559 Dealing with Money Problems 561 Investigating investments and interest 561 Going for the green: Money 564 Practice Questions Answers and Explanations 567 Whaddya Know? Chapter 23 Quiz 571 Answers to Chapter 23 Quiz 572 Book 8: Getting a Grip On Graphing 573 Chapter 24: Getting a Handle on Graphing 575 Thickening the Plot with Points 575 Interpreting ordered pairs 576 Actually Graphing Points 577 Sectioning Off by Quadrants 578 Graphing Lines 579 Using points to lay out lines 579 Going with the horizontal and vertical 581 Graphing Lines Using Intercepts 583 Computing Slopes of Lines 585 Sighting the slope 585 Formulating slope 587 Graphing with the Slope-Intercept Form 590 Changing to the Slope-Intercept Form 591 Writing Equations of Lines 592 Given a point and a slope 593 Given two points 593 Picking on Parallel and Perpendicular Lines 594 Finding Distances between Points 595 Finding Midpoints of Segments 597 Practice Questions Answers and Explanations 598 Whaddya Know? Chapter 24 Quiz 602 Answers to Chapter 24 Quiz 604 Chapter 25: Extending the Graphing Horizon 605 Finding the Intersections of Lines 605 Graphing for intersections 606 Substituting to find intersections 607 Graphing Parabolas and Circles 608 Curling Up with Parabolas 609 Trying out the basic parabola 609 Putting the vertex on an axis 610 Going around in circles with a circular graph 612 Plotting and Plugging in Polynomial Graphs 614 Investigating Graphs of Inequality Functions 618 Taking on Absolute-Value Function Graphs 620 Graphing with Transformations 621 Sliding and multiplying 622 Practice Questions Answers and Explanations 625 Whaddya Know? Chapter 25 Quiz 632 Answers to Chapter 25 Quiz 633 Chapter 26: Coordinating Systems of Equations and Graphing 639 Defining Solutions of Systems of Equations 639 Solving Systems of Linear Equations 641 Using elimination 641 Using substitution 642 Introducing intersections of lines 643 Solving Systems Involving Non-Linear Equations 644 Taking on Systems of Three Linear Equations 647 Practice Problems Answers and Explanations 648 Whaddya Know? Chapter 26 Quiz 651 Answers to Chapter 26 Quiz 652 Index 655

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Book SynopsisPractice your way to a higher grade in Calculus! Calculus is a hands-on skill. You've gotta use it or lose it. And the best way to get the practice you need to develop your mathematical talents is Calculus: 1001 Practice Problems For Dummies. The perfect companion to Calculus For Dummiesand your class this book offers readers challenging practice problems with step-by-step and detailed answer explanations and narrative walkthroughs. You'll get free access to all 1,001 practice problems online so you can create your own study sets for extra-focused learning. Readers will also find: A useful course supplement and resource for students in high school and college taking Calculus IFree, one-year access to all practice problems online, for on-the-go study and practiceAn excellent preparatory resource for faster-paced college classes Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice) is an essential resource for high school and college students looking for more practice and extra help with this challenging math subject. Calculus: 1001 Practice Problems For Dummies (9781119883654) was previously published as 1,001 Calculus Practice Problems For Dummies (9781118496718). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.Table of ContentsIntroduction 1 Part 1: The Questions 5 Chapter 1: Algebra Review 7 Chapter 2: Trigonometry Review 17 Chapter 3: Limits and Rates of Change 29 Chapter 4: Derivative Basics 43 Chapter 5: The Product, Quotient, and Chain Rules 49 Chapter 6: Exponential and Logarithmic Functions and Tangent Lines 55 Chapter 7: Implicit Differentiation 59 Chapter 8: Applications of Derivatives 63 Chapter 9: Areas and Riemann Sums 75 Chapter 10: The Fundamental Theorem of Calculus and the Net Change Theorem 79 Chapter 11: Applications of Integration 87 Chapter 12: Inverse Trigonometric Functions, Hyperbolic Functions, and L’Hôpital’s Rule 101 Chapter 13: U-Substitution and Integration by Parts 109 Chapter 14: Trigonometric Integrals, Trigonometric Substitution, and Partial Fractions 115 Chapter 15: Improper Integrals and More Approximating Techniques 123 Part 2: The Answers 127 Chapter 16: Answers and Explanations 129 Index 581

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Book SynopsisEvery intermediate algebra lesson, example, and practice problem you need in a single, easy-to-use reference Algebra II can be a tough nut to crack when you first meet it. But with the right toolswell, she''s still tough but she gets a heckuva lot easier to manage. In Algebra II All-in-One For Dummies you''ll find your very own step-by-step roadmap to solving even the most challenging Algebra II problems, from conics and systems of equations to exponential and logarithmic functions. In the book, you''ll discover the ins and outs of function transformation and evaluation, work out your brain with complex and imaginary numbers, and apply formulas from statistics and probability theory. You''ll also find: Accessible and practical lessons and practice for second year high-school or university algebra students End-of-chapter quizzes that help you learn and remember! key algebraic concepts, such as quadratic equations, graphing techniqueTable of ContentsIntroduction 1 Part 1: Getting to First Base with the Basics 5 Chapter 1: Beginning at the Beginning of Algebra 7 Chapter 2: Taking on Linear Equations and Inequalities 35 Chapter 3: Handling Quadratic and Other Polynomial Equations 59 Chapter 4: Controlling Quadratic and Rational Inequalities 89 Chapter 5: Soothing the Rational, the Radical, and the Negative 109 Chapter 6: Giving Graphing a Gander 139 Part 2: Figuring on Functions 171 Chapter 7: Formulating Functions 173 Chapter 8: Specializing in Quadratic Functions 201 Chapter 9: Plugging In Polynomials 229 Chapter 10: Acting Rationally with Functions 271 Chapter 11: Exploring Exponential and Logarithmic Functions 303 Chapter 12: Transforming and Critiquing Functions 343 Part 3: Using Conics and Systems of Equations 365 Chapter 13: Slicing the Way You Like It: Conic Sections 367 Chapter 14: Solving Systems of Linear Equations 405 Chapter 15: Solving Systems of Nonlinear Equations 435 Chapter 16: Solving Systems of Inequalities 455 Part 4: Making Lists and Checking for Imaginary Numbers 473 Chapter 17: Getting More Complex with Imaginary Numbers 475 Chapter 18: Making Moves with Matrices 493 Chapter 19: Seeking Out Sequences and Series 521 Chapter 20: Everything You Wanted to Know about Sets and Counting 545 Part 5: Applying Known Formulas 575 Chapter 21: Manipulating Formulas 577 Chapter 22: Taking on Applications 597 Index 613

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Book SynopsisRaymond N. Greenwell earned a B.A. in Mathematics and Physics from the University of San Diego, and an M.S. in Statistics, an M.S. in Applied Mathematics, and a Ph.D. in Applied Mathematics from Michigan State University, where he earned the graduate student teaching award in 1979. After teaching at Albion College in Michigan for four years, he moved to Hofstra University in 1983, where he currently is Professor of Mathematics. Raymond has published articles on fluid mechanics, mathematical biology, genetic algorithms, combinatorics, statistics, and undergraduate mathematics education. He is a member of MAA, AMS, SIAM, NCTM, and AMATYC. He has served as governor of the Metropolitan New York Section of the MAA, as well as webmaster and liaison coordinator, and he received a distinguished service award from the Section in 2003. He is an outdoor enthusiast and leads trips in the Sierra Club's Inner City Outings program. Nathan P. Ritchey Table of ContentsR. Algebra Reference R.1 Polynomials R.2 Factoring R.3 Rational Expressions R.4 Equations R.5 Inequalities R.6 Exponents R.7 Radicals 1. Functions 1.1 Lines and Linear Functions 1.2 The Least Squares Line 1.3 Properties of Functions 1.4 Quadratic Functions; Translation and Reflection 1.5 Polynomial and Rational Functions Chapter Review Extended Application: Using Extrapolation to Predict Life Expectancy2. Exponential, Logarithmic, and Trigonometric Functions 2.1 Exponential Functions 2.2 Logarithmic Functions 2.3 Applications: Growth and Decay 2.4 Trigonometric Functions Chapter Review Extended Application: Power Functions 3. The Derivative 3.1 Limits 3.2 Continuity 3.3 Rates of Change 3.4 Definition of the Derivative 3.5 Graphical Differentiation Chapter Review Extended Application: A Model For Drugs Administered Intravenously 4. Calculating the Derivative 4.1 Techniques for Finding Derivatives 4.2 Derivatives of Products and Quotients 4.3 The Chain Rule 4.4 Derivatives of Exponential Functions 4.5 Derivatives of Logarithmic Functions 4.6 Derivatives of Trigonometric Functions Chapter Review Extended Application: Managing Renewable Resources 5. Graphs and the Derivative 5.1 Increasing and Decreasing Functions 5.2 Relative Extrema 5.3 Higher Derivatives, Concavity, and the Second Derivative Test 5.4 Curve Sketching Chapter Review Extended Application: A Drug Concentration Model for Orally Administered Medications 6. Applications of the Derivative 6.1 Absolute Extrema 6.2 Applications of Extrema 6.3 Implicit Differentiation 6.4 Related Rates 6.5 Differentials: Linear Approximation Chapter Review Extended Application: A Total Cost Model for a Training Program 7. Integration 7.1 Antiderivatives 7.2 Substitution 7.3 Area and the Definite Integral 7.4 The Fundamental Theorem of Calculus 7.5 The Area Between Two Curves Chapter Review Extended Application: Estimating Depletion Dates for Minerals 8. Further Techniques and Applications of Integration 8.1 Numerical Integration 8.2 Integration by Parts 8.3 Volume and Average Value 8.4 Improper Integrals Chapter Review Extended Application: Flow Systems 9. Multivariable Calculus 9.1 Functions of Several Variables 9.2 Partial Derivatives 9.3 Maxima and Minima 9.4 Total Differentials and Approximations 9.5 Double Integrals Chapter Review Extended Application: Optimization for a Predator 10. Matrices 10.1 Solution of Linear Systems 10.2 Addition and Subtraction of Matrices 10.3 Multiplication of Matrices 10.4 Matrix Inverses 10.5 Eigenvalues and Eigenvectors Chapter Review Extended Application: Contagion 11. Differential Equations 11.1 Solutions of Elementary and Separable Differential Equations 11.2 Linear First-Order Differential Equations 11.3 Euler's Method 11.4 Linear Systems of Differential Equations 11.5 Non-Linear Systems of Differential Equations 11.6 Applications of Differential Equations Chapter Review Extended Application: Pollution of the Great Lakes 12. Probability

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Book SynopsisNew 2017 Cambridge A Level Maths and Further Maths resources to help students with learning and revision. Written for the OCR AS/A Level Further Mathematics specification for first teaching from 2017, this print Student Book and Cambridge Elevate edition covers the Pure Core content for AS and first year of A Level. It balances accessible exposition with many worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for progressing through the course. It is underpinned by a strong pedagogical approach, with emphasis on skills development and the synoptic nature of the course. Available online and on tablet devices through the Cambridge Elevate app. Includes answers to aid independent study.

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Book SynopsisNew 2017 Cambridge A Level Maths and Further Maths resources to help students with learning and revision. Written for the OCR AS/A Level Further Mathematics specification for first teaching from 2017, this print Student Book and Cambridge Elevate edition covers the Statistics content for AS and A Level. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for progressing through the course. It is underpinned by a strong pedagogical approach, with an emphasis on skills development and the synoptic nature of the course. Available online and on tablet devices through the Cambridge Elevate app. Includes answers to aid independent study.

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Book SynopsisNew 2017 Cambridge A Level Maths and Further Maths resources to help students with learning and revision. Written for the OCR AS/A Level Further Mathematics specification for first teaching from 2017, this print Student Book covers the Pure Core content for AS and the first year of A Level. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for progressing through the course. It is underpinned by a strong pedagogical approach, with an emphasis on skills development and the synoptic nature of the course. Includes answers to aid independent study.Table of Contents1. Matrices; 2. Further vectors; 3. Applications of matrices; Focus on proof 1; Focus on problem solving 1; Focus on modelling 1; Cross-topic review exercise 1; 4. Complex numbers; 5. Roots of polynomials; 6. Mathematical induction; Focus on proof 2; Focus on problem solving 2; Focus on modelling 2; Cross-topic review exercise 2

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Book SynopsisNew 2017 Cambridge A Level Maths and Further Maths resources help students with learning and revision. Written for the AQA AS/A Level Mathematics specifications for first teaching from 2017, this print Student Book and Cambridge Elevate edition covers the content for AS and first year of A Level. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for progressing through the course. It is underpinned by a strong pedagogical approach, with an emphasis on skills development and the synoptic nature of the course. Available online and on tablet devices through the Cambridge Elevate app. Includes answers to aid independent study.

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Book SynopsisNew 2017 Cambridge A Level Maths and Further Maths resources help students with learning and revision. Written for the AQA A Level Mathematics specification for first teaching from 2017, this print Student Book and Cambridge Elevate edition covers the content for the second year of A Level. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for progressing through the course. It is underpinned by a strong pedagogical approach, with an emphasis on skills development and the synoptic nature of the course. Available online and on tablet devices through the Cambridge Elevate app. Includes answers to aid independent study.

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Book SynopsisStraightforward and easy to read, A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 11E, INTERNATIONAL METRIC EDITION, gives you a thorough overview of the topics typically taught in a first course in differential equations. Your study of differential equations and its applications will be supported by a bounty of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and more.Table of Contents1. INTRODUCTION TO DIFFERENTIAL EQUATIONS. Definitions and Terminology. Initial-Value Problems. Differential Equations as Mathematical Models. Chapter 1 in Review. 2. FIRST-ORDER DIFFERENTIAL EQUATIONS. Solution Curves Without a Solution. Separable Variables. Linear Equations. Exact Equations and Integrating Factors. Solutions by Substitutions. A Numerical Method. Chapter 2 in Review. 3. MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS. Linear Models. Nonlinear Models. Modeling with Systems of First-Order Differential Equations. Chapter 3 in Review. 4. HIGHER-ORDER DIFFERENTIAL EQUATIONS. Preliminary Theory-Linear Equations. Reduction of Order. Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients-Superposition Approach. Undetermined Coefficients-Annihilator Approach. Variation of Parameters. Cauchy-Euler Equation. Solving Systems of Linear Differential Equations by Elimination. Nonlinear Differential Equations. Chapter 4 in Review. 5. MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS. Linear Models: Initial-Value Problems. Linear Models: Boundary-Value Problems. Nonlinear Models. Chapter 5 in Review. 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Review of Power Series Solutions About Ordinary Points. Solutions About Singular Points. Special Functions. Chapter 6 in Review. 7. LAPLACE TRANSFORM. Definition of the Laplace Transform. Inverse Transform and Transforms of Derivatives. Operational Properties I. Operational Properties II. Dirac Delta Function. Systems of Linear Differential Equations. Chapter 7 in Review. 8. SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS. Preliminary Theory. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix Exponential. Chapter 8 in Review. 9. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS. Euler Methods. Runge-Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order Boundary-Value Problems. Chapter 9 in Review. Appendix I. Gamma Function. Appendix II. Matrices. Appendix III. Laplace Transforms. Answers for Selected Odd-Numbered Problems.

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Book SynopsisThis textbook teaches the fundamentals of calculus, keeping points clear, succinct and focused, with plenty of diagrams and practice but relatively few words. It assumes a very basic knowledge but revises the key prerequisites before moving on. Definitions are highlighted for easy understanding and reference, and worked examples illustrate the explanations. Chapters are interwoven with exercises, whilst each chapter also ends with a comprehensive set of exercises, with answers in the back of the book. Introductory paragraphs describe the real-world application of each topic, and also include briefly where relevant any interesting historical facts about the development of the mathematical subject.This text is intended for undergraduate students in engineering taking a course in calculus. It works for the Foundation and 1st year levels. It has a companion volume Foundation Algebra.Table of Contents1. Prerequisites 2. Derivative – I 3. Derivative – II 4. Applications of Derivatives I. 5. Applications of Derivatives II 6. Integration – I 7. Integration II 8. Definite Integration 9. Numerical Integration 10. Applications of Integration 11. Differential Equations 12. Differential Equation Models. Appendix: Proofs Answers to Exercise Questions.

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Book SynopsisWork your way through Calc 2 with crystal clear explanations and tons of practice Calculus II Workbook For Dummies is a hands-on guide to help you practice your way to a greater understanding of Calculus II. You'll get tons of chances to work on intermediate calculus topics such as substitution, integration techniques and when to use them, approximate integration, and improper integrals. This book is packed with practical examples, plenty of practice problems, and access to online quizzes so you'll be ready when it's test time. Plus, every practice problem in the book and online has a complete, step-by-step answer explanation. Great as a supplement to your textbook or a refresher before taking a standardized test like the MCAT, this Dummies workbook has what you need to succeed in this notoriously difficult subject. Review important concepts from Calculus I and pre-calculusWork through practical examples for integration, differentiation, and beyondTest your knowledge with practice probTable of ContentsIntroduction 1 Part 1: Introduction to Integration 3 Chapter 1: An Aerial View of the Area Problem 5 Chapter 2: Forgotten but Not Gone: Review of Algebra and Pre-Calculus 15 Chapter 3: Recent Memories: Calculus Review 37 Part 2: From Definite to Indefinite Integrals 51 Chapter 4: Approximating Area with Riemann Sums 53 Chapter 5: The Fundamental Theorem of Calculus and Indefinite Integrals 69 Part 3: Evaluating Indefinite Integrals 81 Chapter 6: Instant Integration 83 Chapter 7: Sharpening Your Integration Moves 91 Chapter 8: Here’s Looking at u-Substitution 103 Part 4: Advanced Integration Techniques 115 Chapter 9: Integration by Parts 117 Chapter 10: Trig Substitution 131 Chapter 11: Integration with Partial Fractions 151 Part 5: Applications of Integrals 167 Chapter 12: Solving Area Problems 169 Chapter 13: Pump up the Volume — Solving 3-D Problems 189 Chapter 14: Differential Equations 211 Part 6: Infinite Series 219 Chapter 15: Sequences and Series 221 Chapter 16: Convergent and Divergent Series 235 Chapter 17: Taylor and Maclaurin Series 255 Part 7: The Part of Tens 267 Chapter 18: Ten Mathematicians Who Anticipated Calculus before Newton and Leibniz 269 Chapter 19: 10 Skills from Pre-Calculus and Calculus I That Will Help You to Do Well in Calculus II 273 Index 279

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Book SynopsisBreak down biostatistics, make sense of complex concepts, and pass your class If you''re taking biostatistics, you may need or want a little extra assistance as you make your way through. Biostatistics For Dummies follows a typical biostatistics course at the college level, helping you understand even the most difficult concepts, so you can get the grade you need. Start at the beginning by learning how to read and understand mathematical equations and conduct clinical research. Then, use your knowledge to analyze and graph your data. This new edition includes more example problems with step-by-step walkthroughs on how to use statistical software to analyze large datasets. Biostatistics For Dummies is your go-to guide for making sense of it all. Review basic statistics and decode mathematical equations Learn how to analyze and graph data from clinical research studies Look for relationships with correlation and regression U

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Book SynopsisStretch and challenge students with this introduction to higher level mathematics.Including plenty of practice activities and worked examples, this book bridges the gap from GCSE to A-level, building students'' reasoning and problem-solving skills in preparation for the next step.- Develop understanding of mathematics with discussion points, thought-provoking activities and rigorous exercise questions- Build confidence with notes on how prior knowledge can be applied to tackle new concepts- Develop problem-solving skills with step-by-step worked examples and practice questions- Be aware of potential misunderstandings with common pitfalls noted throughout the text- Check progress using a checklist of key points and learning outcomes at the end of each chapter- Help students to achieve their potential with two practice papers at the end of the bookAnswers to exercise questions are at the back of the book and online, alongside full worked

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Book SynopsisSince virtually its first moments as an academic science, women have played a major role in the development of psychology, gaining from the outset research opportunities and academic positions that had been denied them for centuries in other branches of scientific investigation. Look wherever you will, in any branch of psychology or neuroscience in the last century and a half, and what you will find are a plethora of women whose discoveries fundamentally changed how we view the brain and its role in the formation of our perceptions and behaviors.A History of Women in Psychology and Neuroscience tells the story of 267 women whose work opened new doors in humanity''s ongoing attempt to learn about its own nature, from Christine Ladd Franklin''s late 19th century studies of how the brain perceives color to Virginia Johnson''s pioneering studies of the human sexual response, and Augusta Dejerine-Klumpke''s early association of neurological conditions with their underlying brain regions to

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Book SynopsisHighly praised for its broad, practical coverage, the second edition of this popular text incorporated the major statistical models and issues relevant to epidemiological studies. Epidemiology: Study Design and Data Analysis, Third Edition continues to focus on the quantitative aspects of epidemiological research. Updated and expanded, this edition shows students how statistical principles and techniques can help solve epidemiological problems.New to the Third Edition New chapter on risk scores and clinical decision rules New chapter on computer-intensive methods, including the bootstrap, permutation tests, and missing value imputation New sections on binomial regression models, competing risk, information criteria, propensity scoring, and splines Many more exercises and examples using both Stata and SAS More than 60 new figures After introducing study design and reviewTrade Review"This text, like its predecessors, hits the mark. … The author writes extremely well and the text is resplendent with exercises. It would be a crime if Epidemiology: Study Design and Data Analysis were never used as a text! … I wish a text like this had been available for my coursework. Enhancing its value as a text, it will be extremely useful as a reference book for its intended audience—researchers and applied statisticians. … the only excuse for an epidemiologist or applied statistician not to have it on his or her bookshelf is that he or she has not seen or heard of it. Make this book your next purchase!"—Gregory E. Gilbert, The American Statistician, November 2014Praise for Previous Editions:"As a text in quantitative epidemiology, this book also works nicely as a text in biostatistics…The presentation style is relaxed, the examples are helpful, and the level of technical difficulty makes the material approachable without oversimplification…It is sufficiently broad and deep in coverage to compete with standard texts in the field and has the added bonus of emphasizing study design. Methods and issues related to designs commonly used in a wide variety of health sciences are included…"-Ken Hess, Department of Biomathematics and Biostatistics, Anderson Cancer Center"The second edition of this epidemiology text is strengthened to cater to the two audiences the author has in mind: applied statisticians wishing to learn how their statistical expertise can be used in the epidemiology field and statistic-curious researchers who want to understand how statistical techniques can be used to solve epidemiological problems. …The result is a book that will invariably appeal to the intended audience, one with practical applications of techniques and interpretations of results in an epidemiological context. …The book is most certainly an ambitious attempt at covering a broad array of the most important epidemiologic study designs and analytical methods. This is further enforced by the addition of the meta-analysis chapter. …This book will be valuable to statisticians in applying their discipline to epidemiology. Mark Woodward's excellent second edition will effectively serve post-graduate or advanced undergraduate students studying epidemiology, as well as statisticians or researchers who are regularly confronted with epidemiological questions."-Journal of the American Statistical Association"This book provides very good coverage of major issues in the design of epidemiological studies, and a decent, but very quick, tour of commonly used statistical models for such studies."-Short Book Reviews Publication of the International Statistical Institute, K.S. Brown, University of Waterloo, Canada"Amazingly, Woodward manages to describe quite sophisticated models and analysis with nothing more complicated than summation signs. …I highly recommend it."-Statistics in Medicine, 2006"The second edition of this concisely written book covers all statistical methods being of relevance for the planning and analysis of epidemiological studies where the author avoids unnecessary mathematical details for the sake of comprehensibility. The presented statistical principles are always carefully discussed in the context of epidemiological concepts, for instance depending on the different study designs. Detailed practical examples coming from real studies as far as possible illustrate their application. …The book can be highly recommended to researchers in epidemiology who want to understand better the statistical principles being typically applied in this field and to statisticians who want to understand more about statistics in epidemiology, but also to graduate students in epidemiology, public health, medical research and statistics."-Biometrics, Sept. 2005"I think anyone with an interest in both biostatistics and epidemiology will want a copy this book on their bookshelf … it is a first-rate reference book." "I find Professor Woodward's text the most complete and practical introduction to the design and analysis of epidemiological studies I've encountered… an excellent text for either a course introducing epidemiologists to statistical thought and methods or a course introducing statisticians to epidemiological thought and methods… students appreciate having a readable textbook replete with understandable examples and worked exercises…offers a complete introduction to statistical and epidemiological methods in the study of disease in human populations. All of the standard topics are included, and the second edition even has a chapter on meta-analysis. …This book can be used as a text to introduce epidemiological methods to graduate students in statistics who have no background in epidemiology, or vice versa…Professor Woodward is to be congratulated on a job well done."-Dan McGee, Dept of Statistics, Florida State UniversityTable of ContentsFundamental Issues. Basic Analytical Procedures. Assessing Risk Factors. Confounding and Interaction. Cohort Studies. Case-Control Studies. Intervention Studies. Sample Size Determination. Modeling Quantitative Outcome Data. Modeling Binary Outcome Data. Modeling Follow-Up Data. Meta-Analysis. Risk Scores and Clinical Decision Rules. Computer-Intensive Methods. Appendices. Index.

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Book SynopsisThis workbook is designed for students who need a 'refresher course' to increase their fluency and confidence before starting Edexcel GCSE (9-1) Mathematics Foundation course. The write-on format encourages ownership leading to fluency and mastery of the basics, leading on to increased confidence.

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Book Synopsis  Exam Board: Edexcel Level: GCSE Subject: Maths First teaching: September 2015 First exams: June 2017 Our Practice, Problem-solving and Reasoning Books provide students with questions relating to every exercise in the main lessons of the Student Book to give twice the practice. Problem-solving and reasoning questions included throughout. Exam-style questions give students exposure to the sort of questions they will need to answer in their exam. Problem-solving lessons build up strategies from the Student Book so that students need to choose the most appropriate strategy. Mixed problem-solving questions drawing on knowledge from this and previous chapters in the book give students the opportunity to practice using this strategy.

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Book SynopsisThis workbook is designed for students who need a 'refresher course' to increase their fluency and confidence before starting Edexcel GCSE (9-1) Mathematics Foundation course. The write-on format encourages ownership leading to fluency and mastery of the basics, leading on to increased confidence.

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Book SynopsisA stimulating and rigorous approach to Mathematics that goes beyond the requirements of the National Curriculum for Year 6 pupils (aged 10 and above) and lays the foundation for success at Common Entrance and other independent entrance exams at 11+.- Plenty of worked examples to demonstrate method- Develops key skills with clear explanations and diagrams- Challenges pupils with exercises at various levels- Tests understanding with end-of-chapter activities Galore Park Mathematics Year 6 Answers is available to purchase, which includes photocopiable worksheets for selected exercises and activities.Also available from Galore Park www.galorepark.co.uk:- Mathematics Year 5- 11+ Maths Practice Exercises- 11+ Maths Revision Guide- 10-Minute Maths Tests Workbook Age 8-10- 10-Minute Maths Tests Workbook Age 9-11- Mental Arithmetic Workbook Age 8-10- Mental Arithmetic Workbook Age 9-11Table of Contents Chapter 1: Investigations with numbers Chapter 2: Working with numbers Chapter 3: Calculations Chapter 4: Angles and triangles Chapter 5: Number puzzles Chapter 6: More about numbers Chapter 7: Fractions Chapter 8: Ratio and proportion Chapter 9: Congruent and similar shapes Chapter 10: Decimals Chapter 11: Fractions, decimals and percentages Chapter 12: Finding fractions of an amount Chapter 13: Percentages Chapter 14: Negative numbers Chapter 15: Transformations Chapter 16: Formulae Chapter 17: More fractions Chapter 18: Time and travel Chapter 19: Line graphs Chapter 20: 2D shapes Chapter 21: Pie charts and tables Chapter 22: Perimeter and area Chapter 23: 3D shapes Chapter 24: Averages

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Book SynopsisA stimulating and rigorous approach to Mathematics that goes beyond the requirements of the National Curriculum for Year 5 pupils (aged 9 and above) and lays the foundation for success at Common Entrance and other independent entrance exams at 11+. - Plenty of worked examples to demonstrate method- Develops key skills with clear explanations and diagrams- Challenges pupils with exercises at various levels- Tests understanding with end-of-chapter activities Galore Park Mathematics Year 5 Answers is available to purchase, which includes photocopiable worksheets for selected exercises and activities.Also available from Galore Park www.galorepark.co.uk:- Mathematics Year 6- 11+ Maths Practice Exercises- 11+ Maths Revision Guide- 10-Minute Maths Tests Workbook Age 8-10- 10-Minute Maths Tests Workbook Age 9-11- Mental Arithmetic Workbook Age 8-10- Mental Arithmetic Workbook Age 9-11Table of Contents Chapter 1: Introducing investigations Chapter 2: Roman numerals Chapter 3: Place value Chapter 4: Adding and subtracting Chapter 5: Multiplying and dividing Chapter 6: Factors and multiples Chapter 7: Number properties Chapter 8: Angles Chapter 9: Fractions Chapter 10: 2D shapes Chapter 11: Translation Chapter 12: Reflection Chapter 13: Negative numbers Chapter 14: Decimals Chapter 15: More decimals Chapter 16: Decimals, fractions and percentages Chapter 17: Money and measures Chapter 18: Fractions of quantities Chapter 19: Percentages Chapter 20: Long multiplication Chapter 21: More division Chapter 22: Area and perimeter Chapter 23: 3D shapes Chapter 24: Tables and graphs Chapter 25: Time and timetables

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Book SynopsisExam Board: EdexcelLevel: AS/A-levelSubject: MathematicsFirst Teaching: September 2017First Exam: June 2018Endorsed for Edexcel Help students to develop their knowledge and apply their reasoning to mathematical problems with worked examples, stimulating activities and assessment support tailored to the 2017 Edexcel specification.The content benefits from the expertise of subject specialist Keith Pledger and the support of MEI (Mathematics in Education and Industry).-Prepare students for assessment with skills-building activities, worked examples and practice questions tailored to the changed criteria.-Develop a fuller understanding of mathematical concepts with real world examples that help build connections between topics and develop mathematical modelling skills.-Cement understanding of problem-solving, proof and modelling with dedicated sections on these key areas.-Trade ReviewThe content is excellent and I particularly like the link with the Integral website. I would highly recommend these textbooks. -- Mrs Christina Campbell, Head of Maths at Lucton School * Mrs Christina Campbell *

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Book SynopsisDo you need to gain confidence with handling numbers and formulae? Do you want a clear, step-by-step guide to the key concepts and principles of statistics? Nearly all aspects of our lives can be subject to statistical analysis. Statistics: An Introduction shows you how to interpret, analyze and present figures.Assuming minimal knowledge of maths and using examples from a wide variety of everyday contexts, this book makes often complex concepts and techniques easy to get to grips with. This new edition has been fully updated.Whether you want to understand the statistics that you are bombarded with every day or are a student or professional coming to statistics from a wide range of disciplines, Statistics: An Introduction covers it all.

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Book SynopsisPhysics World''s ''Book of the Year'' for 2016 An Entertaining and Enlightening Guide to the Who, What, and Why of String Theory, now also available in an updated reflowable electronic format compatible with mobile devices and e-readers.During the last 50 years, numerous physicists have tried to unravel the secrets of string theory. Yet why do these scientists work on a theory lacking experimental confirmation?Why String Theory? provides the answer, offering a highly readable and accessible panorama of the who, what, and why of this large aspect of modern theoretical physics. The author, a theoretical physics professor at the University of Oxford and a leading string theorist, explains what string theory is and where it originated. He describes how string theory fits into physics and why so many physicists and mathematicians find it appealing when working on topics from M-theory to monsters and from cosmology to superconducTrade Review"There is no direct experimental evidence for string theory. And yet it is one of the biggest games in town. So why do physicists study it and what is it? To answer these questions you need an insider like Conlon, the perfect guide to lead you into the mysterious world of vibrating strings and multidimensional space. Why String Theory? wonderfully unwraps the science, history and philosophy behind one of the most challenging theories of the twenty-first century." —Marcus du Sautoy, Simonyi Professor for the Public Understanding of Science, University of Oxford, UK, and Author of The Music of the Primes"Joe Conlon has taken on the formidable task of explaining string theory, one of the great theoretical developments of the late 20th century. Building on the successes of fundamental particle physics and general relativity, string theory attempts to dig deeper into reality and to come up with a more consistent and mathematically powerful approach to how the universe works. With remarkable clarity and clear prose, Conlon assembles the edifice of string theory in a way that makes it clear why it is such an important intellectual endeavour. He offers a balanced account of its successes and failures and presents a robust response to the critics of string theory. This is a timely, intelligent, and exciting book that describes the joy and pain of working at the frontiers of theoretical physics."—Pedro Ferreira, Author of The Perfect Theory, and Professor of Astrophysics, University of Oxford, UK"A very engaging and up-to-date discussion of string theory that describes its main goals and achievements. It includes the history of how it was developed, with its interesting twists and turns. The surprising connections with other areas of physics and mathematics are clearly explained. Highly recommended for a lay reader with an interest in fundamental physics."—Juan Maldacena, Institute for Advanced Study, Princeton, New Jersey, USA"This is arguably the most compelling set of arguments to explain why string theory has been so attractive to several generations of theoretical physicists in the past three decades despite the lack of experimental evidence. It is written not only with the passion of a practitioner and the broad knowledge and fresh mind of an accomplished young Oxford professor but also with an effort to be understood by enthusiasts of popular science, either young students with an interest in science, researchers in other fields, or the general public. The author introduces subjects with original, witty, and often funny arguments, without offending the intelligence of the reader. Besides being an excellent introduction to string theory, the book is also a unified presentation of the latest developments and open questions in fundamental physics, covering the importance of the basic building blocks of nature, including the recent Higgs discovery, to the latest developments in astrophysics, early universe cosmology, and black hole physics, as well as apparently unrelated subjects such as material science and superconductivity. It also addresses the standard criticisms of string theory and provides honest and thoughtful answers while recognising the weak points and open challenges. In addition, it emphasises the fact that string theory is not only a theory of gravity at the microscopic level but the most ambitious theory ever devised that encompasses all particles and interactions in a consistent manner and deserves to be explored by the most inquisitive and curious minds."—Fernando Quevedo, Director ICTP, Trieste, Italy, and Professor of Theoretical Physics, University of Cambridge, UK "In this book, Professor Conlon has provided—as he promises in his preface—an astonishingly clear tour of modern physics. It is hard to think of a better, clearer, or wittier review, and one that will be particularly useful to science undergraduates curious as to where their field is heading. School students who have done some reading around the subject (e.g., who have read books by Brian Greene) might also find this work of great value. It’s highly recommended."—Nigel Seel on his blog Wading Through Treacle, January 2016"Conlon is a lively, entertaining writer … [he] does a great job of explaining the point of view of typical physicists now working on string theory. He also very ably explains the ‘sociology’ of the field, the different kinds of people who work in this area and their varying sorts of goals and motivations. … I recommend [the book] highly to anyone who cares about these issues."—Peter Woit on his blog Not Even Wrong, December 2015Table of ContentsWhy?: The Long Wait. Scales of Science: Little and Large. Big Lessons of Physics. The Truth Is Out There. What?: What Was String Theory? What Is String Theory? What For?: Direct Experimental Evidence for String Theory. Why Strings? Quantum Field Theory. Why Strings? Mathematics. Why Strings? Cosmology and Particle Physics. Why Strings? Quantum Gravity. Who?: A Thousand Flowers Blooming: Styles of Science. #EpicFail? Criticisms of String Theory. Why String Theory?

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Book SynopsisExam board: AQALevel: A-levelSubject: MathematicsFirst teaching: September 2017First exams: Summer 2019Target success in AQA A Level Mathematics with this proven formula for effective, structured revision; key content coverage and plentiful worked examples are combined with exam-style and multiple choice questions to create a revision guide that students can rely on to review, strengthen and test their knowledge.- Help develop the key skills needed for success with skills-focused questions around problem-solving, proof, modelling and the use of ICT (spreadsheets, graphing software and graphing calculators).- Strategically target revision with diagnostic questions to establish which areas need focus. - Get assessment-ready with exam-style questions and advice on common examination pitfalls.- Embed knowledge and identify weaknesses with hundreds of multiple choice 'Test Yourself' questions, all carefully written to elicit misconceptions; full worked solutions online offer detailed, instructive explanations for all choices (whether they are correct or incorrect)- Consolidate revision with summaries for each topic that focus on what to concentrate on in the build-up to exams, with special focus on common pitfalls such as how to show correct workings.-Access answers at the back of the book, with detailed step-by-step worked solutions for ALL questions available for free online.Includes all Year 1 and Year 2 A-level Maths content.

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Book SynopsisExam board: EdexcelLevel: A-levelSubject: MathematicsFirst teaching: September 2017First exams: Summer 2018Target success in Edexcel A Level Mathematics with this proven formula for effective, structured revision; key content coverage and plentiful worked examples are combined with exam-style and multiple choice questions to create a revision guide that students can rely on to review, strengthen and test their knowledge.- Help develop the key skills needed for success with skills-focused questions around problem-solving, proof, modelling and the use of ICT (spreadsheets, graphing software and graphing calculators).- Strategically target revision with diagnostic questions to establish which areas need focus. - Get assessment-ready with exam-style questions and advice on common examination pitfalls.- Embed knowledge and identify weaknesses with hundreds of multiple choice 'Test Yourself' questions, all carefully written to elicit misconceptions; full worked solutions online offer detailed, instructive explanations for all choices (whether they are correct or incorrect)- Consolidate revision with summaries for each topic that focus on what to concentrate on in the build-up to exams, with special focus on common pitfalls such as how to show correct workings.-Access answers at the back of the book, with detailed step-by-step worked solutions for ALL questions available for free online.Includes all Year 1 and Year 2 A-level Maths content.

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Book SynopsisExam Board: OCRLevel: Free Standing Mathematics QualificationSubject: Additional MathematicsFirst Teaching: September 2018First Exam: June 2019Target success in OCR Additional Mathematics with this proven formula for effective, structured revision. Key content coverage is combined with numerous worked examples and exam-style questions to create a revision guide that students can rely on to review, strengthen and test their knowledge.- Develop the key skills needed for success with skills-focused questions around problem-solving, covering the 2018 specification.- Strategically target revision with diagnostic questions that establish which topics need focus. - Get assessment-ready with exam-style questions and advice on common mistakes and how to show the correct workings.- Reinforce knowledge and identify weaknesses using hundreds of questions supported by answers in the back of the book

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Book Synopsis'Who knew numbers could be so charming? ... Suri takes us on a light-hearted journey all the way from nothing (zero) to infinity' Karen Joy Fowler, New York Times bestselling author of We Are All Completely Beside Ourselves Our universe has multiple origin stories, from religious creation myths to the Big Bang of scientists. But if we leave those behind and start from nothing – no matter, no cosmos, not even empty space – could we create a universe using only maths? In this new mathematical origin story, mathematician and award-winning novelist Manil Suri creates a natural progression of ideas needed to design our world, starting with numbers and continuing through geometry, algebra, and beyond. With evocative and engaging examples ranging from multidimensional crochet to the Mona Lisa’s asymmetrical smile, as well as ingenious storytelling that helps illuminate complex concepts like infinity and relativity, The Big Bang of Numbers charts a playful, inventive course to existence. Distilled from almost four decades of teaching experience, and offering both striking new perspectives for maths aficionados and an accessible introduction for enthusiastic novices, The Big Bang of Numbers proves that we can all fall in love with maths.Trade ReviewThe fundamental[s] of maths presented like a delightful fairy-tale. Hugely enjoyed it * Dara O'Brien *A beautifully written meditation on mathematics: whimsical, thought-provoking and deep * Alex Bellos, author of Alex's Adventures in Numberland *Who knew numbers could be so charming? So industrious? Suri takes us on a light-hearted journey all the way from nothing (zero) to infinity. Math has rarely been so readable. * Karen Joy Fowler, New York Times bestselling author of We Are All Completely Beside Ourselves *In The Big Bang of Numbers, Manil Suri invites the reader to create a universe made of mathematical ideas, sparking a thrill that may catch you off guard—an exhilarating sensation of playfulness, power, and insight. * Steven Strogatz, New York Times bestselling author of Infinite Powers and The Joy of X *Numerophobic? This infinitely fascinating book will cure you ... Manil Suri’s march through maths is brimming with entertaining and yet discombobulating thoughts ... Suri has a knack for clarity and a welcome habit of grounding tricky concepts in the tangible * The Times *A most unusual, creative, and fascinating account of mathematics that relies not on equations or formulas, but on metaphors, paradoxes, and lovely vignettes. * John Allen Paulos, author of Innumeracy and A Mathematician Reads the Newspaper *A delightful ride of a book. Before I knew it, I was rooting for primes, doubting the wisdom of dividing by zero, and holding my breath as the universe starts to emerge from triangles and cones and planes. The book was so enjoyable and understandable, it almost made me want to take another stab at calculus. Almost. Proof that when a smart person who writes well and honestly explores their passion, that passion is contagious. * Ken Krimstein, author of When I Grow Up *An excellent new book that could make anyone fall in love with math * Washingtonian *

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Book SynopsisThis affordable student study guide and workbook to accompany Wendy J. Steinberg and Matthew Price’s Statistics Alive!, Third Edition, helps students get the added review and practice they need to improve their skills and master their Introduction to Statistics course. Bundle and SAVE! Student Study Guide to Accompany Statistics Alive!, Third Edition + Main Text ISBN: 978-1-0718-3088-8Table of ContentsModule 1. Math Review, Vocabulary, and Symbols Module 2. Measurement Scales Module 3. Frequency and Percentile Tables Module 4. Graphs and Plots Module 5. Mode, Median, and Mean Module 6. Range, Variance, and Standard Deviation Module 7. Percent Area and the Normal Curve Module 8. z Scores Module 9. Score Transformations and Their Effects Module 10. Probability Definitions and Theorems Module 11. The Binomial Distribution Module 12. Sampling, Variables, and Hypotheses Module 13. Errors and Significance Module 14. The z Score as a Hypothesis Test Module 15. Standard Error of the Mean Module 16. Normal Deviate Z Test Module 17. One-Sample t Test Module 18. Interpreting and Reporting One-Sample t: Error, Confidence, and Parameter Estimates Module 19. Standard Error of the Difference Between the Means Module 20. t Test With Independent Samples and Equal Sample Sizes Module 21. t Test With Unequal Sample Sizes Module 22. t Test With Related Samples Module 23. Interpreting and Reporting Two-Sample t: Error, Confidence, and Parameter Estimates Module 24. ANOVA Logic: Sums of Squares, Partitioning, and Mean Squares Module 25. One-Way ANOVA: Independent Samples and Equal Sample Sizes Module 26. Tukey HSD Test Module 27. Scheffé Test Module 28. Main Effects and Interaction Effects Module 29. Factorial ANOVA Module 30. One-Variable Chi-Square: Goodness of Fit Module 31. Two-Variable Chi-Square: Test of Independence Module 32. Measures of Effect Size Module 33. Power and the Factors Affecting It Module 34. Relationship Strength and Direction Module 35. Pearson r Module 36. Correlation Pitfalls Module 37. Linear Prediction Module 38. Standard Error of Prediction Module 39. Introduction to Multiple Regression Module 40. Selecting the Appropriate Analysis

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Book SynopsisWhether you are new to Stata graphics or a seasoned veteran, this book will teach you how to use Stata to make publication-quality graphs that will stand out and enhance your statistical results. With over 1,200 illustrated examples and quick-reference tabs, this book quickly guides you to the information you need for creating and customizing high-quality graphs for any type of statistical data. Each graph is displayed in full color with simple and clear instructions that illustrate how to create and customize graphs using Stata commands. Whether you use this book as a learning tool or a quick reference, you will have the power of Stata graphics at your fingertips.Table of Contents1. Introduction 2. Twoway graphs 3. Scatterplot matrix graphs 4. Bar graphs 5. Box plots 6. Dot plots 7. Pie charts 8. Options available for most graphs 9. Standard options available for all graphs 10. Styles for changing the look of graphs 11. Appendix

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Book SynopsisWe all learned that the ratio of the circumference of a circle to its diameter is called pi and that the value of this algebraic symbol is roughly 3.14. What we weren't told, though, is that behind this seemingly mundane fact is a world of mystery, which has fascinated mathematicians from ancient times to the present. Simply put, pi is weird. Mathematicians call it a "transcendental number" because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction. In this delightful layperson's introduction to one of math's most interesting phenomena, Drs. Posamentier and Lehmann review pi's history from prebiblical times to the 21st century, the many amusing and mind-boggling ways of estimating pi over the centuries, quirky examples of obsessing about pi (including an attempt to legislate its exact value), and useful applications of pi in everyday life, including statistics.This enlightening and stimulating approach to mathematics will entertain lay readers while improving their mathematical literacy.Trade Review""There is something for everyone in this book and everyone should read this book because it will be for some, a revelation that mathematics can be fun and beautiful, something they may not have realized during earlier encounters. Math teachers will find a host of ideas to enrich their instruction since Pi, as you know, comes up everywhere. This book is highly recommended and should provide a major step toward increasing the popularity of mathematics.”-Education Update “A joyful exploration…written in a conversational style reminiscent of children's science books. The writing is clear and crisp and draws the reader into the author's enthusiasm…I highly recommend [this book] to high school and college students and teachers of both. The book captures the excitement and fascination of pi and can serve as a starting point for more detailed discussion.”-Mathematics Teacher“I enjoyed reading the book…for its many applications, curiosities, and anecdotes.”-Science “Readers curious about pi could start here…Recommended.” -Choice

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Book Synopsis

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Book SynopsisNeuro-symbolic AI is an emerging subfield of Artificial Intelligence that brings together two hitherto distinct approaches. Neuro refers to the artificial neural networks prominent in machine learning, symbolic refers to algorithmic processing on the level of meaningful symbols, prominent in knowledge representation. In the past, these two fields of AI have been largely separate, with very little crossover, but the so-called third wave of AI is now bringing them together. This book, Neuro-Symbolic Artificial Intelligence: The State of the Art, provides an overview of this development in AI. The two approaches differ significantly in terms of their strengths and weaknesses and, from a cognitive-science perspective, there is a question as to how a neural system can perform symbol manipulation, and how the representational differences between these two approaches can be bridged. The book presents 17 overview papers, all by authors who have made significant contributions in the past few years and starting with a historic overview first seen in 2016. With just seven months elapsed from invitation to authors to final copy, the book is as up-to-date as a published overview of this subject can be. Based on the editors' own desire to understand the current state of the art, this book reflects the breadth and depth of the latest developments in neuro-symbolic AI, and will be of interest to students, researchers, and all those working in the field of Artificial Intelligence.

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