Finite Math For Dummies

Mary Jane Sterling is the author of Algebra I For Dummies, Algebra Workbook For Dummies, and many other For Dummies books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics.

• Introduction 1About This Book 1Foolish Assumptions 2Icons Used in This Book 2Beyond the Book 3Where to Go from Here 3Part 1: Getting Started with Finite Math 5Chapter 1: Feeling Fine with Finite Math 7Getting in Line with Linear Statements 8Making the Most with Matrices 8Staying with the Program 9Getting Set with Sets 10Posing the Probability 11Figuring in Financial Factors 13Finding Statistical Satisfaction 14Considering the Logical Side of Mathematics 15Unlocking the Chains 16Getting into Gaming 18Chapter 2: Lining Up Linear Functions 19Recognizing Equations of Lines 20Identifying slope and its scope 20Creating different forms of the equation 21Writing the equation of a line 21Graphing Lines on the Coordinate Plane 22Graphing a line using two points 23Using the slope and y-intercept to graph a line 24Graphing special lines 25Determining Relationships between Lines 27Parallel and perpendicular lines 27Intersecting versus coincidental lines 29Solving for a Variable 30Chapter 3: Solving Systems of Linear Equations 33Solving Systems Using Elimination 34Solving a system of two linear equations using elimination 34Using elimination to solve a system of three linear equations 36Solving Systems Using Substitution 38Solving a system of two linear equations using substitution 38Taking on a system of three linear equations using substitution 39Dealing with Too Many or No Solutions 41Too many solutions 41No solution at all 42Making Linear Equations Work for You 43Determining the profit 44Mixing it up with a solution 44Counting on change 46Chapter 4: Taking on Systems of Inequalities 49Ruling with Inequalities 49Graphing Linear Inequalities 51Creating graphs of systems 53Making graphs work for you 56Part 2: Making Use of Available Methods 63Chapter 5: Making Way for Matrices 65Squaring Off with Matrix Basics 65Identifying matrices and their components 66Equalizing and transposing matrices 67Performing matrix operations and processes 68Investigating Row Operations 75Performing the row operations 75Creating inverses 77Applying Matrices and Their Operations 80Matrices and motorcycles 81Taking matrices to the zoo 84Chapter 6: Making Matrices Work for You 87Solving Systems of Equations Using Matrices 88Solving a linear system in two variables 89Forging ahead with four variables 90Stopping up short 92Multiplying by the inverse 94Discovering Multiple Solutions 97Applying Matrices to Tasks 99Considering input and output 99Distributing temperatures 103Taking Advantage of Special Formulas 105Inverses of 2 × 2 matrices 105Inverses of 3 × 3 matrices 107Chapter 7: Getting Lined Up with Linear Programming 109Setting Up Linear Programming Problems 110Making the problem structure work 110Solving a maximization problem 112Going for a minimum 115Going Three-Dimensional 118Maximizing in three dimensions 119Going for the minimum 122Chapter 8: Simply the Simplex Method 125Delineating Simplex Method Steps for Maximization 126Setting up for the simplex method 126Solving a maximization application 131Making the Most of Minimization 135Spelling out the format 135Stepping through minimization 136Giving minimization meaning 140Part 3: Using Finite Math to Tackle World Situations 145Chapter 9: Setting Up Sets 147Introducing Set Notation 147Describing large and small sets 148Special types of sets 149Performing Basic Operations 151Using Venn Diagrams for Better Views 152Elements shown 152The number of elements shown 156Chapter 10: Processing the Probability 161Introducing Counting Methods 161Multiplication method of counting 162Using permutations for counting 163Counting with combinations 165Determining the Probability of an Event 167Binomial distributions 169Using probability trees 171Applying Probability Techniques 174Games of chance 174Probability of being chosen 177Chapter 11: Counting on the Mathematics of Finance 181Considering Simple Interest 181Compounding Things with Compound Interest 182Continuous compounding 184Effective interest rate 185Presenting present value 185Analyzing Annuities 188Future value of an annuity 188Present value of an annuity 189Sinking funds 190Amortization 191Creating an amortization schedule 191Accelerating to payoff 193Chapter 12: Telling the Truth with Statistics 195Presenting Data Graphically 195Barring none with a bar graph 196Histograms 197Baking up a pie chart 198Stem-and-leaf graphs 199Measures of Central Tendency 200Meaning it with the mean 200Riding down the middle with the median 202Making the most of the mode 202Recognizing the geometric mean 203Comparing measures of central tendency 203Box-and-whisker plots 207Variance and Standard Deviation 208Variance 208Standard deviation 209Investigating the Normal Distribution 210Chapter 13: Logic 213Logically Presenting the Vocabulary 213Finding the Truth with Truth Tables 215Considering the conjunction 215Displaying the disjunction 216Looking into negativity 217Conditionally making statements 217Analyzing compound statements 218Equivalent Statements 219Studying the Conditional 221Analyzing Arguments 222Applying Logic to Circuits 225Part 4: Employing the Tools of Finite Math to Expand and Investigate 229Chapter 14: Markov Chains 231Recognizing a Markov Chain 231Coming to Terms with Markov Chains 232Working with Transition Matrices 233Using charts and trees 233Dealing with diagrams 236Probability Vectors 239Absorbing Chains 242Making Long-Term Predictions 244Avoiding ruin 244Alternating even and odd 246Chapter 15: Playing Games with Game Theory 249Playing Fairly 249Playing by the Rules 252Matrix representation 252Vocabulary 252Vocabulary illustrated 253Getting Strategic 255Yielding to Domination 258Determining the Moves 259Finding no saddle point 259Getting down to business 263Chapter 16: Applications of Matrices and Game Theory 267Traffic Flow 267Battle of the Bismarck Sea 270The Game of Chicken 271The Prisoner’s Dilemma 272The Traveler’s Dilemma 273Blotto’s Rules 274Jack Be Nimble 275Nim with two heaps 275Upping the Nim stacks to three 277Part 5: the Part of Tens 279Chapter 17: Ten Financial Formulas 281The Rule of 72 281Leverage Ratio 282Gains and Losses 282Determining Depreciation 283Total Return on Investments 283Expected Return 284Inflation-Adjusted Return 284Remaining Balance 285Future Value of Annuity Due 286Bond Pricing Formula 286Chapter 18: Ten Important Graphing Calculator Functions 289Graphing Lines for Intersections 289Adjusting the Window 290Entering Matrices 291Adding, Subtracting, and Multiplying Matrices 292Powering Up Matrices 293Finding Matrix Inverses 294Solving Systems of Equations Using Matrices 295Decimals to Fractions 296Counting with Permutations and Combinations 296Making Statistical Statements 298Glossary 301Index 305