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Finite Math for Dummies


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Table of Contents

Introduction 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 Finite Math 5

Chapter 1: Feeling Fine with Finite Math 7

Getting in Line with Linear Statements 8

Making the Most with Matrices 8

Staying with the Program 9

Getting Set with Sets 10

Posing the Probability 11

Figuring in Financial Factors 13

Finding Statistical Satisfaction 14

Considering the Logical Side of Mathematics 15

Unlocking the Chains 16

Getting into Gaming 18

Chapter 2: Lining Up Linear Functions 19

Recognizing Equations of Lines 20

Identifying slope and its scope 20

Creating different forms of the equation 21

Writing the equation of a line 21

Graphing Lines on the Coordinate Plane 22

Graphing a line using two points 23

Using the slope and y-intercept to graph a line 24

Graphing special lines 25

Determining Relationships between Lines 27

Parallel and perpendicular lines 27

Intersecting versus coincidental lines 29

Solving for a Variable 30

Chapter 3: Solving Systems of Linear Equations 33

Solving Systems Using Elimination 34

Solving a system of two linear equations using elimination 34

Using elimination to solve a system of three linear equations 36

Solving Systems Using Substitution 38

Solving a system of two linear equations using substitution 38

Taking on a system of three linear equations using substitution 39

Dealing with Too Many or No Solutions 41

Too many solutions 41

No solution at all 42

Making Linear Equations Work for You 43

Determining the profit 44

Mixing it up with a solution 44

Counting on change 46

Chapter 4: Taking on Systems of Inequalities 49

Ruling with Inequalities 49

Graphing Linear Inequalities 51

Creating graphs of systems 53

Making graphs work for you 56

Part 2: Making Use of Available Methods 63

Chapter 5: Making Way for Matrices 65

Squaring Off with Matrix Basics 65

Identifying matrices and their components 66

Equalizing and transposing matrices 67

Performing matrix operations and processes 68

Investigating Row Operations 75

Performing the row operations 75

Creating inverses 77

Applying Matrices and Their Operations 80

Matrices and motorcycles 81

Taking matrices to the zoo 84

Chapter 6: Making Matrices Work for You 87

Solving Systems of Equations Using Matrices 88

Solving a linear system in two variables 89

Forging ahead with four variables 90

Stopping up short 92

Multiplying by the inverse 94

Discovering Multiple Solutions 97

Applying Matrices to Tasks 99

Considering input and output 99

Distributing temperatures 103

Taking Advantage of Special Formulas 105

Inverses of 2 × 2 matrices 105

Inverses of 3 × 3 matrices 107

Chapter 7: Getting Lined Up with Linear Programming 109

Setting Up Linear Programming Problems 110

Making the problem structure work 110

Solving a maximization problem 112

Going for a minimum 115

Going Three-Dimensional 118

Maximizing in three dimensions 119

Going for the minimum 122

Chapter 8: Simply the Simplex Method 125

Delineating Simplex Method Steps for Maximization 126

Setting up for the simplex method 126

Solving a maximization application 131

Making the Most of Minimization 135

Spelling out the format 135

Stepping through minimization 136

Giving minimization meaning 140

Part 3: Using Finite Math to Tackle World Situations 145

Chapter 9: Setting Up Sets 147

Introducing Set Notation 147

Describing large and small sets 148

Special types of sets 149

Performing Basic Operations 151

Using Venn Diagrams for Better Views 152

Elements shown 152

The number of elements shown 156

Chapter 10: Processing the Probability 161

Introducing Counting Methods 161

Multiplication method of counting 162

Using permutations for counting 163

Counting with combinations 165

Determining the Probability of an Event 167

Binomial distributions 169

Using probability trees 171

Applying Probability Techniques 174

Games of chance 174

Probability of being chosen 177

Chapter 11: Counting on the Mathematics of Finance 181

Considering Simple Interest 181

Compounding Things with Compound Interest 182

Continuous compounding 184

Effective interest rate 185

Presenting present value 185

Analyzing Annuities 188

Future value of an annuity 188

Present value of an annuity 189

Sinking funds 190

Amortization 191

Creating an amortization schedule 191

Accelerating to payoff 193

Chapter 12: Telling the Truth with Statistics 195

Presenting Data Graphically 195

Barring none with a bar graph 196

Histograms 197

Baking up a pie chart 198

Stem-and-leaf graphs 199

Measures of Central Tendency 200

Meaning it with the mean 200

Riding down the middle with the median 202

Making the most of the mode 202

Recognizing the geometric mean 203

Comparing measures of central tendency 203

Box-and-whisker plots 207

Variance and Standard Deviation 208

Variance 208

Standard deviation 209

Investigating the Normal Distribution 210

Chapter 13: Logic 213

Logically Presenting the Vocabulary 213

Finding the Truth with Truth Tables 215

Considering the conjunction 215

Displaying the disjunction 216

Looking into negativity 217

Conditionally making statements 217

Analyzing compound statements 218

Equivalent Statements 219

Studying the Conditional 221

Analyzing Arguments 222

Applying Logic to Circuits 225

Part 4: Employing the Tools of Finite Math to Expand and Investigate 229

Chapter 14: Markov Chains 231

Recognizing a Markov Chain 231

Coming to Terms with Markov Chains 232

Working with Transition Matrices 233

Using charts and trees 233

Dealing with diagrams 236

Probability Vectors 239

Absorbing Chains 242

Making Long-Term Predictions 244

Avoiding ruin 244

Alternating even and odd 246

Chapter 15: Playing Games with Game Theory 249

Playing Fairly 249

Playing by the Rules 252

Matrix representation 252

Vocabulary 252

Vocabulary illustrated 253

Getting Strategic 255

Yielding to Domination 258

Determining the Moves 259

Finding no saddle point 259

Getting down to business 263

Chapter 16: Applications of Matrices and Game Theory 267

Traffic Flow 267

Battle of the Bismarck Sea 270

The Game of Chicken 271

The Prisoner’s Dilemma 272

The Traveler’s Dilemma 273

Blotto’s Rules 274

Jack Be Nimble 275

Nim with two heaps 275

Upping the Nim stacks to three 277

Part 5: the Part of Tens 279

Chapter 17: Ten Financial Formulas 281

The Rule of 72 281

Leverage Ratio 282

Gains and Losses 282

Determining Depreciation 283

Total Return on Investments 283

Expected Return 284

Inflation-Adjusted Return 284

Remaining Balance 285

Future Value of Annuity Due 286

Bond Pricing Formula 286

Chapter 18: Ten Important Graphing Calculator Functions 289

Graphing Lines for Intersections 289

Adjusting the Window 290

Entering Matrices 291

Adding, Subtracting, and Multiplying Matrices 292

Powering Up Matrices 293

Finding Matrix Inverses 294

Solving Systems of Equations Using Matrices 295

Decimals to Fractions 296

Counting with Permutations and Combinations 296

Making Statistical Statements 298

Glossary 301

Index 305

About the Author

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.

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