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
