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Copyright, ii
Preface, vii
1. Linear Equations and Straight Lines, 1
1.1. Coordinate Systems and Graphs, 1
1.2. Linear Inequalities, 10
1.3. The Intersection Point of a Pair of Lines, 18
1.4. The Slope of a Straight Line, 24
1.5. The Method of Least Squares, 36
Chapter Test, 49
Chapter Project: Break-Even Analysis, 50
2. Matrices, 51
2.1. Solving Systems of Linear Equations, I, 51
2.2. Solving Systems of Linear Equations, II, 63
2.3. Arithmetic Operations on Matrices, 71
2.4. The Inverse of a Matrix, 87
2.5. The Gauss–Jordan Method for Calculating Inverses, 97
2.6. Input–Output Analysis, 102
Chapter Test, 112
Chapter Project: Population Dynamics, 114
3. Linear Programming, A Geometric Approach, 117
3.1. A Linear Programming Problem, 117
3.2. Linear Programming I, 124
3.3. Linear Programming II, 134
Chapter Test, 147
Chapter Project: Shadow Prices, 149
4. The Simplex Method, 151
4.1. Slack Variables and the Simplex Tableau, 151
4.2. The Simplex Method I: Maximum Problems, 160
4.3. The Simplex Method II: Minimum Problems, 172
4.4. Sensitivity Analysis and Matrix Formulations of Linear Programming Problems, 180
4.5. Duality, 188
Chapter Test, 201
Chapter Project: Shadow Prices, 203
5. Sets and Counting, 205
5.1. Sets, 205
5.2. A Fundamental Principle of Counting, 212
5.3. Venn Diagrams and Counting, 218
5.4. The Multiplication Principle, 225
5.5. Permutations and Combinations, 231
5.6. Further Counting Problems, 238
5.7. The Binomial Theorem, 244
5.8. Multinomial Coefficients and Partitions, 250
Chapter Test, 259
Chapter Project: Pascal’s Triangle, 260
6. Probability, 263
6.1. Introduction, 263
6.2. Experiments, Outcomes, Sample Spaces, and Events, 265
6.3. Assignment of Probabilities, 272
6.4. Calculating Probabilities of Events, 284
6.5. Conditional Probability and Independence, 292
6.6. Tree Diagrams, 305
6.7. Bayes’ Theorem, 312
6.8. Simulation, 318
Chapter Test, 328
Chapter Project: Two Paradoxes, 329
7. Probability and Statistics, 331
7.1. Visual Representations of Data, 332
7.2. Frequency and Probability Distributions, 339
7.3. Binomial Trials, 350
7.4. The Mean, 356
7.5. The Variance and Standard Deviation, 366
7.6. The Normal Distribution, 376
7.7. Normal Approximation to the Binomial Distribution, 390
Chapter Test, 398
Chapter Project: An Unexpected Expected Value, 400
8. Markov Processes, 401
8.1. The Transition Matrix, 402
8.2. Regular Stochastic Matrices, 413
8.3. Absorbing Stochastic Matrices, 423
Chapter Test, 436
Chapter Project: Doubly Stochastic Matrices, 437
9. The Theory of Games, 439
9.1. Games and Strategies, 439
9.2. Mixed Strategies, 446
9.3. Determining Optimal Mixed Strategies, 453
Chapter Test, 465
Chapter Project: Simulating the Outcomes of Mixed-Strategy Games, 466
10. The Mathematics of Finance, 469
10.1. Interest, 469
10.2. Annuities, 480
10.3. Amortization of Loans, 490
10.4. Personal Financial Decisions, 499
Chapter Test, 520
Chapter Project: Two Items of Interest, 522
11. Difference Equations and Mathematical Models, 525
11.1. Introduction to Difference Equations I, 525
11.2. Introduction to Difference Equations II, 533
11.3. Graphing Difference Equations, 539
11.4. Mathematics of Personal Finance, 548
11.5. Modeling with Difference Equations, 553
Chapter Test, 561
Chapter Project: Connections to Markov Processes, 562
12. Logic, 563
12.1. Introduction to Logic, 563
12.2. Truth Tables, 568
12.3. Implication, 576
12.4. Logical Implication and Equivalence, 584
12.5. Valid Argument, 592
12.6. Predicate Calculus, 598
12.7. Logic Circuits, 608
Chapter Test, 615
Chapter Project: A Logic Puzzle, 617
Appendix A. Areas Under the Standard Normal Curve, A1
Appendix B. Using the TI-83/84 Plus Graphing Calculators, A2
Appendix C. Spreadsheet Fundamentals, A6
Appendix D. Using the TI-89 Graphing Calculator, A10
Answers, A15
Index, I1
Index of Applications, EP-1
How to With a Calculator, EP-3
How to With a Spreadsheet, EP-3

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