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Copyright, ii
Preface, vii
Student and Instructor Resources, xiii
1. Linear Equations and Straight Lines, 1
1.1. Coordinate Systems and Graphs, 1
1.2. Linear Inequalities, 11
1.3. The Intersection Point of a Pair of Lines, 21
1.4. The Slope of a Straight Line, 26
1.5. The Method of Least Squares, 40
Chapter Test, 54
Chapter Project: Break-Even Analysis, 55
2. Matrices, 57
2.1. Solving Systems of Linear Equations, I, 57
2.2. Solving Systems of Linear Equations, II, 70
2.3. Arithmetic Operations on Matrices, 78
2.4. The Inverse of a Matrix, 93
2.5. The Gauss–Jordan Method for Calculating Inverses, 103
2.6. Input–Output Analysis, 108
Chapter Test, 118
Chapter Project: Population Dynamics, 120
3. Linear Programming, A Geometric Approach, 123
3.1. A Linear Programming Problem, 123
3.2. Linear Programming I, 130
3.3. Linear Programming II, 141
Chapter Test, 155
Chapter Project: Shadow Prices, 157
4. The Simplex Method, 159
4.1. Slack Variables and the Simplex Tableau, 159
4.2. The Simplex Method I: Maximum Problems, 168
4.3. The Simplex Method II: Minimum Problems, 180
4.4. Sensitivity Analysis and Matrix Formulations of Linear Programming Problems, 188
4.5. Duality, 196
Chapter Test, 211
Chapter Project: Shadow Prices, 212
5. Sets and Counting, 213
5.1. Sets, 213
5.2. A Fundamental Principle of Counting, 220
5.3. Venn Diagrams and Counting, 226
5.4. The Multiplication Principle, 232
5.5. Permutations and Combinations, 239
5.6. Further Counting Problems, 246
5.7. The Binomial Theorem, 252
5.8. Multinomial Coefficients and Partitions, 258
Chapter Test, 267
Chapter Project: Pascal’s Triangle, 269
6. Probability, 273
6.1. Introduction, 273
6.2. Experiments, Outcomes, and Events, 275
6.3. Assignment of Probabilities, 284
6.4. Calculating Probabilities of Events, 295
6.5. Conditional Probability and Independence, 304
6.6. Tree Diagrams, 316
6.7. Bayes’ Theorem, 324
6.8. Simulation, 330
Chapter Test, 340
Chapter Project: Two Paradoxes, 341
7. Probability and Statistics, 343
7.1. Visual Representations of Data, 344
7.2. Frequency and Probability Distributions, 352
7.3. Binomial Trials, 364
7.4. The Mean, 370
7.5. The Variance and Standard Deviation, 381
7.6. The Normal Distribution, 392
7.7. Normal Approximation to the Binomial Distribution, 406
Chapter Test, 415
Chapter Project: An Unexpected Expected Value, 417
8. Markov Processes, 419
8.1. The Transition Matrix, 419
8.2. Regular Stochastic Matrices, 430
8.3. Absorbing Stochastic Matrices, 438
Chapter Test, 451
Chapter Project: Doubly Stochastic Matrices, 452
9. The Theory of Games, 455
9.1. Games and Strategies, 455
9.2. Mixed Strategies, 462
9.3. Determining Optimal Mixed Strategies, 469
Chapter Test, 482
Chapter Project: Simulating the Outcomes of Mixed-Strategy Games, 483
10. The Mathematics of Finance, 485
10.1. Interest, 485
10.2. Annuities, 496
10.3. Amortization of Loans, 506
10.4. Personal Financial Decisions, 515
Chapter Test, 533
Chapter Project: Two Items of Interest, 534
11. Difference Equations and Mathematical Models, 537
11.1. Introduction to Difference Equations I, 537
11.2. Introduction to Difference Equations II, 545
11.3. Graphing Difference Equations, 552
11.4. Mathematics of Personal Finance, 561
11.5. Modeling with Difference Equations, 567
Chapter Test, 574
Chapter Project: Connections to Markov Processes, 576
12. Logic, 577
12.1. Introduction to Logic, 577
12.2. Truth Tables, 582
12.3. Implication, 591
12.4. Logical Implication and Equivalence, 599
12.5. Valid Argument, 608
12.6. Predicate Calculus, 614
12.7. Logic Circuits, 624
Chapter Test, 632
Chapter Project: A Logic Puzzle, 634
Appendices, A1
Appendix A. Tables, A1
Table 1 Areas under the standard normal curve, A2
Table 2 (1 + i)^n Compound amount of $1 invested for n interest periods at interest rate i per period, A3
Table 3 1/(1 + i)^n Present value of $1. Principal that will accumulate to $1 in n interest periods at a compound rate of i per period, A4
Table 4 S_ni Future value of an ordinary annuity of n $1 payments each, immediately after the last payment at compound interest rate of i per period, A5
Table 5 1/S_ni Rent per period for an ordinary annuity of n payments, with compounded interest rate i per period, and future value $1, A6
Table 6 a_ni Present value of an ordinary annuity of n payments of $1 one period before the first payment, with interest compounded at i per period, A7
Table 7 1/a_ni Rent per period for an ordinary annuity of n payments whose present value is $1, with interest compounded at i per period, A8
Appendix B. Using the TI−83/TI−83+/TI−84+ Graphing Calculators, A9
Appendix C. Spreadsheet Fundamentals, A12
Appendix D. Using the TI−89 Graphing Calculator, A16
Answers, A21
Solutions to Circled Exercises, A63
Index, I1
Index of Applications, EP-1
Index of Applications, BM-1

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