Preface
Index of Applications
1. Linear Equations and Straight Lines
1.1 Coordinate Systems and Graphs
1.2 Linear Inequalities
1.3 The Intersection Point of a Pair of Lines
1.4 The Slope of a Straight Line
1.5 The Method of Least Squares
Chapter Project: Break-even Analysis
2. Matrices
2.1 Solving Systems of Linear Equations, I
2.2 Solving Systems of Linear Equations, II
2.3 Arithmetic Operations on Matrices
2.4 The Inverse of a Matrix
2.5 The Gauss-Jordan Method for Calculating Inverses
2.6 Input-Output Analysis
Chapter Project: Population Dynamics
3. Linear Programming, A Geometric Approach
3.1 A Linear Programming Problem
3.2 Linear Programming, I
3.3 Linear Programming, II
Chapter Project: Shadow Prices
4. The Simplex Method
4.1 Slack Variables and the Simplex Tableau
4.2 The Simplex Method, I: Maximum Problems
4.3 The Simplex Method, II: Minimum Problems
4.4 Sensitivity Analysis and Matrix Formulations of Linear Programming Problems
4.5 Duality
Chapter Project: Shadow Prices
5. Sets and Counting
5.1 Sets
5.2 A Fundamental Principle of Counting
5.3 Venn Diagrams and Counting
5.4 The Multiplication Principle
5.5 Permutations and Combinations
5.6 Further Counting Problems
5.7 The Binomial Theorem
5.8 Multinomial Coefficients and Partitions
Chapter Project: Pascal's Triangle
6. Probability
6.1 Introduction
6.2 Experiments, Outcomes, Samples and Events
6.3 Assignment of Probabilities
6.4 Calculating Probabilities of Events
6.5 Conditional Probability and Independence
6.6 Tree Diagrams
6.7 Bayes' Theorem
6.8 Simulation
Chapter Project: Two Paradoxes
7. Probability and Statistics
7.1 Representation of Data
7.2 Frequency and Probability Distributions
7.3 Binomial Trials
7.4 The Mean
7.5 The Variance and Standard Deviation
7.6 The Normal Distribution
7.7 Normal Approximation to the Binomial Distribution
Chapter Project: An Unexpected Expected Value
8. Markov Processes
8.1 The Transition Matrix
8.2 Regular Stochastic Matrices
8.3 Absorbing Stochastic Matrices
Chapter Project: Doubly Stochastic Matrices
9. The Theory of Games
9.1 Games and Strategies
9.2 Mixed Strategies
9.3 Determining Optimal Mixed Strategies
Chapter Project: Simulating the Outcomes of Mixed-Strategy Games
10. The Mathematics of Finance
10.1 Interest
10.2 Annuities
10.3 Amortization of Loans
10.4 Personal Financial Decisions
Chapter Project: Two Items of Interest
11. Difference Equations and Mathematical Models
11.1 Introduction to Difference Equations, I
11.2 Introduction to Difference Equations, II
11.3 Graphing Difference Equations
11.4 Mathematics of Personal Finance
11.5 Modeling with Difference Equations
Chapter Project: Connections to Markov Processes
12. Logic
12.1 Introduction to Logic
12.2 Truth Tables
12.3 Implication
12.4 Logical Implication and Equivalence
12.5 Valid Argument
12.6 Predicate Calculus
12.7 Logic Circuits
Chapter Project: A Logic Puzzle
Appendix A: Areas under the Standard Normal Curve
Appendix B: Using the TI-83/84 Plus Graphing Calculators
Appendix C: Spreadsheet Fundamentals
Appendix D: Using the TI-89 Graphing Calculators
Answers to Odd-Numbered Exercises
Index