1. FUNCTIONS AND LINEAR MODELS 

Introduction 

Functions from the Numerical and Algebraic Viewpoints 

Functions from the Graphical Viewpoint 

Linear Functions 

Linear Models 

Linear Regression 

Case Study: Modeling Spending on Internet Advertising 

Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions 

2. SYSTEMS OF LINEAR EQUATIONS AND MATRICES 

Introduction 

Systems of Two Equations in Two Unknowns 

Using Matrices to Solve Systems of Equations 

Applications of Systems of Linear Equations 

Case Study: The Impact of Regulating Sulfur Emissions 

3. MATRIX ALGEBRA AND APPLICATIONS 

Introduction 

Matrix Addition and Scalar Multiplication 

Matrix Multiplication 

Matrix Inversion 

InputOutput Models 

Case Study: The Japanese Economy 

4. LINEAR PROGRAMMING 

Introduction 

Graphing Linear Inequalities 

Solving Linear Programming Problems Graphically 

The Simplex Method: Solving Standard Maximization Problems 

The Simplex Method: Solving General Linear Programming Problems 

The Simplex Method and Duality (Optional) 

Case Study: Airline Scheduling 

5. THE MATHEMATICS OF FINANACE 

Introduction 

Simple Interest 

Compound Interest 

Annuities, Loans, and Bonds 

Case Study: Saving for College 

6. SETS AND COUNTING 

Introduction 

Set Operations 

Cardinality 

The Addition and Multiplication Principles 

Permutations and Combinations 

Case Study: Designing a Puzzle 

7. PROBABILITY 

Introduction 

Sample Spaces and Events 

Estimated Probability 

Empirical Probability 

Probability and Counting Techniques 

Probability Distributions 

Conditional Probability and Independence 

Bayes' Theorem and Applications 

Case Study: The Monty Hall Problem 

8. RANDOM VARIABLES AND STATISTICS 

Introduction 

Random Variables and Distributions 

Bernoulli Trials and Binomial Random Variables 

Measures of Central Tendency 

Measures of Dispersion 

Normal Distributions 

Case Study: Spotting Tax Fraud with Benford's Law 

Optional Internet Topics: Sampling Distributions and the Central Limit Theorem 

Confidence Intervals 

Hypothesis Testing 

9. MARKOV SYSTEMS 

Introduction 

Markov Systems 

Distribution Vectors and Powers of the Transition Matrix 

LongRange Behavior of Regular Markov Systems 

Absorbing Markov Systems 

Case Study: Predicting the Price of Gold 

OPTIONAL INTERNET CHAPTERS 

G 

Game Theory 

Introduction 

TwoPerson Zero Sum Games; Reduction by Dominance 

Strictly Determined Games 

Solving Games using the Simplex Method 

Expert Opinionarvesting Forests 

L 

Introduction to Logic 

Introduction 

Statements and Logical Operators 

Logical Equivalence, Tautologies and Contradictions 

The Conditional and the Biconditional 

Tautological Implications and Tautological Equivalences 

Rules of Inference 

Arguments and Proofs 

Appendix A: Real Numbers 

Appendix B: Table: Area Under a Normal Curve 

Answers to Selected Exercises 

Index 
