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What is included with this book?
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 | |
Input-Output 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 | |
Long-Range Behavior of Regular Markov Systems | |
Absorbing Markov Systems | |
Case Study: Predicting the Price of Gold | |
OPTIONAL INTERNET CHAPTERS | |
G | |
Game Theory | |
Introduction | |
Two-Person Zero Sum Games; Reduction by Dominance | |
Strictly Determined Games | |
Solving Games using the Simplex Method | |
Expert Opinion--arvesting 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 |