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ISBN: 9780534419493 | 0534419496

Format: HardcoverPublisher: Brooks Cole

Pub. Date: 6/19/2003

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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 APPLICA TIONS. 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: Designi ng a Puz zle. 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--arves ting 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.