| 1. FUNCTIONS AND LINES. Functions. Graphs and Lines. Mathematical Models and Applications of Linear Functions. 2. LINEAR SYSTEMS. Systems of Two Equations. Systems with Three Variables: An Introduction to a Matrix Representation of a Linear System of Equations. Gauss-Jordan Method for General Systems of Equations. Matrix Operations. Multiplication of Matrices. The Inverse of a Matrix. Leontief Input-Output Model in Economics. Linear Regression. 3. LINEAR PROGRAMMING. Linear Inequalities in Two Variables. Solutions of Systems of Inequalities: A Geometric Picture. Linear Programming: A Geometric Approach. Applications. 4. LINEAR PROGRAMMING: THE SIMPLEX METHOD. Setting Up the Simplex Methods. The Simplex Method. The Standard Minimum Problem: Duality. Mixed Constraints. Multiple Solutions, Unbounded Solutions, and No Solutions. What's Happening in the Simplex Method? (Optional). 5. MATHEMATICS OF FINANCE. Simple Interest. Compound Interest. Annuities and Sinking Funds. Present Value of an Annuity and Amortization. 6. SETS AND COUNTING. Sets. Counting Elements in a Subset Using a Venn Diagram. Basic Counting Principles. Permutations. Combinations. A Mixture of Counting Problems. Partitions (Optional). 7. PROBABILITY. Introduction to Probability. Equally Likely Events. Compound Events: Union, Intersection, and Complement. Conditional Probability. Independent Events. Bayes' Rule. Markov Chains. 8. STATISTICS. Frequency Distributions. Measures of Central Tendency. Measures of Dispersion: Range, Variance, and Standard Deviation. Random Variables and Probability Distributions of Discrete Random Variables. Expected Value of a Random Variable. Binomial Experiments and Binomial Distribution. Normal Distribution. Estimating Bounds on a Proportion. 9. GAME THEORY. Two-Person Games. Mixed Strategy Games. 10. LOGIC. Statements. Conditional Statements. Equivalent Statements. Valid Arguments. APPENDIX A: REVIEW TOPICS. Properties of Real Numbers. Solving Linear Equations. Coordinate Systems. Linear Inequalities and Interval Notation. APPENDIX B: USING A TI-83 GRAPHING CALCULATOR. Notation. Arithmetic Operations. Graphing. Evaluating A Function. Finding the Intersection of Two Graphs. Constructing a Table. Matrices. Statistics. APPENDIX C: USING EXCEL. |
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