Table of Contents
1. Applications of Linear Functions. The Cartesian Plane and Graphing.
Equations of Straight Lines.
Linear Modeling.
Two Lines: Relating the Geometry to the Equations.
Regression and Correlation.
2. Systems of Linear Equations. Linear Systems as Mathematical Models.
Linear Systems Having One or No Solutions.
Linear Systems having Many Solutions.
3. Matrix Algebra. Matrix Addition and Applications.
Matrix Multiplication and Applications.
The Inverse of a Matrix.
More Applications of Inverses.
4. Linear Programming: The Graphical Method. Modeling Linear Programming Problems.
Linear Inequalities in Two variables.
Solving Linear Programming Problems Graphically.
5. Linear Programming: The Simplex Method. Slack Variables and Pivoting.
The Simplex Algorithm: Maximization.
The Simplex Algorithm: Minimization.
Nonstandard Problems: Crown's Rules.
The Dual Problem.
6. Mathematics of Finance. Simple and Compound Interest.
Ordinary Annuities.
Consumer Loans and Amortization.
7. Logic, Sets, and Counting Techniques. Logic.
Truth Tables.
Sets, Set Operations, and Venn Diagrams.
Applications of Venn Diagrams.
Counting: The Multiplication Principle.
Permutations.
Combinations.
8. Basic Concepts of Probability. Sample Spaces with Equally Likely Outcomes.
Outcomes with Unequal Probability; Odds.
Discrete Random Variables and Expected Value.
9. Additional Topics in Probability. Addition Rules for Probability and Mutually Exclusive Events.
Conditional Probability.
Multiplications Rules Probability and Independent Events.
Bayes' Theorem.
The Binomial Distribution.
10. Statistics. Organizing Data; Frequency Distributions.
Measures of Central Tendency.
Measures of Dispersion.
Continuous Random Variables and the Normal Distribution.
11. Markov Chains. Markov Chains as Mathematical Models.
State Vectors.
Regular Markov Chains.
12. Game Theory: Two Player, Zero-Sum Games. Strictly Determined Games.
The Expected Value of Games with Mixed Strategies.
Solving Mixed-Strategy Games.
Appendices. Appendix I: Algebra Review.
Appendix II: Introduction to Spreadsheets.
Appendix III: Standard Normal Table.
Appendix IV: Solutions to Odd Numbered Exercises.
Index.
