| |
| |
| Preface | |
| |
| |
| Index of Applications | |
| |
| |
| |
| Linear Equations and Straight Lines | |
| |
| |
| |
| Coordinate Systems and Graphs | |
| |
| |
| |
| Linear Inequalities | |
| |
| |
| |
| The InterSection Point of a Pair of Lines | |
| |
| |
| |
| The Slope of a Straight Line | |
| |
| |
| |
| The Method of Least Squares | |
| |
| |
| Chapter Project: Break-even Analysis | |
| |
| |
| |
| Matrices | |
| |
| |
| |
| Solving Systems of Linear Equations, I | |
| |
| |
| |
| Solving Systems of Linear Equations, II | |
| |
| |
| |
| Arithmetic Operations on Matrices | |
| |
| |
| |
| The Inverse of a Matrix | |
| |
| |
| |
| The Gauss-Jordan Method for Calculating Inverses | |
| |
| |
| |
| Input-Output Analysis | |
| |
| |
| Chapter Project: Population Dynamics | |
| |
| |
| |
| Linear Programming, A Geometric Approach | |
| |
| |
| |
| A Linear Programming Problem | |
| |
| |
| |
| Linear Programming, I | |
| |
| |
| |
| Linear Programming, II | |
| |
| |
| Chapter Project: Shadow Prices | |
| |
| |
| |
| The Simplex Method | |
| |
| |
| |
| Slack Variables and the Simplex Tableau | |
| |
| |
| |
| The Simplex Method, I: Maximum Problems | |
| |
| |
| |
| The Simplex Method, II: Minimum Problems | |
| |
| |
| |
| Sensitivity Analysis and Matrix Formulations of Linear Programming Problems | |
| |
| |
| |
| Duality | |
| |
| |
| Chapter Project: Shadow Prices | |
| |
| |
| |
| Sets and Counting | |
| |
| |
| |
| Sets | |
| |
| |
| |
| A Fundamental Principle of Counting | |
| |
| |
| |
| Venn Diagrams and Counting | |
| |
| |
| |
| The Multiplication Principle | |
| |
| |
| |
| Permutations and Combinations | |
| |
| |
| |
| Further Counting Problems | |
| |
| |
| |
| The Binomial Theorem | |
| |
| |
| |
| Multinomial Coefficients and Partitions | |
| |
| |
| Chapter Project: Pascal's Triangle | |
| |
| |
| |
| Probability | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Experiments, Outcomes, and Events | |
| |
| |
| |
| Assignment of Probabilities | |
| |
| |
| |
| Calculating Probabilities of Events | |
| |
| |
| |
| Conditional Probability and Independence | |
| |
| |
| |
| Tree Diagrams | |
| |
| |
| |
| Bayes' Theorem | |
| |
| |
| |
| Simulation | |
| |
| |
| Chapter Project: Two Paradoxes | |
| |
| |
| |
| Probability and Statistics | |
| |
| |
| |
| Representation of Data | |
| |
| |
| |
| Frequency and Probability Distributions | |
| |
| |
| |
| Binomial Trials | |
| |
| |
| |
| The Mean | |
| |
| |
| |
| The Variance and Standard Deviation | |
| |
| |
| |
| The Normal Distribution | |
| |
| |
| |
| Normal Approximation to the Binomial Distribution | |
| |
| |
| Chapter Project: An Unexpected Expected Value | |
| |
| |
| |
| Markov Processes | |
| |
| |
| |
| The Transition Matrix | |
| |
| |
| |
| Regular Stochastic Matrices | |
| |
| |
| |
| Absorbing Stochastic Matrices | |
| |
| |
| Chapter Project: Doubly Stochastic Matrices | |
| |
| |
| |
| The Theory of Games | |
| |
| |
| |
| Games and Strategies | |
| |
| |
| |
| Mixed Strategies | |
| |
| |
| |
| Determining Optimal Mixed Strategies | |
| |
| |
| Chapter Project: Simulating the Outcomes of Mixed-Strategy Games | |
| |
| |
| |
| The Mathematics of Finance | |
| |
| |
| |
| Interest | |
| |
| |
| |
| Annuities | |
| |
| |
| |
| Amortization of Loans | |
| |
| |
| |
| Personal Financial Decisions | |
| |
| |
| Chapter Project: Two Items of Interest | |
| |
| |
| |
| Difference Equations and Mathematical Models | |
| |
| |
| |
| Introduction to Difference Equations, I | |
| |
| |
| |
| Introduction to Difference Equations, II | |
| |
| |
| |
| Graphing Difference Equations | |
| |
| |
| |
| Mathematics of Personal Finance | |
| |
| |
| |
| Modelling with Difference Equations | |
| |
| |
| Chapter Project: Connections to Markov Processes | |
| |
| |
| |
| Logic | |
| |
| |
| |
| Introduction to Logic | |
| |
| |
| |
| Truth Tables | |
| |
| |
| |
| Implication | |
| |
| |
| |
| Logical Implication and Equivalence | |
| |
| |
| |
| Valid Argument | |
| |
| |
| |
| Predicate Calculus | |
| |
| |
| |
| Logic Circuits | |
| |
| |
| Chapter Project: A Logic Puzzle | |
| |
| |
| |
| Tables | |
| |
| |
| |
| Using the TI-83, TI-83 Plus, and TI-84 Plus Graphing Calculators | |
| |
| |
| |
| Spreadsheet Fundamentals | |
| |
| |
| |
| Using the TI-89 Graphing Calculators | |
| |
| |
| Answers to Odd-Numbered Exercises | |
| |
| |
| Solutions to Selected Exercises | |
| |
| |
| Index | |
