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