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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 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 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 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 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 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 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 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 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 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 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 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 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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