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| Functions | |
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| Real Numbers, Inequalities, and Lines | |
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| Real Numbers and Inequalities | |
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| Sets and Intervals | |
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| The Cartesian Plane | |
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| Lines and Slopes | |
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| Equations of Lines | |
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| General Linear Equation | |
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| Exponents | |
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| Positive Integer Exponents | |
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| Properties of Exponents | |
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| Zero and Negative Exponents | |
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| Roots and Fractional Exponents | |
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| Fractional Exponents | |
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| Avoiding Pitfalls in Simplifying | |
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| Learning Curves in Airplane Production | |
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| Functions | |
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| Functions | |
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| Solving Quadratic Equations | |
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| Derivation of the Vertex Formula | |
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| Derivation of the Quadratic Formula | |
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| More About Functions | |
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| Polynomial Functions | |
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| Rational Functions | |
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| Piecewise Linear Functions | |
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| Composite Functions | |
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| Shifts of Graphs | |
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| Exponential Functions | |
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| Exponential Functions | |
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| Compound IntereSt. Depreciation by a Fixed Percentage | |
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| The Number e | |
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| Continuous Compounding of IntereSt | |
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| Intuitive Meaning of Continuous Compounding | |
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| The Function y = ex | |
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| Exponential Growth | |
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| Justification of the Formula for Continuous Compounding | |
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| Logarithmic Functions | |
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| Common Logarithms | |
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| Properties of Common Logarithms | |
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| Graphs of Logarithmic and Exponential Functions | |
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| Logarithms to Other Bases | |
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| Natural Logarithms | |
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| Carbon-14 Dating | |
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| Mathematics Of Finance | |
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| Simple IntereSt | |
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| Simple Interest Formula | |
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| Total Amount Due on a Loan | |
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| Discounted Loans and Effective Interest Rates | |
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| Compound IntereSt | |
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| Compound Interest Formula | |
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| Growth Times | |
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| Rule of | |
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| Effective Rates | |
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| Recap | |
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| Annuities | |
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| A First Example | |
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| Geometric Series | |
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| Accumulated Account Formula | |
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| Sinking Funds | |
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| How Long Will It Take? | |
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| Amortization | |
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| Present Value of an Annuity | |
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| Amortization | |
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| Unpaid Balance | |
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| Equity | |
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| Systems Of Equations And Matrices | |
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| Systems of Two Linear Equations in Two Variables | |
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| Systems of Equations | |
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| Graphical Representations of Equations | |
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| Equivalent Systems of Equations | |
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| Elimination Method | |
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| Matrices and Linear Equations in Two Variables | |
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| Matrices | |
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| Augmented Matrices from Systems of Equations | |
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| Row Operations | |
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| Solving Equations by Row Reduction | |
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| Systems of Linear Equations and the Gauss-Jordan Method | |
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| Names for Many Variables | |
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| Row-Reduced Form | |
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| Matrix Arithmetic | |
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| Equality of Matrices | |
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| Transpose of a Matrix | |
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| Identity Matrix | |
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| Scalar Multiplication | |
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| Matrix Addition and Subtraction | |
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| Matrix Multiplication as Evaluation | |
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| Identity Matrices | |
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| Matrix Multiplication with Systems of Equations | |
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| Matrix Multiplication and Row Operations | |
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| Inverse Matrices and Systems of Linear Equations | |
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| Inverse Matrices | |
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| How to Find Inverse Matrices | |
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| Solving AX = B Using A-1 | |
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| Introduction to Modeling: Leontief Models | |
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| Linear Programming | |
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| Linear Inequalities | |
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| Inequalities in Two Variables | |
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| Vertices of Feasible Regions | |
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| Bounded and Unbounded Regions | |
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| Applications | |
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| Two-Variable Linear Programming Problems | |
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| Linear Programming Problems | |
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| Fundamental Theorem of Linear Programming | |
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| Extensions to Larger Problems | |
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| The Simplex Method for Standard Maximum Problems | |
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| Standard Maximum Problems | |
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| Matrix Form of a Standard Maximum Problem | |
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| The Initial Simplex Tableau | |
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| Basic and Nonbasic Variables | |
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| The Pivot Element | |
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| The Pivot Operation | |
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| The Simplex Method | |
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| Standard Minimum Problems and Duality | |
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| Standard Minimum Problems | |
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| The Dual of a Standard Minimum Problem | |
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| Matrix Form | |
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| Mixed Constraints: A Transportation Problem | |
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| Probability | |
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| Sets, Counting, and Venn Diagrams | |
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| Sets and Set Operations | |
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| Addition Principle for Counting | |
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| The Multiplication Principle for Counting | |
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| The Number of Subsets of a Set | |
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| Permutations and Combinations | |
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| Factorials | |
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| Permutations | |
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| Combinations | |
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| Probability Spaces | |
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| Random Experiments and Sample Spaces | |
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| Events | |
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| Probabilities of Possible Outcomes | |
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| Probabilities of Events | |
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| Probability That an Event Does Not Occur | |
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| Probability Space | |
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| Addition Rule for Probability | |
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| Conditional Probability and Independence | |
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| Conditional Probability | |
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| The Product Rule for Probability | |
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| Independent Events | |
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| Bayes' Formula | |
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| Bayes' Formula | |
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| Random Variables and Distributions | |
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| Random Variables | |
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| Expected Value | |
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| Binomial Distribution | |
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| Statistics | |
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| Random Samples and Data Organization | |
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| Random Samples | |
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| Bar Chart | |
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| Histogram | |
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| Measures of Central Tendency | |
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| Mode | |
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| Median | |
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| Mean | |
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| Mean, Median, and Mode | |
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| Measures of Variation | |
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| Range | |
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| Box-and-Whisker Plot | |
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| Interpreting Box-and-Whisker Plots | |
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| Sample Standard Deviation | |
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| Normal Distributions and Binomial Approximation | |
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| Discrete and Continuous Random Variables | |
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| Normal Distribution | |
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| z-Scores | |
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| The Normal and Binomial Distributions | |
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| Markov Chains | |
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| States and Transitions | |
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| States and Transitions | |
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| Markov Chains | |
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| Types of Transition Matrices | |
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| State Distribution Vectors | |
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| The kth State Distribution Vector | |
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| Duration in a Given State | |
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| Regular Markov Chains | |
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| Regular Markov Chains | |
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| The Fundamental Theorem of Regular Markov Chains | |
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| How to Solve D ? T = D | |
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| Absorbing Markov Chains | |
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| Absorbing Markov Chains | |
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| Standard Form | |
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| Transition Times and Absorption Probabilities | |
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| Game Theory | |
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| Two-Person Games and Saddle Points | |
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| Payoff Matrix | |
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| Optimal Strategy | |
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| Finding Saddle Points | |
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| Mixed Strategies | |
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| Mixed Strategies and Expected Values | |
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| Optimal Mixed Strategies for 2 ? 2 Games | |
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| Other Interpretations of Mixed Strategies | |
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| Games and Linear Programming | |
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| Games as Linear Programming Problems | |
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| Every Game Has a Solution | |
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| Index | |