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R. Algebra Reference | |
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Polynomials | |
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Factoring | |
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Rational Expressions | |
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Equations | |
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Inequalities | |
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Exponents | |
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Radicals | |
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Linear Functions | |
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Slope and Equations of a Line | |
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Linear Functions | |
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Linear Mathematical Models | |
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Constructing a Mathematical Model | |
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Review Exercises | |
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Extended Application: Using Marginal Cost to Estimate the Cost of Educating Immigrants | |
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Extended Application: Depreciation | |
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Systems of Linear Equations and Matrices | |
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Solution of Linear Systems by the Echelon Method | |
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Solution of Linear Systems by the Gauss-Jordan Method | |
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Addition and Subtraction of Matrices | |
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Multiplication of Matrices | |
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Matrix Inverses | |
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Input-Output Models | |
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Review Exercises | |
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Extended Application: Contagion | |
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Linear Programming: The Graphical Method | |
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Graphing Linear Inequalities | |
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Solving Linear Programming Problems Graphically | |
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Applications of Linear Programming | |
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Review Exercises | |
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Linear Programming: The Simplex Method | |
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Slack Variables and the Pivot | |
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Maximization Problems | |
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Minimization Problems; Duality | |
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Nonstandard Problems | |
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Review Exercises | |
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Extended Application: A Minimum Cost Balanced Organic Fertilizer Mix | |
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Mathematics of Finance | |
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Simple and Compound Interest | |
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Future Value of an Annuity | |
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Present Value of an Annuity; Amortization | |
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A Strategy for Solving Finance Problems | |
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Review Exercises | |
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Extended Application: Time, Money, and Polynomials | |
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Sets and Probability | |
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Sets | |
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Applications of Venn Diagrams | |
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Introduction to Probability | |
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Basic Concepts of Probability | |
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Conditional Probability; Independent Events | |
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Bayes' Theorem | |
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Probability Summary | |
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Review Exercises | |
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Extended Application: Medical Diagnosis | |
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Counting Principles; Further Probability Topics | |
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The Multiplication Principle; Permutations | |
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Combinations | |
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Probability Applications of Counting Principles | |
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Binomial Probability | |
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Probability Distributions; Expected Value | |
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Review Exercises | |
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Extended Application: Optimal Inventory for a Service Truck | |
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Statistics | |
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Frequency Distributions; Measures of Central Tendency | |
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Measures of Variation | |
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The Normal Distribution | |
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Normal Approximation to the Binomial Distribution | |
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Review Exercises | |
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Markov Chains | |
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Basic Properties of Markov Chains | |
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Regular Markov Chains | |
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Absorbing Markov Chains | |
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Review Exercises | |
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Extended Application: Cavities and Restoration | |
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Game Theory | |
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Strictly Determined Games | |
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Mixed Strategies | |
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Game Theory and Linear Programming | |
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Review Exercises | |
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Extended Application: Decision Making in the Military | |