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Algebra Review | |
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Real Numbers | |
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Exponents and Radicals | |
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Multiplying and Factoring Algebraic Equations | |
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Rational Expressions | |
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Solving Polynomial Equations | |
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Solving Miscellaneous Equations | |
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Functions and Linear Models | |
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Functions from the Numerical and Algebraic Viewpoints | |
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Functions from the Graphical Viewpoint | |
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Linear Functions | |
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Linear Models | |
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Linear Regression | |
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Key Concepts | |
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Review Exercises | |
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Case Study: Modeling Spending on Internet Advertising | |
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Technology Guides | |
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Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions | |
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Systems of Linear Equations and Matrices | |
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Systems of Two Equations in Two Unknowns | |
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Using Matrices to Solve Systems of Equations | |
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Applications of Systems of Linear Equations | |
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Key Concepts | |
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Review Exercises | |
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Case Study: The Impact of Regulating Sulfur Emissions | |
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Technology Guides | |
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Matrix Algebra and Applications | |
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Matrix Addition and Scalar Multiplication | |
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Matrix Multiplication | |
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Matrix Inversion | |
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Matrices in Practice: Game Theory | |
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Matrices in Practice: Input-Output Models | |
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Key Concepts | |
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Review Exercises | |
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Case Study: The Japanese Economy | |
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Technology Guides | |
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Linear Programming | |
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Graphing Linear Inequalities | |
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Solving Linear Programming Problems Graphically | |
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The Simplex Method: Solving Standard Maximization Problems | |
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The Simplex Method: Solving General Linear Programming Problems | |
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The Simplex Method and Duality (Optional) | |
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Key Concepts | |
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Review Exercises | |
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Case Study: Airline Scheduling | |
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Technology Guides | |
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The Mathematics of Finance | |
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Simple Interest | |
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Compound Interest | |
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Annuities, Loans, and Bonds | |
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Key Concepts | |
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Review Exercises | |
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Case Study: Saving for College | |
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Technology Guides | |
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Sets and Counting | |
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Sets and Set Operations | |
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Cardinality | |
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The Addition and Multiplication Principles | |
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Permutations and Combinations | |
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Key Concepts | |
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Review Exercises | |
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Case Study: Designing a Puzzle | |
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Technology Guides | |
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Probability | |
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Sample Spaces and Events | |
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Estimated Probability | |
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Theoretical Probability and Probability Distributions | |
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Probability and Counting Techniques (optional) | |
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Conditional Probability and Independence | |
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Bayes' Theorem and Applications | |
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Probability in Practice: Markov Systems | |
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Key Concepts | |
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Review Exercises | |
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Case Study: The Monty Hall Problem | |
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Technology Guides | |
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Random Variables and Statistics | |
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Random Variables and Distributions | |
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Bernoulli Trials and Binomial Random Variables | |
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Measures of Central Tendency | |
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Measures of Dispersion | |
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Normal Distributions | |
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Key Concepts | |
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Review Exercises | |
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Case Study: Spotting Tax Fraud with Benford's Law | |
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Technology Guides | |
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Optional Internet Topics: Sampling Distributions and the Central Limit Theorem | |
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Confidence Intervals | |
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Hypothesis Testing | |
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Nonlinear Models | |
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Quadratic Functions and Models | |
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Exponential Functions and Models | |
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Logarithmic Functions and Models | |
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Logistic Functions and Models | |
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Key Concepts | |
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Review Exercises | |
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Case Study: Checking up on Malthus | |
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Technology Guides | |
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Optional Internet Topics: Inverse Functions | |
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Using and Deriving Algebraic Properties of Logarithms | |
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Introduction to the Derivative | |
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Limits: Numerical and Graphical Approaches | |
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Limits and Continuity | |
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Limits: Algebraic Approach | |
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Average Rate of Change | |
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Derivatives: Numerical and Graphical Viewpoints | |
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Derivatives: Algebraic Viewpoint | |
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Derivatives of Powers, Sums, and Constant Multiples | |
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A First Application: Marginal Analysis | |
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Key Concepts | |
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Review Exercises | |
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Case Study: Reducing Sulfur Emissions | |
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Technology Guides | |
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Optional Internet Topics: Sketching the Graph of the Derivative | |
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Proof of the Power Rule | |
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Continuity and Differentiability | |
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Techniques of Differentiation | |
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The Product and Quotient Rules | |
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The Chain Rule | |
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Derivatives of Logarithmic and Exponential Functions | |
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Implicit Differentiation | |
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Key Concepts | |
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Review Exercises | |
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Case Study: Projecting Market Growth | |
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Technology Guides | |
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Optional Internet Topic: Linear Approximation and Error Estimation | |
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Applications of the Derivative | |
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Maxima and Minima | |
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Applications of Maxima and Minima | |
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The Second Derivative and Analyzing Graphs | |
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