Functions and Linear Models | |
Functions from the Numerical and Algebraic Viewpoints | |
Functions from the Graphical Viewpoint | |
Linear Functions | |
Linear Models | |
Linear Regression | |
Modeling Spending on Internet Advertising | |
Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions | |
Systems of Linear Equations and Matrices | |
Systems of Two Equations in Two Unknowns | |
Using Matrices to Solve Systems of Equations | |
Applications of Systems of Linear Equations | |
The Impact of Regulating Sulfur Emissions | |
Matrix Algebra and Applications | |
Matrix Addition and Scalar Multiplication | |
Matrix Multiplication | |
Matrix Inversion | |
Input-Output Models | |
Chapter Project: The Japanese Economy | |
Linear Programming | |
Graphing Linear Inequalities | |
Solving Linear Programming Problems Graphically | |
The Simplex Method: Solving Standard Maximization Problems | |
The Simplex Method: Solving General Linear Programming Problems | |
The Simplex Method and Duality (Optional) | |
Chapter Project: Airline Scheduling | |
The Mathematics of Finanace | |
Simple Interest | |
Compound Interest | |
Annuities, Loans, and Bonds | |
Chapter Project: Saving for College | |
Sets and Counting | |
Set Operations | |
Cardinality | |
The Addition and Multiplication Principles | |
Permutations and Combinations | |
Designing a Puzzle | |
Probability | |
Sample Spaces and Events | |
Estimated Probability | |
Empirical Probability | |
Probability and Counting Techniques | |
Probability Distributions | |
Conditional Probability and Independence | |
Bayes' Theorem and Applications | |
Chapter Project: The Monty Hall Problem | |
Random Variables and Statistics | |
Random Variables and Distributions | |
Bernoulli Trials and Binomial Random Variables | |
Measures of Central Tendency | |
Measures of Dispersion | |
Normal Distributions | |
Chapter Project: Spotting Tax Fraud with Benford's Law | |
Optional Internet Topics: Sampling Distributions and the Central Limit Theorem | |
Confidence Intervals | |
Hypothesis Testing | |
Markov Systems | |
Markov Systems | |
Distribution Vectors and Powers of the Transition Matrix | |
Long-Range Behavior of Regular Markov Systems | |
Absorbing Markov Systems | |
Chapter Project: Predicting the Price of Gold | |
AppendiceS | |
Real Numbers | |
Table: Area Under a Normal Curve | |
Optional Internet Chapters | |
G. Game Theory | |
Two-Person Zero Sum Games | |
Reduction by Dominance | |
Strictly Determined Games | |
Solving Games using the Simplex Method | |
Expert Opinion--Harvesting Forests | |
L. Introduction to Logic | |
Statements and Logical Operators | |
Logical Equivalence, Tautologies and Contradictions | |
The Conditional and the Biconditional | |
Tautological Implications and Tautological Equivalences | |
Rules of Inference | |
Arguments and Proofs | |
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