Preface
1. Linear Equations and Straight Lines
1.1 Coordinate Systems and Graphs
1.2 The Slope of a Straight Line
1.3 The Intersection Point of a Pair of Lines
1.4 The Method of Least Squares
Chapter Project: Break-Even Analysis
2. Matrices
2.1 Systems of Linear Equations with Unique Solutions
2.2 General Systems of Linear Equations
2.3 Arithmetic Operations on Matrices
2.4 The Inverse of a Matrix
2.5 The Gauss-Jordan Method for Calculating Inverses
2.6 Input-Output Analysis
Chapter Project: Population Dynamics
3. Linear Programming, A Geometric Approach
3.1 Linear Inequalities
3.2 A Linear Programming Problem
3.3 Fundamental Theorem of Linear Programming
3.4 Linear Programming
Chapter Project: Shadow Prices
4. The Simplex Method
4.1 Slack Variables and the Simplex Tableau
4.2 The Simplex Method I: Maximum Problems
4.3 The Simplex Method II: Nonstandard and Minimum Problems
4.4 Sensitivity Analysis and Matrix Formulations of Linear Programming Problems
4.5 Duality
Chapter Project: Shadow Prices
5. Sets and Counting
5.1 Sets
5.2 A Fundamental Principle of Counting
5.3 Venn Diagrams and Counting
5.4 The Multiplication Principle
5.5 Permutations and Combinations
5.6 Further Counting Techniques
5.7 The Binomial Theorem
5.8 Multinomial Coefficients and Partitions
Chapter Project: Pascal's Triangle
6. Probability
6.1 Experiments, Outcomes, Sample Spaces, and Events
6.2 Assignment of Probabilities
6.3 Calculating Probabilities of Events
6.4 Conditional Probability and Independence
6.5 Tree Diagrams
6.6 Bayes' Theorem, Natural Frequencies
6.7 Simulation
Chapter Project: Two Paradoxes
7. Probability and Statistics
7.1 Visual Representations of Data
7.2 Frequency and Probability Distributions
7.3 Binomial Trials
7.4 The Mean
7.5 The Variance and Standard Deviation
7.6 The Normal Distribution
7.7 Normal Approximation to the Binomial Distribution
Chapter Project: An Unexpected Expected Value
8. Markov Processes
8.1 The Transition Matrix
8.2 Regular Stochastic Matrices
8.3 Absorbing Stochastic Matrices
Chapter Project: Doubly Stochastic Matrices
9. The Theory of Games
9.1 Games and Strategies
9.2 Mixed Strategies
9.3 Determining Optimal Mixed Strategies
Chapter Project: Simulating The Outcomes of Mixed-Strategy Games
10. The Mathematics of Finance
10.1 Interest
10.2 Annuities
10.3 Amortization of Loans
10.4 Personal Financial Decisions
10.5 A Unifying Equation
Chapter Project: Two Items of Interest
11. Logic
11.1 Introduction to Logic
11.2 Truth Tables
11.3 Implication
11.4 Logical Implication and Equivalence
11.5 Valid Argument
11.6 Predicate Calculus
11.7 Logic Circuits
Chapter Project: A Logic Puzzle
12. Difference Equations and Mathematical Models (Online at www.pearsonhighered.com/mathstatsresources)
12.1 Introduction to Difference Equations
12.2 Difference Equations and Interest
12.3 Graphing Difference Equations
12.4 Mathematics of Personal Finance
12.5 Modeling with Difference Equations
Chapter Project: Connections to Markov Processes
Appendix A. Areas Under the Standard Normal Curve
Appendix B. The TI-83/84 Plus Graphing Calculators
Appendix C. Spreadsheet Fundamentals
Appendix D. Wolfram Alpha
Answers to Odd-Numbered Exercises
Index
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