Finite Mathematics Book

R. Algebra Reference

R.1 Polynomials

R.2 Factoring

R.3 Rational Expressions

R.4 Equations

R.5 Inequalities

R.6 Exponents

R.7 Radicals

1. Linear Functions

1.1 Slopes and Equations of Lines

1.2 Linear Functions and Applications

1.3 The Least Squares Line

Chapter 1 Review

Extended Application: Using Extrapolation to Predict Life Expectancy

2. Systems of Linear Equations and Matrices

2.1 Solution of Linear Systems by the Echelon Method

2.2 Solution of Linear Systems by the Gauss-Jordan Method

2.3 Addition and Subtraction of Matrices

2.4 Multiplication of Matrices

2.5 Matrix Inverses

2.6 Input-Output Models

Chapter 2 Review

Extended Application: Contagion

3. Linear Programming: The Graphical Method

3.1 Graphing Linear Inequalities

3.2 Solving Linear Programming Problems Graphically

3.3 Applications of Linear Programming

Chapter 3 Review

Extended Application: Sensitivity Analysis

4. Linear Programming: The Simplex Method

4.1 Slack Variables and the Pivot

4.2 Maximization Problems

4.3 Minimization Problems; Duality

4.4 Nonstandard Problems

Chapter 4 Review

Extended Application: Using Integer Programming in the Stock-Cutting Problem

5. Mathematics of Finance

5.1 Simple and Compound Interest

5.2 Future Value of an Annuity

5.3 Present Value of an Annuity; Amortization

Chapter 5 Review

Extended Application: Time, Money, and Polynomials

6. Logic

6.1 Statements

6.2 Truth Tables and Equivalent Statements

6.3 The Conditional and Circuits

6.4 More on the Conditional

6.5 Analyzing Arguments and Proofs

6.6 Analyzing Arguments with Quantifiers

Chapter 6 Review

Extended Application: Logic Puzzles

7. Sets and Probability

7.1 Sets

7.2 Applications of Venn Diagrams

7.3 Introduction to Probability

7.4 Basic Concepts of Probability

7.5 Conditional Probability; Independent Events

7.6 Bayes’ Theorem

Chapter 7 Review

Extended Application: Medical Diagnosis

8. Counting Principles; Further Probability Topics

8.1 The Multiplication Principle; Permutations

8.2 Combinations

8.3 Probability Applications of Counting Principles

8.4 Binomial Probability

8.5 Probability Distributions; Expected Value

Chapter 8 Review

Extended Application: Optimal Inventory for a Service Truck

9. Statistics

9.1 Frequency Distributions; Measures of Central Tendency

9.2 Measures of Variation

9.3 The Normal Distribution

9.4 Normal Approximation to the Binomial Distribution

Chapter 9 Review

Extended Application: Statistics in the Law—The Castaneda Decision

10. Markov Chains

10.1 Basic Properties of Markov Chains

10.2 Regular Markov Chains

10.3 Absorbing Markov Chains

Chapter 10 Review

Extended Application: A Markov Chain Model for Teacher Retention

11. Game Theory

11.1 Strictly Determined Games

11.2 Mixed Strategies

11.3 Game Theory and Linear Programming

Chapter 11 Review

Extended Application: The Prisoner’s Dilemma—Non-Zero-Sum Games in Economics