Finite Mathematics (with InfoTrac)

by Waner, Stefan; Costenoble, Steven

• ISBN13: 9780534419493
• ISBN10: 0534419496
• Format: Hardcover
• Copyright: 2003-06-19
• Publisher: Brooks Cole

Summary

1. FUNCTIONS AND LINEAR MODELS. Introduction. Functions from the Numerical and Algebraic Viewpoints. Functions from the Graphical Viewpoint. Linear Functions. Linear Models. Linear Regression. Case Study: Modeling Spending on Internet Advertising. Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions. 2. SYSTEMS OF LINEAR EQUATIONS AND MATRICES. Introduction. Systems of Two Equations in Two Unknowns. Using Matrices to Solve Systems of Equations. Applications of Systems of Linear Equations. Case Study: The Impact of Regulating Sulfur Emissions. 3. MATRIX ALGEBRA AND APPLICA TIONS. Introduction. Matrix Addition and Scalar Multiplication. Matrix Multiplication. Matrix Inversion. Input-Output Models. Case Study: The Japanese Economy. 4. LINEAR PROGRAMMING. Introduction. 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). Case Study: Airline Scheduling. 5. THE MATHEMATICS OF FINANACE. Introduction. Simple Interest. Compound Interest. Annuities, Loans, and Bonds. Case Study: Saving for College. 6. SETS AND COUNTING. Introduction. Set Operations. Cardinality. The Addition and Multiplication Principles. Permutations and Combinations. Case Study: Designi ng a Puz zle. 7. PROBABILITY. Introduction. Sample Spaces and Events. Estimated Probability. Empirical Probability. Probability and Counting Techniques. Probability Distributions. Conditional Probability and Independence. Bayes' Theorem and Applications. Case Study: The Monty Hall Problem. 8. RANDOM VARIABLES AND STATISTICS. Introduction. Random Variables and Distributions. Bernoulli Trials and Binomial Random Variables. Measures of Central Tendency. Measures of Dispersion. Normal Distributions. Case Study: Spotting Tax Fraud with Benford's Law. Optional Internet Topics: Sampling Distributions and the Central Limit Theorem. Confidence Intervals. Hypothesis Testing. 9. MARKOV SYSTEMS. Introduction. Markov Systems. Distribution Vectors and Powers of the Transition Matrix. Long-Range Behavior of Regular Markov Systems. Absorbing Markov Systems. Case Study: Predicting the Price of Gold. OPTIONAL INTERNET CHAPTERS. G. Game Theory. Introduction. Two-Person Zero Sum Games; Reduction by Dominance. Strictly Determined Games. Solving Games using the Simplex Method. Expert Opinion--arves ting Forests. L. Introduction to Logic. Introduction. 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. Appendix A: Real Numbers. Appendix B: Table: Area Under a Normal Curve. Answers to Selected Exercises. Index.

Table of Contents

1. FUNCTIONS AND LINEAR MODELS

Introduction

Functions from the Numerical and Algebraic Viewpoints

Functions from the Graphical Viewpoint

Linear Functions

Linear Models

Linear Regression

Case Study: Modeling Spending on Internet Advertising

Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions

2. SYSTEMS OF LINEAR EQUATIONS AND MATRICES

Introduction

Systems of Two Equations in Two Unknowns

Using Matrices to Solve Systems of Equations

Applications of Systems of Linear Equations

Case Study: The Impact of Regulating Sulfur Emissions

3. MATRIX ALGEBRA AND APPLICATIONS

Introduction

Matrix Addition and Scalar Multiplication

Matrix Multiplication

Matrix Inversion

Input-Output Models

Case Study: The Japanese Economy

4. LINEAR PROGRAMMING

Introduction

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)

Case Study: Airline Scheduling

5. THE MATHEMATICS OF FINANACE

Introduction

Simple Interest

Compound Interest

Annuities, Loans, and Bonds

Case Study: Saving for College

6. SETS AND COUNTING

Introduction

Set Operations

Cardinality

The Addition and Multiplication Principles

Permutations and Combinations

Case Study: Designing a Puzzle

7. PROBABILITY

Introduction

Sample Spaces and Events

Estimated Probability

Empirical Probability

Probability and Counting Techniques

Probability Distributions

Conditional Probability and Independence

Bayes' Theorem and Applications

Case Study: The Monty Hall Problem

8. RANDOM VARIABLES AND STATISTICS

Introduction

Random Variables and Distributions

Bernoulli Trials and Binomial Random Variables

Measures of Central Tendency

Measures of Dispersion

Normal Distributions

Case Study: Spotting Tax Fraud with Benford's Law

Optional Internet Topics: Sampling Distributions and the Central Limit Theorem

Confidence Intervals

Hypothesis Testing

9. MARKOV SYSTEMS

Introduction

Markov Systems

Distribution Vectors and Powers of the Transition Matrix

Long-Range Behavior of Regular Markov Systems

Absorbing Markov Systems

Case Study: Predicting the Price of Gold

OPTIONAL INTERNET CHAPTERS

G

Game Theory

Introduction

Two-Person Zero Sum Games; Reduction by Dominance

Strictly Determined Games

Solving Games using the Simplex Method

Expert Opinion--arvesting Forests

L

Introduction to Logic

Introduction

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

Appendix A: Real Numbers

Appendix B: Table: Area Under a Normal Curve

Answers to Selected Exercises

Index