Finite Math & Its Application Book

Preface

Index of Applications

Chapter 1 Linear Equations and Straight Lines

1.1 Coordinate Systems and Graphs

1.2 Linear Inequalities

1.3 The Intersection Point of a Pair of Lines

1.4 The Slope of a Straight Line

1.5 The Method of Least Squares

Chapter Project: Break-even Analysis

Chapter 2 Matrices

2.1 Solving Systems of Linear Equations, I

2.2 Solving Systems of Linear Equations, II

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

Chapter 3  Linear Programming, A Geometric Approach  

3.1 A Linear Programming Problem

3.2 Linear Programming, I

3.3 Linear Programming, II

Chapter Project: Shadow Prices

Chapter 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: Minimum Problems

4.4 Sensitivity Analysis and Matrix Formulations of Linear Programming Problems

4.5 Duality

Chapter Project: Shadow Prices

Chapter 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 Problems

5.7 The Binomial Theorem

5.8 Multinomial Coefficients and Partitions

Chapter Project: Pascal's Triangle

Chapter 6  Probability

6.1 Introduction

6.2 Experiments, Outcomes, and Events

6.3 Assignment of Probabilities

6.4 Calculating Probabilities of Events

6.5 ConditionalProbability and Independence

6.6 Tree Diagrams

6.7 Bayes' Theorem

6.8 Simulation

Chapter Project: Two Paradoxes

Chapter 7  Probability and Statistics

7.1 Representation 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

Chapter 8  Markov Processes

8.1 The Transition Matrix

8.2 Regular Stochastic Matrices

8.3 Absorbing Stochastic Matrices

Chapter Project: Doubly Stochastic Matrices

Chapter 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

Chapter 10  The Mathematics of Finance

10.1 Interest

10.2 Annuities

10.3 Amortization of Loans

10.4 Personal Financial Decisions

Chapter Project: Two Items of Interest

Chapter 11  Difference Equations and Mathematical Models

11.1 Introduction to Difference Equations, I

11.2 Introduction to Difference Equations, II

11.3 Graphing Difference Equations

11.4 Mathematics of Personal Finance

11.5 Modelling with Difference Equations

Chapter Project: Connections to Markov Processes

Chapter 12  Logic

12.1 Introduction to Logic

12.2 Truth Tables

12.3 Implication

12.4 Logical Implication and Equivalence

12.5 Valid Argument

12.6 Predicate Calculus

12.7 Logic Circuits

Chapter Project: A Logic Puzzle

 Appendix  A  Tables

Appendix B  Using the TI-83, TI-83 Plus, and TI-84 Plus Graphing Calculators

Appendix C  Spreadsheet Fundamentals

Appendix D  Using the TI-89 Graphing Calculators

Answers to Odd-Numbered Exercises

Solutions to Selected Exercises

Index