A “tried and true” favorite of both students and instructors alike, this text offers extremely readable coverage of the principles of finite mathematics and their applications in business, social science, and the life sciences. Topics are presented in a straightforward, interesting manner, with considerable attention given to the applications of the mathematics. The goal is for the students' mathematical maturity and appreciation for the usefulness of mathematics to grow simultaneously. Many sections contain specially designed technology exercises.

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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 Conditional Probability 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\n

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