Finite Mathematics

Michael Sullivan is Professor Emeritus in the Department of Mathematics and Computer Science at Chicago State University where he taught for 35 years before retiring a few years ago. Dr. Sullivan is a member of American Mathematical Society, the Mathematical Association of America, and the American Mathematical Association of Two Year Colleges. He is President of Text and Academic Authors Association and represents that organization on the Authors Coalition of America, Mike has been writing textbooks in mathematics for over 30 years. He currently has 13 books in print: 3 texts with John Wiley & Sons and 10 with Prentice-Hall. Six of these titles are co-authored with his son, Michael Sullivan III. He has four children: Kathleen, who teaches college mathematics; Michael, who teaches college mathematics, Dan who is a Prentice-Hall sales representative, and Colleen, who teaches middle school mathematics. Nine grandchildren round out the family.

Chapter 1: Linear Equations 1.1.   Lines

1.2.   Pairs of Lines

1.3.   Applications to Business and Economics

1.4.   Scatter Diagrams; Linear Curve Fitting

Chapter Review

Chapter Project

Chapter 2: Systems of Linear Equations

2.1 Systems of Linear Equations: Substitution; Elimination

2.2 Systems of Linear Equations: Gauss-Jordan Method

2.3 Systems of m Linear Equations Containing n Variables

Chapter Review

Chapter Project

Chapter 3: Matrices

3.1 Matrix Algebra

3.2 Multiplication of Matrices

3.3 The Inverse of a Matrix

3.4 Applications in Economics (the Leontief Model), Accounting, and Statistics (the Method of Least Squares)

Chapter Review

Chapter Project

Chapter 4: Linear Programming with Two Variables

4.1 Systems of Linear Inequalities

4.2 A Geometric Approach to Linear Programming Problems

Chapter Review

Chapter Project

Chapter 5: Linear Programming: Simplex Method

5.1 The Simplex Tableau; Pivoting

5.2 The Simplex Method; Solving Maximum Problems in Standard Form

5.3 Solving Minimum Problems Using the Daily Principle

5.4 The Simplex Method for Problems Not in Standard Form

Chapter Review

Chapter Project

Chapter 6: Finance

6.1 Interest

6.2 Compound Interest

6.3 Annuities; Sinking Funds

6.4 Present Value of an Annuity; Amortization

6.5 Annuities and Amortization Using Recursive Sequences

Chapter Review

Chapter Project

Chapter 7: Probability

7.1 Sets

7.2 The Number of Elements in a Set

7.3 The Multiplication Principle

7.4 Sample Spaces and the Assignment of Probabilities

7.5 Properties of the Probability of an Event

7.6 Expected Value

Chapter Review

Chapter Project

Chapter 8: Bayes' Theorem; The Binomial Probability Model

8.1 Conditional Probability

8.2 Independent Events

8.3 Bayes' Theorem

8.4 Permutations

8.5 Combinations

8.6 The Binomial Probability Model

Chapter Review

Chapter Project

Chapter 9: Statistics

9.1 Introduction to Statistics: Data and Sampling

9.2 Representing Qualitative Data Graphically: Bar Graphs; Pie Charts

9.3 Organizing and Displaying Quantitative Data

9.4 Measures of Central Tendency

9.5 Measures of Dispersion

9.6 The Normal Distribution

Chapter Review

Chapter Project

Chapter 10: Markov Chains; Games

10.1 Markov Chains and Transition Matrices

10.2 Regular Markov Chains

10.3 Absorbing Markov Chains

10.4 Two-Person Games

10.5 Mixed Strategies

10.6 Optimal Strategy in Two-Person Zero-Sum Games with 2 X 2 Matrices

Chapter Review

Chapter Project

Chapter 11: Logic

11.1 Propositions

11.2 Truth Tables

11.3 Implications; The Biconditional Connective; Tautologies

11.4 Arguments

11.5 Logic Circuits

Chapter Review

Chapter Project

Appendix A: Review

A.1 Real Numbers

A.2 Algebra Essentials

A.3 Exponents and Logarithms

A.4 Recursive Defined Sequences: Geometric Sequences

Appendix B: Using LINDO to Solve Linear Programming Problems

Appendix C: Graphing Utilities

C.1 The Viewing Rectangle

C.2 Using a Graphing Utility to Graph Equations

C.3 Square Screens

C.4 Using a Graphing Utility to Graph Inequalities

Answers to Odd-Numbered Problems

Photo Credits

Index