Finite Mathematics & Its Applications

Larry Goldstein has received several distinguished teaching awards, given more than fifty Conference and Colloquium talks & addresses, and written more than fifty books in math and computer programming.  He received his PhD at Princeton and his BA and MA at the University of Pennsylvania. He also teaches part time at Drexel University.   David Schneider, who is known widely for his tutorial software, holds a BA degree from Oberlin College and a PhD from MIT.  He is currently an associate professor of mathematics at the University of Maryland. He has authored eight widely used math texts, fourteen highly acclaimed computer books, and three widely used mathematics software packages. He has also produced instructional videotapes at both the University of Maryland and the BBC.   Martha Siegel holds a BA from Russell Sage College, attended Rensselear Polytechnic Institute as a special student, and received her PhD at the University of Rochester. From 1966 until 1971 she taught at Goucher University in Baltimore. Since 1971 she has been a professor at Towson State University, also in Maryland. Professor Siegel has been on the writing team of this book since the fifth edition and is also the co-author of a precalculus reform book.

Preface

 

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

 

2. Matrices

Systems of Linear Equations with Unique Solutions

2.1 Systems of Linear Equations with Unique Solutions

2.2 General Systems of Linear Equations

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

 

3. Linear Programming, A Geometric Approach

3.1 A Linear Programming Application

3.2 The Fundamental Theorem of Linear Programming

3.3 Linear Programming

   Chapter Project: Shadow Prices

 

4. The Simplex Method

4.1 Slack Variables and the Simplex Tableau

4.2 Maximum Problems

4.3 Minimum Problems

4.4 Sensitivity Analysis and Matrix Formulations of Linear Programming Problems

4.5 Duality

   Chapter Project: Shadow Prices

 

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 Techniques

5.7 The Binomial Theorem

5.8 Multinomial Coefficients and Partitions

   Chapter Project: Pascal's Triangle

 

6. Probability

6.1 Experiments, Outcomes, SampleSapces, and Events

6.2 Assignment of Probabilities

6.3 Calculating Probabilities of Events

6.4 Conditional Probability and Independence

6.5 Tree Diagrams

6.6 Bayes' Theorem, Natural Frequencies

6.7 Simulation

   Chapter Project: Two Paradoxes

 

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

 

8. Markov Processes

8.1 The Transition Matrix

8.2 Regular Stochastic Matrices

8.3 Absorbing Stochastic Matrices

   Chapter Project: Doubly Stochastic Matrices

 

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

 

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

 

11. Difference Equations and Mathematical Models

11.1 Introduction to Difference Equations

11.2 Difference Equations and Interest

11.3 Graphing Difference Equations

11.4 Mathematics of Personal Finance

11.5 Modeling with Difference Equations

   Chapter Project: Connections to Markov Processes

 

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. Areas Under the Standard Normal Curve

Appendix B. The TI-83/84 Plus Graphing Calculators

Appendix C. Spreadsheet Fundamentals

Appendix D. Wolfram Alpha

 

Answers to Odd-Numbered Exercises

Index