Applied Finite Mathematics

1st Edition - January 1, 1974
Authors: Howard Anton, Bernard Kolman
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 7 1 3 7 - 8

Applied Finite Mathematics presents the fundamentals of finite mathematics in a style tailored for beginners, but at the same time covers the subject matter in sufficient depth so… Read more

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Applied Finite Mathematics presents the fundamentals of finite mathematics in a style tailored for beginners, but at the same time covers the subject matter in sufficient depth so that the student can see a rich variety of realistic and relevant applications. Applications in fields such as business, biology, behavioral sciences, and social sciences are included. Comprised of nine chapters, this book begins with an introduction to set theory, explaining concepts such as sets and union and intersection of sets as well as counting elements in sets. The next chapter deals with coordinate systems and graphs, along with applications of linear equations and graphs of linear inequalities. The discussion then turns to linear programming; matrices and linear systems; probability; and statistics. Examples of applications are given, including those of game theory, Markov chains, and probability. The final chapter is devoted to computers and programming languages such as FORTRAN. This monograph is intended for students and instructors of applied mathematics.

Preface

Acknowledgments

1 Set Theory

1.1 Introduction to Sets

1.2 Union and Intersection of Sets

1.3 Complementation and Cartesian Product of Sets

1.4 Counting Elements in Sets

2 Coordinate Systems and Graphs

2.1 Coordinate Systems

2.2 The Straight Line

2.3 Applications of Linear Equations

2.4 Linear Inequalities and Their Graphs

3 Linear Programming (A Geometric Approach)

3.1 What Is Linear Programming?

3.2 Solving Linear Programming Problems Geometrically

4 Matrices and Linear Systems

4.1 Linear Systems

4.2 Gauss-Jordan Elimination

4.3 Matrices; Matrix Addition and Scalar Multiplication

4.4 Matrix Multiplication

4.5 Inverses of Matrices

5 Linear Programming (An Algebraic Approach)

5.1 Introduction; Slack Variables

5.2 The Key Ideas of the Simplex Method

5.3 The Simplex Method

5.4 Nonstandard Linear Programming Problems; Duality

6 Probability

6.1 Introduction; Sample Space and Events

6.2 Probability Models for Finite Sample Spaces

6.3 Basic Theorems of Probability

6.4 Counting Techniques; Permutations and Combinations

6.5 Conditional Probability; Independence

6.6 Bayes' Formula

7 Statistics

7.1 Introduction; Random Variables

7.2 Expected Value of a Random Variable

7.3 Variance of a Random Variable

7.4 Chebyshev's Inequality; Applications of Mean and Variance

7.5 Binomial Random Variables

7.6 The Normal Approximation to the Binomial

7.7 Hypothesis Testing; The Chi-Square Test

8 Applications

8.1 An Application of Conditional Probability to Medical Diagnosis

8.2 An Application of Probability to Genetics ; The Hardy-Weinberg Stability Principle

8.3 Applications of Probability and Expected Value to Life Insurance and Mortality

8.4 Introduction to Game Theory and Applications

8.5 Games with Mixed Strategies

8.6 Markov Chains and Applications

9 Computers

9.1 What Is a Computer?

9.2 Communicating with the Computer

9.3 FORTRAN, A Programming Language of Science

9.4 FORTRAN, Continued (Loops and Decisions)

9.5 Flow Charts

9.6 Other Programming Languages

Appendix/Tables

I Area under the Standard Normal Curve

II Table of Binomial Probabilities

III Table of 5% Critical Levels for x2-Curves

IV Table of Square Roots

Answer to Selected Exercises

Index

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Bernard Kolman