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Applied Finite Mathematics

2nd Edition - January 1, 1978

Authors: Howard Anton, Bernard Kolman

eBook ISBN:

9 7 8 - 1 - 4 8 3 2 - 7 0 9 6 - 8

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

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Applied Finite Mathematics, Second Edition 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. Some applications of probability, game theory, and Markov chains are given. Comprised of 10 chapters, this book begins with an introduction to set theory, followed by a discussion on Cartesian coordinate systems and graphs. Subsequent chapters focus on linear programming from a geometric and algebraic point of view; matrices, the solution of linear systems, and applications; the simplex method for solving linear programming problems; and probability and probability models for finite sample spaces as well as permutations, combinations, and counting methods. Basic concepts in statistics are also considered, along with the mathematics of finance. The final chapter is devoted to computers and programming languages such as BASIC. 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 Mathematics of Finance

9.1. Exponents and Logarithms—A Review

9.2. Mathematics of Finance

10 Computers

10.1. What is a Computer?

10.2. Communicating with the Computer

10.3. BASIC, A Programming Language

10.4. BASIC Continued (Print and Data Instructions)

10.5. BASIC Continued (Loops and Decisions)

10.6. Flow Charts

10.7. Other Programming Languages

Appendix/Tables

Answers to Odd-Numbered Exercises

Index