FINITE MATH

MA 230

Catalogue Description

Topics include set theory, symbolic logic, combinations, elementary probability, linear equations and matrices, linear programming and decisions and games. 3 credits.

Prerequisite: Ma 165 or equivalent

Goals

A. To increase the student's knowledge of non-calculus portions of mathematics.

B. To improve the level of quantitative sophistication.

C. To make the student as comfortable as possible in an environment which increasingly makes use of quantitative analysis and the computer.

D. To provide the student with basic tools of decision making analysis.

Procedures

A. Lecture/Discussion

B. Computer Tutorials

C. Classroom Computer Demonstration

Course Content

A. Set Theory

1. Basic Concepts of Sets

2. Set Operations

3. Venn Diagrams

4. Truth Sets

5. Properties of Sets

6. Cartesian Product

B. Symbolic Logic

1. Validity of Arguments by Euler Circles

2. Truth Tables

3. Related Statements

4. Properties of Connectives

5. Arguments

6. Quantification

7. Applications

C. Combinations

1. Counting Principle

2. Permutations

3. Combinations

4. Pascal's Triangle

5. Binomial Theorem

6. Multinomial Theorem

D. Elementary Probability

1. Events & Sample Spaces

2. Compound Events

3. Equally Likely Events

4. Experiments with Outcomes Not Equally Likely

5. Binomial Experiments

6. Conditional Probability

7. Stochastic Processes

8. Bayes' Theorem

E. Linear Equations & Matrices

1. Coordinate Systems & Linear Equations

2. Systems of two Linear Equations

3. Linear Systems in Several Unknowns

4. Matrices and Linear Equations

5. Some Matrix Computations

6. Matrix Multiplication

7. Inverses of Square Matrices

F. Decisions and Games

1. Expected Value and Decisions True Analysis

2. Game Theory and Pure Strategies

3. Mixed Strategies for 2 x 2 Games

4. Higher Order Games

Evaluation methods at the discretion of the Instructor

Bibliography

Required Text: Lial, Margaret L. and Miller, Charles D., Finite Mathematics and Calculus with Applications, 3rd Ed., Scott, Foresman & Co., Glenview, Ill., 1989.

Budnick, Frank, Finite Mathematics with Applications, McGraw-Hill, Inc., 1985.

Costello, Gowdy and Rash, Finite Mathematics with Applications, Harcourt Brace Jovanovich, Inc., New York, N.Y., 1987.

Hardy, F. Lane, Finite Mathematics, Harper & Row Publ., New York, N.Y., 1987.

Maki, Daniel and Thompson, Maynard, Finite Mathematics, McGraw Hill Book Co., New York, N.Y., 1986.

Smith, Karl, Finite Mathematics, Brooks Cole Publ., Monterey, Ca., 1985.

Software

Avery & Barker, Computer-Aided Finite Mathematics.

Kemeny, Kurt, True-Basic Discrete Mathematics, Hanover, N.H., 1986.

Kemeny, Kurt, True-Basic Pre-Calculus, Hanover, N.H., 1987.

Student Edition of Math Cad, Addison-Wesley, Reading, Ma., 1988.