STATE UNIVERSITY COLLEGE AT BUFFALO

Department of Mathematics

Course Proposal

I. Number and Title of Course

Mathematics 119-Finite Mathematics

II. Reasons for Addition to the Present Curricula

To serve students, in areas other than mathematics, who need or desire some elementary concepts of sets, probability, vectors, matrices, and linear functions. This course should be suitable background for any elementary statistics course. The students best served will probably be those studying psychology, economics, sociology, elementary education, and the non-mathematical sciences. III. The major objectives of the course are to introduce non-mathematics majors to concepts of modern mathematics in a setting different from other mathematics electives. IV. Topical Outline A. Sets and Subsets 1. Set operations
2. Venn diagrams and partitions
3. Number of elements in a set
4. Sets of outcomes and tree diagrams B. Counting Problems


B. Counting Problems

1. General principle of counting
2. Permutations
3. Combinations
4. Binomial theorem C. Probability 1. Properties of probability measure
2. Equiprobable measure
3. Conditional probability
4. Finite stochastic processes
5. Bayes' probability
6. Bernoulli trials
7. Expected value of a random variable   D. Linear Models in Two Variables 1. Equations and graphs of lines
2. Systems of lines
3. Systems of linear inequalities in two variables
4. Linear programming problems in two variables   E. Matrices 1. Linear equations and matrix notation
2. Solution of systems of linear equations
3. Matrix inverses F. Applications 1. Markov chains
2. Digraphs and networks
3. Two person zero-sum game
4. Computational methods for linear programming V. Bibliography

Anton, H., and Kolman, B., Applied Finite Mathematics 3rd Ed., New York, NY, Academic Press, 1982.

Barnett, R..and Ziegler, M., Finite Mathematics for Management Life and Social Sciences 3rd Ed., Santa Clara, CA, Dellen Publishing Co., 1984.

Gallin D., Finite Mathematics, Glenview, IL, Scott Foresman, 1984.

Gilbert, G.,and Koehler, D., Applied Finite Mathematics, New York, NY, McGraw Hill, 1984.

Goldstein L.,and Schneider, D., Finite Mathematics and Its Applications 2nd Ed., Englewood Cliff, NJ, Prentice Hall, 1974.

Goodman, A.,and Ratti, J., Finite Mathematics with Applications 4th Ed., New York, NY, Macmillan, 1986.

Grossman, S., Finite Mathematics, Belmont, CA, Wadsworth, 1983.

Kemeny, J., Snell, L., Thompson G.,Introduction to Finite Mathematics 3rd Ed., Englewood Cliffs, NJ, Prentice Hall, 1974.

Liall, M.,and Miller, C., Finite Mathematics 3rd Ed., Glenview, IL, Scott Foresman, 1985.

Maki, P.,and Thompson, M.,Finite Mathematics 3rd. Ed., New York, NY, McGraw Hill, 1983.
 

VI. Presentation and Evaluation

Lectures, class discussion,assigned problems, written examinations,
VII. Prerequisite
3 years of high school Regents mathematics or equivalent.
VIII. Credit
Three semester hours
IX. Statement of Approval
This course proposal was examined in accord with established- procedures and was approved by the Department of Mathematics on May 8, 1986.
Department Chairperson
X. Catalog Description
Mat 119- FINITE MATHEMATICS. Sets, partitions, probability, vectors, matrices, linear programming, linear functions .
X1. Statement of qualifications of faculty who will teach course
Any member of the mathematics faculty may teach this course .
XII. Support Services Required:
Adequate classroom facilities already available on campus.