State University College at Buffalo

Department of Mathematics

Request for Course

I. Number and title of course

MATHEMATICS 593 - Mathematics for Elementary Teachers - Finite Mathematics
II.Reasons for addition to the present curricula
A. To provide an elective for graduate elementary education majors having the undergraduate equivalent of Math. 121-122.

B. To improve the quality of mathematics instruction in the elementary schools through increased teacher mathematical maturity.

C. To carry out and evaluate the recommendations of national advisory groups concerned with elementary mathematics teacher preparation.

III. Major objectives of the course
A. To acquaint the elementary teacher with mathematics concepts currently included, or proposed for inclusion, in the elementary school curriculum.

B. To illustrate how mathematics concepts are abstracted from concrete situations; how the concepts are used in building a mathematical system; and how the resulting system is used to benefit man.

IV. Topical Outline
A. Partitions
1. Partitions

2. The number of elements of a set

3. Permutations

4. Ordered partitions

5. Properties of the numbers

6. Binomial theorem

B. Probability Theory
1. Probability measure
2. Properties

3. Equiprobable measure

4. Conditional probability

5. Finite Stochastic processes

6. Bay's' probability

7. Independent trials with two outcomes

C. Vectors and Matrices
1. Column and Row vectors
2. Product of vectors

3. Matrices and their combination with vectors

4. Addition and multiplication of vectors

5. Solution of linear equations

6. The inverse of a square matrix

D. Linear programming
1. Convex sets
2. Maxima and Minima of linear functions

3. Linear programming problems


V. Bibliography, texts, and readings
 

Davis, P. J. The Mathematics of Matrices, brew York: Blaisdell, 1965.
Kemeny, J. G.., J. L.. Snell, G. L. Thompson. Introduction to Finite Mathematics, Second Edition. Englewood Cliffs 3 N.J. Prentice Hall, 1966.
Lipschutz, S. Finite Mathematics, New York. McGraw-Hill Book Co., 1966.
Marcus M. A Survey of Finite Mathematics. New York. Houghton Mifflin Co.,1969.
Schwartz, J. T. Introduction to Matrices and Vectors. New York. McGraw-Hill, 1961.
VI. Presentation and Evaluation
Lectures, class discussion, assigned problems, written examinations.
VII. Prerequisites
Mathematics 121 and 122, or equivalent.
VIII. Credit
Three semester hours
IX. Statement of Approval
This course proposal was examined in accord with recommended procedures and was approved by the Mathematics Department Graduate Mathematics Education Faculty.

_______________________________    Chairman

X. Catalog Description
MATH. 593 - MATHEMATICS FOR ELEMENTARY TEACHERS: FINITE MATHEMATICS: Partitions; permutations, probability measure; conditional probability' vectors; matrices, operations, properties; linear programming; applications.

Prerequisites: Math. 121 and 122, or equivalent.

Credit: Three semester hours.

XI. Statement of qualifications of faculty who will teach the course.
Faculty designated as Graduate Mathematics Education Faculty. (Although most mathematics faculty would have the subject matter background to teach this course, this is not in itself a sufficient qualification. Experience in, interest in or attitude towards the elementary school program and objectives would be prerequisite to selection for teaching this course.)