STATE UNIVERSITY COLLEGE AT BUFFALO

Department of Mathematics

Request for Course

I. Number and Title of Course

Mathematics 552 - Mathematics for Elementary Teachers: Number Theory

II. Reasons for addition to the present curricula

A. To provide an elective for graduate elementary education majors who wish to broaden their experience in the area of number theory.

B. To improve the quality of instruction in mathematics in the elementary school by providing an opportunity for the student to experience involvement in the processes of mathematics.

III. Major Objectives

A. To review the fundamental algebraic properties of the integers.

B. To observe patterns, make conjectures, test hypotheses and develop arguments on properties of the system of integers.

C. To introduce the student to the rich heritage of number theory by tracing some of the major developments.

D. To provide the student with suggestions for classroom activities based on the topics discussed in the course.

IV. Topical Outline

A. The Integers -a review

B. Divisibility

1. Division

2. Greatest common divisor

3. Primes and relatively prime integers

4. Fundamental Theorem of Arithmetic

C. Congruence

1. Clock arithmetic, equivalence classes and representatives

2. Divisibility of large numbers

3. Linear congruencies

4. Simultaneous linear congruencies

5. Euler Phi function

6. Fermat's Theorem and Euler's Theorem

D. Diophantine Equations

1. Linear problems

2. Pythagorean triples

E. Fibonacci numbers

F. Magic numbers

G. Polygonal numbers

V. Bibliography, texts and readings

A. Texts

Courant, R. and Robbins, H. What is Mathematics, New York: Oxford University Press, 1953

Dickson, Leonard Eugene, Introduction to the Theory of Numbers, New York: Dover Publications, Inc., 1957

Dudley, Underwood, Elementary Number Theory, San Francisco: T. E'. Freeman and Company, 1969

Landaw, Edmund, Elementary Number Theory, New York: Chelsean Publishing Co., 1966

Maxfield, Julin E. and Maxfield, Margaret T., Discovering .,Number Theory Philadelphia: r!.D. Saunders Company, 1972

McCoy, Real., The Theory of Numbers . New York: The Macmillan Company, 1965

Ogilvy, C. Stanley and Anderson, John t., Excursions in Number Theory, New York: Oxford University Press, l966

Rademacher, H. and Toeplitz, O. The Enjoyment of Ma thematics , Princeton, N.J. : Princeton university Press 1957

Stark Harold M., An Introduction to 'lumber Theory, Chicaco: Markham Publishing Co. ?

Vinogradov, I . M., Elements of lumber Theory, New York : Dover Publications

'Wright, Harry N., First Course in Theory of Numbers, New York: John

Wiley Sons, Inc. 1939

B. Journal Articles

Adkins, Julia, An Application of Modular Number Systems The Arithmetic Teacher XV (December 1968), 113-4

Hansen, Rodney T. "Modular Palindromes" Mathematics Magazine XLIV (January 1970), 41-42 .

Hervey Margaret A. and LitwiIler, Bonnie H. 'Polygonal Numbers: A Study of Patterns The Arithmetic Teacher XVII (January 1970 ) 33-38

Klamkin, HAS. and Newman' D.J. "Some Combinatorial Problems of Arithmetic Mathematics Magazine. XLII ( March 1969), 53-57

Pervin, J. ''Binary Digital Arithmetic's' Mathematics Magazine XLIII ( January 1970), 41-42

VI. Presentation and Evaluation Lectures, class discussions, demonstrations, capers, written and/or oral examinations .

VII. Prerequisites Math 121 122 or the 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 on March 27, 1973.

X. Catalog Description

Math 552 MATHEMATICS FOR ELEMENTARY TEACHERS: NUMBER THEORY

A study of the structure of the integers, divisibility, primes, congruence classes, linear congruenceis, Diophantine equations, Fibonacci numbers and selected topics. Some topics will be developed and adapted by the students for the elementary classroom.

Classification: Elective

Prerequisites: Math 121-122 or equivalent

Credit: Three semester hours

XI. Statement of qualifications of faculty who will teach the course
Experienced Faculty designated as Graduate Mathematics Education Faculty. Preparation and experience with number theory and the teaching of this is recommended although not an absolute necessity. 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 positive attitude toward the elementary school program and objectives would be prerequisite to selection for teaching this course.