COURSE SYLLABUS

Course Number: MATH6840
Course Title: FOUNDATIONS OF NUMBER THEORY FOR SECONDARY SCHOOL TEACHERS
Credit Hours: 3
Prerequisites: MATH 2630
Corequisite: 

Objectives: 
This course is an introduction to some basic topics in number theory intended for teachers of mathematics at the high school level.

Course Content (typical):
Basic properties of the integers: definition, mathematical induction, divisibility, representation in various bases, prime numbers. (8 days)

Greatest common divisors and prime factorization: The Euclidean Algorithm, The Fundamental Theorem of Arithmetic,
techniques for factoring integers, linear diophantine equations. (10 days)

Modular arithmetic, linear congruences, and the Chinese Remainder Theorem. (10 days)

Divisibility tests based on congruences (such as n is divisible by 3 if the sum of the digits of n is divisible by 3). (2 days)

Wilson's Theorem, Fermat's Little theorem, and Euler's Theorem.  Psuedoprimes. (10 days)


Possible textbook:
Elementary Number Theory and its Applications, 2nd ed., Kenneth H. Rosen, Addison Wesley, 1988.

Grading and Evaluation Procedures:
Quizzes, tests, final exam, graded homework and in-class presentations at the instructors discretion.

Statement related to policies on unannounced quizzes and class attendance and participation:
Individual instructors have different policies concerning pop quizzes, class participation, homework grades, and attendance, which are announced at the beginning of the semester. 

JUSTIFICATION FOR COURSE AND JUSTIFICATION FOR GRADUATE CREDIT

	This course has been designed for secondary school teachers who are pursuing Master's degrees in education. Such students usually do not have the same preparatory background as mathematics majors and the course has been designed so that these students can receive graduate level instruction aimed for their specific background and needs.  In addition to these graduate students, education majors and fifth year students who plan to teach mathematics in secondary schools register for the course.  Credit for students who are not secondary education students may only be received by special permission of the mathematics department.  As we have done in the past we intend to flag this course as one which is not available to majors or graduate students in the area of science and mathematics.