MATH 319 01 Theory of Numbers (53254)

INSTRUCTOR: G. Towsley, 324C South Hall, x5388, towsleyg@uno.cc.geneseo.edu

TIME AND PLACE: 9:30-10:20 MWF Sturges 113

TEXTS: An Introduction to the Theory of Numbers, Fifth Edition , Niven, Zuckerman, and Montgomery . John Wiley and Sons( New York, 1991)

EVALUATION PROCEDURES:

The grade for this course will be based on an in-class test, a project, and homework assignments. The portions of the evaluation are weighted as follows:

Homework………………………..35%

Mid-term Exam.………………….30%

Final Exam.………………………35%

The mid-term exam will be given on or near Friday, March 14. The final exam is scheduled for Friday, May 16 at 8 AM. The homework assignments may be completed by groups of 3-4 students with a single submission from each group or individuals may complete them. Part of the homework will consist of laboratory exercises in Number Theory using Maple. The final grade will be determined on the following schedule:

A 93-100% A^- 90-92% B⁺ 87-89% B 83-86% B^- 80-82%

C⁺ 77-79% C 73-76% C^- 70-72% D 60-69% E 0-59%

CONTENT OUTLINE:

The course covers some or all of the first five chapters of the text. In detail:

1. Divisibility, Primes, and the Euclidean Algorithm

2. Congruence, Solutions of Congruences, The Chinese Remainder Theorem

3. Fermat’s Little Theorem and Factorization

4. Quadratic Reciprocity

5. Arithmetic Functions

6. Diophantine Equations

7. Factoring, Primality Testing, and Public-key Cryptography

MAKE-UP POLICY:

A make-up exam will be given only if I am supplied with a valid excuse prior to the exam.