MATH
319 01 Theory of Numbers (53254)
INSTRUCTOR: G. Towsley, 324C South Hall, x5388, towsleyg@uno.cc.geneseo.edu
TIME
AND PLACE: 11:30-12:20
MWF Fraser 213
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%
Project
.30%
In-class
Test
35%
The
in-class test will be given on or near March 9. The homework assignments that are called Problem Sets 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 project will consist of group work on a topic in Number Theory that
will be due near the end of the semester.
There will be a written submission of work for the project and an oral
presentation at the end of the semester. More details on the projects will be
given on the first day of class. 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.
Fermats
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.