:
MATH 325
COURSE SYLLABUS
(20011-2012, Spring Semester)
MATH 325 Elementary Number Theory
(3-0)3
Instructor: Cansu Betin
Catalog Data: Divisibility, congruences, Euler, Chinese Remainder and Wilson's Theorems. Arithmetic
functions. Primitive roots. Quadratic residues and quadratic reciprocity. Diophantine equations.
Textbook: David Burton, Elementary Number Theory, McGraw-Hill, Fifth Edition, 2002
Prerequisite: Math 111
Grading Policy:
Exam I
Exam II
Homeworks & Quizzes
Final
30 points
30 points
10 points
35 points
Exam Dates
Exam I will be held on TBA
Exam II will be held on TBA
Final Exam: To be announced later
Make-up: Make-up exams will be given only if the proper medical documentation for the absence is
received.
REMARK: All the students should PROVIDE student ID cards to proctors to serve as identification. Any
student without an ID card CAN NOT take the exam.
Attendance Policy:
Attendance is an essential requirement of this course. Any student should attend more than %80 of the
lecture hours. If any do attend less than %80 of the lecture hours will get an “NA” for letter grade.
WEEKLY SCHEDULE AND PRE-STUDY PAGES
Week
Topics
Pre-study Pages
1
Preliminaries, Division Algorithm
pp. 1-18
2
Greatest Common Divisor
pp. 18-26
3
Euclidean Algorithm, Linear Diophantine
Equations
pp. 26-40
4
The Fundamental Theorem of Arithmetic,
pp. 40-62
Prime Numbers and Their Distribution
5
Basic Properties of Congruences, Special
pp. 62-72
Divisibility Tests
6
7
8
9
10
11
12
13
14
Chinese Remainder Theorem, Solving
Linear Congruences
Fermat’s Factorization Method, Fermat’s
Little Theorem
Wilson’s Theorem, Some Number Theoretic
Functions
Number Theoretic Functions and Möbius
Inversion Formula
Euler’s Phi-Function, Euler’s Theorem,
Some Properties of the Phi-Function
Primitive Roots for Primes
pp. 75-85
pp. 84-98
pp. 98-111
pp. 111-127
pp. 129-156
pp. 157-168
Composite Numbers Having Primitive
pp. 168-178
Roots, The Theory of Indices
Euler’s Criterion, The Legendre Symbol and
pp. 179-195
Its Properties
Quadratic Reciprocity, Quadratic
pp. 195-207
Congruences