Syllabus Application
MATH 317
Elementary Number Theory
Faculty
Faculty of Engineering and Natural Sciences
Semester
Fall 2026-2027
Course
MATH 317 -
Elementary Number Theory
Time/Place
Time
Week Day
Place
Date
10:40-11:30
Tue
FENS-L062
Sep 28-Dec 31, 2026
09:40-11:30
Wed
FENS-G029
Sep 28-Dec 31, 2026
Level of course
Undergraduate
Course Credits
SU Credit:3, ECTS:6, Basic:6
Prerequisites
MATH 102 and ( MATH 201 or MATH 212)
Corequisites
Course Type
Lecture
Instructor(s) Information
Nurdagül Anbar Meidl
- Email: nanbar@sabanciuniv.edu
Course Information
Catalog Course Description
Divisibility, prime numbers, congruences, quadratic residues, arithmetic functions, the Riemann Zeta function.
Learning Outcomes:
| 1. | Prove simple facts about divisibility, greatest common divisors, least common multiples, |
|---|---|
| 2. | Understand the Euclidean Algorithm |
| 3. | Understand the Fundamental Theorem of Arithmetic |
| 4. | Solve linear Diophantine equations and linear congruences |
| 5. | Understand and apply Fermat's Little Theorem |
| 6. | Determine Euler Phi Function and prove simple facts about Euler Phi Function |
| 7. | Prove simple facts about primitive roots |
| 8. | Apply the Law of Quadratic Reciprocity |
| 9. | Show simple facts about quadratic residues |
| 10. | Decide if an integer can be written as a Sum of Squares |
| 11. | Apply standard proof methods like mathematical induction, direct and indirect proofs |
| 12. | Present simple proofs in a precise and formally correct way. |
Course Objective
The course covers the following topics, and it is subject to change.
1) Divisibility of integer numbers and the Euclidean algorithm
2) The Fundamental Theorem of Arithmetic
3) Multiplicative arithmetic functions and interesting numbers: perfect numbers, Fermat numbers and Mersenne numbers
4) Congruences and polynomial congruences
5) Chinese Remainder Theorem
6) Primitive roots
7) Quadratic residues, Jacobi symbols and Quadratic reciprocity
8) Pseudoprimes
9) Pythagorean triangles
-
1) Divisibility of integer numbers and the Euclidean algorithm
2) The Fundamental Theorem of Arithmetic
3) Multiplicative arithmetic functions and interesting numbers: perfect numbers, Fermat numbers and Mersenne numbers
4) Congruences and polynomial congruences
5) Chinese Remainder Theorem
6) Primitive roots
7) Quadratic residues, Jacobi symbols and Quadratic reciprocity
8) Pseudoprimes
9) Pythagorean triangles
Course Materials
Resources:
A Friendly Introduction to Number Theory, by Joseph H. Silverman, Fourth Edition-ISBN: 978-0-321-81619-1 2012 Pearson Education, Inc.