Syllabus Application
Elementary Number Theory
MATH 317
Faculty:
Faculty of Engineering and Natural Sciences
Semester:
Fall 2025-2026
Course:
Elementary Number Theory - MATH 317
Classroom:
FENS-L035,FENS-L062
Level of course:
Undergraduate
Course Credits:
SU Credit:3.000, ECTS:6, Basic:6
Prerequisites:
MATH 102 and MATH 201
Corequisites:
Course Type:
Lecture
Instructor(s) Information
Kağan Kurşungöz
- Email: kursungoz@sabanciuniv.edu
Course Information
Catalog Course Description
Divisibility, prime numbers, congruences, quadratic residues, arithmetic functions, the Riemann Zeta function.
Course 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
Refer to the course content
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Course Materials
Resources:
Andrews, George E.. Number Theory. United Kingdom, Dover Publications, 1994.