Rapor Tarihi: 13.04.2026 03:15
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Number Theory | MAT406 | Turkish | Compulsory | 8. Semester | 3 + 0 | 3.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing |
| Course Coordinator | Prof. Dr. Arzu ÖZKOÇ ÖZTÜRK |
| Instructor(s) | |
| Goals | To teach content of the lesson. |
| Course Content | The course covers topics such as divisibility, division and Euclidean algorithms, the Fundamental Theorem of Arithmetic, Euler's phi function, properties of the Euler phi function, linear Diophantine equations, congruences, linear congruences, the Chinese remainder theorem, the Fermat-Euler theorem, and primitive roots. |
| # | Öğrenme Kazanımı |
| 1 | It explains the fundamental properties of the set of integers and expresses divisibility rules mathematically. |
| 2 | It calculates the greatest common divisor (GCD) and least common multiple (LCM) using the division algorithm and the Euclidean algorithm. |
| 3 | It explains the fundamental theorem of arithmetic and analyzes the prime factorization of integers. |
| 4 | Euler defines the phi function, describes its properties, and calculates its value for various numbers. |
| 5 | It applies methods for solving linear Diophantine equations and characterizes the solution set. |
| 6 | t explains the concept of congruence; solves linear congruences; and uses the Chinese Remainder Theorem in problem solving. |
| 7 | t explains the Fermat–Euler Theorem and the concept of primitive roots, and applies these results to modular arithmetic problems. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Introduction to number theory | Preparation, After Class Study, Research, Other Activities, Interview |
| 2. Week | General information about integers | Preparation, After Class Study, Research, Other Activities, Interview |
| 3. Week | Divisibility | Preparation, After Class Study, Research, Other Activities, Interview |
| 4. Week | Division and Euclidean algorithms | |
| 5. Week | Fundamental Theorem of Arithmetic | Preparation, After Class Study, Research, Other Activities, Interview |
| 6. Week | Euler phi function | Preparation, After Class Study, Research, Other Activities, Interview |
| 7. Week | Euler phi function and Applications | Preparation, After Class Study, Research, Other Activities, Interview |
| 8. Week | Linear Diophantine equations | Preparation, After Class Study, Research, Other Activities, Interview |
| 9. Week | Lineer Diophantine equations | Preparation, After Class Study, Research, Other Activities, Interview |
| 10. Week | Congruences | Preparation, After Class Study, Research, Other Activities, Interview |
| 11. Week | Linear Congruences | Preparation, After Class Study, Research, Other Activities, Interview |
| 12. Week | Chinese remainder theorem | Preparation, After Class Study, Research, Other Activities, Interview |
| 13. Week | Fermat-Euler Theorem | Preparation, After Class Study, Research, Other Activities, Interview |
| 14. Week | Primitive roots | Preparation, After Class Study, Research, Other Activities, Interview |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Possesses theoretical and applied knowledge of the fundamental areas of mathematics (Analysis and Function Theory, Algebra and Number Theory, Geometry, Applied Mathematics, Topology and Foundations of Mathematics, and Mathematical Logic). | ✔ | |||||
| 2 | Explains the historical development of mathematical concepts, their relationship with other branches of science, and their application areas. | ✔ | |||||
| 3 | Defines mathematical problems, selects appropriate methods, and solves them using analytical/numerical techniques. | ✔ | |||||
| 4 | Constructs mathematical expressions with logical integrity and reaches conclusions using proof methods. | ✔ | |||||
| 5 | Formulates and interprets real-life problems by performing mathematical modeling. | ✔ | |||||
| 6 | Effectively uses information technologies and mathematical software in data analysis and computation processes. | ✔ | |||||
| 7 | Takes responsibility in individual or team work; plans and executes projects. | ✔ | |||||
| 8 | Follows current developments in their field; improves themselves with a lifelong learning awareness. | ✔ | |||||
| 9 | Expresses mathematical ideas verbally and in writing clearly and in accordance with academic rules. | ✔ | |||||
| 10 | Acts in accordance with professional and academic ethical values; acts with a sense of social responsibility. | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | DK7 |
|---|---|---|---|---|---|---|---|
| PY1 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY5 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| PY6 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| PY7 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY8 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| PY9 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY10 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 3 | 42 |
|
Ders Dışı |
Homework | 14 | 1 | 14 |
| Preparation, After Class Study | 14 | 2 | 28 | |
| Practice | 14 | 2 | 28 | |
| Other Activities | 14 | 1 | 14 | |
|
Sınavlar |
Midterm | 1 | 2 | 2 |
| Final | 1 | 2 | 2 | |
| Total Workload | 130 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
