| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Modular Functions | MAT521 | 3 + 0 | 3.0 | 8.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Graduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator |
Res. Assist. Zehra İŞBİLİR |
| Instructors |
Nejla ÖZMEN |
| Assistants | |
| Goals | Teaching high level of mathematics to graduate degree students. |
| Course Content | Double periodic functions Fundamental period pairs Elliptic functions Mobius transformations Modular Group Fundamental region Modular functions Dedekind Eta functions ,Modular forms midterm Dedekind additions and properties Eisenstein Function Modular forms ve Dirichlet series Modular forms ve Dirichlet series Modular forms ve Dirichlet series Modular forms ve Dirichlet series |
| Learning Outcomes |
- Students will learn theoretical concepts in mathematics - Students will learn how to read academical journals |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Double periodic functions | |
| 2. Week | Fundamental period pairs | |
| 3. Week | Elliptic functions | |
| 4. Week | Mobius transformations | |
| 5. Week | Modular Group Fundamental region | |
| 6. Week | Modular functions | |
| 7. Week | Dedekind Eta functions ,Modular forms, Dedekind sums and properties | |
| 8. Week | midterm | |
| 9. Week | Eisenstein Function | |
| 10. Week | Modular forms ve Dirichlet series | |
| 11. Week | Modular forms ve Dirichlet series | |
| 12. Week | Modular forms ve Dirichlet series | |
| 13. Week | Modular forms ve Dirichlet series | |
| 14. Week | Modular forms ve Dirichlet series |
| Tom M Apostol.,Modular Functions and Dirihlet Series in Number Theory |
| Roberta Rankın.,Modular form and Functions |
| Tom M Apostol.,Modular Functions and Dirihlet Series in Number Theory |
| Roberta Rankın.,Modular form and Functions |
| Program Requirements | Contribution Level | DK1 | DK2 | Measurement Method |
|---|---|---|---|---|
| PY1 | 2 | 1 | 1 | 60 |
| PY2 | 2 | 1 | 1 | 60 |
| PY3 | 2 | 1 | 1 | 60 |
| PY4 | 2 | 1 | 1 | 60 |
| PY5 | 2 | 1 | 1 | 60 |
| PY6 | 2 | 1 | 1 | 60 |
| PY7 | 2 | 1 | 1 | 60 |
| PY8 | 2 | 1 | 1 | 60 |
| PY9 | 2 | 1 | 1 | 60 |
| PY10 | 2 | 1 | 1 | 60 |
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| Course's Level of contribution | None | Very Low | Low | Fair | High | Very High |
| Method of assessment/evaluation | Written exam | Oral Exams | Assignment/Project | Laboratory work | Presentation/Seminar |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 15 | 2 | 30 |
| Homework 2 | 15 | 2 | 30 |
| Final | 1 | 2 | 2 |
| Practice | 15 | 3 | 45 |
| Practice End-Of-Term | 15 | 3 | 45 |
| Classroom Activities | 15 | 3 | 45 |
| Total Workload | 199 | ||
| ECTS Credit of the Course | 8.0 | ||
