| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Theory of Linear Operators I | MAT513 | 3 + 0 | 3.0 | 8.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Graduate |
| Course Type | |
| Mode of delivery | Lecturing |
| Course Coordinator |
Prof. Dr. Emrah Evren KARA |
| Instructors |
Pınar ZENGİN ALP |
| Assistants | |
| Goals | Teaching about linear operators and their properties to master and Ph.D students |
| Course Content | Vector spaces, Normed spaces, Inner product spaces, Linear operators, Linear functionals, Bounded(continuous) linear functionals, Adjoint operators, Compact Operators |
| Learning Outcomes |
- Student’s ability of commenting and thinking truely will improve and the students will get basic information about mathematics. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Vector spaces | Research Course Hours Other Activities |
| 2. Week | Normed Spaces | Other Activities Preparation, After Class Study Research Course Hours |
| 3. Week | Banach Spaces | Preparation, After Class Study Research Course Hours Other Activities |
| 4. Week | Inner Product Spaces | Course Hours Preparation, After Class Study Research Other Activities |
| 5. Week | Linear Operators | Course Hours Other Activities Research |
| 6. Week | Bounded Linear Operators | Course Hours Research Other Activities |
| 7. Week | Bounded Linear Operators | Course Hours Research Other Activities |
| 8. Week | Midterm | Other Activities |
| 9. Week | Adjoint Operators | Other Activities Preparation, After Class Study Course Hours Research |
| 10. Week | Adjoint Operators | Research Other Activities Preparation, After Class Study Course Hours |
| 11. Week | Adjoint Operators | Course Hours Research Preparation, After Class Study Other Activities |
| 12. Week | Compact Operators | Preparation, After Class Study Research Other Activities Course Hours |
| 13. Week | Compact Operators | Research Other Activities Course Hours Preparation, After Class Study |
| 14. Week | Compact Operators | Research Other Activities Preparation, After Class Study Course Hours |
| Istratescu, Introduction to Linear Operator Theory, 1981, CRC Press |
| Program Requirements | Contribution Level | DK1 | Measurement Method |
|---|---|---|---|
| PY1 | 5 | 5 | 40,60 |
| PY2 | 5 | 5 | 40,60 |
| PY3 | 2 | 2 | 40,60 |
| PY4 | 1 | 1 | 40,60 |
| PY5 | 4 | 4 | 40,60 |
| PY6 | 3 | 3 | 40,60 |
| PY7 | 5 | 5 | 40,60 |
| PY8 | 3 | 3 | 40,60 |
| PY9 | 4 | 4 | 40,60 |
| PY10 | 2 | 2 | 40,60 |
| 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) |
|---|---|---|---|
| Course Hours | 14 | 3 | 42 |
| Preparation, After Class Study | 14 | 1 | 14 |
| Research | 14 | 1 | 14 |
| Other Activities | 14 | 1 | 14 |
| Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 7 | 3.5 | 24.5 |
| Homework 2 | 7 | 3 | 21 |
| Final | 1 | 2.5 | 2.5 |
| Practice | 14 | 1 | 14 |
| Practice End-Of-Term | 14 | 2 | 28 |
| Classroom Activities | 14 | 2 | 28 |
| Total Workload | 204 | ||
| ECTS Credit of the Course | 8.0 | ||
