| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Rings and Modules | MAT515 | 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. Arzu ÖZKOÇ ÖZTÜRK |
| Instructors | |
| Assistants | |
| Goals | To give the basics about rings and modules. |
| Course Content | Structures of rings and modules, tensor product and its applications |
| Learning Outcomes |
- The student's ability to think and interpret correctly will improve and the student will gain basic knowledge about mathematics. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Introduction | |
| 2. Week | Module definition and examples | |
| 3. Week | Module homomorphisms and integral sequences | |
| 4. Week | Module homomorphisms and integral sequences | |
| 5. Week | Free modules and vector spaces | |
| 6. Week | Projective and injective modules | |
| 7. Week | Projective and injective modules | |
| 8. Week | Midterm | |
| 9. Week | Tensor products ve applications | |
| 10. Week | Tensor products and applications | |
| 11. Week | Structure of rings and modules | |
| 12. Week | Structure of rings and modules | |
| 13. Week | Modules on principal ideal domains | |
| 14. Week | Algebras |
| 1.Algebra Thomas w.Hungerford |
| 2.Rings and Modules:Paulo Ribenboim |
| 1.Algebra Thomas w.Hungerford |
| 2.Rings and Modules:Paulo Ribenboim |
| Program Requirements | Contribution Level | DK1 | Measurement Method |
|---|---|---|---|
| PY1 | 2 | 0 | 40 |
| PY2 | 5 | 0 | 40 |
| PY3 | 3 | 0 | 40 |
| PY4 | 1 | 0 | 40 |
| PY5 | 0 | 0 | 40 |
| PY6 | 2 | 0 | 40 |
| PY7 | 5 | 0 | 40 |
| PY8 | 4 | 0 | 40 |
| PY9 | 2 | 0 | 60 |
| PY10 | 0 | 0 | 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 | 14 | 2 | 28 |
| Homework 2 | 14 | 1 | 14 |
| Final | 1 | 2 | 2 |
| Practice | 14 | 2 | 28 |
| Practice End-Of-Term | 14 | 1 | 14 |
| Classroom Activities | 14 | 2 | 28 |
| Total Workload | 200 | ||
| ECTS Credit of the Course | 8.0 | ||
