MTK746 - HOMOLOGICAL ALGEBRA II
| Course Name | Code | Semester | Theory (hours/week) |
Application (hours/week) |
Credit | ECTS |
|---|---|---|---|---|---|---|
| HOMOLOGICAL ALGEBRA II | MTK746 | 2nd Semester | 3 | 0 | 3 | 12 |
| Prequisites | MTK 745 Homolojik Algebra I | |||||
| Course language | Turkish | |||||
| Course type | Elective | |||||
| Mode of Delivery | Face-to-Face | |||||
| Learning and teaching strategies | Lecture Discussion Question and Answer | |||||
| Instructor (s) | Ass. Prof. Ali ErdoÄŸan | |||||
| Course objective | The aim of this course is to introduce the theory of functors to the students who are willing to study module theory. | |||||
| Learning outcomes |
| |||||
| Course Content | I. Sequences of Projective and injective modules II. Exact sequences III. Global and homological dimensions IV. Dimensions of certain rings V. Spectral sequences | |||||
| References | H. Cartan; S. Eilenberg; Homological Algebra, Princeton University Press, 1956. | |||||
Course outline weekly
| Weeks | Topics |
|---|---|
| Week 1 | Sequences |
| Week 2 | Exact sequences |
| Week 3 | Projective resolution |
| Week 4 | Injective resolutions |
| Week 5 | Flat resolutions |
| Week 6 | Projective dimensions |
| Week 7 | Injective dimensions |
| Week 8 | Flat dimensions |
| Week 9 | Global and homological dimensions |
| Week 10 | Global and homological dimensions of some rings Tor functors |
| Week 11 | Künneth relations |
| Week 12 | Change of rings |
| Week 13 | Applications to local rings |
| Week 14 | Applications to local rings |
| Week 15 | Preparation for the final examination |
| Week 16 | Final exam |
Assesment methods
| Course activities | Number | Percentage |
|---|---|---|
| Attendance | 0 | 0 |
| Laboratory | 0 | 0 |
| Application | 0 | 0 |
| Field activities | 0 | 0 |
| Specific practical training | 0 | 0 |
| Assignments | 2 | 20 |
| Presentation | 0 | 0 |
| Project | 0 | 0 |
| Seminar | 1 | 20 |
| Midterms | 0 | 0 |
| Final exam | 1 | 60 |
| Total | 100 | |
| Percentage of semester activities contributing grade succes | 0 | 40 |
| Percentage of final exam contributing grade succes | 0 | 60 |
| Total | 100 | |
WORKLOAD AND ECTS CALCULATION
| Activities | Number | Duration (hour) | Total Work Load |
|---|---|---|---|
| Course Duration (x14) | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Specific practical training | 0 | 0 | 0 |
| Field activities | 0 | 0 | 0 |
| Study Hours Out of Class (Preliminary work, reinforcement, ect) | 14 | 17 | 238 |
| Presentation / Seminar Preparation | 1 | 25 | 25 |
| Project | 0 | 0 | 0 |
| Homework assignment | 2 | 20 | 40 |
| Midterms (Study duration) | 0 | 0 | 0 |
| Final Exam (Study duration) | 1 | 15 | 15 |
| Total Workload | 32 | 80 | 360 |
Matrix Of The Course Learning Outcomes Versus Program Outcomes
| D.9. Key Learning Outcomes | Contrubition level* | ||||
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |
| 1. Deepens the concepts of mathematics in the level of expertise. | X | ||||
| 2. Grasps the inter-disciplinary interaction related to the area; reaches original results by using the specialist knowledge in analyzing and evaluating new ideas. | X | ||||
| 3. Gains the ability to think independently and develops theoretical concepts. | X | ||||
| 4. Develops original mathematical models by using interrelations between mathematics and other disciplines and applies them to other disciplines. | X | ||||
| 5. Uses high level research methods in studies in the area. | X | ||||
| 6. Develops a new idea, method and/or application independently, finds a solution, and contributes to the progress in the area by carrying out original studies. | X | ||||
| 7. Fulfills the leader role in the environments where solutions are thought for the area and/or inter-disciplinary problems. | X | ||||
| 8. Develops continually the skills of creativity, decision making and problem solving. | X | ||||
| 9. Defends original opinions by communicating with experts in the area. | X | ||||
| 10. Uses a foreign language- at least C1 Level-, communicates with foreign colleagues and follows the international literature. | X | ||||
| 11. Follows the latest developments in the information and communication technologies and uses them in the area. | X | ||||
| 12. Does research in national and international research groups. | X | ||||
| 13. Makes strategic decision in the solution of problems in the area. | X | ||||
| 14. Protects the rights of other researchers in regards to ethics, privacy, ownership and copyright. | X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest