MATH771 HOMOLOGICAL ALGEBRA
| Course Code: | 2360771 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 6.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Assoc.Prof.Dr. SEMRA PAMUK |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
1-To introduce standart concepts of homological algebra such as Ext and Tor and apply these in the setting of specific areas chosen depending the consent of the instructor.
2-To prepare students to a current research area, introduce them open questions.
3-To enable students with the computational skills such as computation of homology groups, cohomology groups which are needed in algebraic topology, algebraic geometry, etc...
Course Content
Categories, functors, derived functors, extensions, resolutions, homology and cohomology of complexes. Some applications depending on the consent of the instructor such as modular representation theory or cohomology of groups or Lie algebras, algenraic topology.
Course Learning Outcomes
Obtain knowledge of the facts and techniques from homological algebra e.g. diagram chasing etc.
Apply homological algebra methods to problems in algebra and topology.
Compute homology and cohomology groups of spaces and groups.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution