MATH728 HOMOLOGICAL METHODS IN TOPOLOGY
| Course Code: | 2360728 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Assoc.Prof.Dr. SEMRA PAMUK |
| Offered Semester: | Fall Semesters. |
Course Objectives
This course is designed to provide the students with some of the necessary potential research background from the homological algebra for reading and understanding research articles in algebraic topology. In particular, it is designed to equip the students with the essential computational technique of spectral sequences and Steenrod algebra, to give applications to spaces with a group action, to introduce some topics of algebraic topology such as group cohomology and transformation groups, which are potential research areas for graduate students.
Course Content
For course details, see https://catalog2.metu.edu.tr.Course Learning Outcomes
Obtain knowledge of the facts and computational techniques of spectral sequences and Steenrod algebra.
Apply these computational methods to deal with problems in algebraic 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