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: | |
| 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.