MATH512 INFINITE GROUPS
| Course Code: | 2360512 |
| 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: | Prof.Dr. MAHMUT KUZUCUOĞLU |
| Offered Semester: | Fall Semesters. |
Course Objectives
Students learn the free groups of finite rank and infinite rank, lower and upper central series, finitely generated groups, finitely presented groups, existentially closed groups. We expect they to use the proof techniques learn in the course, and they should be able to them in other subjects and courses.
Course Content
Locally finite groups. Maximal and minimal condition on subgroups, Cernikov groups and automorphisms of Cernikov groups, direct limit inverse limit of groups, linear groups, locally finite simple groups, Hall universal group, centralizers of elements in simple locally finite groups.
Course Learning Outcomes
The subjects described in the course syllabus mastered, the proof techniques are understood and students are able to use them in different proof and courses.
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