MATH511 FINITE GROUPS
| Course Code: | 2360511 |
| 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. GÜLİN ERCAN |
| Offered Semester: | Fall Semesters. |
Course Objectives
This course aims
· to teach the concepts listed in the Catalog Description, such as
Abelian groups; torsion, divisible, torsion-free groups, pure subgroups, finitely generated Abelian groups. Solvable and nilpotent groups, Hall-subgroups. Permutation groups. Representations. Fixed-point free automorphisms. Locally nilpotent groups, locally solvable groups. Finiteness properties. Infinite solvable groups.
· to improve the proficiency in giving examples of the abstract concepts.
Course Content
Abelian groups; torsion, divisible, torsion-free groups, pure subgroups, finitely generated abelian groups. Solvable and nilpotent groups, Hall ?-subgroups. Permutation groups. Representations. Fixed-point free automorphisms. Locally nilpotent groups, locally solvable groups. Finiteness properties. Infinite solvable 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