| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Algebra | MTÖ307 | 5. Semester | 2 + 0 | 2.0 | 2.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | Distance Education |
| Course Coordinator |
Assist. Prof. Dr. Duygu ARABACI |
| Instructor(s) |
EMİNE NUR ÜNVEREN BİLGİÇ |
| Assistants | |
| Goals | To teach algebraic stuctures such that groups, rings and fields and to work on the relations between these |
| Course Content | Binary operations; definition of algebraic groups and its basic properties; subgroups; permutation groups; cyclic groups; symmetry group of regular polygons; cyclic permutations; odd and even permutations; homomorphisms; Cosets and Lagrange theorem; isomorphism theorems; an action of a group on a set; rings, subrings and ideals; prime and maximal ideals; homomorphisms on rings; arithmetics on rings; polynomial rins; Burnside theorem and its applications; fields; p-groups and related theorems. |
| Learning Outcomes |
- Students know group structures and proves important theorems related to group structures - Students observe the pros of equivalency of two algebraic structures by understanding the isomorphism theorems. - Students know the notions of cosets and normal subspaces. - Students understand the notion of rings. - Students know homomorphisms on rings. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Preliminaries, Binary Operations | Course Hours Verbal Expression |
| 2. Week | Groups | Course Hours Verbal Expression |
| 3. Week | Subgroups | Verbal Expression Course Hours |
| 4. Week | Permutation groups | Verbal Expression Course Hours |
| 5. Week | Dihedral Groups and Symmetry Groups | Verbal Expression Course Hours |
| 6. Week | Cyclic Permutations | Course Hours Verbal Expression |
| 7. Week | Even and odd permutations and homomorphisms | Verbal Expression Course Hours |
| 8. Week | Midterm | |
| 9. Week | Isomorphism and isomorphism theorems | Verbal Expression Course Hours |
| 10. Week | Cosets and Lagrange Theorem | Course Hours Verbal Expression |
| 11. Week | Action of a group on a set | Course Hours Verbal Expression |
| 12. Week | Rings, Subrings, and Ideals | Course Hours Verbal Expression |
| 13. Week | Ring homomorphisms and operations on rings | Course Hours Verbal Expression |
| 14. Week | Final | Verbal Expression Course Hours |
| Soyut Cebir, İsmail Naci Cangül, Dora Yayınları. |
| Örneklerle Soyut Cebir, Fethi Çallıalp, Birsen Yayınevi. |
| Program Requirements | Contribution Level | DK1 | DK2 | DK3 | DK4 | DK5 | Measurement Method |
|---|---|---|---|---|---|---|---|
| PY1 | 5 | 5 | 5 | 5 | 5 | 5 | - |
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| Course's Level of contribution | None | Very Low | Low | Fair | High | Very High |
| Method of assessment/evaluation | Written exam | Oral Exams | Assignment/Project | Laboratory work | Presentation/Seminar |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Course Hours | 13 | 2 | 26 |
| Midterm 1 | 1 | 8 | 8 |
| Homework 1 | 1 | 5 | 5 |
| Final | 1 | 12 | 12 |
| Total Workload | 51 | ||
| ECTS Credit of the Course | 2.0 | ||
