Rapor Tarihi: 24.02.2026 22:01
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Abstract Algebra I | MAT301 | Turkish | Compulsory | 5. Semester | 2 + 2 | 3.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing |
| Course Coordinator | Prof. Dr. Arzu ÖZKOÇ ÖZTÜRK |
| Instructor(s) | |
| Goals | 1. To give the Fundamentals of the subject 2. To make the students comprehend the concept of groups and results of these concepts |
| Course Content | Groups, subgroups, Cyclic groups, Dihedral groups, permutation groups, Cosets and Lagrange’s theorem Normal subgroups and quotient groups, Group homomorphisms, Cayley’s Theorem, Group isomorphisms and automorphisms, Direct product of groups, Fundamental theorem of finite abelian groups, Group actions, p-Groups and Sylow theorems, Applications of Sylow theorems |
| # | Öğrenme Kazanımı |
| 1 | It recognizes basic algebraic structures. It solves algebraic problems. It explains group structures. |
| 2 | This section defines the concepts of Group, Subgroup, and Normal Subgroup, provides examples, and presents relevant proofs. |
| 3 | It explains the concepts of group homomorphisms and isomorphisms. |
| 4 | The student has knowledge of Quotient Groups, Symmetric (Permutation) Groups, Cyclic Groups, and Direct Product Groups. |
| 5 | The person is familiar with and able to answer questions related to p-groups and Sylow's theorems. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Groups, subgroups | |
| 2. Week | Subgroups and examples | |
| 3. Week | Cosets and Lagrange’s theorem | |
| 4. Week | Normal subgroups and quotient groups | |
| 5. Week | Group homomorphisms, Cayley’s Theorem | |
| 6. Week | Group isomorphisms and automorphisms | |
| 7. Week | permutation groups | |
| 8. Week | Cycling groups | |
| 9. Week | Cyclic groups | |
| 10. Week | Dihedral groups | |
| 11. Week | Direct product of groups | |
| 12. Week | p-Groups and Sylow theorems | |
| 13. Week | Fundamental theorem of finite abelian groups | |
| 14. Week | Applications of Sylow theorems |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Acquiring knowledge on theories and practice of education in general, subject teaching in particular, and the basic concepts and theories of the related disciplines, | ✔ | |||||
| 3 | Doing effective educational planning, organizing and evaluating based on theoretical and practical content matter and in relation to the needs of the learners, | ✔ | |||||
| 5 | Analyzing studies in the field with a scientific perspective, assessing the findings and offering solutions, | ✔ | |||||
| 7 | Pursuing the scientific discussions in the field and interpreting them through scientific examination, | ✔ | |||||
| 8 | Forming scientific study platforms in order to solve the problems in practice, | ✔ | |||||
| 8 | Forming scientific study platforms in order to solve the problems in practice, | ✔ | |||||
| 10 | Following the developments in the field through professional activities such as literature reviews, seminars, conferences and workshops, and sharing them with other expert and non-expert individuals, | ✔ | |||||
| 12 | To be able to analyse the notions and ideas in the field by using scientific methods, to identify problems, and to develop solutions based on proofs and researches | ✔ | |||||
| 13 | To be able to gain ability of doing academic research | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 |
|---|---|---|---|---|---|
| PY1 | 4 | 4 | 4 | 4 | 4 |
| PY3 | 5 | 5 | 5 | 5 | 5 |
| PY5 | 4 | 4 | 4 | 4 | 4 |
| PY7 | 2 | 2 | 2 | 2 | 2 |
| PY8 | 2 | 2 | 2 | 2 | 2 |
| PY10 | 1 | 1 | 1 | 1 | 1 |
| PY12 | 4 | 4 | 4 | 4 | 4 |
| PY13 | 2 | 2 | 2 | 2 | 2 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 4 | 56 |
|
Sınavlar |
Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 14 | 1 | 14 | |
| Final | 1 | 2 | 2 | |
| Practice | 14 | 2 | 28 | |
| Practice End-Of-Term | 14 | 1 | 14 | |
| Classroom Activities | 12 | 1 | 12 | |
| Total Workload | 128 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
