Rapor Tarihi: 13.04.2026 03:07
| 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. Basic information related to the lesson is provided. 2. The student understands the concepts and results of group theory. |
| Course Content | Groups, subgroups, Cyclic groups, permutation groups, Cosets and Lagrange’s theorem Normal subgroups and quotient groups, Group homomorphisms, Cayley’s Theorem, Group isomorphisms and automorphisms, |
| # | Öğrenme Kazanımı |
| 1 | It explains the concepts of group and subgroup, provides examples, and applies subgroup criteria. |
| 2 | It analyzes order relations in finite groups using cosets and Lagrangian Theorem. |
| 3 | It explains normal subgroups and quotient groups and interprets the relationships between group structures. |
| 4 | It explains group homomorphisms and isomorphisms, performs structural analysis using the concepts of kernel and image, and interprets Cayley's Theorem. |
| 5 | It analyzes structural similarities between groups using the concepts of isomorphism and automorphism. |
| 6 | It defines permutations and cyclic groups; it applies the basic properties and operations of these groups. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Groups, subgroups | Preparation, After Class Study, Research, Other Activities, Interview |
| 2. Week | Subgroups and examples | Preparation, After Class Study, Research, Other Activities, Interview |
| 3. Week | Cosets and Lagrange’s theorem | Preparation, After Class Study, Research, Other Activities, Interview, Presentation (Preparation), Practice |
| 4. Week | Cosets and Lagrangian Theorem | Preparation, After Class Study, Research, Other Activities, Interview |
| 5. Week | Normal subgroups, quotient groups | Preparation, After Class Study, Research, Other Activities, Interview |
| 6. Week | Normal subgroups, quotient groups | Preparation, After Class Study, Research, Other Activities, Interview |
| 7. Week | Group homomorphisms, Cayley's Theorem | Preparation, After Class Study, Research, Other Activities, Interview |
| 8. Week | Group homomorphisms, Cayley's Theorem | Preparation, After Class Study, Research, Other Activities, Interview |
| 9. Week | Group isomorphisms and automorphisms | Preparation, After Class Study, Research, Other Activities, Interview |
| 10. Week | Group isomorphisms and automorphisms | Preparation, After Class Study, Research, Other Activities, Interview |
| 11. Week | Permutation groups | Preparation, After Class Study, Research, Other Activities, Interview |
| 12. Week | Permutation groups | Preparation, After Class Study, Research, Other Activities, Interview |
| 13. Week | Rotating groups | Preparation, After Class Study, Research, Other Activities, Interview |
| 14. Week | Rotating groups | Preparation, After Class Study, Research, Other Activities, Interview |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Possesses theoretical and applied knowledge of the fundamental areas of mathematics (Analysis and Function Theory, Algebra and Number Theory, Geometry, Applied Mathematics, Topology and Foundations of Mathematics, and Mathematical Logic). | ✔ | |||||
| 2 | Explains the historical development of mathematical concepts, their relationship with other branches of science, and their application areas. | ✔ | |||||
| 3 | Defines mathematical problems, selects appropriate methods, and solves them using analytical/numerical techniques. | ✔ | |||||
| 4 | Constructs mathematical expressions with logical integrity and reaches conclusions using proof methods. | ✔ | |||||
| 5 | Formulates and interprets real-life problems by performing mathematical modeling. | ✔ | |||||
| 6 | Effectively uses information technologies and mathematical software in data analysis and computation processes. | ✔ | |||||
| 7 | Takes responsibility in individual or team work; plans and executes projects. | ✔ | |||||
| 8 | Follows current developments in their field; improves themselves with a lifelong learning awareness. | ✔ | |||||
| 9 | Expresses mathematical ideas verbally and in writing clearly and in accordance with academic rules. | ✔ | |||||
| 10 | Acts in accordance with professional and academic ethical values; acts with a sense of social responsibility. | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 |
|---|---|---|---|---|---|---|
| PY1 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY2 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY3 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY4 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY5 | 2 | 2 | 2 | 2 | 2 | 2 |
| PY6 | 2 | 2 | 2 | 2 | 2 | 2 |
| PY7 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY8 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY9 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY10 | 5 | 5 | 5 | 5 | 5 | 5 |
| 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 |
|
Ders Dışı |
Homework | 14 | 1 | 14 |
| Preparation, After Class Study | 14 | 1 | 14 | |
| Practice | 14 | 2 | 28 | |
| Other Activities | 12 | 1 | 12 | |
|
Sınavlar |
Midterm | 1 | 2 | 2 |
| Final | 1 | 2 | 2 | |
| Total Workload | 128 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
