Rapor Tarihi: 13.04.2026 03:08
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Abstract Algebra II | MAT302 | Turkish | Compulsory | 6. 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 | To understand the algebraic structure of the rings through some fundamental theorems and definitions |
| Course Content | The definition, properties, and examples of rings; Sub-rings and their examples; Integrity domains and fields; Prime and maximal ideals; Quotient rings; Ring homomorphisms and isomorphism theorems; Fields of fractions and polynomial rings; Fundamental Ideal Domain; Field extensions. |
| # | Öğrenme Kazanımı |
| 1 | t explains the structure of finite abelian groups, applies Sylow's theorems, and analyzes subgroup structures of finite groups. |
| 2 | It defines basic group structures such as dihedral groups and direct products, and compares the properties of these structures. |
| 3 | It explains the concept of rings, subrings, and basic ring examples; it determines whether a given structure is a ring or not. |
| 4 | It defines domains of wholeness, fields, prime and maximal ideals, and quotient rings, and analyzes the relationships between them. |
| 5 | It examines the relationships between algebraic structures using ring homomorphisms and isomorphism theorems. |
| 6 | It explains the concepts of polynomial rings and fields of fractions; it applies basic operations and structural properties to these structures. |
| 7 | It defines fundamental ideal domains and field extensions, calculates the degree of extension, and uses algebraic structures in problem solving. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Fundamental theorem of finite abelian groups | Preparation, After Class Study, Research, Other Activities, Interview |
| 2. Week | p-groups and Sylow's theorems | Preparation, After Class Study, Research, Other Activities, Interview |
| 3. Week | Dihedral groups, direct product groups | Preparation, After Class Study, Research, Other Activities, Interview |
| 4. Week | Rings and ring examples | Preparation, After Class Study, Research, Other Activities, Interview |
| 5. Week | Subrings and examples | Preparation, After Class Study, Research, Other Activities, Interview |
| 6. Week | Integral domains and fields | Preparation, After Class Study, Research, Other Activities, Interview |
| 7. Week | Prime and maximal ideals, quotient rings | Preparation, After Class Study, Research, Other Activities, Interview |
| 8. Week | Ring homomorphisms and isomorphism theorems | Preparation, After Class Study, Research, Other Activities, Interview |
| 9. Week | Fields of quotients | Preparation, After Class Study, Research, Other Activities, Interview |
| 10. Week | polynomial rings | Preparation, After Class Study, Research, Other Activities, Interview |
| 11. Week | Polynomial rings | Preparation, After Class Study, Research, Other Activities, Interview |
| 12. Week | Basic Ideal Region | Preparation, After Class Study, Research, Other Activities, Interview |
| 13. Week | Field extensions | Preparation, After Class Study, Research, Other Activities, Interview |
| 14. Week | Field extensions | 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 | DK7 |
|---|---|---|---|---|---|---|---|
| PY1 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| PY3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY6 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY7 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY8 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY9 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY10 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| 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 | ||
