| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT6001 | Advanced Algebra I | Fall | 3 | 0 | 3 | 12 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | Tr |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Assoc. Prof. ATABEY KAYGUN |
| Course Objectives: | To provide the necessary algebraic tools and techniques to a graduate student who would go into a doctoral program in mathematics. |
|
The students who have succeeded in this course; A student who finished this course successfully will have acquired the necessary basic knowledge to be able to follow a course in algebra in a doctoral program in mathematics. |
| Groups. Symmetric groups. Matrix groups. Abelian groups. Groups by generators and relations. p-groups. Central series and nilpotent groups. Group actions. Sylow Theorems. Group representations. Finite groups and their characters. Character tables. Commutative rings and fields. Polynomial rings. Rings of matrices. Ideals, subrings and modules. Commutative rings and fields. Polynomial rings. Rings of matrices. Ideals, subrings and modules. Chains of ideals and modules. Artinian and Noetherian rings. Hopkins-Levitzki Theorem. Chains of ideals and modules. Artinian and Noetherian rings. Hopkins-Levitzki Theorem. |
| Week | Subject | Related Preparation | |
| 1) | Set theory. | ||
| 2) | Groups. Symmetric groups. Matrix groups. Abelian groups. | ||
| 3) | Groups by generators and relations. | ||
| 4) | p-groups. Central series and nilpotent groups. Group actions. Sylow Theorems. | ||
| 5) | p-groups. Central series and nilpotent groups. Group actions. Sylow Theorems. | ||
| 6) | Group representations. | ||
| 7) | Group representations. | ||
| 8) | Finite groups and their characters. Character tables. | ||
| 9) | Finite groups and their characters. Character tables. | ||
| 10) | Calculations of group character tables. | ||
| 11) | Commutative rings and fields. Polynomial rings. Rings of matrices. Ideals, subrings and modules. | ||
| 12) | Commutative rings and fields. Polynomial rings. Rings of matrices. Ideals, subrings and modules. | ||
| 13) | Chains of ideals and modules. Artinian and Noetherian rings. Hopkins-Levitzki Theorem. | ||
| 14) | Chains of ideals and modules. Artinian and Noetherian rings. Hopkins-Levitzki Theorem. | ||
| Course Notes: | Instructor's own lectures. S. Lang, "Algebra" |
| References: |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | % 0 | |
| Laboratory | % 0 | |
| Application | % 0 | |
| Field Work | % 0 | |
| Special Course Internship (Work Placement) | % 0 | |
| Quizzes | % 0 | |
| Homework Assignments | % 0 | |
| Presentation | % 0 | |
| Project | 1 | % 20 |
| Seminar | % 0 | |
| Midterms | 2 | % 40 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 40 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 40 | |
| PERCENTAGE OF FINAL WORK | % 60 | |
| Total | % 100 | |
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Special Course Internship (Work Placement) | 0 | 0 | 0 |
| Field Work | 0 | 0 | 0 |
| Study Hours Out of Class | 14 | 7 | 98 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 1 | 33 | 33 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 2 | 2 | 4 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 23 | 23 |
| Total Workload | 200 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |