| 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 |
| MAT5002 | Abstract Algebra II | 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. |
|
The students who have succeeded in this course; A student who finishes this class successfully will have acquired the minimum background to be able to follow a graduate level algebra course. |
| Week | Subject | Related Preparation | |
| 1) | Rings and ideals. Morphisms of rings. | ||
| 2) | Fields and vector spaces. | ||
| 3) | Examples of rings and fields. | ||
| 4) | Zero divisors. Principal Ideal Domains and Integral Domains. | ||
| 5) | Euclidean Domains. Unique Factorizations Domains. | ||
| 6) | Principal ideals, primary ideals, prime ideals and maximal ideals. | ||
| 7) | Radicals of ideals and rings. Nil radical and Jacobson radical. | ||
| 8) | Local and semi-local rings. | ||
| 9) | Basics of Lie algebras and Lie brackets. Structure constants. Jacobi identity. | ||
| 10) | Residue field and the cotangent space of a local ring. | ||
| 11) | The lattice of ideals of a ring, and operations in this lattice. | ||
| 12) | Alexandroff topology in a poset. Distributive lattices and Birhoff transform. | ||
| 13) | Selected topics from ring theory. | ||
| 14) | Selected topics from ring theory. | ||
| Course Notes: | Instructor's own lectures notes. 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 | 1 | % 30 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 50 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 30 | |
| PERCENTAGE OF FINAL WORK | % 70 | |
| 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 | 6 | 84 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 1 | 49 | 49 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 0 | 0 | 0 |
| Preliminary Jury | 0 | ||
| Midterms | 1 | 12 | 12 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 13 | 13 |
| Total Workload | 200 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |