| 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 |
| MAT4066 | Rings and Modules | Fall | 3 | 0 | 3 | 6 |
| The course opens with the approval of the Department at the beginning of each semester |
| Language of instruction: | En |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Dr. Öğr. Üyesi TUĞCAN DEMİR |
| Course Objectives: | To provide the necessary background in rings and modules for mathematics students who would go into a graduate program in mathematics.konu |
|
The students who have succeeded in this course; A student who finishes this course successfully will have acquired the fundamental concepts of ring theory and will enough background to take a graduate class in ring theory. |
| Abelian groups. Rings and fields. Vector spaces. Polynomial algebras over commuting variables. Ideals. Modules over commutative polynomial algebras. Radicals of ideals. Nil radical and Jacobson radical. Tensor product. Modules and morphisms. Kernel and image modules. Submodules and quotient modules. Chains of ideals and modules. Zorn's Lemma. Artinian and Notherian rings and modules. Free modules and bases. Semi-simple modules and rings. Artin–Wedderburn Theorem. |
| Week | Subject | Related Preparation | |
| 1) | Abelian groups. Rings and fields. | ||
| 2) | Abelian groups. Rings and fields. | ||
| 3) | Vector spaces. Polynomial algebras over commuting variables. Ideals. Modules over commutative polynomial algebras. | ||
| 4) | Radicals of ideals. Nil radical and Jacobson radical. | ||
| 5) | Radicals of ideals. Nil radical and Jacobson radical. | ||
| 7) | Tensor product. Modules and morphisms. Kernel and image modules. Submodules and quotient modules. | ||
| 8) | Tensor product. Modules and morphisms. Kernel and image modules. Submodules and quotient modules. | ||
| 9) | Chains of ideals and modules. Zorn's Lemma. Artinian and Notherian rings and modules. | ||
| 10) | Chains of ideals and modules. Zorn's Lemma. Artinian and Notherian rings and modules. | ||
| 11) | Free modules and bases. Semi-simple modules and rings. | ||
| 12) | Simple modules and composition series. | ||
| 13) | Artin–Wedderburn Theorem. | ||
| 14) | Artin-Wedderburn Theorem. | ||
| Course Notes: | Instructor's own lecture notes. S. Lang, "Algebra". T. Y. Lam, "Lectures on Modules and Rings." |
| References: |
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 0 | % 0 |
| Laboratory | 0 | % 0 |
| Application | 0 | % 0 |
| Field Work | 0 | % 0 |
| Special Course Internship (Work Placement) | 0 | % 0 |
| Quizzes | 3 | % 10 |
| Homework Assignments | 0 | % 0 |
| Presentation | 0 | % 0 |
| Project | 0 | % 0 |
| Seminar | 0 | % 0 |
| Midterms | 2 | % 40 |
| Preliminary Jury | % 0 | |
| Final | 1 | % 50 |
| Paper Submission | % 0 | |
| Jury | % 0 | |
| Bütünleme | % 0 | |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 50 | |
| PERCENTAGE OF FINAL WORK | % 50 | |
| 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 | 3 | 42 |
| Presentations / Seminar | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework Assignments | 0 | 0 | 0 |
| Quizzes | 3 | 3 | 9 |
| Preliminary Jury | 0 | ||
| Midterms | 2 | 10 | 20 |
| Paper Submission | 0 | ||
| Jury | 0 | ||
| Final | 1 | 12 | 12 |
| Total Workload | 125 | ||
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |