BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| APPLIED MATHEMATICS (TURKISH, THESIS) | |||||
| Master | TR-NQF-HE: Level 7 | QF-EHEA: Second Cycle | EQF-LLL: Level 7 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT5002 | Abstract Algebra II | Spring | 3 | 0 | 3 | 12 |
| This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Basic information
| Language of instruction: | Turkish |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Assoc. Prof. ATABEY KAYGUN |
| Recommended Optional Program Components: | None |
| Course Objectives: | To provide the necessary algebraic tools and techniques to a graduate student. |
Learning Outcomes
|
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. |
Course Content
Weekly Detailed Course Contents
| 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. |
Sources
| Course Notes / Textbooks: | Instructor's own lectures notes. S. Lang, "Algebra" |
| References: |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Project | 1 | % 20 |
| Midterms | 1 | % 30 |
| Final | 1 | % 50 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 30 | |
| PERCENTAGE OF FINAL WORK | % 70 | |
| Total | % 100 | |
ECTS / Workload Table
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 14 | 6 | 84 |
| Project | 1 | 49 | 49 |
| Midterms | 1 | 12 | 12 |
| Final | 1 | 13 | 13 |
| Total Workload | 200 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |