BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT6023 | Advanced Differential Geometry I | Spring | 3 | 0 | 3 | 8 |
| 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 : | Prof. Dr. ERTUĞRUL ÖZDAMAR |
| Recommended Optional Program Components: | None |
| Course Objectives: | In this course,first of all, fundamental topics for Kähler manifolds will be given. These are parts of differential geometry (vector bundles and connections, curvature and holonomy) and global analysis. In addition, the course includes basic facts about the Laplace and the Hodge operators on differential forms, vector fields and forms on complex manifolds. |
Learning Outcomes
|
The students who have succeeded in this course; The students who succeeded in this course; o will be able to know the concepts of Vector bundles, connections,Curvature and holonomy and do basic calculations about them. o will be able to design and perform operations on The Laplace and the Hodge operators on vector fields and forms on complex manifolds. o will be able to apply the fundemental theorems of Global analysis o will be able to use The Laplace and the Hodge operators on vector fields and forms on complex manifolds |
Course Content
| Vector bundles and connections Curvature and holonomy Global analysis Differential forms and the Laplace and the Hodge operators on differential forms The Laplace and the Hodge operators on vector fields and forms on complex manifolds |
Weekly Detailed Course Contents
| Week | Subject | Related Preparation |
| 1) | Vector bundles and connections | |
| 2) | Vector bundles and connections | |
| 3) | Vector bundles and connections | |
| 4) | Curvature and holonomy | |
| 5) | Curvature and holonomy | |
| 6) | Curvature and holonomy | |
| 7) | Global analysis | |
| 8) | Global analysis | |
| 9) | Global analysis | |
| 10) | Differential forms and the Laplace and the Hodge operators on differential forms | |
| 11) | Differential forms and the Laplace and the Hodge operators on differential forms | |
| 12) | Differential forms and the Laplace and the Hodge operators on differential forms | |
| 13) | Differential forms and the Laplace and the Hodge operators on differential forms | |
| 14) | The Laplace and the Hodge operators on vector fields and forms on complex manifolds |
Sources
| Course Notes / Textbooks: | Lectures on Kahler Manifolds,3-03719-025-6,W. Ballmann, 2006 |
| References: | . |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Attendance | 14 | % 10 |
| Homework Assignments | 1 | % 10 |
| Midterms | 1 | % 35 |
| Final | 1 | % 45 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 55 | |
| PERCENTAGE OF FINAL WORK | % 45 | |
| Total | % 100 | |
ECTS / Workload Table
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 3 | 30 | 90 |
| Homework Assignments | 1 | 20 | 20 |
| Midterms | 1 | 20 | 20 |
| Final | 1 | 20 | 20 |
| Total Workload | 192 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |