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 |
MAT6023 | Advanced Differential Geometry I | Fall Spring |
3 | 0 | 3 | 8 |
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 : | Prof. Dr. ERTUĞRUL ÖZDAMAR |
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. |
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 |
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 |
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 |
Course Notes: | Lectures on Kahler Manifolds,3-03719-025-6,W. Ballmann, 2006 |
References: | . |
Semester Requirements | Number of Activities | Level of Contribution |
Attendance | 14 | % 10 |
Laboratory | % 0 | |
Application | % 0 | |
Field Work | % 0 | |
Special Course Internship (Work Placement) | % 0 | |
Quizzes | % 0 | |
Homework Assignments | 1 | % 10 |
Presentation | % 0 | |
Project | % 0 | |
Seminar | % 0 | |
Midterms | 1 | % 35 |
Preliminary Jury | % 0 | |
Final | 1 | % 45 |
Paper Submission | % 0 | |
Jury | % 0 | |
Bütünleme | % 0 | |
Total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 55 | |
PERCENTAGE OF FINAL WORK | % 45 | |
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 | 3 | 30 | 90 |
Presentations / Seminar | 0 | 0 | 0 |
Project | 0 | 0 | 0 |
Homework Assignments | 1 | 20 | 20 |
Quizzes | 0 | 0 | 0 |
Preliminary Jury | 0 | ||
Midterms | 1 | 20 | 20 |
Paper Submission | 0 | ||
Jury | 0 | ||
Final | 1 | 20 | 20 |
Total Workload | 192 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |