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 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
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. |
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 / Textbooks: | Lectures on Kahler Manifolds,3-03719-025-6,W. Ballmann, 2006 |
References: | . |
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 |
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 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution | |
1) | Ability to assimilate mathematic related concepts and associate these concepts with each other. | 5 |
2) | Ability to gain qualifications based on basic mathematical skills, problem solving, reasoning, association and generalization. | 5 |
3) | Be able to organize events, for the development of critical and creative thinking and problem solving skills, by using appropriate methods and techniques. | 5 |
4) | Ability to make individual and team work on issues related to working and social life. | |
5) | Ability to transfer ideas and suggestions, related to topics about his/her field of interest, written and verball. | 5 |
6) | Ability to use mathematical knowledge in technology. | 3 |
7) | To apply mathematical principles to real world problems. | 3 |
8) | Ability to use the approaches and knowledge of other disciplines in Mathematics. | 3 |
9) | Be able to set up and develope a solution method for a problem in mathematics independently, be able to solve and evaluate the results and to apply them if necessary. | 5 |
10) | To be able to link abstract thought that one has to concrete events and to transfer the solutions and examine and interpret the results scientifically by forming experiments and collecting data. | 4 |
11) | To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. | 3 |
12) | To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself. | 3 |