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 |
MAT6024 | Advanced Differential Geometry II | Fall | 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: | The object of the course is to provide basic concepts to students,of complex structures, holomorphic transformations, Hermitian and Kähler metrics, Riemannian manifolds and Kähler 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 complex structures and holomorphic maps and do basic calculations about them. o will be able to know Hodge and Dolbeault theories. o will be able to apply concepts of Complex and holomorphic vector bundles and Hermitian bundles o will be able to give examples of Kähler metrics o will be able to use natural operators on Riemannian and Kähler manifolds and the Ricci form of Kahler manifolds |
Complex structures and holomorphic maps Holomorphic forms and vector fields Complex and holomorphic vector bundles Hermitian bundles Hermitian and Kähler metrics The curvature tensor of Kähler manifolds Examples of Kähler metrics Natural operators on Riemannian and Kähler manifolds Hodge and Dolbeault theories The Ricci form of Kahler manifolds Kahler–Einstein metrics |
Week | Subject | Related Preparation |
1) | Complex structures and holomorphic maps | |
2) | Complex structures and holomorphic maps | |
3) | Holomorphic forms and vector fields | |
4) | Holomorphic forms and vector fields | |
5) | Complex and holomorphic vector bundles | |
6) | Complex and holomorphic vector bundles | |
7) | Hermitian bundles | |
8) | Hermitian and Kähler metrics | |
9) | The curvature tensor of Kähler manifolds | |
10) | Examples of Kähler metrics | |
11) | Natural operators on Riemannian and Kähler manifolds | |
12) | Hodge and Dolbeault theories | |
13) | The Ricci form of Kahler manifolds | |
14) | Kahler–Einstein metrics |
Course Notes / Textbooks: | Lectures on Kähler Geometry By Andrei Moroianu |
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. | 3 |
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. | |
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. | 3 |
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. | 4 |