Differential Topology(MATH 523)
Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
---|---|---|---|---|---|---|---|
MATH 523 | Differential Topology | 2 | 3 | 0 | 0 | 3 | 7 |
Prerequisites | |
Admission Requirements |
Language of Instruction | English |
Course Type | Elective |
Course Level | Masters Degree |
Course Instructor(s) | Serap GÜRER serapgurer@gmail.com (Email) |
Assistant | |
Objective | This course is an introduction to smooth manifolds and their topology (differential topology). |
Content | In the first part of the course, we will introduce basic objects on smooth manifolds, including: differentiable manifolds, smooth maps, tangent and cotangent vectors, differential forms, integration, stokes theorem and de Rham cohomology. In the second part, we will study differential topology (topology of smooth manifolds), including: Whitney immersion and embedding theorems, approximation theorem, Sard theorem, transversality, intersection numbers, Morse functions and Morse theory. |
Course Learning Outcomes | |
Teaching and Learning Methods | |
References |
1)John Lee, Introduction to smooth manifolds? 2)Victor Guillemin & Alan Pollack, Differential topology |
Theory Topics
Week | Weekly Contents |
---|
Practice Topics
Week | Weekly Contents |
---|
Contribution to Overall Grade
Number | Contribution | |
---|---|---|
Contribution of in-term studies to overall grade | 4 | 15 |
Contribution of final exam to overall grade | 1 | 40 |
Toplam | 5 | 55 |
In-Term Studies
Number | Contribution | |
---|---|---|
Assignments | 0 | 0 |
Presentation | 0 | 0 |
Midterm Examinations (including preparation) | 0 | 0 |
Project | 0 | 0 |
Laboratory | 0 | 0 |
Other Applications | 0 | 0 |
Quiz | 0 | 0 |
Term Paper/ Project | 0 | 0 |
Portfolio Study | 0 | 0 |
Reports | 0 | 0 |
Learning Diary | 0 | 0 |
Thesis/ Project | 0 | 0 |
Seminar | 0 | 0 |
Other | 0 | 0 |
Toplam | 0 | 0 |
No | Program Learning Outcomes | Contribution | ||||
---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 |
Activities | Number | Period | Total Workload |
---|---|---|---|
Total Workload | 0 | ||
Total Workload / 25 | 0,00 | ||
Credits ECTS | 0 |