MATH541 DIFFERENTIAL TOPOLOGY
| Course Code: | 2360541 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. MOHAN LAL BHUPAL |
| Offered Semester: | Fall Semesters. |
Course Objectives
The objective of this course is to provide the student with a solid foundation in differential topology that can both serve as an entry point to the literature or as a basis for more advanced courses in topology such as low dimensional topology or symplectic topology. Starting with the definition of a manifold and the notion of differential structures on manifolds, students will progress to cover topics such as vector bundles, embeddings, transversality and Sard's Theorem.
Course Content
Manifolds and differentiable structures. Tangent Space. Vector bundles. Immersions, submersions, embeddings. Transversality. Sard's theorem. Whitney Embedding Theorem. The exponential map and tubular neighborhoods. Manifolds with boundary. Thom's tranversality Theorem.
Course Learning Outcomes
After successfully completing the course, students will know:
- basic notions and techniques about the topology of manifolds like transversality techniques,
- basic theorems of differential topology like Whitney Embedding Theorem, Sard's Theorem, Transversality Homotopy Theorem etc.,
- some applications of transversality like Intersection Theory.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution