MATH737 VECTOR BUNDLES AND CHARACTERIST.CLASSES
| Course Code: | 2360737 |
| 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: | Assoc.Prof.Dr. SEMRA PAMUK |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of the course student will learn:
- the definition and examples of vector bundles, basic constructions about them and their main properties,
- definition and basic properties of Stiefel -Whitney classes, Euler class, Chern classes and Pontrjagin classes, basic calculations and some applications.
Course Content
Courses not listed in catalogue. Contents vary from year to year according to interest of students and instructor in charge. Typical contents include contemporary developments in Algebra, Analysis, Geometry, Topology, Applied Mathematics.
Course Learning Outcomes
By the end of the course the student will know
- the concept of vector bundle and basic constructions about vector bundles,
- the basics of Stiefel-Whitney classes and some methods to compute them,
- the concept of oriented bundle and Euler class,
- the concept of complex structure on a real vector bundle,
- the basics of Chern classes and some methods to compute them,
- the basics of Pontrjagin classes and some methods to compute them,
- some geometric and topological applications of characteristic classes,
- the concept of Grassmann manifold and its importance for the classification of vector bundles.
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