PHYS491 GEOMETRY AND TOPOLOGY IN PHYSICS I
| Course Code: | 2300491 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 5.0 |
| Department: | Physics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Prof.Dr. ATALAY KARASU |
| Offered Semester: | Fall Semesters. |
Course Objectives
The subject matter of this course is important for appreciating the differential geometric aspects of gravitation and modern developments in mathematical and theoretical physics. The greater aim is to prepare beginning students to be able to read the modern literature on their own with relative ease.
Course Content
Vector spaces; algebras; topological spaces; simplicial homology; homotopy groups; differentiable manifolds; vectors and tensors; calculus of exterior forms; Stokes theorem; conservation laws and de Rham cohomology; parallel transport; connection and covariant derivative; geodesics; curvature and torsion. geometry of space-time.
Course Learning Outcomes
Officially the following topics will be covered
Vector spaces; algebras; topological spaces; simplicial homology; homotopy groups; differentiable manifolds; vectors and tensors; calculus of exterior forms; Stokes’ theorem; conservation laws and de Rham cohomology; parallel transport; connection and covariant derivative; geodesics; curvature and torsion, geometry of spacetime
These are all necessary for being able to follow the recent literature in mathematical physics.
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Can understand, model and analyze the fundamental physical processes of nature. | ✔ | |||
| 2 | Can suggest mathematical models to problems they face and solve them by various (approximate/analytical/numerical) approaches. | ✔ | |||
| 3 | Can use basic measurement devices; can choose and apply the best measurement technique. | ✔ | |||
| 4 | Can adequately record their observations, e.g., in a lab book. | ✔ | |||
| 5 | Can design and carry out experiments. | ✔ | |||
| 6 | Can access scientific information sources. | ✔ | |||
| 7 | Can critically analyze and contribute to scientific information. | ✔ | |||
| 8 | Can present scientific information clearly. | ✔ | |||
| 9 | Can analyze systems that contain probabilistic parts; can do error analysis. | ✔ | |||
| 10 | Has the basic programming skills; can solve a simple physical problem or can simulate one with an appropriate language they choose. | ✔ | |||
| 11 | Can actively and skillfully conceptualize, apply, analyze, synthesize and evaluate information. | ✔ | |||
| 12 | Can produce new ideas and products by using their background in physics. | ✔ | |||
| 13 | Can systematically design, evaluate, and implement a strategy to respond to an existing problem. | ✔ | |||
| 14 | Is effective in oral and written communication skills by using both Turkish and English languages. | ✔ | |||
| 15 | Can do leadership and take initiative. | ✔ | |||
| 16 | Tries to find physics based solutions to the problems of the world that we live in. | ✔ | |||
| 17 | Obeys the ethical rules in the workplace and the society and ascertains that they are obeyed by others. | ✔ | |||
| 18 | Can use the digital communication and computation tools in the most efficient and effective way. | ✔ | |||
| 19 | Can effectively use the knowledge and skills they gained in physics, in observing, analyzing, modeling and solving other societal problems. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution