MATH471 HYPERBOLIC GEOMETRY
| Course Code: | 2360471 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 6.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Prof.Dr. MUSTAFA KORKMAZ |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course, the students are expected to explain Euclid's Parallel Postulate and why there are other geometries in which it does not hold, provide models of the hyperbolic plane, describe the Möbius transformations of the hyperbolic plane, and perform calculations involving lengths, distances, angles and areas in the hyperbolic plane.
Course Content
Parallel postulate and the need for non-Euclidean geometry, models of the hyperbolic plane, Möbius group, classification of Möbius transformations, classical geometric notions such as length, distance, isometry, parallelism, convexity, area, trigonometry in the hyperbolic plane, groups acting on the hyperbolic plane, fundamental domains.
Course Learning Outcomes
By the end of this course, students will be able to:
Explain the historical and logical foundations of non-Euclidean geometry, including the role of the parallel postulate and why its modification leads to alternative geometries.
Describe and analyze various models of the hyperbolic plane, such as the Poincaré disk and upper half-plane models, and translate between them.
Understand the structure and action of the Möbius group on the hyperbolic plane, including identification and classification of Möbius transformations.
Apply classical geometric notions (e.g., length, distance, isometry, parallelism, convexity, area) within the context of hyperbolic geometry.
Analyze group actions on the hyperbolic plane, and understand the significance of such actions in hyperbolic geometry.
Identify and construct fundamental domains for group actions on the hyperbolic plane.
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 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 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 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 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