MATH466 GROUPS AND GEOMETRY
| Course Code: | 2360466 |
| 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: | Lecturer Dr. EMİNE YASEMİN TALU |
| Offered Semester: | Fall Semesters. |
Course Objectives
The aim of this course is to introduce students to the basic principles of geometric symmetries. We will study certain finitely generated groups by exploring the geometric properties of spaces on which these groups act. In summary, the main purpose is to teach how to relate groups and geometry.
Course Content
Symmetry. Isometrics of R?, the Euclidean group, symmetry groups of regular polygons and polyhedra, classification of finite subgroups of the three dimensional rotation group. Frieze groups, crystals, wallpaper groups, groups of acting on trees. Reflection groups, root systems, classification of finite reflection groups, crystallographic root systems and Weyl groups.
Course Learning Outcomes
If a student completes this course successfully he/she is expected to
- know different types of isometries of the Euclidean plane
- know the relationship between the group of isometries of the plane and reflections
- finite groups of isometries of the plane
- learn different types of isometries of the Euclidean spaces
- learn Frieze groups, wallpaper groups and recognize the symmetry groups of frieze patterns and wallpaper patterns
- learn tessellations (tilings) of the plane
- know different types of Platonic solids and their symmetry groups
- know root systems, Weyl groups
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