GEOMETRY AND GROUPS
| Title | ΓΕΩΜΕΤΡΙΑ ΚΑΙ ΟΜΑΔΕΣ / GEOMETRY AND GROUPS |
| Code | 0308 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Common | No |
| Status | Active |
| Course ID | 600018925 |
Programme of Study: Merikīs Foítīsīs (2014-sīmera)
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| KORMOS | Elective Courses belonging to the selected specialization | Winter | - | 5.5 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 23
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | 6 | 3 | 5.5 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors | |
| Class ID | 600276093
|
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600276093
Erasmus
The course is also offered to exchange programme students.
Prerequisites
Required Courses
- 0332 Classical Differential Geometry II
- 0110 ELEMENTS OF LINEAR ALGEBRA
- 0306 INTRODUCTION TO GEOMETRY I
Course Content (Syllabus)
Crash courses on Group Theory. Complex numbers and rotations of the plane. Quaternions. Rotations of the 2- sphere, rotations of R^3 , rotations of R^4. Reflections.
Isometry group of of R^2 and R^3. Isometry subgroups (discrete, finite, fixed point).
Circle and SO(2). Spherical geometry, isometries of the sphere, the groups O(3), SO(3).
Stereographic projection, real projective line, Mobius transformations, SL(2,r) and action on RP(1), the group PSL(2,R).
Complex projective line, SL(2,C) and action on CP(1). Riemann sphere, the group PSL(2,C). Hyperbolic plane. Inversion.
Real projective plane and SL(3,R). Groups of matrices and Topology. Rudiments of Lie groups.
Bibliography
Additional bibliography for study
Vaughn Climenhaga, Anatole Katok, From Groups to Geometry and Back, Student
Mathematical Library, Vol. 81, A.M.S. 2017.
2) David A. Brannan, Matthew F. Esplen, Jeremy J. Gray, Geometry, Cambridge University
Press, 2012.
3) Kristopher Tapp, Matrix Groups for Undergraduates, Student Mathematical Library, Vol. 79,
A.M.S. 2016.
Last Update
15-09-2025
