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: UPS of School of Mathematics (2014-today)
Registered students: 112
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Winter | - | 5.5 |
| Academic Year | 2020 – 2021 |
| Class Period | Winter |
| Faculty Instructors |
|
| Weekly Hours | 3 |
| Class ID | 600166776
|
Course Type 2011-2015
Knowledge Deepening / Consolidation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600166776
Erasmus
The course is also offered to exchange programme students.
Prerequisites
Required Courses
- 0108 Linear Algebra
- 0306 INTRODUCTION TO GEOMETRY I
Learning Outcomes
Students taking this course will not only aquire further mathematical knowledge, but they will deepen and better understand the interrelations between the Algebra and Geometry courses they took in the first two years of the undergraduate program. In addition, they will familiarize with the interdisciplinary approach to mathematical problems and enforce their mathematical perception. The techniques used in the course are fundamental for many mathematical disciplines but are also used extensively for many applications of any kind of motion simulation and graphic design.
General Competences
- Work autonomously
- Work in teams
Course Content (Syllabus)
(Note: Special attention will be given to the cases n=2,3.)
The group Aff(n). Short reminder on the isometries of the plane and space. The group ISO(n). Subgroups of Isometries (discrete, finite, fixed point). Circle and the group SO(2). Spherical geometry (spherical coordinates, triangles, great circles). Isometries of the sphere, the groups O(3), SO(3). Stereographic projection, real projective line, Mobius tranformations. SL(2,R) and 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, real projective plane and SL(3,R).
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | |||
| Reading Assigment | 46 | 1.5 | ✓ | ||
| Exams | 80 | 2.7 | |||
| Total | 165 | 5.5 |
Student Assessment
Description
Written exam
Student Assessment methods
- Written Exam with Multiple Choice Questions (Formative, Summative)
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Oral Exams (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Γεωμετρία και Συμμετρία, L. C. Kinsey, T. E. Moore, E. Prassidis, ISBN 978-960-461-854-5, ΕΚΔΟΣΕΙΣ ΚΛΕΙΔΑΡΙΘΜΟΣ ΕΠΕ, Κωδικός στον Εύδοξο 77108682
Additional bibliography for study
1) 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
11-11-2020
