INTRODUCTION TO GEOMETRY II
| Title | ΕΙΣΑΓΩΓΗ ΣΤΗ ΓΕΩΜΕΤΡΙΑ ΙΙ / INTRODUCTION TO GEOMETRY II |
| Code | 0307 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Common | No |
| Status | Active |
| Course ID | 600018924 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 12
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
| Academic Year | 2022 – 2023 |
| Class Period | Spring |
| Faculty Instructors |
|
| Weekly Hours | 4 |
| Class ID | 600211851
|
Course Type 2011-2015
Knowledge Deepening / Consolidation
Mode of Delivery
- Distance learning
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600211851
- eLearning: https://elearning.auth.gr/course/view.php?id=15088
Erasmus
The course is also offered to exchange programme students.
Prerequisites
Required Courses
- 0306 INTRODUCTION TO GEOMETRY I
Course Content (Syllabus)
Affine spaces and the affine group. Projective spaces: charts, their topology. Group actions and examples. Projective maps (homographies) and the projective group. Projective bases, they determine unique homography, examples. Projective subspaces, independence. Theorems of Pappus and Desargues, proofs. Perspectives. Cross ratio. Duality for vector spaces, annihilator, pencils. Projective quadrics.
Spherical and elliptic geometry: area, angle, Girard’s formula. Intrinsic metric.
Introduction to hyperbolic geometry: the three geometries, need for models of hyperbolic space. The hyperboloid model, elementary geometry and trigonometry, the projective model, other models (Klein, Poincaré, half-space).
Student Assessment
Student Assessment methods
- Written Exam with Problem Solving (Summative)
Bibliography
Additional bibliography for study
1. Σημειώσεις διδασκόντων
2. Brannan D.A., Esplen M., Gray J. Geometry (2nd ed. OU-CUP 2012)
3. Kinsey C., Moore T., Πρασσίδης Ε. Γεωμετρία και Συμμετρία (Ευδοξος)
Last Update
09-02-2023
