| Area of Mathematics: | Algebra and Geometry (EAG) | ||
| Semester: | 4ο | ||
| Course ID: | 42201 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 4 | Practice: 0 | Laboratory: 0 |
| ECTS : | 5 | ||
| Eclass: | For the course’s material, click here. | ||
| Instructors: | Marina Statha | ||
Description
- Axiomatic definition of affine and projective plane. The principle of duality. Completion and deletion. Morphisms and collinearity. The groups of homologies and elations.
- The construction of P2(R) and its relationship with real projective plane of synthetic projective geometry. Classification of homologies and elations of P2(R).
- Theorems of Pascal-Brianchon.
- Projective Geometry over finite fields.
- The division ring P. The construction of the projective plane from an (algebraic) ring D. Relationship between the rings R and D. Relationships between the projective planes P and P2(R).
Bibliography
- S.M. Coxeter Projective Geometry, Second Edition
- J. Mihalek Projective Geometry and Algebraic Structures, Academic Press.
