There is no midterm during the semester. The final grade at the end of the semester is determined solely by the oral exam.

Oral exam: 12 topics 6 from projective geometry, 6 from non-Euclidean geometry. Everyone gets one from both parts and, after a short preparation, they have to report on the given topics.

Topic list:

First part
I. Axioms and dimension of a projective geometry
II. Desargues' and Pappus' theorem
III. Fundamental Theorem for Projectivities on a Line and Pappus' theorem
IV. Projective spaces P(V)
V. Cross ratio and projectivities on a line
VI. The algebra of points on a line
Second part
VII. Spherical trigonometry
VIII. Locus problems on the sphere
IX. Models of the hyperbolic geometry and the connection between them
X. Distance, angle and area in hyperbolic geometry
XI. Hyperbolic coordinate systems, n-dimensional hyperbolic volume
XII. Thurston geometries

Lecture notes from non-Euclidean geometry.
Lecture notes from geometry (Can be usefull for some topics)