one midterm, one rendez-vous, one final, homework assignments.
25% each.
no "tek ders sinavi"; will be given.

Geometry and Algebra:
Introduction, basic definitions, axioms.
Projective spaces, linear subspaces, homogeneous coordinates.
Projective transformations and general position.
Desargues' and Pappus theorem.
Finite projective geometries
Dual projective spaces, duality between points and lines in the plane.
Collineation.
Projections and correlations.
The cross-ratio.
Use of cross-ratio to define hyperbolic and spherical geometry.
Comparison with Euclidean geometry.
Polarity.
Klein's point of view on geometry.
The projective group and the affine group.
Passage to affine and metric spaces.
Plane algebraic curves and their singular points, conics and cubics. Topology
The topology of real projective plane, affine charts.
Nonsingular compact curves in the projective plane with degree less than 6.
Prohibitions via Bezout's theorem.
Harnack theorem and M-curves.