Affine and projective geometry

Completed course Algebra 1.

Affine Geometry: affine spaces, affine transformations, the fundamental theorem of affine geometry.
Projective Geometry: projective spaces, embedding of affine spaces into projective spaces, collineations and projectivities, the fundamental theorem of projective geometry, projective coordinates, cross-ratio, harmonic ratio, perspectivities.
Conics in projective plane: poles and polars, cross-ration on a conic, Pascal's Theorem, classification of conics.
Additional topics: classification of isometries in the Euclidean plane, Leonardo's Theorem, frieze groups and wallpaper groups, finite groups of isometries in Euclidean 3-space.

T. Košir, B. Magajna: Transformacije v geometriji, DMFA-založništvo, Ljubljana, 1997.
Vidav: Afina in projektivna geometrija, DMFA-založništvo, Ljubljana, 1981.
M. Berger: Geometry I, Springer, Berlin, 2004.
M. Berger: Geometry II, Springer, Berlin, 1996.
E. G. Rees: Notes on Geometry, Springer, Berlin-New York, 2005.
R. A. Rosenbaum: Introduction to Projective Geometry and Modern Algebra, Addison-Wesley, Reading, 1963.

The main objective is to introduce affine and projective geometry using the tools from algebra and linear algebra. The student develops geometric intution.

Knowledge and understanding: The understanding of the fundamental notions of affine and projective geometry. The ability to apply the knowledge obtained in algebra and mathemetical analysis courses in geometry.
Application: The application of geometric techniques in other subjects and in practice.
Reflection: The ability to connect different approaches: analytical, algebraic and geometric.
Transferable skills: The ability to apply theoretical knowledge in practice.

Lectures, exercises, consultations

2 midterm exams instead of written exam, written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Tomaž Košir:
BUCKLEY, Anita, KOŠIR, Tomaž. Plane curves as Pfaffians. Annali della Scuola normale superiore di Pisa, Classe di scienze, ISSN 0391-173X, 2011, vol. 10, iss. 2, str. 363-388. [COBISS-SI-ID 15928409]
BINDING, Paul, KOŠIR, Tomaž. Root vectors for geometrically simple two-parameter eigenvalues. Transactions of the American Mathematical Society, ISSN 0002-9947, 2004, vol. 356, no. 5, str. 1705-1726. [COBISS-SI-ID 13013081]
KOŠIR, Tomaž. Root vectors for geometrically simple multiparameter eigenvalues. Integral equations and operator theory, ISSN 0378-620X, 2004, vol. 48, no. 3, str. 365-396. [COBISS-SI-ID 12895321]
Aleš Vavpetič:
CENCELJ, Matija, DYDAK, Jerzy, VAVPETIČ, Aleš, VIRK, Žiga. A combinatorial approach to coarse geometry. Topology and its Applications, ISSN 0166-8641. [Print ed.], 2012, vol. 159, iss. 3, str. 646-658. [COBISS-SI-ID 16094809]
CENCELJ, Matija, DYDAK, Jerzy, MITRA, Atish, VAVPETIČ, Aleš. Hurewicz-Serre theorem in extension theory. Fundamenta mathematicae, ISSN 0016-2736, 2008, vol. 198, no. 2, str. 113-123. [COBISS-SI-ID 14551385]
VAVPETIČ, Aleš, VIRUEL, Antonio. Symplectic groups are N-determined 2-compact groups. Fundamenta mathematicae, ISSN 0016-2736, 2006, vol. 192, no. 2, str. 121-139. [COBISS-SI-ID 14185305]
VAVPETIČ, Aleš. Afina in projektivna geometrija. Ljubljana: samozal. A. Vavpetič, 2011. VI, 114 str., ilustr. [COBISS-SI-ID 15994969]