Course for international guest/part time students

Faculty

Faculty of Science

Organization

TTK Department of Geometry

Code

kombge1u0um17em

Title

Combinatorial geometry (l)

Usual semester

Autumn

ECTS

3

Language

en

Learning outcomes

Knowledge: Knowledge of basic concepts, results and methods in the field. Ability: Application of knowledge in the field, understanding of interrelationships and problem solving. Attitude: Desire to improve mathematical knowledge and to learn as much as possible, and to apply knowledge as widely as possible. Autonomy and responsibility: Formulate and analyze mathematical questions independently and evaluate the limits of their applicability responsibly.

Course content

Combinatorial properties of projective and affine spaces built on finite fields. Collineations and polarities. Second-order surfaces, Hermite varieties, zero polarities and combinatorial structures related to them (circular geometries, generalized quadrilaterals). Special shapes that can be selected from finite sets of Euclidean geometry (collinear points, convex polygons), and their number. Helly-type theorems, transversals. Lattices, lattice-like arrangements. Polyhedra and tessellations of Euclidean, hyperbolic and spherical geometries. Cell systems that can be connected to point systems. Placements and coverings. Density. Circular and spherical arrangements. Prerequisite knowledge: linear and abstract algebra, basic affine geometry

Assessment method

(written or oral) exam plus term mark

Bibliography

lecture notes

Recommended bibliography

Kiss György, Szőnyi Tamás: Finite Geometries, CRC Press, Boca Raton, 2019. Boltyanski, V., Martini, H. and Soltan, P.S.: Excursions into Combinatorial Geometry, Springer-Verlag, Berlin-Heidelberg-New York, 1997. Fejes Tóth L.: Regular Figures, Pergamon Press, Oxford-London-New York-Paris, 1964. Fejes Tóth L.: Lagerungen in der Ebene auf der Kugel und im Raum, Springer-Verlag, Berlin-Heidelberg-New York, 1972.

Programmes of the course