Date of Graduation

Spring 2018

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Les Reid

Keywords

Affine Geometry, Projective Geometry, Latin Square, Ternary Ring, Perfect Difference Set, Bruck-Ryser Theorem

Subject Categories

Geometry and Topology

Abstract

In this thesis, we investigate affine and projective geometries. An affine geometry is an incidence geometry where for every line and every point not incident to it, there is a unique line parallel to the given line. Affine geometry is a generalization of the Euclidean geometry studied in high school. A projective geometry is an incidence geometry where every pair of lines meet. We study basic properties of affine and projective planes and a number of methods of constructing them. We end by prov- ing the Bruck-Ryser Theorem on the non-existence of projective planes of certain orders.

Copyright

© Abraham Pascoe

Open Access

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