We will use axiomatic systems to explore properties of affine and projective planes. The emphasis will be on the relationship between the number of lines and the number of points in a finite plane. We will then generalize affine space over an arbitrary field F and dimension n. The discussion of affine space will lead to a family of functions called collineations. These are the bijective functions which map any 3 points on a line to 3 points on another line. We will conclude with an attempt to classify all collineations as linear transformations up to automorphisms of the field F.
|Commitee:||Brevik, John, Murray, Will|
|School:||California State University, Long Beach|
|Department:||Mathematics and Statistics|
|School Location:||United States -- California|
|Source:||MAI 53/06M(E), Masters Abstracts International|
|Keywords:||Affine, Collineation, Projective|
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