Explorations of geometric combinatorics in vector spaces over finite fields

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file (viewed on June 8, 2009)Vita.Thesis (Ph. D.) University of Missouri-Columbia 2008.We study how large a set of points needs to be in a vector space over a finite field in order for the points to determine all of a certain type of geometric structure. In addition we show that there are key differences between the finite field version of these questions and the corresponding euclidean versions. Several arithmetic consequences are also explored.Includes bibliographical reference