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dc.contributor.advisorIosevich, Alex, 1967-en_US
dc.contributor.authorCovert, David
dc.contributor.otherUniversity of Missouri-Columbia. Graduate School. Theses and Dissertations. Dissertations. 2011 Dissertationsen_US
dc.date.issued2011
dc.date.submitted2011 Springen_US
dc.descriptionTitle from PDF of title page (University of Missouri--Columbia, viewed on October 18, 2012).en_US
dc.descriptionThe entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.en_US
dc.descriptionDissertation advisor: Dr. Alex Iosevichen_US
dc.descriptionIncludes bibliographical references.en_US
dc.descriptionVita.en_US
dc.descriptionPh. D. University of Missouri--Columbia 2011.en_US
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Mathematicsen_US
dc.description"May 2011"en_US
dc.description.abstractThis thesis is a compilation of work in which the author studies geometric configurations in finite fields and the integers modulo q. The results of this dissertation are threefold. First, we prove a finite field analog of the Furstenberg-Katznelson-Weiss theorem on triangles in R2. Second, we study volume sets in Fd/q and discuss some applications to sum-product problems. Finally, we study geometric combinatorics in Z/qZ. We generalize a result of Hart and Iosevich [27] which has applications to sum-product problems. Finally, we show that the Zd/q analogue of a sphere with unital radius is qd−1-dimensional.en_US
dc.format.extentv, 52 pagesen_US
dc.identifier.otherCovertD-042011-D5439
dc.identifier.urihttp://hdl.handle.net/10355/15768
dc.publisherUniversity of Missouri--Columbiaen_US
dc.relation.ispartof2011 Freely available dissertations (MU)en_US
dc.subjectgeometric combinatoricsen_US
dc.subjectfinite fieldsen_US
dc.subjectsum-product problemen_US
dc.titleGeometric combinatorics in discrete settingsen_US
dc.typeThesisen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineMathematicseng
thesis.degree.grantorUniversity of Missouri--Columbiaen_US
thesis.degree.levelDoctoralen_US
thesis.degree.namePh. D.en_US


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