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dc.contributor.advisorIosevich, Alex, 1967-eng
dc.contributor.authorCovert, Davideng
dc.date.issued2011eng
dc.date.submitted2011 Springeng
dc.descriptionTitle from PDF of title page (University of Missouri--Columbia, viewed on October 18, 2012).eng
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.eng
dc.descriptionDissertation advisor: Dr. Alex Iosevicheng
dc.descriptionIncludes bibliographical references.eng
dc.descriptionVita.eng
dc.descriptionPh. D. University of Missouri--Columbia 2011.eng
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Mathematicseng
dc.description"May 2011"eng
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.eng
dc.format.extentv, 52 pageseng
dc.identifier.oclc872560909eng
dc.identifier.otherCovertD-042011-D5439eng
dc.identifier.urihttp://hdl.handle.net/10355/15768eng
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcollectionUniversity of Missouri--Columbia. Graduate School. Theses and Dissertations.eng
dc.subjectgeometric combinatoricseng
dc.subjectfinite fieldseng
dc.subjectsum-product problemeng
dc.titleGeometric combinatorics in discrete settingseng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


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