Boston University. University Professors Program Senior theses. / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / 2031-01-02

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Univ., Diss.--Göttingen, 2004.

Zugl.: Heidelberg, Univ., Diss.

Recent work on many problems in additive combinatorics, such as Roth's Theorem, has shown the usefulness of first studying the problem in a finite field environment. Using the techniques of Bourgain to give a result in other settings such as general abelian groups, the author gives a walk through, including proof, of Roth's theorem in both the one dimensional and two dimensional cases (it would be more accurate to refer to the two dimensional case as Shkredov's Theorem). In the one dimensional case the argument is at its base Meshulam's but the structure will be essentially Green's. Let Ϝⁿ [subscript p], p ≠ 2 be the finite field of cardinality N = pⁿ. For large N, any subset A ⊂ Ϝⁿ [subscript p] of cardinality ∣A ∣≳ N ∕ log N must contain a triple of the form {x, x + d, x + 2d} for x, d ∈ Ϝⁿ [subscript p], d ≠ 0. In the two dimensional case the argument is Lacey and McClain who made considerable refinements to this argument of Green who was bringing the argument to the finite field case from a paper of Shkredov. Let Ϝ ⁿ ₂ be the finite field of cardinality N = 2ⁿ. For all large N, any subset A⊂ Ϝⁿ ₂ × Ϝⁿ ₂ of cardinality ∣A ∣≳ N ² (log n) − [superscript epsilon], ε <, 1, must contain a corner {(x, y), (x + d, y), (x, y + d)} for x, y, d ∈ Ϝⁿ₂ and d ≠ 0.

Thesis (M.A.)--University of North Carolina at Wilmington, 2003. / Includes bibliographical references (leaves : [41]-42).

Thesis (M.A.)--Kutztown State College. / Source: Masters Abstracts International, Volume: 45-06, page: 2830. Typescript. Abstract precedes thesis as preliminary leaves. Includes bibliographical references (leaves [138]-142).

This thesis takes as its focus several works in the late period of Philip Roth’s writing and examines the way in which these particular texts address issues of American national experience since the Depression. In particular, this study looks at Roth’s assessment of a distinctly modern liberal vision that came to prominence during the 1930s and was to dominate American political and cultural life until the late 1960s. In thus covering the wider historical sweep of these novels, the research will draw attention to the way in which such broader matters of American cultural and political life intersect with more local issues of Jewish-American subjectivity and literary style that have been explored recurrently throughout Roth’s greater body of fiction. This study thus aims to show how the more recent ‘historical turn’ in Roth’s novelistic focus is in fact consistent with certain pivotal themes that have helped to define his overall development as a writer.

Thesis (M.A.)--University of Missouri-Columbia, 2007. / 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 November 5, 2007) Includes bibliographical references.