Electronic Theses and Dissertations

Identifier

4953

Date

2017

Date of Award

4-19-2017

Document Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematical Sciences

Concentration

Mathematics

Committee Member

Bela Bollobas

Committee Member

Paul Balister

Committee Member

Mate Wierdl

Abstract

The foundational belief that guides the work in this dissertation is that the pursuit of questions that are the most "basic" or "simply put" will ultimately lead to the greatest impact and application within and beyond mathematics. The reader shall see that we study only the most basic objects (finite sets of integers, finite sets of unordered pairs, colourings of the integers) and that the questions we consider assume very little about the underlying system that we study; we often assume only that our systems are "large", "dense" or do not contain a given substructure.

Comments

Data is provided by the student.

Library Comment

dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.

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