Date of Award
Doctor of Philosophy
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.
dissertation or thesis originally submitted to the local University of Memphis Electronic Theses & dissertation (ETD) Repository.
Sahasrabudhe, Julian David Raja, "Extremal and Ramsey Problems on Graphs and the Integers" (2017). Electronic Theses and Dissertations. 1654.