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On Cup-Products Of Cofibers Of Maps Between Moore Spaces, Hopf Invariant, And Lusternik-Schnirelmann Category, Marwa A.S. Mosallam

Masters Theses

In this thesis we make a detailed investigation of the cohomology rings of the cofibers C_β of Moore spaces of dimension 2 by computing the cup products in cofibers and to do so we prove that the Hopf invariant in case of Moore spaces in the zero and nonzero homomorphism case is a homomorphism. We have shown when is 𝓍_r,_k a Co-H-Map. We calculated the homologies and cohomologies of Moore spaces of dimension 2 and of the cofibers C_β where β=𝓍_r,k. We used Lusternik-Schnirelmann category to determine the complexity of C …

Characterizing Undergraduate Students’ Proving Processes Around “Stuck Points”, Yaomingxin Lu

Dissertations

Learning to prove mathematical propositions is a cornerstone of mathematics as a discipline (de Villiers, 1990). However, since proving is a different mathematical activity as compared to students’ prior experience, research has also shown that many undergraduate students struggle to learn to prove, including those who major in mathematics (Moore, 1994; Selden, 2012). While the field has generated research that has analyzed the final products of proof (Selden & Selden, 2009) and there are frameworks for analyzing problem-solving processes (e.g., Carlson & Bloom, 2005; Schoenfeld, 1985, 2010), much remains to be known about analyzing undergraduate students’ proving processes. With a …

Dominating Functions In Graphs, Maria Talanda-Fisher

Dissertations

Domination in graphs has become one of the most popular areas of graph the- ory, no doubt due to its many fascinating problems and applications to modern society, as well as the sheer mathematical beauty of the subject. While this area evidently began with the work by the French mathematician Claude Berge in 1958 and the Norwegian-American mathematician Oystein Ore in 1962, domination did not become an active area of research until 1977 with the appearance of the survey paper by Ernest Cockayne and Stephen Hedetniemi. Since then a large number of variations of domination have surfaced and provided numerous …

From Multi-Prime To Subset Labelings Of Graphs, Bethel I. Mcgrew

Dissertations

A graph labeling is an assignment of labels (elements of some set) to the vertices or edges (or both) of a graph G. If only the vertices of G are labeled, then the resulting graph is a vertex-labeled graph. If only the edges are labeled, the resulting graph is an edge-labeled graph. The concept was first introduced in the 19th century when Arthur Cayley established Cayley’s Tree Formula, which proved that there are n^n-2 distinct labeled trees of order n. Since then, it has grown into a popular research area.

In this study, we first review several types …

On Problems In Random Structures, Ryan Cushman

Dissertations

This work addresses two problems in optimizing substructures within larger random structures. In the first, we study the triangle-packing number v(G), which is the maximum size of a set of edge-disjoint triangles in a graph. In particular we study this parameter for the random graph G(n,m). We analyze a random process called the online triangle packing process in order to bound v(G). The lower bound on v(G(n,m)) that this produces allows for the verification of a conjecture of Tuza for G( …