W&L Dept. of Mathematics
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This collection contains the scholarship of students in the W&L Dept. of Mathematics.
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Recent Submissions

On the Realizability of Projective Configurations (thesis)
Many natural questions emerge from the work of this thesis. The first chapter may inspire a budding mathematician to work (in the fashion of my thesis advisor) on area relations and equidissections. From the second chapter, ... 
Linear Algebraic Methods in Data Science and Neural Networks (thesis)
This thesis is about some of the methods and concepts of linear algebra that are particularly helpful for data analysis. After a brief review of some linear algebra concepts in chapter 1, the second chapter of the thesis ... 
The Lambda Property and Isometries for Higher Order Schreier Spaces (thesis)
For each n in N, let Sn be the Schreier set of order n and XSn be the corresponding Schreier space of order n. In their 1989 paper "The lambdaproperty in Schreier space S and the Lorentz space d(a, 1)," Th. Shura and D. ... 
Realizability of nVertex Graphs with Prescribed Vertex Connectivity, Edge Connectivity, Minimum Degree, and Maximum Degree (thesis)
This is the fourth and nal thesis that concludes ProfessorWayne M. Dymacek's research project Realizability of nVertex Graphs with Prescribed Vertex Connectivity, Edge Connectivity, Minimum Degree, and Maximum Degree. ... 
Upgrowing Online Linear Discrepancy of Tripleoptimal Partially Ordered Sets (thesis)
Whether we acknowledge it as a poset or not, posets arise in many natural contexts, and many also seem to warrant linear extensions (or rankings) of the poset. In some sense, the linear discrepancy of a linear extension L ... 
Exploring Extreme Points and Related Properties of Tsirelson Space (thesis)
Tsirelson space was constructed in 1974 as the first example of a Banach space without an embedded c0 or lp space. In 1989, Casazza and Shura wrote a book Tsirelson's Space devoted to Tsirelson space and its many properties. ... 
Realizability of nVertex Graphs with Prescribed Vertex Connectivity, Edge Connectivity, Minimum Degree, and Maximum Degree (thesis)
Our work continues a long tradition in graph theory studying the relation ship between vertex connectivity, edge connectivity, and minimum degree. [From Introduction] 
Towards an Automated and Customizable Linear Cryptanalysis of SubstitutionPermutation Network Cipher (thesis)
The increasing scale of the Internet of Things exposes the proprietors and users to a number of security threats in terms of invasion of privacy, identity thefts and the like. It is therefore absolutely necessary that the ... 
Periods of Linearly Recurring Sequences (thesis)
In this thesis, we investigate sequences defined by linear recurrence relations. These are sequences whose subsequent terms are generated using some linear combination of the previous terms. We call the equation that ... 
Permutation Formula (thesis)
Runs in permutations and similar topics have been studied by various authors under different names. Hegarty examined permutations of finite abelian groups which avoid what he called progressions. Riordan studied 3runs ... 
Finding Cycles In The Kth Power Diagraphs Over Integers Modulo A Prime And Over Gaussian Integers Modulo a Gaussian Prime (thesis)
Given Zp where p is an integer prime, let's de ne G(k) p to be the digraph whose set of vertices is Zp such that there is a directed edge from a vertex a to a vertex b if ak b mod p. First, we nd our own way to decide ... 
Arithmetic Progressions in Permutations (thesis)
In this thesis we will examine progressions in permutations. We will analyze regular and circular permutations with progressions either modular or regular with rise one or two. We will calculate the number of permutations ... 
Steinhaus Graphs and Pendent Vertices (thesis)
Steinhaus graphs have many interesting properties, yet there are many things about them that are not yet known. In [1], a formula was discovered for the total number of Steinhaus graphs on 11 vertices with at least one ...