Browsing by Subject "Washington and Lee University -- Honors in Mathematics"
Now showing items 1-20 of 30
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An Elementary Theorem-Proving Program
My goal is to write a theorem-proving assistant that can , to s ome extent, take a hypothesis (that works on IF-THEN rules) and make some progress toward a realizable goal. However, since I need a more concrete problem ... -
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 ... -
Chaos and Linearity
Mathematically, one may define chaos in relation to the behavior of discrete dynamical systems, i.e., the behavior of operators (functions) under iteration. R. Devaney, in his book An Introduction to Chaotic Dynamical ... -
Chaos and the Dynamics of Quadratic Mappings
The immediate aim of this paper is to systematically investigate dynamical systems governed by a certain class of difference equations. The results obtained do not, however, constitute an isolated piece in a sprawling ... -
Compressing Operators to Obtain Single-Point Numerical Ranges
We are all familiar with vector spaces and their basic properties. We understand linear operators, dot products, and maybe even norms. What the reader may not be as familiar with, however, is the concept of numerical range. ... -
Compressions of Linear Operators Yielding a Single Point Numerical Range
This thesis will focus on finding subspaces M such that the compression of T to M, denoted TM, has a single point numerical range. . . . The motivation for finding such subspaces lies in a theorem from quantum coding ... -
Differential Hyperbolic Geometry
In this paper, we develop two model spaces for hyperbolic geometry using differential calculus. Our approach is to first develop the Euclidean model space R[2] and then mirror the development for hyperbolic geometry. The ... -
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. ... -
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 ... -
Julia Sets: An Introduction to Chaos in the Plane
In this paper we introduce the reader to a family of functions which give rise to Julia sets. Making their home in the complex plane, these sets exhibit many interesting properties, including chaotic dynamics . The aesthetic ... -
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 lambda-property in Schreier space S and the Lorentz space d(a, 1)," Th. Shura and D. ... -
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 ... -
Norms of Composition Operators on the Hardy Space
This thesis covers Hilbert spaces, Hardy spaces, their properties, and composition operators. -
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, ... -
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 3-runs ... -
Rado's Selection Principle: Equivalences and Applications
Rado's Selection Principle is a combinatorial theorem which allows the characterization of infinite objects (e.g. graphs, groups, partially-ordered sets) based on the characterization of their finite subparts. That is, a ... -
Realizability of n-Vertex 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] -
Realizability of n-Vertex 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 n-Vertex Graphs with Prescribed Vertex Connectivity, Edge Connectivity, Minimum Degree, and Maximum Degree. ...