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ThesisHermiz, RaniThe SPHAERICA (in English: Spherics) of Menelaus of Alexandria (dating to roughly 100 AD) is among the oldest known works on spherical geometry and trigonometry. Spherical geometry is the study of geometric objects on the surface of a sphere and spher . . .

ThesisWilson, Jason RA major part of topology is the study of properties of topological spaces that are invariant under homeomorphisms. Such properties allow us to classify spaces. Some basic examples are compactness and connectedness. Although quite useful, these propert . . .

ThesisTimmons, CraigThe focus of this thesis is star coloring planar graphs. A star coloring of a planar graph is a proper coloring in which no path on four vertices is colored with just two colors. A graph G is said to be kstarcolorable if G has a star coloring with a . . .

ThesisStewart, MaryIn this thesis, we study finite simple groups as well as the Classification Theorem, which classifies all such groups. We will see by the Classification Theorem that all simple groups are one of the following four types: cyclic of prime order, alterna . . .

ThesisSanders, GinaIn this thesis, we investigate a coloring problem on a special class of graphs. A proper coloring of a graph is a coloring of the vertices of the graph so that vertices joined by an edge get different colors. A starcoloring of a graph is a proper col . . .

ThesisMelcher, MichaelA monochromatic sink in an arccolored tournament is a vertex that can be reached by every other vertex in the tournament by a monochromatic path. A rainbow k cycle in an arccolored tournament is a cycle with k arcs such that no two arcs in the cycl . . .

ThesisLovelace, Joshua WalterThis thesis will briefly go over definitions and properties of continuous time Markov chains and describe the definition of reversibility and conditions for positive recurrence. We then discuss the evolution of the Markov chains studied in [12] which . . .

ThesisJones, Jessica MThe focus of this thesis is to use Galois Theory to prove results in Number Theory. As a result, we begin by familiarizing ourselves with some significant results in Galois Theory. We then proceed to discuss other pertinent results in Algebraic Number . . .

ThesisEddo, Timothy JComputing the k dominant singular values of a matrix A by computing the singular value decomposition may require an exorbitant amount time when A is large sparse and rectangular. Instead, the iterative Lanczos method may be used to compute a partial t . . .

ThesisSastre, IaneThis work is based on the article" A Guide to Entropy and the Second Law of Thermodynamics" [1] by E. H. Lieb of Princeton University and J. Yngvason of Vienna University. The article appeared on the May 1998 issue of Notices of the American Mathemati . . .

ThesisOrloff, Mai TThis thesis examines methods to estimate errors of calculated solutions of linear systems. These methods include the traditional condition number, Skeel's condition numbers, and Chandrasekaran and Ipsen's component condition numbers. The thesis concen . . .

ThesisBuchwald, Charles ThomasThis thesis involves the study of a two person game played on a tournament and some results concerning the topic of score sets for tournaments. A goal, in studying the game, is to determine if winning strategies for the game exist and if so, for which . . .

ThesisAlidaee, BahramWe discuss the generalized Davidson's algorithm for computing accurate approximations of the k principal eigenpairs of a large, sparse, and symmetric n x n matrix. Our implementation of the iterative algorithm in the Matlab language is based on the ps . . .

ThesisBotica, JoshuaLittle’s law arises naturally in the modeling and analysis of queueing systems. It relates the long run average number of items in an inputoutput system to the long run average time spent in the system by each item. It is given implied validity and j . . .

ThesisLi, YuanThe business of Reaction Network Theory is to model and study the dynamical properties of biochemical processes and certain biological systems such ecological dynamics and spread of epidemics. When large number of reactants are present, a system of OD . . .

ThesisMulvany, JustinA multiclass processor sharing queue consists of a single server and a buffer that contains jobs that require service. At each time, the server simultaneously processes the work associated with each job in the buffer at a rate equal to the reciprocal . . .

ThesisNewberg, StevenA moduli problem seeks to find a bijection between a class of objects and a topological space that describes the parameters of the class of objects. We will present the moduli problem for a type of curve used in cryptography, elliptic curves. The topo . . .

ThesisMartinez, MarthaThe purpose of this paper is to utilize algebraicgeometric ideas in the study of polynomials for which the associated polynomial functions are permuta tions of a given finite field. Polynomials of this type are called permutation polynomials. Due to . . .

ThesisSantana, MichaelThis thesis focuses on two ideas in tournament theory: cycle intersections in tournaments (i.e., intersection spectra of tournaments) and some work done on score sequences of tournaments. Chapter 2 deals with the intersection spectrum of a specific fa . . .

ThesisKnapp, Randall GThis is a survey of various results concerning the extremity of graphs and digraphs. Given a graph, there are various subsets of the vertex set that can be interpreted as the "extremity of the graph"; we investigate several of these: the periphery, th . . .

ThesisHultman, JasonHospital emergency room patients often experience lengthy delays while waiting for an open bed and treatment. Some patients become frustrated and leave without being seen, which results in lost hospital revenue. Hospital administrators are responding . . .

ThesisMariscal, EduardoThe thesis goal is to prove unique prime factorization (UPF) for ideals in a cyclotomic integers in the most elementary and efficient way. This way it can later be formally verified. The reason is to help prepare a formal verification of Fermat's Last . . .

ThesisBrich, JenniferThis thesis focuses on the formalization of basic topics in commutative algebra using the proof assistant Isabelle. This written exposition will provide an overview of the work that was completed to formalize the following objectives in Isabelle: 1. D . . .

ThesisReeves, TonyaA repetition is a sequence of symbols in which the first half is the same as the second half. An edgecoloring of a graph is repetitionfree if there is no path with a color pattern that is a repetition. The minimum number of colors so that a graph ha . . .

ThesisShinsato, TinaOver the past century golf has become an obsession among many Americans. With the popularity of any sport, the opportunity to gamble will usually follow. It is clear that a matchup between a casual golfer and an avid golfer would not be fair. Therefo . . .

ThesisSpangler, MeganWe start by familiarizing ourselves with edge covers. We review several interesting results for covers using triangles and covers using cycles. We then consider covering a graph with cuts. Determining the minimum total number of edges in a cut cover o . . .

ThesisPatno, Janina Silvana PWe consider the problem of sending a message in a communication network. Our networks are modeled by graphs. In our graphs we want to send a message from a vertex s, the sender, to a vertex r, the receiver, via paths from s tor. One difficulty we may . . .

ThesisMercado, SerenaThis thesis focuses on pricing derivatives securities such as stock options in incomplete financial markets. The goal is to determine arbitrage free prices for these securities. For this we consider a finite state, discrete time stochastic model of a . . .

ThesisMay, BrianThis paper begins with a brief discussion of algebraic geometry. Elliptic curves are algebraic varieties of genus one. We conclude the discussion of algebraic geometry with the definition of a function field. We then define an elliptic curve and prese . . .

ThesisAlAzem, KassemThis presentation has two main parts. In the first part we start with introducing an extension of the Schwarz lemma, called the SchwarzPick lemma, in the complex plane. We then define a special type of automorphism, called the Mobius transformation, . . .

ThesisBobkoski, CarlGeneticists wish to pairwise align protein sequences in order to determine if the two sequences have a similar function. This thesis explains the use of hidden Markov models (HMM's) in the pairwise alignment of protein sequences. The pairwise alignmen . . .

ThesisToole, AlexA repetitionfree coloring of a graph is a coloring of its vertices such that there are no paths for which the color pattern on the first half is repeated on the second half. The Thue chromatic number of a graph is the minimum number of colors require . . .

ThesisTalsania, BhavishaThis thesis discusses the formalization of basic results from linear algebra up to the following theorems, using the computer proof checker Isabelle. Chapter 1 provides a discussion of informal and formal proofs and an introduction to the thesis topic . . .

ThesisChen, LixianThis thesis examines the predatorprey models with harvesting of the prey. We first introduce the basic LotkaVolterra predatorprey model and then discuss different harvesting strategies. Then we focus on two types of harvesting functions, and combin . . .

ThesisCuriel, NemoThis thesis focuses on formalizing results involving automorphism groups of fields using the proof assistant Isabelle. Chapter 1 serves as an introduction to the thesis topic and includes a short history of computer proof assistants. In Chapter 2, we . . .

ThesisHernandez Hernandez, JesusThis thesis explores bond percolation on rary trees and then moves on to 3regular infinite trees. The last chapter explores bond percolation on the square lattice where horizontal bonds are open in a periodic fashion.

ThesisCaldwell, James DavidThis paper examines the problem of rank ordering a set of players or objects on the basis of a tournament arising from a complete set of pairwise comparisons.

ThesisSingh, LeenaDigitized as part of the "Retrospective Thesis and Dissertation Project." No abstract is available.

ThesisEllinger, Paul NDigitized as part of the "Retrospective Thesis and Dissertation Project." No abstract is available. Item only available to the CSUSM community. Authentication with campus user name and password required.

ThesisLarson, Gregory SDigitized as part of the "Retrospective Thesis and Dissertation Project." No abstract is available.

ThesisMcNulty, AnneThis paper begins with the definition of an elliptic curve. We define the group law on elliptic curves and discuss methods for finding points on elliptic curves. We discuss torsion points and the use of division polynomials to calculate them. We inves . . .

ThesisDePalma, Eli DDigitized as part of the "Retrospective Thesis and Dissertation Digitization Project." No abstract is available.

ThesisSafaralian, LeilaDigitized as part of the "Retrospective Thesis and Dissertation Digitization Project." No abstract is available.

ThesisDamon, Linn EDigitized as part of the "Retrospective Thesis and Dissertation Digitization Project." No abstract is available.

ThesisDunbar, Keith AllanDigitized as part of the "Retrospective Thesis and Dissertation Digitization Project." No abstract is available.



ThesisWilson, Jason RA major part of topology is the study of properties of topological spaces that are invariant under homeomorphisms. Such properties allow us to classify spaces. Some basic examples are compactness and connectedness. Although quite useful, these propert . . .

ThesisVargas, BrianA search engine is intended to crawl the world wide web and retrieve a list of sites that match the user's search terms. Listing the search results in a proper order is crucial but it is far from being a trivial task. Prior to the rise of Google, sear . . .

ThesisStewart, MaryIn this thesis, we study finite simple groups as well as the Classification Theorem, which classifies all such groups. We will see by the Classification Theorem that all simple groups are one of the following four types: cyclic of prime order, alterna . . .