Browsing Student Works by Department "Mathematics"
Now showing items 120 of 20

Coherence of triangle artin groups
(2009)Artin groups have attracted a great deal of current research due to their strong connections to geometry. We investigate the relationship of Artin groups to 3manifold groups and analyze the properties of their subgroups. 
Contact network epidemiology: Mathematical methods of modeling a mutating pathogen on a twotype network
(200805)With the threat of diseases like Sudden Acute Respiratory Syndrome (SARS) and Avian Flu that can lead to global pandemics, it is important to be able to understand how diseases spread through a population and predict how ... 
Developing scalable quartet tree encodings
(200912)Reconstructing the Tree of Life, the evolutionary history of all species, stands as one of the most significant and intensive problems in computational biology. One approach to this grand project is to use supertree ... 
Equilibrium and nonequilibrium molecular absorption: A study of the Ising Model and the infinite parking limit problem
(20121207)Randomness is present in so many everyday systems that we often forget its importance in both mathematical and chemical situations. Chemical reactions depend on random interactions and collisions, the movement of particles ... 
Even more CappellShaneson spheres are standard
(201405)This thesis examines an important problem in the field of differential topology: the 4dimensional smooth Poincaré conjecture. More specifically we analyze a class of objects known as CappellShaneson spheres and the ... 
Fiberedness of almostMontesinos knots
(201505)In this paper we begin to classify fiberedness of "AlmostMontesinos" knots, a generalization of Montesinos knots. We employ the method used in the classification of fiberedness of Montesinos knots due to Hirasawa and ... 
Global coordinate systems: Continuously moving finitedimensional unit norm tight frames on smooth manifolds
(201205)Continuously moving bases for tangent spaces of manifolds are important in the study of differential geometry and mathematical physics. However, globally continuous bases do not exist for the tangent spaces of all manifolds, ... 
Incorporating the Effects of Designated Hitters in the Pythagorean Expectation
(2015)The Pythagorean Expectation is widely used in the field of sabermetrics to estimate a baseball team’s overall season winning percentage based on the number of runs scored and allowed in its games thus far. Bill James ... 
Modeling the spread of disease through a population
(2009)As disease spreads through a population, scientists want to know who gets sick, how best to prevent a large outbreak, and if an epidemic may occur. For many years, mathematicians used models to approximate answers to ... 
Modular representations of symmetric groups
(201305)I have studied representation theory of finite groups, in particular of the symmetric group over fields of prime characteristics. Over C, there is a nice classification of the simple representations of symmetric groups. ... 
On Lfunctions and the Selberg class
(201005)The purpose of this thesis will be to explore the relationship between elliptic curves and Lfunctions. We will start o with a section giving some necessary defi nitions that will be used throughout the entire paper. ... 
On the optimal stopping of Brownian motion
(2013)In this thesis, first we briefly outline the general theory surrounding optimal stopping problems with respect primarily to Brownian motion and other continuoustime stochastic processes. In Chapter 1, we provide motivation ... 
Optimized mosquito surveillance in St. Tammany's Parish, LA
(20140502)Since its emergence in the United States in 1999, West Nile Virus has caused hundreds of deaths and has been spreading geographically. In order to efficiently control West Nile Virus outbreaks, it is necessary to monitor ... 
Parabolic Anderson Model on R^2
(2016)For my thesis project we have been studying the analysis of the parabolic Anderson model in 2 spatial dimensions on the whole plane, performed by Hairer and Labbe in early 2015. This problem is a nice example as it requires ... 
Photonic topological insulators: Building topological states of matter
(201305)The discovery of topological insulators  materials which are conventional insulators in the bulk but support dissipationless, "topologically protected" edge states  has revolutionized condensed matter physics in recent ... 
Quantum Field Theory for Homological Algebraists
(2016)The BV formalism in quantum field theory provides a homological theory of integration that can be used to compute path integrals. The present note is an overview of such ideas. Starting with a discussion of the combinatorial ... 
Simulation Controlled Seamless Phase II/III Clinical Trials
(2015)Clinical trials have become a standard part of modern medicine, creating great interest in the field of adaptive clinical trials. The goal of adaptive trials is greater efficiency in the use of patients and time, higher ... 
Statistical consistency of maximum parsimony: A 3state, 3taxa model
(2008)Phylogenetics, the study of evolutionary relationships among species, bridges numerous disciplines, notably mathematics and biology. While biologists and computer scientists might be more concerned with the net result ... 
Trapezoidality and the Alexander polynomial
(2012)We study the Alexander polynomial of a class of alternating Montesinos links, and show that this class of links satisfies a conjecture of Ralph Fox that states that alternating links have trapezoidal polynomials. 
When is a graph knotted?
(200905)Knot theory, as traditionally studied, asks whether or not a loop of string is knotted. That is, can we deform the loop in question into a circle without cutting or breaking it. In this thesis, I take a less traditional ...