Theses and DissertationsMathematics
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Using Knot Theory to Model and Analyze DNA Replication and Recombination
(20181113)Due to DNA supercoiling inside the nucleus of a cell, DNA can be modeled as a mathematical knot. We will analyze and examine the knots and links that arise after single or multiple rounds of DNA recombi nation using the ... 
Bounding the Index of a Normal Subgroup with a large class size
(20180409)No abstract prepared. 
Orbit Sizes and a New Classification of the Dihedral Group of Order Eight
(20180418)No abstract prepared. 
Motivation Intervention Through Calculus Tasks with Science and Engineering Applications
(20180420)Although national interest has been focused on increasing STEM graduates, calculus courses still pose a challenge for most STEM major students. As recent statistics show, only half of the students are successful in calculus ... 
A Solid Object Floating in a Bath of Three Fluids
(20180420)We consider a bounded container filled by three immiscible fluids and a solid object, presumably floating at one or more of the interfaces. Fluids are modeled by Caccioppoli sets. The energy in our model is assumed to come ... 
Kernel Estimation of Probability Density Functions for Intervalcensored Sexually Transmitted Disease Data with Diary Information
(20180420)The purpose of this study is to propose a method to reliably estimate the survival function of the true infection time of a sexually transmitted disease (STD) based on intervalcensored data with diary information. The ... 

Investigating How an Informal Summer Program Sustains Teachers in Their Profession
(20180720)Teacher turnover is a significant problem in the United States. Research has examined how to retain teachers through teacher induction and continuing education programs, mentoring, and building a supportive community and ... 
Numerical Approach to Energy Minimization of Fluid Configurations Using PhaseField Models
(20180723)We consider a fluid, under isothermal conditions and confined to a bounded container of homogeneous makeup, whose Gibbs free energy, per unit volume, is a prescribed function of its density distribution. Based on the Van ... 
Bruhat Order and Coxeter Hyperplane Arrangements
(20180720)In the paper “Bruhat order, rationally smooth Schubert varieties, and hyperplane arrangements,” S. Oh and H. Yoo studied Schubert varieties in generalized flag manifolds by linking them with a certain hyperplane arrangement ... 
Aspects that Arise in the Transition from the Montessori Method to a Traditional Method: A Fourth Grade Mathematics View
(20170725)The purpose of the dissertation is to investigate three particular aspects that may affect the transition between a third grade Montessori system and a fourth grade nonMontessori system, specifically within the context ... 
Estimation of Survival Function for Intervalcensored Sexually Transmitted Disease Data.
(20160422)Attention often pivots on the distribution of the sexually transmitted disease (STD) true infection time based on intervalcensored event time data. It occurs in biological and medical studies such as medical followup ... 
Creating a pathway to STEM: Role of an informal mathematics program
(20160707)This dissertation presents the findings of a singlesite, qualitative, embedded case study involving four former (1990 – 2008) participants of an informal math program in US. The purpose of this study is to describe in my ... 
Computation of Liquid Drops Geometry with Motion of the Contact Curves
(20170725)This paper covers the modeling of homogenous liquids adhering to a uniform solid surface. It is divided into two separate problems: the sessile drop on a horizontal plane, and the liquid bridge between two horizontal planes ... 
The Double Sessile Drop
(20170711)We consider the double sessile drop, which is formed of two connected drops of liquid with prescribed volumes V1 and V2 resting in equilibrium on a horizontal plane P in a vertical gravity field directed toward P. We suppose ... 
Numerical Solutions to Poisson's Equation Over NonUniform Discretizations with Associated Fast Solvers
(20170419)Partial differential equations (PDE's) lay the foundation for the physical sciences and many engineering disciplines. Unfortunately, most PDE's can't be solved analytically. This limitation necessitates approximate solutions ... 
A Characterization of Oriented Hypergraphic Laplacian and Adjacency Coefficients and Minors
(20170420)No abstract prepared. 
Cultivating Mathematical Affections: Developing a Productive Disposition through Engagement in ServiceLearning
(20170320)This research explores the impact of servicelearning on the affective outcomes of secondary mathematics curricula. This was a qualitative case study of high school students who recently completed a servicelearning project ... 
Is Tutoring Teaching? Exploring Tutoring's Potential to Improve Mathematics Teacher Education
(20170424)This study investigated the tutoring practices of mathematics tutors working in one university tutoring center and the corresponding rationale exhibited by the mathematics tutors. This study illustrates how the tutoring ... 
Identifying Developmental Levels and Learning Trajectories in Statistics for Grade 612 Students
(20130712)Since the early 80s, reform movements have recommended increasing the content and rigor of statistics in school mathematics curriculum. Two important curriculum documents, the Guidelines for Assessment and Instruction in ...