Theses and DissertationsMathematics
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On Depth of Powers of Ideals
(201104)The paper “The depth of powers of an ideal," by Herzog and Hibi is expanded to include background information and proof details. The numerical function f(k)=depth(S/Ik] is discussed where S is Noetherian local or standard ... 

A Fast Solver for the Expanded Mixed Finite Element Method
(20180416)We present a fast solver for expanded mixed finite element method with a discontinuous coefficient. Our result is based on the auxiliary space preconditioning method and the CrouzeixRaviart Finite Element Method. 
Evolving Mathematical Identity for PostSecondary Students
(201805)Mathematics encompasses more than formulas, theorems and proofs. For many, mathematics can be a way of life or even a culture and like within any culture, an individual who associates with that culture has an identity: a ... 

Assessing ITP Students' Validating Ability: Framing, Developing and Validating a Pilot Assessment
(20190712)In this paper I discuss the process of creating a closedform multiplechoice assessment of students’ ability to validate mathematical proofs at the introduction to proof (ITP) level. This process involved: (1) creating ... 
Chinese middle school mathematics teachers' pedagogical content knowledge and cultural beliefs towards teaching
(20190426)This study investigated the pedagogical content knowledge and cultural beliefs towards teaching of middle school mathematics teachers in Shandong, China. The study illustrates how four middle school mathematics teachers ...

A new 5step perturbationbased multicollinearity diagnostic package
(20190416)The ordinary least squares method, for estimating unknown parameters of a multiple linear regression (MLR) model, produces an idealistic solution if the column vectors (regressors) of the design matrix X are linearly ... 
Chipfiring on graphs: stability, the dollar game, and the Tutte polynomial
(20190416)No abstract prepared. 
Using Knot Theory to Model and Analyze DNA Replication and Recombination
(201811)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 ... 
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 ... 

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 ... 
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 ... 
Investigating How an Informal 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 ... 
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 ...