Electronic Dissertations and Theses  Mathematics
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This collection contains theses and dissertations by students in the Department of Mathematics and Statistics at Washington State University.
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High School Student Representational Adaptivity and Transfer in Multiplying Polynomials
(2018)While there is an extensive amount of research on representations for solving problems involving functions, there are few studies on high school student use of multiple representations for multiplying polynomials. This ... 
MATHEMATICAL MODELING AND BAYESIAN PARAMETER ESTIMATION IN CANCER
(2018)Recent works have highlighted the role of the differentiation of fibroblast into myofibroblast in cancer initiation and progression. Fibroblasts respond in a variety of ways to concentrations of activated transforming ... 
Median Shapes
(2018)In this paper, we generalized the variational definition of median numbers to median shapes. We represent shapes with currents and use flat norms as the distances between currents. Under this setting, the median shapes ... 
Stability Analysis, Convex Hulls of Matrix Powers and their Relations to Pmatrices
(2018)Invertibility of all convex combinations of an $n\times n$ matrix $A$ and the $n\times n$ identity matrix $I$ is equivalent to the real eigenvalues of $A$, if any, being positive. Moreover, invertibility of all matrices ... 
Boundary Measures and Cubical Covers of Sets in R^n
(2018)The art of analysis involves the subtle combination of approximation, inequalities, and geometric intuition as well as being able to work at different scales. Even the restriction to sets in R^n affords us the opportunity ... 
Examining Student Agency in an ActiveLearning Business Calculus Course
(2017)This study explored student agency in an activelearning business calculus course. The lecturestyle instructional practices typically used in this course at this institution allow few opportunities for students to interact ... 
AN ENERGYBASED INTERACTION MODEL FOR POPULATION OPINION DYNAMICS WITH TOPIC COUPLING
(2017)Opinion dynamics, also called the opinion game, has gained a great deal of attention during past several decades. It tries to model and explain the evolution of opinions of people in a society. How individuals learn, how ... 
Eventual Cone Invariance
(2017)If $K$ is a proper cone in $\RR^{n}$ some results in the theory of eventually (entrywise) nonnegative matrices have equivalent analogues in eventual $K$invariance. We develop these analogues using the classical ... 
Studying and supporting the teaching practice of calculus teaching assistants
(2017)Graduate teaching assistants (TAs) are an important group of math instructors whose practice deserves to be supported and studied. In this action research study, I lead a customized regimen of professional development ... 
Portfolio Optimization on Jump Diffusion
(2016)Portfolio optimization problem is an important research topic in financial applications. In this research, we focus on a consumption process and a terminal wealth problem. A portfolio including a riskless asset, a zero ... 
On the computation of eigenvalues, spectral bounds, and Hessenberg form for matrix polynomials
(2016)In this dissertation we focus on rootfinding methods, such as Laguerre's method, for solving the polynomial eigenvalue problem. Serious consideration is given to the initial conditions and stopping criteria. Cost efficient ... 
Interior Point Algorithms for Stochastic Semidefinite Programming
(2016)Twostage stochastic semidefinite programming with recourse (SSDP) has been proposed and studied during the last 10 years, as a twostage stochastic counterpart of semidefinite programming (SDP). To design efficient ... 
Identification and Establishment of Social and Sociomathematical Norms Associated with Mathematically Productive Discourse
(2016)For some time, the mathematics education community has sought to involve students more actively in classroom mathematical discourse, but realizing this goal has been problematic. This study has two goals: the first is to ... 
Numerical Methods for American Option Pricing with Nonlinear Volatility
(2015)Options are a fundamental and important type of financial derivatives with stocks as the underlying asset. Investors frequently trade options, making option pricing an important research area in both finance and applied ... 
First Collegiate Mathematics Grade and Persistence to Graduation in STEM
(2015)This study explores the relationship between college students’ first mathematics course and persistence to graduation with a bachelor’s degree in a Scientific, Technical, Engineering, or Mathematical (STEM) field. Half of ... 
On alphacritical graphs and their construction
(2015)A graph G is alphacritical (or removalcritical) if alpha(Ge)=alpha(G)+1 for all edges e in E(G), where alpha(G) is the vertex independence number of G. Similarly, a graph G is contractioncritical if alpha(G\setminus ... 
Pattern formation properties of a system of interactiondiffusion equations relevant to a musselalgae ecosystem in a quiescent marine layer
(2014)A particular interactiondiffusion musselalgae model system for the development of spontaneous stationary young mussel bed patterning on a homogeneous substrate covered by a quiescent marine layer containing algae as a ... 
Mathematical models of immersed boundary complex fluids
(2014)A major research interest in recent computational rheology has been on modeling complex biological fluid and fluidstructure interaction. With considerable progress in formulating methods for Newtonian fluids and given the ... 
GPU Accelerated Polynomial Spectral Transformation Methods
(2014)A new class of methods for accelerating linear system solving and eigenvalue computations for positive definite matrices using GPUs is presented. This method makes use of techniques from polynomial approximation theory to ... 
Applications of Generalized Laplacian Matrices in Graph Tiling
(2014)This dissertation is an examination of how generalized Laplacian matrices (in particular, their determinants) may be useful in determining graph tilings. Since there is a very strong connection between the generalized ...