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 ... 
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 ... 
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 ... 
TAIL DENSITIES OF COPULAS AND THEIR APPLICATIONS TO EXTREMAL DEPENDENCE ANALYSIS OF VINES
(2013)Extreme events occur everywhere, and analyzing impacts of these events becomes fundamentally important in many areas such as financial risk management, electrical grid reliability analysis, and environmental impact assessment. ... 
Simplicial Complexes and the Optimal Homologous Chain Problem
(2013)This dissertation examines topological properties of a finite simplicial complex 
COMPUTATION OF MULTIVARIATE NORMAL PROBABILITIES USING BIVARIATE CONDITIONING WITH SIMULATION
(2013)We introduce algorithms for block LDL^{t} decompositions of positive definite covariance matrices. These are extensions of the LDL^t decomposition which requires D to be a diagonal matrix. We make use of these algorithms ... 
A Method of Applying an Unbiased Estimator for Monitoring the Weibull Shape Parameter and TimetoEvent Model Using Copula with Accelerated Life Testing
(2013)Two topics are discussed in this dissertation. In chapter 1, we introduce a method for monitoring the Weibull shape parameter beta without specifying the values of nuisance parameters. The control limits depend on the ... 
Matrix Roots of Nonnegative and Eventually Nonnegative Matrices
(2013)Eventually nonnegative matrices are real matrices whose powers become and remain nonnegative. As such, eventually nonnegative matrices are, a fortiori, matrix roots of nonnegative matrices, which motivates us to study the ... 
ASYMPTOTIC ANALYSIS AND BOUNDS OF MULTIVARIATE COHERENT RISK
(2012)A central topic in modern financial and insurance mathematics is the search for new methods to estimate extreme risk (or tail risk) for multivariate financial assets. This research targets this fundamental question about ... 
Experimental investigations of a proposed chromophore correlation model of self healing of Disperse Orange 11 doped in Poly (methyl methacrylate)
(2012)We studied photodegradation and recovery of amplified spontaneous emission (ASE) in Disperse Orange 11 dye doped in Poly(methyl methacrylate)(PMMA) as a function of dye concentration and sample temperature. A simple ... 
EIGENSPACES OF TOURNAMENT MATRICES
(2012)In this dissertation we investigate the eigenspaces of tournament matrices. These matrices (and their generalizations) appear in a variety of combinatorial applications (e.g., in biology, sociology, statistics, and networks); ... 
Recurrence Representations
(2012)A new method of representing positive integers using recurrence sequences, related to tiling a 1 x n board, is developed for recurrences with positive coefficients. This is then extended to many sequences that have negative ... 
Mathematical models of species' responses to habitat destruction
(2012)Anthropogenic habitat destruction is the leading cause of the high rate of extinctions of species observed around the world today. With a growing human population, it is vitally important for conservationists to understand ...