Mathematics and Statistics, Department of
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This community features research by the Department of Mathematics and Statistics at Washington State University. Primary research interests include mathematical modeling in fluid mechanical, cellular biological, and population epidemiological systems; optimization problems on high performance computing environments, with nonsmooth functions, and integer programming; partial differential equations in materials research, microwave heating, and inverse problems; matrix algebra including both computational and theoretical analyses; mathematical education research associated with teacher preparation, use of technology, and culturally relevant pedagogy; discrete mathematics that includes cryptography, combinatorics and number theory; environmental mathematics such as contaminant transport in groundwater, population ecology, and predatorprey problems; geometric analysis with applications to data analysis; statistics related to bioinformatics and large data, multiple comparisons, experimental design, linear models, changepoint problems, quality control, engineering reliability and risk analysis; and probability including martingale methods, stochastic differential equations, stochastic simulation, and extreme value theory.
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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 ... 
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 ... 
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 ... 
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 
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); ... 
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 ... 
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 ... 
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 ... 
Optimization Models on Protein Structure and Function
(2011)Traditional experimental methods to study protein structure and function are often time consuming and expensive. Scoring functions are common computational methods for predictions. This dissertation is enclosed with the ... 
A Nonlinear Stability Analysis of Vegetative Turing Pattern Formation for an InteractionDiffusion PlantSurface Water Model System in an Arid Flat Environment
(2011)The development of spontaneous stationary vegetative patterns in an arid flat environment is investigated by means of a weakly nonlinear diffusive instability analysis applied to the appropriate model system for this ... 
Optimization Over Symmetric Cones Under Uncertainty
(2011)We introduce and study twostage stochastic symmetric programs (SSPs) with recourse to handle uncertainty in data defining (deterministic) symmetric programs in which a linear function is minimized over the intersection ... 
Operator Splitting Method and Applications for Semilinear Parabolic Partial Differential Equations
(2011)This dissertation presents a redefined operator splitting method used in solving semilinear parabolic partial differential equations. As one such form, the reactiondiffusion equation is highly prevalent in mathematical ... 
Optimal Control Problem for American Put Option
(2011)In the dissertation, we study an inverse free boundary problem associated with the American put option, where the free boundary is called the early exercise boundary and separates the option holding region from the stopping ... 
Super Fair Divisions: A Minimum Number of Cuts
(2011)This dissertation develops procedures for super fair division that use marks to reduce the number of cuts required for super fair division when compared to all known existing procedures that use marks or can be modified ...