This page lists all the PhD theses in the Department of Mathematics since 1990. Each entry provides the students name, thesis title, advisor or coadvisors, and program. Degrees are awarded in May, August, and December. Graduation ceremonies are held in May and December. Thesis are designated as Mathematics (MA), Applied Mathematics (AMA), Computational Mathematics (CMA), and Operations Research (ORM), and Biomathematics (BMM). A number of the AMA theses could have been CMA theses but the student chose to meet the AMA course requirements. ORM students are students in the Operations Research Program whose thesis advisor is from the Mathematics Department. BMM students are students in the Biomathematics Program whose thesis advisor is from the Mathematics Department. A list of all PhD students since the PhD program began can be found in the Departmental History.

December 2007

• Braun, Thomas R.; High Speed Model Implementation and Inversion Techniques for Smart Material Transducers. Smith, AMA.
• David, John; Estimation, and Shape Design: Analysis and Applications. Tran, AMA.
• Dillard, Karen Edna Michele; An Application of Implicit Filtering to Water Resources Management. Kelley, AMA.
• Gong, Yan; Immersed-Interface Finite-Element Methods for Elliptic and Elasticity Interface Problems. Li, AMA.
• Grove, Sarah Lynn; Dissertation: Optimization Problems in the Presence of Uncertainty.
  Banks, AMA.

August 2007

• Gong, Yan; Immersed-Interface Finite-Element Methods for Elliptic and Elasticity Interface Problems. Li, AMA.
• Osborne, Jason; On Geometric Control Design for Holonomic and Nonholonomic Mechanical Systems. Zenkov, MA.
• Wills, Rebecca Smith; When Rank Trumps Precision: Using the Power Method to Compute Google’s PageRank. Ipsen, MA.

May 2007

• Chanchana, Prakash; An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix. Meyer, AMA.
• Choe, Dongkyoung; Digital Signal Design for Fault Detection in Linear Continuous Dynamical Systems. Campbell, ORM.
• Hong, Chung-Chien; Nonlinear Programming and Optimal Control Approach To the study of Social Network. Medhin, ORM.
• Kermes, Jeremiah Mitchell; Fermat Curves on Weighted Projective Planes. Fauntleroy, MA.
• Lin, Chuan; Heavy Traffic and Markov Modulated Models for Wireless Queueing Systems and Numerical Methods for Associated Resource Allocation Problems. Buche, ORM.
• Ovchinnikov, Alexey; Tannakian Categories and Linear Differential Algebraic Groups. Singer, MA.
• Zack, Laurie Margaret; Nilpotent Lie Algebras with a Small Second Derived Quotient. Stitzinger, MA.

December 2006

• Ball, Brian L; Characterization of Stress-Effects in Ferroelectrics with Application to Transducer Design. Smith, AMA.
• Luke, Nicholas Stephen; Modeling Shear Wave Propagation in Biotissue: An Internal Variable Approach to Dissipation. Banks, CMA.
• Reese, Jill Paula; Examining the Significance of Advective Acceleration to Single-Phase Flow Through Heterogeneous Porous Media. Kelley, CMA.
• Suanmali, Suthathip; On the Relationship Between the Class of a Lie Algebra and the Classes of its Subalgebras. Stitzinger, MA.

August 2006

• Engelsone, Anna; Direct Transcription Methods in Optimal Control: Theory and Practice. Campbell, ORM.
• Kuster, Christopher Mark; Fast Numerical Methods for Evolving Interfaces. Gremaud, MA.
• Wan, Xiaohai; Numerical Simulation Methods for Biological Tissue Interactions. Lubkin and Zhilin Li, BMM.

May 2006

• Cabbage, Brian William; The Stone-ech Compactification of the Plane. Faulkner, MA.
• Cicco, Tracey Martine Westbrook; Algorithms for Computing Restricted Root Systems and Weyl Groups. Helminck, MA.
• Finkel, Daniel Edwin; Global Optimization with the DIRECT Algorithm. Kelley, ORM.
• Glotov, Petr Evgenyevich; Time Reversal of Electromagnetic Waves in Randomly Layered Media. Fouque, MA.
• Ingram, Frank III; On the Wreath Product of Schur Functions. Jing and Stitzinger, MA.
• Taylor, Padraic Whittingham; On the Solvability of Nonlinear Discrete Multipoint Boundry Value Problems. Rodriguez, MA.
• Zhou, Xianwen; Application of Perturbation Methods to Modeling Correlated Defaults in Financial Markets. Fouque, AMA.

December 2005

• Adams, Brian Michael; Non-parametric Parameter Estimation and Clinical DataFitting with a Model of HIV Infection. Banks, CMA. Computational Mathematics
• Hood, Jeffrey Braidon Hood; Molecular-based Models for Viscoelasticity of Polymers. Banks and Medhin, CMA.
• Lasater, Matthew Scott; Numerical Methods for the Wigner-Poisson Equations. Kelley, CMA.

August 2005

• Gao, Jining;  The Algebraic Structure of BRST Operators and Their Applications.  Fulp,  MA.
• May, John Paul; Approximate Factorization of Polynomials in Many Variables and Other Problems in Approximate Alegebra via Singular Value Decomposition Methods. Kaltofen, MA.
• Ray, Robert Charles;  Quantum Symmetric Spaces and Quantum Symplectic Invariants. Jing, MA.
• Schugart, Richard Charles;  Mathematical Models and Numerical Methods for Analysis of Mechanical and Chemical Loading in Articular Cartilage. Haider, AMA.
• Yokley, Karen Alyse;  Physiologically Based Model Development and Parameter Estimation:  Benzene Dosimetry in Humans and Respiratory Irritation Response in Rodents. Tran, CMA.

• Bidwell, John Charles; On the Periodic Nature of Solutions to the Reciprocal Delay Difference Equation with Maximum. Franke, MA.
• Cook , William Jeffrey; Affine Lie Algebras, Vertex Operator Algebras and Combinatorial Identities. Misra, MA.
• Dozier , Richard Brent; Existence and Analysis of the Limiting Spectral Distribution of Large Dimensional Information-plus-noise Type Matrices. Silverstein, AMA.
• He, Taiping; Reaction-diffusion Systems with Discontinuous Reaction Functions. Pao, MA.
• Hillman, Rebecca Ann; Relationship between Symmetric Brace Algebras and Pre-lie Algebras. Lada, MA.
• Jackson, Farrah Monique; Characterization of Involutions of SP (2N, K), Helminck, MA.
• Levy, Rachel; Partial Differential Equations of Thin Liquid Films: Analysis and Numerical Simulation. Shearer, AMA.
• Perry, John Edward III; Combinatorial Criteria for Gröbner Bases.Hong, MA.

December, 2004

• Wood, Lisa M; On the Solvable length of Associative Algebras, Matrix Groups, and Lie Algebras. Stitzinger, AMA.
• Hatch, Andrew Graydon; Model Development and Control Design for Atomic Force Microscopy. Smith, MA.
  

• Gibson, Nathan Louis; Terahertz-based Electromagnetic Interrogation Techniques for Damage Detection. Banks, CMA.
• Kyei, Yaw; Higher-order Cartesian Grid Based Finite Difference Methods for Elliptic Equations on Irregular Domains and Interface Problems and Their Applications. Ito, CMA.
• Taylor, Dewey Teres; Fine Bruhat Intersections for Reductive Monoids. Putcha, MA.
• Yang, Xingzhou; Immersed Interface Method for Elasticity Problems with Interfaces. Li, CMA.

May 2004

• Attiogbe, Cyril Efoe; On Characterizing Nilpotent Lie Algebras by their Multipliers. Stitzinger, MA.
• Chen, Guo; Immersed Interface Method for the Biharmonic Equation on Irregular Domain and its Applications. Li, AMA.
• Daily, Marilyn Elizabeth; L(Infinity) Structures on Spaces of Low Dimension. Lada, MA.
• Kharebava, Zviad ; Singular Cochains and Rational Homotopy Type. Lada, MA.
• Seaton, Gerald Arthur; The Lattice of Equivalence Classes of Closed Sets and the Stone-Cech Compactification. Faulkner, MA.
• Williams, Ellison Anne; A Formula for N-Row Macdonald Polynomials Mathematics. Stitzinger and Jing, MA.
• Williams, Michael Peretzian ; Nilpotent N-Lie Algebras. Stitzinger, MA.

December 2003

• Al-Ashhab, Samer Shafiq; The Role of sh-Lie Algebras in Lagrangian Field Theory. Fulp, AMA.
• Drake, Kimberly Jean; Analysis of Numerical Methods for Fault Detection and Model Identification in Linear Systems with Delays. Campbell, AMA.
• Hicks, Gregory Philip; Modeling and Control of a Snake-like Serial-link Structure. Ito, AMA.
• Kavanagh, Kathleen Rose; A Nonsmooth Nonlinearities in Applications From Hydrology. Kelley, AMA.
• Wieman, Robert Edward; Granular Flow Models: Analysis and Numerical Simulations. Shearer, CMA.
• Zager, Michael Gary; Modeling the Distribution and Metabolism of the Phytoestrogen Genistein in Rats. Tran, CMA.

August 2003

• Dometrius ,Christopher Edward; Relationship between Symmetric and Skew-symmetric Bilinear Forms and Involutions on SL (N,K) and SO(N, K). Helminck, MA
• Han, Chuan-Hsiang; Singular Perturbations on Non-smooth Boundary Problems in Finance.  Fouque, AMA.
• Lewis, Brian Matthew; Applied Mathematics Malvern, Optimal Control and Shape Design:  Theory and Applications. Tran, AMA.
• Massad, Jordan Elias; Macroscopic Models for Shape Memory Alloy Characterization and Design.   Smith, CMA.
• Nealis, James Matthew; Model-based Robust Control Designs for High Performance Magnetostrictive Transducers. Smith, AMA.
• Williams, Vicky Lynn; Root Multiplicities of the Indefinite KAC-Moody Algebras HCn (1). Misra, MA.

May 2003

• Fowler, Jennifer Renee; Algorithms for Computations in Local Symmetric Spaces. Helminck, MA.
• Gagliardi, Daniel James; Relations Between Characters of Lie Algebras and Symmetric Spaces.   Helminck, MA.
• Mawhinney, Katherine Joyner; Characteristics of Complexity Within the Lattice of Compactifications. Faulkner, MA.
• Williams, Scott Everett; The Lageos Satellite: A Comprehensive Spin Model and Analysis. Arkady Kheyfets, AMA

December 2002

• Bortz, David Matthew; Modeling, Analysis, and Estimation of an in vitro HIV Infection Using Functional Differential Equations. Banks,  AMA
• Coffey, Todd Stirling; Temporal and Pseudo-temporal Numerical Integration Methods.  Kelley, CMA
• Person, Axelle Claude; Solving Homogeneous Linear Differential Equations of Order 4 in Terms of Equations of Smaller Order. Singer, MA

August 2002

• Raye, Julie Knowles; An Electromagnetic Interrogation Technique Utilizing Pressure-dependent Polarization. Banks, AMA
• Tullie, Tracey Andrew; Variance Reduction for Monte Carlo Simulation of European, American or Barrier Options in a Stochastic Volatility Environment. Fouque, AMA
• Turner, William Jonathan; Black Box Linear Algebra with the Linbox Library. Kaltofen, CMA
• Wu, Ling; Classification of Involutions of SL(N, K) and SO (2N + 1, K). Helminck, AMA

May 2002

• Haws, John; Preconditioning KKT System. Meyer, AMA
• Burns, Brenda Darlene; The Staircase Decomposition for Reductive Monoids. Putcha, MA
• Ye, Yuanqing; Semiclean Rings and Clean Rings. Luh, MA

December 2001

• Berman, Peter Hillel; Computing Galois Groups for Certain Classes of Ordinary Differential Equations. Singer, MA
• Bihari, Kathleen Louise; Analysis of Thermal Conductivity in Composite Adhesives. Banks, AMA
• Gray, Scott Thomas; A Distributed Parameter Liver Model of Benzene Transport and Metabolism in Humans and Mice-Developmental, Theoretical, and Numerical Considerations. Tran. CMA
• Harris, Leona Ann; Differential Equation Models for the Hormonal Regulation of the Menstrual Cycle. Selgrade, AMA
• Lee, Wen-Shin; Early Termination Strategies in Sparse Interpolation Algorithms. Kaltofen, CMA

August 2001

• Cole, Cammey Elizabeth; Benzene and its Effect on Erythropoiesis: Models, Optimal Controls, and Analyses. Tran, CMA
• Gablonsky, Jörg Maximilian Xaver; Modifications of the Direct Algorithm. Kelley, AMA
• Joyner, Michele Lynn ; An Application of a Reduced Order Computational Methodology for Eddy Current Based Nondestructive Evaluation Techniques. Banks, CMA
• Potter, Laura Kay; Physiologically Based Pharmacokinetic Models for the Systemic Transport of Trichloroethylene. Banks, AMA
• Segal, Rebecca Anne; Patterns of Air Flow and Particle Deposition in the Diseased Human Lung. Shearer, CMA

May 2001

• Biehn, Neil; Implicit Runge-Kutta Methods for Stiff and State Constrained Optimal Control Problems. Campbell, ORM.
• Deng, Shaozhong; Immersed Interface Method for Three Dimensional Interface Problems and Applications. Li, AMA
• Horton, Kirk; Fault Detection and Model Identification in Linear Systems. Campbell, ORM.
• McLean, Michael Allen; N-Symplectic Analysis of Field Theory. Norris, MA
• Minimair, Manfred; Resultants of Composed Polynomials. Hong, AMA

December 2000

• Matthews III, John; An Analytical and Numerical Study of Granular Flows in Hoppers. Gremaud, AMA
• Beeler, Scott Colvin; Modeling and Control of Thin Film Growth in a Chemical Vapor Deposition Reactor. Tran, AMA
• Poplin, Phillip Lamar; The Semiring of Multisets. Hartwig, MA
• Wang, Yonghong; Multiple Internal Layer Solutions in Singularly Perturbed Boundary Value Problems. Lin, MA
• Whitaker, Shree Yvonne; A Biologically Based Controlled Growth and Differentiation Model Using Delay Differential Equations: Development, Applications and Stability Analysis. Tran. AMA

August 2000

• Horton, Michael; Consistency of Least Squares Estimators for Imaging through Turbulence. Ito, AMA
• Jenkins, Eleanor; The Application of Two-level Domain Decomposition Preconditioners to Problems in Hydrology.  Kelley, MA

May 2000

• Cho, Eun; Computation for Markov Chains. Meyer, AMA.

December 1999

• Choi, Melissa; Analysis and Implementation of a Model for Radio-frequency Bonding of Adhesives in Composites. Banks, AMA.

August 1999

• Choi, Tony; Bound Constrained Optimization. Kelley, AMA.
• Yankosky, George; Topics on Nilpotent Lie Algebras. Stitzinger, MA

May 1999

• Simon, Tammy; Modeling and computation of the effective magnetic properties of magnetoheological fluids. Ito, AMA.
• Sprague, John; Analytic functions of a generalized complex variable. Chung, MA
• Brauer, Craig; Triangular monoids. Putcha, MA
• Chan, David; Asymptotic dynamics in multi-species, discrete competitive systems. Franke, MA
• Holmes, Karen; Finite dimensional nilpotent Lie algebras with isomorphic maximal subalgebras. Stitzinger, MA
• Schroeter, Jeffry; Simulation and control of the Navier-Stockes equations using the reduced basis method. Ito, CMA

December 1998

• Batzel, Jerry; Modeling and stability analysis of the human respiratory control system. Tran, AMA
• Buksas, Michael; Modeling, analysis, and implementation of forward and inverse problems in one dimensional electromagnetic scattering with differential and hysteric polarization. Banks, AMA
• DelRosario, Ricardo; Computational methods for feedback control in structural systems. Banks, AMA
• Hontz, Jennifer; Root multiplicities of some Kac-Moody Lie algebras of indefinite type. Misra, MA
• Cynthia Musante; A distributed parameter model for spatially dependent hepatic processing of 2,3,7,8-tetrachlorodibenzo-p-dioxin. Tran/Banks, CMA
• Obersnel, Franco; On compactifications of the set of natural numbers and the half line. Faulkner, MA

May 1998

• Hardy, Peter; On characterizing nilpotent Lie algebras by their multipliers, t(L)8. Stitzinger, MA
• Hu, Xueqing; Derivation on Prime Gamma Rings. Luh, AMA
• Jeffris, Michael; Analysis and Simulations of Unsaturated Groundwater Flow and Heterogeneous Media. Fitzpatrick, CMA
• Lyerly, Christopher; Explicit Construction of a Level-Two Representation of G2(1). Jing, MA
• Schmidt, Michael; Quotient Rings of T-Rings. Luh, MA
• Tocci, Michael; Numerical Methods for Variably Saturated Flow and Transport Models. Kelley, AMA
• Velummylum, Somasundaram; Interior Transition Layers in Singularly Perturbed Boundary Value Problems. Lin, MA
• Yang, Zhi-Ping; Monotone Methods for Analytic and Numerical Solutions of Reaction Diffusion Systems. Pao, AMA
• Yeomans, Kevin; Initialization Issues in General Differential Algebraic Equation Integrators. Campbell, AMA

December 1997

• Hessinger, Sabrina; Computing Galois Groups of Linear Differential Equations of Order Four. Singer, MA
• Zhong, Yangchun; Efficient Numerical Solutions of General Nonlinear Higher Index Differential Algebraic Equations. Campbell, CMA

August 1997

• Banoczi, James M.; Multilevel Methods for Conductive-Radiative Heat Transfer. Kelley, CMA
• Butera, Jeffrey V.; A Random Process Model for Dispersion in Containment Transport through Porous Media: Analysis and Computation. Fitzpatrick, AMA
• Klima, Richard E.; Involutory Commutants of the Seventh Order with Applications to Algebraic Cryptography. Stitzinger, AMA

May 1997

• Marszalek, Wieslaw; Analysis of Partial Differential Algebraic Equations. Campbell/Chukwu, AMA
• Zhang, Yue; Mathematical Formulation of Vibrations of a Composite Curved Beam Structure: Aluminum Core Material with Viscoelastic Layers, Constraining Layers, and Piezoceramic Patches. Banks, AMA

December 1996

• Wang, Jianhua; Monotone Iterative Method for Diffusion Equations with Nonlinear Diffusion Coefficients. Pao, AMA

August 1996

• None

May 1996

• Chen, Xuzhou; The Matrix Iterative Analysis. Hartwig, AMA
• Harger, Robert; Realization of Level Two Integrable Highest Weight Representations of the Affine Lie Algebra A7(2). Misra, MA
• Mani, Vaidyanath; On Black Box Interpolation over Arbitrary Fields. Hartwig, AMA

December 1995

• Xue, Zhaoqing; Mesh-Independence of GMRES for Integral Equations. Kelley, AMA

August 1995

• Sigmon, Neil P.; Involutory Commutants of the Sixth Order with Applications Algebraic Cryptography. Stitzinger, AMA

May 1995

• Etheridge, Debra L; Existence and Behavior of Solutions of Nonlinear Discrete-time Boundary Value Problems. Rodriguez, MA
• Pennell, Edwin A.; Generalized Bruhat Order on Reductive Monoids. Putcha, MA

December 1994

• None

August 1994

• Lawson, Jeffrey; Generalized Symplectic Geometry for Classical Fields and Spinors. Fulp / Norris, MA

May 1994

• Bos, Margaret K.; Embedding of Affine Lie Algebra Representations and Principle Characters. Misra, MA
• Carscadden, Rob L.; The Orbit Structure of Finite Monoids. Putcha, MA
• Gibson, Gregory A.; Extension Problems in Lie Algebras. Stitzinger, MA
• Moore, Edward; Constraint Preserving Multistep Integrators for Differential Algebraic Equations. Campbell / Clark, AMA
• Shutt, John; Heteroclinic and Homoclinic Orbits in a Class. Schecter, MA

December 1993

• Benzi, Michele, A Direct Row-Projection Method for Sparse Linear Systems. Meyer, AMA
• Choi, Sang-Il, Analysis of Limiting Empirical Spectral Distribution Function of Large Dimensional Random Matrices. Silverstein, MA
• Lu, Yiyuan, Centralizing Derivations of Higher Order on Prime Rings. Luh, MA

August 1993

• Gilmore, Paul; An Algorithm for Optimizing Functions with Multiple Minima. Kelley, AMA
• Kim Hok; Solutions of Perturbed Nonlinear Differential Equations. Marlin, MA
• Lu, Xin; Nonlinear Parabolic Boundary-Valey Problems with Time Delays. Pao, AMA
• Oppegaard, Dean; Generalizations of Continuity, Symmetry, and Symmetric Continuity. Evans, MA
• Renfro, Dave; Some Supertypical Nowhere Differentiability Results for C[0,1]. Evans, MA

May 1993

• Batten, Peggy; Multipliers and Covers of Lie Algebras, Stitzinger, MA
• Buchanan, James; Asymptotic Behavior of n-Dimensional Systems of ODEs of Kolmogorov-type. Selgrade, AMA
• Chaussalet, Thierry; On Bounded Growth of Density Dependent Stochastic Population Models. Bishir, AMA

December 1992

• None

August 1992

• Tian, Tiehong; Convengence Analysis of a Projected Gradient Method for a Class of Optimal Control Problems. Dunn, AMA

May 1992

• Matthews, David; Valuations Defined by Ostwoski Nets. Cohen, MA
• Sumner, Suzanne; Dynamical Systems Associated with Pioneer-Climax Models, Marlin, AMA

December 1991

• Ferng, Ruennhwa; Lanczos-based Condition Estimation in Signal Processing and Optimization. Plemmons, AMA .
• Jang, Ho-Jong; The Equilibrium Equation: Substructuring and the Force Method. Plemmons/ White, AMA .
• Mukundan, Lakshmi; Convergence Analysis of the Harmonic Balance Method. Kelley, MA .
• Nagy, James; Toeplitz Least Squares Computations. Plemmons, AMA .
• Vallin, Robert; Shell Porosity in Metric Spaces. Evans, MA .
• Yang, Yadong; Explicit Solutions of a Class of Riemann Problems of Mixed Type. Shearer, AMA.

August 1991

• Chen, Hong-Wei; Blow-up of Solutions for Nonlinear Parabolic Boundary Value Problems, Pao, MA.
• Hwang, Dong-Ming; Convergence of Broyden's Method in Banach Spaces. Kelley, MA.

May 1991

• Benzi, Michele.; A Direct Row-Projection Method for Sparse Linear Systems. Meyer, AMA.

December 1990

• None

August 1990

• Augustine, Mathai; Monoids of Lie Type and Their Congruence. Putcha, MA.
• Han, Jun Cheol; Involutions in Left Artinian Rings. Koh, MA .
• James, Douglas; Conjugate Gradient Methods for Constrained Least Squares Problems. Meyer/Plemmons, AMA .
• Moneyhun, Kay; Isoclinisms in Lie Algebras. Stitzinger, MA.
• Talmadge, Andrew; A Geometric Formulation of the Higgs Mechanism via Internal Metric Fields. Fulp, AMA.
• Terrell, William; Observability and External Description of Linear Time Varying Singular Control System. Campbell, MA.

May 1990

• Li, Zhongshan; The Embedding of Rings in Regular Rings and Non-Regular Rings. Luh/ Putcha, MA.
• Marquardt, Vera; Factoring the Group of Units of a Ring. Putcha, MA.
• Yakubu, Abdul; Global Stability, Bifurcation, and Chaos in Discrete Competitive Systems. Franke, AMA .