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.

August 2009

• Heller, Martin A.; Robust Minimum Density Estimators and Stochastic Resonance for Classification Algorithms. Ito, AMA.
• Xie, Hui; Finite Element Methods for Interface Problems with Locally Modified Triangulations. Li, AMA.
• Zhang, Qin; Control of Infinite Dimensional Bilinear Systems: Applications to Quantum Control Systems. Ito, AMA.

May 2009

• Kalhorn, Rebecca I.B.; On the Solvability of Nonlinear Boundary Value Problems on Time Scales. Rodriguez, MA.
• Kim, Eun Jung; Computational biomechanical models for the pericellular matrix of
  articular cartilage. Haider, AMA .
• Levy, Louis A.; Multipliers for the Lower Central Series of Strictly Upper Triangular Matrices. Stitzinger, MA.
• Pope, Scott R.; Parameter Identification in Lumped Compartment Cardiorespiratory Models. Kelley, AMA.
• Porter, Gloria L.; Multiobjective Optimal Control Methodology for the Analysis of Certain Sociodynamic Problems. Medhin, AMA.
• Selee, Teresa M.; Stochastic matrices: ergodicity coefficients and applications to ranking. Ipsen, AMA.
• Yuhasz, George L.; Berlekamp/Massey Algorithms for Linearly Generated Matrix Sequences. Kaltofen, MA.

December 2008

• Davis, Jimena L.; Uncertainty Quantification in the Estimation of Probability Distributions on Parameters in Size-Structured Population Models. Banks, CMA.
• Ellwein, Laura M.; Cardiovascular and Respiratory Regulation, Modeling and Parameter Estimation. Olufsen, AMA.
• Ernstberger, Stacey L.; Sensitivity Methods for Dynamical Systems. Banks, CMA.
• Govan, Anjela Y.; Ranking Theory with Application to Popular Sports. Meyer, AMA.
• Okay, Irfan; The Additional Dynamics of the Least Squares Completions of Linear Differential Algebraic Equations. Campbell, MA.
• Qasimov, Heydar R. O.; Lacunae Based Stabilization of PMLs. Tsynkov, AMA.
• Siskind, Ryan D.; Model Development for Shape Memory Polymers. Smith, AMA.

August 2008

• Andjelkovic, Ivan; Auxiliary Signal Design for Fault Detection for Nonlinear Systems:
  Direct Approach. Campbell, AMA.
• Benedict, Brandy A.; Axisymmetric Poroelastic Boundary Element Methods for Biphasic Mechanics of Articular Cartilage. Haider, CMA.
• Dickson, Kelly I.; Condition Estimates for Numerical Continuation with Applications to Atomic and Molecular Fluids. Kelley, AMA.
• Ernstberger, Jon M.; High Speed Parameter Estimation for a Homogenized Energy Model. Smith, CMA.
• Janovitz-Freireich, Itnuit; Computation of the Exact and Approximate Radicals of Ideals: Techniques Based on Matrices of Traces, Moment Matrices and Bezoutians. Szanto, MA.
• Jiang, Qunlei; Analysis and Computation for a Fluid Mixture Model of Tissue Deformations. Li & Lubkin, CMA.
• Olson, Sarah D.; Mathematical models for analysis of tissue regeneration in articular cartilage. Haider, BMM.
• Pasteur, Roger D. II; A Multiple Inhibin Model of the Human Menstrual Cycle. Selgrade, AMA.
• Samuels, John R. , Jr.; Inverse Problems and Post Analysis Techniques for a Stenosis-Driven Acoustic Wave Propagation Model. Banks, CMA.
• Yang, Yipeng; Path Dependent Stochastic Models and Their Applications in Finance and Communications. Pang, ORM.
• Wan, Wei; Dynamic Game Theoretic Models in Marketing and Finance. Medhin, ORM.

May 2008

• Beier, Julie Catherine; Crystals for Demazure Modules of Special Linear Quantum Affine Type. Misra, MA.
• Beun, Stacy Leigh; On the Classification of Orbits of Minimal Parabolic k-subgroups Acting
  on Symmetric k-varieties of SL(n,k). Helminck, MA.
• Brown, Jonathan Dale; N-Symplectic Quantization. Norris, MA.
• Cook, James Steven; Foundations of Supermathematics with Applications to N=1 Supersymmetric Field Theory. Fulp, MA.
• DeVault, Kristen Jean; Numerical Study of Two Problems in Fluid Flow: Cavitation and Cerebral Circulation. Gremaud, AMA.
• Petersen, Richard Francis; Transformation Semigroups Over Groups. Putcha, MA.
• Sweetingham, Kelly Ann: Auxiliary Signal Design for Fault Detection in Nonlinear Systems.
  Campbell, AMA.

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.