The department offers students the opportunity to explore more advanced topics through an independent study, which could have the added benefit of leading to an honors project. Students interested in completing an independent study should consult with a faculty member who is interested in directing a student in the desired field. Here is a list of faculty and their independent study interests:
Yuan-Jen Chiang has worked with students on the following topics: topics in analysis, differential geometry, tensors and relativity, partial differential equations, introduction to harmonic maps, applications of mathematics in electrical engineering, fractional calculus, topics in Euclidean and non-Euclidean geometries, tensor analysis in physics and engineering, Fourier analysis, and minimal surfaces.
Jeb Collins welcomes the opportunity to work with students on problems in applied mathematics and scientific computing. Examples of projects include developing error estimates for a particular numerical method or implementing the finite element method for solving a differential equation. He is also interested in numerical algebraic geometry, which involves computational methods for solving polynomial systems. These projects could involve heavy programming or utilizing known software to solve models involving polynomial systems.
Melody Denhere is interested in working with students on problems in probability
and statistics. Future projects may include simulation studies, statistical modelling
and analysis of real world problems in preparation for careers in mathematics and
statistics. Melody is also keen to direct studies in big data analytics, biostatistics,
regression analysis, multivariate data analysis, robust statistical methods, and outlier analysis.
Julius Esunge welcomes the opportunity to work with students on problems in probability, statistics and financial mathematics. Examples of possible topics include the following: simulation of random variables and probability distributions; properties and applications of Brownian motion, Brownian bridge and fractional Brownian motion; applications of limit theorems in probability; applications of stable distributions for heavy tailed data; statistical analysis and properties of actuarial models. Julius also enjoys directing reading courses/seminars towards actuarial examination preparation.
Randall Helmstutler has directed students in cryptology, digital topology, homotopy and Lie theory, category theory, advanced group theory, and linear algebra. His general interest is in working with students wishing to delve into advanced topics in abstract algebra and topology. In the field of algebra this includes group theory, ring theory, and applications of group theory to cryptographic protocols. Topologically, he would enjoy directing studies in homotopy and covering spaces, differential topology, and topological group theory. To see what students have done under Dr. H., visit his undergraduate research page at doctorh.umwblogs.org/student-research/.
Debra Hydorn is interested in working with students on research projects in probability and statistics, including simulations and statistical modelling. In addition to projects in multivariate statistics and simulations of statistical methods, she has comentored several undergraduate research projects with mathematicians at the Naval Surface Warfare Division Dahlgren. She has also led directed studies on regression analysis, linear models, statistical computing, statistics education, mathematical art, and multivariate statistics. Details about projects that Dr. Hydorn has conducted with students are available at hydornpage.umwblogs.org/undergraduate-research/
Janusz Konieczny has directed students in the study of field theory, topics in geometry, applications of linear algebra, and semigroup theory.
Jangwoon “Leo” Lee is interested in working with students in various areas of applied mathematics including partial differential equations, scientific computations, optimal control problems, and numerical methods for mathematical model equations such as stochastic/partial differential equations.
J. Larry Lehman has led directed studies in Galois theory, algebraic number theory, and elliptic curves. He would also be interested in working with students in analytic number theory and other advanced topics in number theory.
Keith Mellinger has directed students in various areas of discrete mathematics including coding theory, design theory, finite geometry, combinatorics, graph theory, and cryptography. He also directed a joint project with a student and a Navy scientist as part of the Dahlgren Research Collaboration. Dr. Mellinger is interested in working with students in any of these areas and more information about his projects with students can be found on his Student Research webpage, located at www.keithmellinger.com/student-research/
Suzanne Sumner has worked with students on mathematical modelling, fractal geometry, dynamical systems, applications in finite mathematics, operations research, epidemiological models, and differential equations.