Student Research Opportunities in Mathematics

Below you will find a listing of all available research opportunities in Mathematics. Please use the contact information listed in each posting for further information regarding the research opportunity.


John Davis

I work at the intersection of differential equations/dynamical systems and control theory, on problems usually motivated by applications in engineering. Much of our recent work has focused on stochastic control problems as well as the analysis, design, and stability of switched dynamical systems with an emphasis on Lyapunov techniques.

Required Courses: MTH 3325
Course Credit Offered: Yes
Begin Date: January 8, 2018
Contact Information: john_m_davis@baylor.edu


Jameson Graber

I specialize in the analysis of differential equations. I mostly care about theoretical questions: Does a solution exist? Is it unique? How does it behave? Is it smooth or rough? Does it conserve, dissipate or accumulate energy? The answers often tell us something about how the real-world situations we are trying to model. Although some of my work applies to physics, I also study lots of models related to economics and game theory.

Required Courses: MTH 2311, 3325, & 3326
Course Credit Offered: Yes
Begin date: January 8, 2018
Contact Information: Jameson_graber@baylor.edu


Paul Hagelstein

I am currently interested in problems on the interface of combinatorics and harmonic analysis.   There are fascinating unsolved problems in this area that are readily understood by undergraduates!   For example:  Suppose you are given N^2 rectangles in the plane whose sides are parallel to the coordinate axes.    Out of these N^2 rectangles, can you find a subset of N of them that are either a) pairwise disjoint; or b) have a point of common intersection?    The research involved is frequently done in collaboration with Dr. Daniel Herden.   Students interested in undergraduate research in this area should anticipate needing at least three semesters of research to complete suitable projects.  Recently, undergraduate research projects have led to the following publications:

Hagelstein, P. A., Herden, D., and Young, D.   Ramsey--type theorems for sets satisfying a geometric regularity condition, J. Math. Anal. Appl. 447  (2017), 951--956.
Gwaltney, E., Hagelstein, P. A., and Herden, D.  A probabilistic proof of the Vitali covering lemma, Methods of Functional Analysis and Topology, to appear.

Required Courses: MTH 3323 & 3312
Course Credit Offered: Yes
Begin Date: January 8, 2018
Contact Information: paul_hagelstein@baylor.edu


Jon Harrison

I work on problems in quantum chaos, investigating how the mathematics of chaos theory and quantum mechanics are connected.  A lot of the examples I work with use networks models and random matrices.

Required Courses: MTH 2311 & 3300
Course Credit Offered: Yes
Begin Date: January 8, 2018
Contact Information: jon_harrison@baylor.edu


Ron Morgan

I work in the area of numerical analysis or computer math.  More specifically, I look at improving algorithms for solving large systems of linear equations and large eigenvalue problems.  To start research in this area, one must project/pretend confidence around large, ill-conditioned matrices, so they don’t think you are afraid of them.  

Required Courses: MTH 2311 & 3300
Course Credit Offered: Yes
Begin Date: January 8, 2018
Contact Information: Ronald_morgan@baylor.edu


Brian Raines

I study the structure of strange, pathological spaces that arise from chaotic dynamical systems.  Recent student research has included examinations of bimodal maps and families of cubic polynomials as well as the dynamical properties of the shift operator on a countable alphabet.

Required Courses: MTH 3323 & 3312
Course Credit Offered: Yes
Begin Date: January 8, 2018
Contact Information: brian_raines@baylor.edu


Tim Sheng

I have been interested in solving interesting problems in computational mathematics. Examples including numerical approximations of the derivatives, anti-derivatives and data obtained from real applications such as those in engineering, physics and finance.

Here are selected research publications by my previous undergraduate students after their projects:

   [1] Brian Jain and AS, An Exploration of the Approximation of Derivative Functions via Finite Differences, Rose-Hulman Undergraduate Math Journal, 8 (2007),  172-188.

   [2] Myles Baker and DS, Modeling Turbulent Financial Derivatives: Experiments of Nonuniform Schemes for the Black-Scholes Equations, Involve, A Mathematics Journal, 2 (2009), 477-492.

   [3] Myles Baker and DS, Approximations of the Financial Derivatives, The Pulse, 7 (2010), 1-16.

Required courses: MTH 2311, 3325, & 3326
Course Credit Offered: Yes
Course Begin Date: January 8, 2018
Contact Information: Qin_sheng@baylor.edu


Brian Simanek

My research focuses on polynomials in many different forms.  I think about approximating complicated functions by polynomials, properties of randomly selected polynomials, the location of zeros of polynomials, orthogonal polynomials, and applications of these ideas to certain problems in mathematical physics.  The most important unsolved problem in this field is known as the Sendov Conjecture and it is an attempt to give a precise answer to the following question: if you know the location of the zeros of a polynomial, what can you say about the zeros of the derivative of that polynomial?

Required Courses: MTH 3323 & 3312
Course Credit Offered: Yes
Begin Date: January 8, 2018
Contact Information: brian_simanek@baylor.edu