Undergraduate Mathematics Research
Thanks to Drexel's Co-op program, the Department of Mathematics offers unique opportunities for undergraduates to work on long-term, full-time research projects with internationally known mathematicians. These projects take place during the Spring and Summer Quarters, and applications are typically submitted through the Steinbright Career Development Center’s co-op matching system. Projects vary in topic and are derived from individual faculty’s research programs. Funding comes from the National Science Foundation, Drexel University’s Office of the Provost, the College of Arts and Sciences, and/or the Department of Mathematics. There are also sometimes opportunities for summer research projects that are smaller in scope. For more information, contact the department’s undergraduate adviser, Ronald Perline at perlinrk@drexel.edu.
Examples of Past Projects
Student: Sean Miller, '17
Faculty Adviser: Hugo Woerdeman, PhD
Undergraduate Sean Miller worked with Hugo Woerdeman, PhD, to identify the specific properties that multivariable polynomials have that can be written in the form det(I-KZ), where I is the identity matrix, K is a Hermitian contraction, and Z is a diagonal matrix with the variables on the diagonal. Determinantal representations of polynomials appear in areas such as Systems Theory, Signal Processing, and also Algebraic Geometry. A summary of Miller's results maybe found via the link below.
This project was supported by NSF grant DMS-0901628
Students: Ryan Wasson and David Kimsey
Faculty Adviser: Hugo Woerdeman, PhD
Undergraduates Ryan Wasson and David Kimsey worked with Professor Hugo Woerdeman, PhD, to find missing data in a matrix (double array of numbers). This area of research is referred to as "Matrix completion problems" and has several applications, including 'guessing’ consumer preferences (e.g. movie ratings) and predicting future trends. In a matrix completion problem, the objective is to obtain a completed matrix (i.e. to find values for the missing entries) based on the known entries as well as on some global property of the matrix (which matrices in that context are known to have). The following two peer-reviewed papers are the result of these successful projects:
Students: Jeremy Gaison and Qimin Zhang
Faculty Advisers: J. Douglas Wright, PhD and Shari Moskow, PhD
Undergraduate students Jeremy Gaison and Qimin Zhang worked on understanding the bulk effects of a nonlinear infinite chain of oscillators. The materials in this model vary periodically, and for long wavelengths there are unexpected averaging effects. The students derived equations, did asymptotic analysis, and ran numerical experiments. This work resulted in the jointly authored SIAM MMS peer-reviewed journal article:
The project was funded partially by the National Science Foundation grants DMS-1108858 and DMS-1105635.
Students: Mark Kondrla, Jr. and Michael Valle
Faculty Adviser: David Ambrose, PhD
Mark Kondrla, Jr. and Michael Valle worked with faculty mentor David Ambrose, PhD, on a project about fluid motion, by computing time-periodic solutions of nonlinear systems of partial differential equations. Usually such motion is modeled by Euler’s equations. In this research project, Kondrla and Valle performed computations on a simplified model, helping to validate its use. Ambrose, Kondrla and Valle have written a paper on this subject, "Computing time-periodic solutions of a model for the vortex sheet with surface tension," which has been accepted for publication by the journal Quarterly of Applied Mathematics.
Learn More About Research in the Mathematics Department