The department has been actively supporting undergraduate research for many years. Below is a partial list of undergraduate projects undertaken with faculty from the department, roughly listed by year and alphabetically by student.

This is a very partial list and new content that will be updated as time goes on. It is currently just a template.

Current Research Projects

Spatial Graphs
Abstract: We are using 3D printers to make 3D visualizations of various graphs that are more visually pleasing than the traditional versions drawn on paper. Recent examples include bipartite graphs and complete graphs. We have also discovered that book embeddings of graphs can be constructed as "dome graphs" that build curved edges between vertices laid out on a circle.
Faculty: Stephen Lucas, Laura Taalman
Current Students: Abby Eget, William Nettles 
Past Students: Hannah Critchfield, Benjamin Flint, Harley Mead
Areas: Graph theory, 3D printing
When: Fall 2017 to current


Rolling Knots & Developable Surfaces
Abstract: We began by 3D printing Morton's tritangentless knot, and discovered it's convex hull is a developable surface. By varying parameters and stretching, we came up with a collection of knots that rolled as smoothly as possible, although not as smoothly as the oloid. We wish to understand the relationship of these knots to other developable surfaces .
Faculty: Stephen Lucas and Laura Taalman
Current Students: Abby Eget,  William Nettles 
Areas: Knot theory, 3D printing
When: Spring 2019 to current

Past Undergraduate Research Projects

Analytic Solutions for Parrando’s Paradox
Abstract: Parrando’s paradox shows how two losing games can be combined into a winning game. Past solutions were available for random selection between games, but only simulations for specific patterns. We came up with analytic solutions for specific patterns and optimized the random selection approach.
Faculty: Stephen Lucas
Student: Volkan Bakiran
Areas: Probability theory, linear algebra, computational mathematics
When: Fall 2017, Spring 2018
Outcomes: A half draft of a paper outlining results is available.


Approximating the Wiener Process, and a Simple Approach to Stochastic ODEs.
Abstract: The Wiener process is an important random process that is continuous and differentiable no-where. We developed a variation of the Karhunen-Loeve expansion that has the same variance as the Wiener process and nearly the correct covariance, which is smooth. This can be used to numerical solve stochastics ODEs far more easily than current methods.
Faculty: Stephen Lucas
Student: Adam Diehl
Areas: Probability theory, linear algebra, computational mathematics
When: Spring 2017, Fall 2017
Outcomes: A half draft of a paper outlining results is available. Adam presented his research at SUMS in 2017.

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