Sample Undergraduate Research Projects

Here is a list of recent undergraduate research projects. When available, we have added images that give you a flavor of some of the topics studied. If the student wrote a thesis, you can look it up at USM's library.

• Samuel Dent, "Applications of the Sierpiński Triangle to Musical Composition", Honors Thesis
• Brandon Hollingsworth, "A time integration method for nonlinear ordinary differential equations", undergraduate research thesis.
• Haley Dozier, "Ideal Nim", undergraduate research project.
• Sean Patterson, "Generalizing the Relation between the 2-Domination and Annihilation Number of a Graph", Honors Thesis.
• Elyse Garon, "Modeling the Diffusion of Heat Energy within Composites of Homogeneous Materials Using the Uncertainty Principle", Honors Thesis.
• Brandi Moore, "Magic Surfaces", Mathematics Undergraduate Thesis.
• Amber Robertson, "Chebyshev Polynomial Approximation to Solutions of Ordinary Differential Equations", Mathematics Undergraduate Thesis
• Kinsey Ann Zarske, "Surfaces of Revolution with Constant Mean Curvature H=c in Hyperbolic 3-Space H 3 (-c 2 )", Undergraduate Student Paper Competition, 2013 meeting of the LA/MS Section of the MAA.

Examples of the near-triangularity of the Macaulay matrix.

reduced tropical polynomial" width="150" height="150" />	reduced tropical polynomial" width="150" height="150" />
One line contributes nothing to the tropical polynomial on the left. The tropical polynomial on the right is fully reduced, because all the lines contribute.		A dense tropical polynomial: if the slope of line i is mi, then mi+1 = mi+1.

Trying to compute a vector common to L1 and L2 gives rise to an interesting multivariate, polynomial system.

Dodgson's Method fails if an interior matrix has determinant zero.	The double-crossing method fixes this by choosing a different matrix for the division. More details in the full paper.