# Sample Undergraduate Research Projects

Recent projects appear at the top; older projects appear below.

## Recent 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.

- 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.
- "Magic Surfaces", Brandi Moore.
- "Surfaces of Revolution with Constant Mean Curvature
*H=c*in Hyperbolic 3-Space**H**^{3}(-*c*^{2})", Kinseyann Zarske, Undergraduate Student Paper Competition, 2013 meeting of the LA/MS Section of the MAA.

- "Triangularizing matrices without swapping columns", Lorrin Debenport, Honors Thesis, 2011.
Examples of the near-triangularity of the **Macaulay matrix**. - "Special Matrices, the Centrosymmetric Matrices", Benjamin Benson, Undergraduate Thesis, 2010.
- "Tropical Mathematics", Matthew Dixon, Undergraduate Project, 2010.
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*m*, then_{i}*m*_{i}_{+1}=*m*+1._{i} - "A criterion for identifying stressors in non-linear equations using Gröbner bases", Elisabeth Palchak, Honors Thesis, 2010.
Trying to compute a vector common to *L*_{1}and*L*_{2}gives rise to an interesting multivariate, polynomial system. - "Method of approximate fundamental solutions for ill-posed elliptic boundary value problems", Christopher R. Mills, Honors Thesis, 2009.
- "Problems in the College Math Journal", Ashley Sanders, Undergraduate Project, 2009.
- "Dodgson's method of computing determinants", Deanna Leggett, Undergraduate Project, 2008.
**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.

## Older projects

- "Estimation of convergence rates of approximation methods", Joshua Dove and Wesley Duffee-Braun, NSF REU project, Spring 2003.
- "Error Correcting Codes," Sarah Graham, 2003.
- " x'' + P(x) = 0, where P(x) is a quartic polynomial," Amanda Adams, 2002.
- "Assessing Random Iteration," Rochelle Jenkins, 2001.
- "Mathematics of Biology," Chrissy Dear, 2001.
- "Coupled Spring Models," Sarah Graham, 2001.
- "Periodic Solutions to the Forced Duffing Equation," Aaron Lott, 2001.
- "The Gibbs' Phenomenon from a Signal Processing Point of View, K.G. Schultz, 2001.
- "A Visual Bridge to Geometry," Jennifer Heidemann, 2000.
- "Number Sense and Mental Math - A Meaningful Combination," Melissa Avery, 2000.
- "Using Visual Dsolve to Investigate Nonlinear Differential Equations," P. Aaron Lott, 2000.
- "Convolution is a Folding," Jennifer Alsworth, 1999.
- "The Gibbs Phenomenon and Solutions to the Forced Harmonic Oscillator," P. Aaron Lott, 1999.
- "Do you LOGO?" Robin Lofton, 1999.
- "Extending Bernstein Mollifyers in Two Dimensions in Data Analysis," Shywanda Ruffin, 1999.
- "The Period of a Beat," Craig Collier, 1998.
- "Coupled Springs," John Sample, 1998.