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 H3(-c2)", Kinseyann Zarske, Undergraduate Student Paper Competition, 2013 meeting of the LA/MS Section of the MAA.

Animation of profiles curves for CMC H=c surfaces of revolution in H3(−c2) tendi Animation of CMC H=c surfaces of revolution in H3(−c2) tending toward catenoid i

  • "Triangularizing matrices without swapping columns", Lorrin Debenport, Honors Thesis, 2011.
    M6 matrixM5 matrixM4 matrix
     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.

    A non-reduced tropical polynomial

    A fully reduced tropical polynomialA dense tropical polynomial
    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.
  • "A criterion for identifying stressors in non-linear equations using  Gröbner bases", Elisabeth Palchak, Honors Thesis, 2010.
    Finding a common vector
     Trying to compute a vector common to L1 and L2 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 from Jacobi's Theorem  The double-crossing method
    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.