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.

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

  • Lorrin Debenport, "Row Reduction of Macauley Matrices", Honors Thesis, 2011.
    M6 matrixM5 matrixM4 matrix
     Examples of the near-triangularity of the Macaulay matrix.
  • Benjamin Benson, "Special Matrices, the Centrosymmetric Matrices", Undergraduate Thesis, 2010.
  • Matthew Dixon, "Tropical Mathematics", 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.
  • Elisabeth Palchak, "A criterion for identifying stressors in non-linear equations using  Gröbner bases", 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.
  • Christopher R. Mills, "Method of approximate fundamental solutions for ill-posed elliptic boundary value problems", Honors Thesis, 2009.
  • Ashley Sanders, "Problems in the College Math Journal", Undergraduate Project, 2009.
  • Deanna Leggett, "Dodgson's method of computing determinants", 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.