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School of Mathematics and Natural Sciences

Sample Undergraduate Research Projects

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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 matrix M5 matrix M4 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 polynomial A 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.