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Areas of Interest

My areas of interest are analysis and differential equations, particularly using tools built from complex and functional analysis to investigate various properties of differential operators. Most recently, I have been working on problems relating to the spectral theory of ordinary differential operators via various methods for constructing spectral measures. Prior research interests include investigations of invariants for specific classes of knots and some problems in inverse scattering theory.

Courses Taught
  • Calculus 1
  • Calculus 2
  • Linear Algebra
Publications
  • M. Bush, D. Frymark, and C. Liaw. Singular boundary conditions for Sturm–Liouville operators via perturbation theory. Canad. J. Math., 2022
  • M. Bush, C. Liaw, and R.T.W. Martin. Spectral measures for derivative powers via matrix-valued Clark theory. J. Math. Anal. Appl., 514, 2022
  • D. Shepherd, J. Smith, S. Smith-Polderman, M. Bush, J. Bowen, and J. Ramsay. Braid computations for the crossing number of Klein links. Involve, 8(1):169–179,2015.
  • M. Bush, K. French, and J. Smith. Total linking numbers of torus links and Klein links. Rose-Hulman Undergraduate Mathematics Journal, 15(1):72–92, 2014
Professional Affiliations

Society for Industrial and Applied Mathematics