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
  • 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
  • Anesu Munyanyi – Predicting the Behaviour of Breast Cancer Cells Using Data Analytics and Mathematical Modelling
  • Raisa Raofa – Analysis of Nonlinear Phase Accumulation from Transformations of the Polarization States of Light in Connection to Quantum Information
  • John Schmidt – Modelling Stable Equilibrium Orientations of a Submerged Dipolar Particle in an Electromagnetic Field
  • Chin Chin Soe – The Foundations of Romance: Tracing the Impact of Childhood and Adolescent Experiences on Adult Relationships
Professional Affiliations

Society for Industrial and Applied Mathematics