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Andrea Bruder

Assistant Professor

Andrea Bruder received her Diploma in Mathematics at the University of Technology in Munich, Germany, and earned her Ph.D. in Mathematics at Baylor University.

My research interests are in the theory of differential equations and their applications in mathematical biology. In my dissertation, I studied the spectral theory of the Jacobi differential equation. Most recently, I have worked with David Brown in CC's math/computer science department and Miro Kummel in CC's environmental program on modeling an insect predator-prey system.

Our field system consists of ladybugs (Coccinella septempunctata, Hippodamia convergens) and aphids (Aphis helianthi), which are patchily distributed on racemes of yucca plants (Yucca glauca) in the Rocky Mountains of Colorado. The 107 patches are connected by the relatively fast dispersal of the ladybugs, whereas the aphids are relatively sessile. In a 30-day field study we observed a split of the aphid population sizes into extremely large and extremely small populations, a phenomenon known as spatial self-organization or pattern formation. In order to study the effects of density independent predator and prey immigration into the system and migration due to the predator's attraction to predation, work in progress includes the study of a two-patch, ordinary differential equations model, which is continuous in time and discrete in space (with David Brown, Miro Kummel, and Hannah Thompson).

Activities & Interests

When I am not in the classroom or in Tutt Science, I enjoy rock climbing and mountain biking. About once a year, I do a presentation about the Mathematics of Rock Climbing ("The Forces of Falling") in collaboration with the downtown gym, CityRock.

Publications

  1. M. Kummel, D. Brown, A. Bruder, How the aphids got their spots: Predation drives self-organization of aphid colonies in a patchy habitat, Oikos, to appear.
  2. A. Bruder, L. L. Littlejohn, Classical and Sobolev orthogonality of the nonclassical Jacobi polynomials with parameters α=β=-1, Ann. Mat. Pura Appl., to appear.
  3. A. Bruder, L. L. Littlejohn, Non-classical Jacobi polynomials and Sobolev orthogonality, Results Math., 61 (2012), no. 3-4, 283-313.
  4. A. Bruder, L. L. Littlejohn, D. Tuncer, R. Wellman, Left-definite theory with applications to orthogonal polynomials, J. Comput. Appl. Math., 233 (2010), 1380-1398.

Regular Classes

  • Precalculus/Calculus
  • Calculus 1, 2
  • Linear Algebra
  • Differential Equations
  • FYE: Calculus and Chaos (with Jane McDougall)
  • Mathematical Modeling Adjunct (with Amelia Taylor)

Courses

  • MA220 – Linear Algebra

Education

    Ph.D. Baylor University, 2009