She, her, hers

Associate Dean of the Faculty

Mathematics & Computer Science

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. 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. This 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 and Miro Kummel).

Activities & Interests

When I am not in the classroom or in Tutt Science, I enjoy reading and climbing.

Publications

1. An Eigenvalue Problem for the Associated Askey-Wilson Polynomials (with S. Suslov and C. Krattenthaler), to appear.
2. Modeling Transport in Streams (with M. Kummel), PRIMUS 29:7, 2019.
3. Coffee to Go! Modeling Thermoclines in Multivariable Calculus (with B. Kohler), PRIMUS, 2018.
4. Numbers: Histories, Mysteries, Theories. By Albrecht Beutelspacher. Translated by A. Bruder, A. Easterday, and John J. Watkins, Dover Publications, 2016.
5. M. Kummel, D. Brown, A. Bruder, How the aphids got their spots: Predation drives self-organization of aphid colonies in a patchy habitat, Oikos 122 (6), 2013.
6. 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.
7. A. Bruder, L. L. Littlejohn, Non-classical Jacobi polynomials and Sobolev orthogonality, Results Math., 61 (2012), no. 3-4, 283-313.
8. 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.
9. Topological Symmetries in Krichever-Novikov Algebras, (with M. Meiler and A. Ruffing), Nonlinear Phenomena in Complex Systems, 9 (3), 288-293, 2006.

Articles published by my students:

1. E. Campbell, M. Jay, and N. Mankovich: Searching for a Lost Plane: A Probabilistic, Neighborhood-Based Model for Locating Transoceanic Flights, UMAP Vol. 36, No.3, 2015
2. A. Sood, N. Angmo, and Y. Iwasaki: Water, Water Everywhere: Meeting the Demands of Saudi Arabias Water Needs, SIAM Undergraduate Research Online (SIURO), September 15, 2014

Regular Classes

• Precalculus/Calculus
• Calculus 1, 2, 3
• Introduction to Probability and Statistics
• Linear Algebra
• Differential Equations
• Special Topics: Difference Equations
• Real Analysis, Complex Analysis
• FYE: Calculus and Chaos
• Mathematical Modeling
• Mathematical Models in Biology
• Partial Differential Equations
• Numerical Analysis

Committees & Governance