| Application | Key Mathematics Areas |
| Animal behavior transitions | probability, statistics, Markov chain transition matrix |
| Planning emergancy population relocation for the San Francisco Bay Area | linear optimization, transportation problem |
| Evaluating the effectiveness of different emergency notification methods | probability distribution functions, Laplace transform, convolution |
| Biological Patch-Clamp Instrument | signal processing, filtering, FFT |
| Modeling the energy field generated by an ultrasound probe | PDE, Hankel functions |
| Simulating time-series data for Jackknife statistical research | statistics, resampling, Jackknife |
| Writing assembler routines for matrix/vector operations on an IBM 3090 Vector Facility | linear algebra, assembler language |
| Elements Engineering-Scientific Workspace, providing an interactive environment with matrix, vector, polynomial, and other aggregate data types | linear algebra, numerical analysis |
| Multivariate range searching in engineering material property database | interval analysis, programming, user-interface design issues |
| Modeling of multidimensional, recursive, deforming (bumpy) manifolds | differential geometry, tensor analysis, orthogonal polynomials |
| Writing a 3D computer graphics renderer | parametric representation, tessellation, projective geometry |
| Writing a minimum-length geodesic computation routine Geodes for multidimensional manifolds. It is stored in the Netlib repository of scientific software | differential geometry, system of nonlinear ODEs |
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