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We discuss mesh-moving, static mesh-regeneration, and local mesh-refinement algorithms that can be used with a finite difference or finite element scheme to solve initial-boundary value problems for vector systems of time-dependent partial differential equations in two space dimensions and time. A coarse base mesh of quadrilateral cells is moved by an algebraic mesh-movement function so as to follow and isolate spatially distinct phenomena. The local mesh-refinement method recursively divides the time step and spatial cells of the moving base mesh in regions where error indicators are high until a prescribed tolerance is satisfied. The static mesh-regeneration procedure is used to create a new base mesh when the existing one becomes too distorted. The adaptive methods have been combined with a MacCormack finite difference scheme for hyperbolic systems and an error indicator based upon estimates of the local discretization error obtained by Richardson extrapolation. Results are presented for several computational examples.

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The Department of Mathematical Sciences at the United States Military Academy is prepared to lead the young minds of America into the 21st century with a bold and innovative curriculum coupled with student and faculty growth models and interdisciplinary lively applications. In 1990, the mathematics department began its first iteration of their "7 into 4" core curriculum. Each year improvements have been incorporated into the core mathematics program. In 1992 , interdisciplinary applications appeared in the core program as an opportunity t o communicate and work with the academic disciplines. Our core curriculum is tied together both vertically and horizontally with threads. These threads tie together both the content within each course as well as among all the courses. Student attitudes are measured through course surveys as we attempt to develop "life long learners". Student performance is measured or calibrated throughout their four years.

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