This activity arises from the common interest of six faculty members at the Florida Institute of Technology in computers with advanced architectures which enable vector and parallel processing, and in developing attendant mathematical software to run on them. The target machines for this work are at the Argonne National Laboratory and the Cornell Supercomputer Center. The areas in which software development for parallel computers are proposed: (1) Scheduling Problems for Multiprocessors (2) Ordinary Differential Equations, Boundary Value and Eigenvalue Problems (3) Parallel Versions of Certain Linear Algebra Algorithms (4) Monte Carlo Algorithms for Problems in Partial Differential Equations (5) Multigrid Methods in Computational Fluid Dynamics. These research activities are expected to stimulate undergraduates' interest in this popular area of research and attact them into further graduate study.