This is a grant under the Scientific Computing Research Equipment for the Mathematical Sciences program of the Division of Mathematical Sciences of the National Science Foundation. This program supports the purchase of special purpose computing equipment dedicated to the conduct of research in the mathematical sciences. This equipment is required for several research projects and would be difficult to justify for one project alone. Support from the National Science Foundation is coupled with discounts and contributions from manufacturers and with substantial cost-sharing from the institutions submitting the proposal. This program is an example of academic, corporate, and government cooperation in the support of basic research in the mathematical sciences. This equipment will be used to support three research projects in the Department of Mathematics at Kansas State University: Numerical Solution of Inverse Scattering Problems, directed by Alexander Ramm and Qisu Zou; The CAYLEY Program in Group Theory Research, directed by Andrew Chermak, Alberto Delgado, Ernest Shult, and David Surowski; and Investigation of Steady-State and Dynamical Bifurcations in Poorly-Stirred Premixed and Nonpremixed Chemically-Reacting Systems, directed by Wendell Dan Curtis, Rodney Fox, and Kadosa Halasi.