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PREFACE The National Research Council's Panel on the Mathematical Sciences in High-Performance Computing and Communications was established at the request of the National Science Foundation and charged with producing a timely report and briefing to . examine the elements of the federal government's High Performance Computing and Communications (HPCC) program and explicitly identify the role of the mathematical sciences community in that effort; and . identify the role of mathematical sciences research in an illustrative subset of the "Grand Challenges" of computational science, which are the ultimate targets of the infrastructure to be built by the HP CC program. It was clear to the panel that mathematical sciences research has contributed greatly in the past to high-performance computing and communications, and continued mathematical research must be an integral part of the HPCC program in order for it to meet its goals. Likewise, the mathematical sciences have made fundamental contributions to attacks on grand challenge problems, and the development of new mathematics will continue to be critical to ongoing progress. This report documents these claims. The panel is very grateful to the anonymous reviewers who provided excellent feedback in a short time. These colleagues strengthened the report significantly. . V11

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