Performs research and maintains expertise in the methodology and application of mathematical algorithms and software in support of computational science within NIST as well as in industry and academia; in particular, maintains and applies expertise in mathematical subdisciplines such as numerical analysis, special functions, linear algebra, partial differential equations, and symbolic computing, as well as in high performance computing, computer arithmetic, mathematical software design, testing and evaluation methodology, advanced mathematical graphics, and repository technology; supports and advances the NIST scientific computing environment by developing fundamental mathematical algorithms of particular concern to NIST programs, implementing them in high-quality software, and consulting and collaborating with NIST scientists in their use; develops computational techniques, tools, and standards for representation, search, visualization, and exchange of mathematical objects and databases; and works with academia, industry, professional societies, consortia, and standards bodies on tools to ensure the performance, usability, reliability, portability, and compatibility of mathematical software via demonstrations, testbeds, prototypes, reference implementations and the wide dissemination of information.