KDI: Mathematical Foundations for a Networked Scientific Knowledge Base

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9980036This project addresses the problems of generation, validation, organization, distribution and use of a Web-oriented knowledge base of mathematical concepts. The field of coverage is the special functions of applied mathematics. The investigator and his colleagues develop a Digital Library of Mathematical Functions (DLMF), a Web-accessible knowledge base of validated mathematical data obtained by a completely new survey of the archival literature. The DLMF delivers reference information in the concise style of the classic NBS Handbook of Mathematical Functions (Abramowitz and Stegun, eds.), but within a rich structure of semantic-based representation, metadata, interactive features, and internal/external links. It supports diverse user requirements such as simple lookup, complex search and retrieval, formula validation and discovery, automatic rule generation, interactive visualization, custom data on demand, and pointers to software and evaluated numerical methodology. As successor to the NBS Handbook, the DLMF provides an authoritative source of mathematical concepts traceable to a NIST definition. The basic research issues are associated with content, representation, and interaction of humans and other agents with the DLMF knowledge base. Such issues include identification and validation of relevant material; development of semantic-based representations of mathematical information; structure of metadata; search and retrieval in mathematical databases; and conversion of mathematical data between formats suitable for composition, display, and computation. These problems are being solved by an international team of experts, overseen by an editorial board. The DLMF will be disseminated in a print edition with CD-ROM as well as from a free Web service that will be maintained indefinitely at NIST.The project personnel are constructing a Digital Library of Mathematical Functions (DLMF) which provides NIST-certified reference data and associated information for the higher functions of applied mathematics. Such functions possess a wealth of critically important and highly technical properties that are used by engineers, scientists, statisticians and others to aid in the construction and analysis of computational models of materials and processes in a wide variety of applications. TheDLMF assists its users in locating formulas, algorithms and software; in understanding complex relationships through interactive graphics and typical applications; in tracing mathematical definitions and properties to a NIST standard; and in transcribing intricate mathematical information into documents and computer programs with complete reliability and accuracy. For example, software companies will be able to use the DLMF to produce vastly improved libraries and software packages. This is very significant because software provides the most effective means for practitioners to employ mathematical methods easily and reliably. The current standard reference for mathematical functions, developed by NIST with NSF support in the 1950s, is seriously out-of-date. A myriad of new properties, functions, applications and computational techniques have come into importance since then. This gap needs to be filled, and done so in a way that takes full advantage of modern information technology. The data are presented at a state-of-the-art World Wide Web site that will become a focus for the community of researchers and users of mathematical function technology, as well as in a book with CD-ROM. It is expected that the DLMF will be a model for other projects of similar type. This KDI project is supported by the Division of Mathematical Sciences and the Division of Information and Intelligent Systems.