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Advancements in Knowledge Management for Mathematics: The NIST DLMF Project Overview

This document outlines the developments in knowledge management (KM) for mathematics through the NIST Digital Library of Mathematical Functions (DLMF) project, initiated in 1998 and funded by the NSF. It highlights traditional and modern KM methods, interactive graphics, computer algebra systems, and math-aware search technologies. With contributions from editors, authors, and staff, the project aims to provide comprehensive mathematical content, facilitating effective research options for users. The document also describes the DLMF’s innovative search capabilities and tools for improved mathematical exploration.

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Advancements in Knowledge Management for Mathematics: The NIST DLMF Project Overview

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  1. MKM and the NIST DLMF Dan Lozier National Institute of Standards and Technology Gaithersburg, MD 20899-8910 NA-MKM 2004 Phoenix

  2. Traditional Methods of KM • Handbooks, dictionaries, encyclopedias, atlases • Springer-NY search: Keyword “handbook”: 1125 hits “Handbook” in title/subtitle: 802 hits • CRC Press search: “Handbook” in title/subtitle, “mathematics” as subject/discipline: 41 hits NA-MKM 2004 Phoenix

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  8. New Methods of KM for Math • Stimulus: • CD/DVD, web sites, “digital technology” • Interactive graphics (scientific visualization) • Computer algebra, theorem provers • Key research areas • Math notation and definition • Presentation/representation of math • Math-aware search • Hardware/software standards • Formal methods NA-MKM 2004 Phoenix

  9. NIST Digital Library of Mathematical Functions Project • - project conceived 1998 - sample chapter & prototype web site 1999 - NSF funding received 2000 – 2004 Math content development, editing, validation Web development, inc. search & graphics 2005 – book published, web site released NA-MKM 2004 Phoenix

  10. Personnel • 4 principal editors • 10 associate editors • 35 authors • 25 validators • 15 NIST staff NA-MKM 2004 Phoenix

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  13. DLMF Web Site • Features • Math content • Metadata • Interactive graphics • Math-aware search • Demonstration NA-MKM 2004 Phoenix

  14. DLMF Equation Search System DLMF Database Query Input Query Processing Search Engine Query Output Presentation Module NA-MKM 2004 Phoenix

  15. Query Expression and Entry • Simplified, Latex-like query language • Operators & symbols that can be expressed with 1 or 2 keyboard strokes are so entered • Otherwise, alphabetical names are used (both full-names and short-hand names) • “\” not needed • {} and () are equivalent NA-MKM 2004 Phoenix

  16. Examples NA-MKM 2004 Phoenix

  17. Query Results: 2 Choices • Document list • Links to DLMF sections • Matching equations highlighted • Equation list • Created on-the-fly • Links to containing document, positioned with matching equation at top of window NA-MKM 2004 Phoenix

  18. Recent Developments • Mathematica and Maple nomenclature • function names • order of arguments • Wild cards • $ matches any one token • \* matches any alphanumeric string in a token • Null in argument list, e.g. Euler’s generalized beta integral Beta[z0,z1,,] NA-MKM 2004 Phoenix

  19. DLMF Search Demonstrations Mathematica and Maple Illustrations Equation Search Page NA-MKM 2004 Phoenix

  20. Legendre Functions NA-MKM 2004 Phoenix

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  28. Spheroidal Wave Functions NA-MKM 2004 Phoenix

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