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Nov 9, 2005SIAM Johns Hopkins University1 Math on the Web and the DLMF Project Daniel W Lozier...
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Transcript of Nov 9, 2005SIAM Johns Hopkins University1 Math on the Web and the DLMF Project Daniel W Lozier...
Nov 9, 2005 SIAM Johns Hopkins University 1
Math on the Weband the DLMF Project
Daniel W LozierNational Institute of Standards and
TechnologyGaithersburg, MD 20899-8910 USA
[email protected]://dlmf.nist.gov
Nov 9, 2005 SIAM Johns Hopkins University 2
Outline
• Introduction• Some Math on the Web issues• The DLMF Project• DLMF website demonstration• DLMF search demonstration• Concluding remarks and future work
Nov 9, 2005 SIAM Johns Hopkins University 3
Online Access to Papers
• Author’s home pages• Department websites• Preprint servers• Professional society
websites• University libraries
• Journal websites • Commercial
clearinghouses• MathSciNet• Zentralblatt MATH
Nov 9, 2005 SIAM Johns Hopkins University 4
So What’s the Problem?And What’s the Solution?
• Only recently have papers begun to exist electronically. And there are too many different ways to access the electronic ones. We need a standard way to access all papers electronically.
• WDML (the World Digital Mathematics Library) to the rescue! (well, it’s a possibility, anyway)
• http://www.wdml.org/
Nov 9, 2005 SIAM Johns Hopkins University 5
WDML Vision In light of mathematicians’ reliance on their
discipline’s rich published heritage and the key role of mathematics in enabling other scientific disciplines, the DML strives to make the entirety of past mathematics scholarship available online, at reasonable cost, in the form of an authoritative and enduring digital collection, developed and curated by a network of institutions.
Cornell University DML Project, 2003-2004Funded by NSF
Nov 9, 2005 SIAM Johns Hopkins University 6
Selected Retrodigitization Projects
• JSTOR (US, 30 math/stat journals)• NUMDAM (France, 10 math journals)• GDZ (Germany, 38 math journals)• EMANI (105 math journals from 4 libraries
in China, Germany, US, France; German-Russian initiative in progress for ~70 Russian journals)
Nov 9, 2005 SIAM Johns Hopkins University 7
For Further Information…
• Allyn Jackson, The Digital Mathematics Library, Notices of the AMS, Sep 2003, pp. 918-923
• John Ball, The IMU and You, Notices of the AMS, Nov 2005, pp. 1208-1210
Nov 9, 2005 SIAM Johns Hopkins University 8
A (Much) Bigger View
• MK “Mathematical Knowledge”– Not just traditional math– Procedural as well as declarative– Produced as much by nonmathematicians as
mathematicians– Example: software development– Not always well communicated in journals and
textbooks
Nov 9, 2005 SIAM Johns Hopkins University 9
How Should MK Be Managed?
• We want to use computers, Internet, Web to:– store MK (how to encode?)– display MK (with which browser?)– transform MK (by computer algebra?)– locate MK (with a search engine?)– identify MK (by URLs?)– etc.
Nov 9, 2005 SIAM Johns Hopkins University 10
MK Management MKM is a new interdisciplinary field of
research involving math, computer science, library science, and scientific publishing. Its objective is to develop new and better ways of managing MK using sophisticated software tools.
William M. FarmerACM SIGSAM Bulletin 38(2), June 2004, pp. 47-52
Nov 9, 2005 SIAM Johns Hopkins University 11
MKM Kickoff
• Conference: September 2001, Hagenburg, Austria
• Special Issue: Ann. Math and AI 38, May 2003– 11 papers on, e.g., formula presentation, semantic
markup, authoring systems, formal math systems, theorem provers, new knowledge libraries
– Includes 2 papers on DLMF and 1 on EMANI
Nov 9, 2005 SIAM Johns Hopkins University 12
Major MKM Events To Date
• Hagenburg (2001)• Bertinoro (2003)• Bialystok (2004)• Bremen (2005)• England (2006)
• McMaster U (2002)• Herriot-Watt U (2003)• JMM Phoenix (2004)
Nov 9, 2005 SIAM Johns Hopkins University 13
The DLMF: What is the Model?GPO (1964) Dover (1965)
Nov 9, 2005 SIAM Johns Hopkins University 14
GPO & Dover Impacts
Sales to Date: >150,000 (GPO), >600,000 (Dover)
Citing Journals: Physics, engineering, math, stat
Citations:
Nov 9, 2005 SIAM Johns Hopkins University 15
Nov 9, 2005 SIAM Johns Hopkins University 16
DLMF Approach
Math Database + Special Software Tools
DLMF HandbookDLMF Web Site
DLMF CD-ROMOther DLMF Documents (future)
Nov 9, 2005 SIAM Johns Hopkins University 17
Personnel
• 4 principal editors• 10 associate editors• 35 authors• 25 validators• 15 NIST staff
Nov 9, 2005 SIAM Johns Hopkins University 18
Web Demonstration• Features
– Strong coverage of special functions– References to proofs for every equation– Links to online references, reviews,
constants, software, ...– State-of-the-art 2D and 3D graphics– (Math-aware search)
• Demonstration
Nov 9, 2005 SIAM Johns Hopkins University 19
Search Demonstration• Features
– Accepts math and text queries (with “wild cards”)
– Understands DLMF, Maple, Mathematica names
– Targets are equations, figures, tables, sections– Still very much an object of R&D
• Demonstration
Nov 9, 2005 SIAM Johns Hopkins University 20
Computer Algebra
• DLMF chapter provides basic algorithms, references to additional algorithms, links to software
• A few CA proofs have been provided for DLMF equations – an example follows
Nov 9, 2005 SIAM Johns Hopkins University 21
Nov 9, 2005 SIAM Johns Hopkins University 22
Idea of the Proof
• Construct 4th order homogeneous ODE for LHS (differentiate modified Bessel ODE, annihilate inhomogeneous term, substitute ½)
• Construct general solution of 4th order ODE• Develop a few terms of asymptotic expansions of
the LHS and the 4th order ODE• Match the first 4 coefficients (solve 4th order linear
system)
Nov 9, 2005 SIAM Johns Hopkins University 23
Nov 9, 2005 SIAM Johns Hopkins University 24
Nov 9, 2005 SIAM Johns Hopkins University 25
Future Directions• (Complete basic DLMF content)• (Publish DLMF book, release DLMF web site)• Conduct research in MKM
– semantic math (XML, MathML, …)– math search (Xquery, Xpath, …)– active math (tables, graphs & software “on
demand”)• Use DLMF as research laboratory for
development, application, testing and evaluation of MKM in the field of special functions