1. Nov 9, 2005SIAM Johns Hopkins University1 Math on the Web and the DLMF Project Daniel W Lozier National Institute of Standards and Technology Gaithersburg, MD 20899-8910 USA lozier@nist.gov http://dlmf.nist.gov

2. Nov 9, 2005SIAM Johns Hopkins University2 Outline Introduction Some Math on the Web issues The DLMF Project DLMF website demonstration DLMF search demonstration Concluding remarks and future work

3. Nov 9, 2005SIAM Johns Hopkins University3 Online Access to Papers Author’s home pages Department websites Preprint servers Professional society websites University libraries Journal websites Commercial clearinghouses MathSciNet Zentralblatt MATH

4. Nov 9, 2005SIAM Johns Hopkins University4 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/

5. Nov 9, 2005SIAM Johns Hopkins University5 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, 2003-2004 Funded by NSF

6. Nov 9, 2005SIAM Johns Hopkins University6 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)

7. Nov 9, 2005SIAM Johns Hopkins University7 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

8. Nov 9, 2005SIAM Johns Hopkins University8 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

9. Nov 9, 2005SIAM Johns Hopkins University9 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.

10. Nov 9, 2005SIAM Johns Hopkins University10 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. Farmer ACM SIGSAM Bulletin 38(2), June 2004, pp. 47-52

11. Nov 9, 2005SIAM Johns Hopkins University11 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

12. Nov 9, 2005SIAM Johns Hopkins University12 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)

13. Nov 9, 2005SIAM Johns Hopkins University13 The DLMF: What is the Model? GPO (1964)Dover (1965)

14. Nov 9, 2005SIAM Johns Hopkins University14 GPO & Dover Impacts Sales to Date: >150,000 (GPO), >600,000 (Dover) Citing Journals: Physics, engineering, math, stat Citations:

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16. Nov 9, 2005SIAM Johns Hopkins University16 DLMF Approach Math Database + Special Software Tools DLMF Handbook DLMF Web Site DLMF CD-ROM Other DLMF Documents (future)

17. Nov 9, 2005SIAM Johns Hopkins University17 Personnel 4 principal editors 10 associate editors 35 authors 25 validators 15 NIST staff

18. Nov 9, 2005SIAM Johns Hopkins University18 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

19. Nov 9, 2005SIAM Johns Hopkins University19 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

20. Nov 9, 2005SIAM Johns Hopkins University20 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

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22. Nov 9, 2005SIAM Johns Hopkins University22 Idea of the Proof Construct 4 th order homogeneous ODE for LHS (differentiate modified Bessel ODE, annihilate inhomogeneous term, substitute ½) Construct general solution of 4 th order ODE Develop a few terms of asymptotic expansions of the LHS and the 4 th order ODE Match the first 4 coefficients (solve 4 th order linear system)

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25. Nov 9, 2005SIAM Johns Hopkins University25 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