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Mathematics in the internet

Mathematics in the internet. Mika Seppälä University of Helsinki and Florida State University. We need to be able to. Cut and paste mathematical objects Search information using the context of a formula as a key word Exchange scientific data so that the meaning gets understood automatically

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Mathematics in the internet

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  1. Mathematics in the internet Mika Seppälä University of Helsinki and Florida State University

  2. We need to be able to • Cut and paste mathematical objects • Search information using the context of a formula as a key word • Exchange scientific data so that the meaning gets understood automatically • Produce scientific web material with live formulae

  3. Proper standard encoding helps to avoid costly mistakes • Ariane V explosion • Mars orbiter

  4. Standard encoding of mathematics Needed for proper educational web material used for a virtual university

  5. OpenMath and MathML • Languages to define the meaning of mathematical formulae • MathML covers K12 mathematics • OpenMath extends MathML to all areas of mathematics (via extensible content dictionaries)

  6. OpenMath solution Maple Translation between OM and proprietary presentations by phrasebooks Mathem. OpenMath language as defined by CD’s Editor Database Browser

  7. Preamble of an OpenMath CD OpenMath Content Dictionary: arith1

  8. Preamble of an OpenMath CD OpenMath Content Dictionary: arith1Canonical URL: http://www.openmath.org/cd/arith1.ocd

  9. Preamble of an OpenMath CD OpenMath Content Dictionary: arith1Canonical URL: http://www.openmath.org/cd/arith1.ocd CD File: arith1.ocd CD as XML Encoded OpenMath: arith1.omcd

  10. Preamble of an OpenMath CD OpenMath Content Dictionary: arith1Canonical URL: http://www.openmath.org/cd/arith1.ocd CD File: arith1.ocd CD as XML Encoded OpenMath: arith1.omcd Defines: abs, divide, gcd, lcm, minus, plus, power, product, root, sum, times, unary_minus

  11. Preamble of an OpenMath CD OpenMath Content Dictionary: arith1Canonical URL: http://www.openmath.org/cd/arith1.ocd CD File: arith1.ocd CD as XML Encoded OpenMath: arith1.omcd Defines: abs, divide, gcd, lcm, minus, plus, power, product, root, sum, times, unary_minus Date: 2001-03-12 Version: 2 Review Date: 2003-04-01

  12. Preamble of an OpenMath CD OpenMath Content Dictionary: arith1Canonical URL: http://www.openmath.org/cd/arith1.ocd CD File: arith1.ocd CD as XML Encoded OpenMath: arith1.omcd Defines: abs, divide, gcd, lcm, minus, plus, power, product, root, sum, times, unary_minus Date: 2001-03-12 Version: 2 Review Date: 2003-04-01 Status: official Uses CD: alg1, fns1, integer1, interval1, linalg2, logic1, quant1, relation1, set1, setname1, transc1

  13. OpenMath CD definitions lcm The symbol to represent the n-ary function to return the least common multiple of its arguments. Commented Mathematical property (CMP): lcm(a,b) = a*b/gcd(a,b)

  14. OpenMath CD definitions Formal Mathematical property (FMP): <OMOBJ> <OMA> <OMS cd="relation1" name="eq"/> <OMA> <OMS cd="arith1" name="lcm"/> <OMV name="a"/> <OMV name="b"/> </OMA> <OMA> <OMS cd="arith1" name="divide"/> <OMA> <OMS cd="arith1" name="times"/> <OMV name="a"/> <OMV name="b"/> </OMA> <OMA> <OMS cd="arith1" name="gcd"/> <OMV name="a"/> <OMV name="b"/> </OMA></OMA> </OMA></OMOBJ>eq (lcm ( a, b) , divide (times ( a, b) , gcd ( a, b) ) )

  15. OM definition of sin(x2+1) x2 <OMOBJ>………. <OMS cd="arith1" name="power"/><OMV name="x"/> <OMI>2</OMI>………. </OMOBJ>

  16. OM definition of sin(x2+1) x2+1 <OMOBJ>………. <OMA> <OMS cd = "arith1" name="plus"/> <OMA> <OMS cd="arith1" name="power"/><OMV name="x"/> <OMI>2</OMI> </OMA> <OMI>1</OMI> </OMA>………. </OMOBJ>

  17. OM definition of sin(x2+1) (x2+1) <OMOBJ>…… <OMATP> <OMS cd="presentation" name="left"/><OMSTR>(</OMSTR> <OMS cd="presentation" name="right"/> <OMSTR>)</OMSTR></OMATP> <OMA> <OMS cd = "arith1" name="plus"/> <OMA> <OMS cd="arith1" name="power"/><OMV name="x"/> <OMI>2</OMI> </OMA> <OMI>1</OMI> </OMA> </OMATTR> </OMA></OMOBJ>

  18. OM definition of sin(x2+1) sin(x2+1) <OMOBJ><OMA> <OMS cd="transc1" name="sin"/><OMATTR> <OMATP> <OMS cd="presentation" name="left"/><OMSTR>(</OMSTR> <OMS cd="presentation" name="right"/> <OMSTR>)</OMSTR></OMATP> <OMA> <OMS cd = "arith1" name="plus"/> <OMA> <OMS cd="arith1" name="power"/><OMV name="x"/> <OMI>2</OMI> </OMA> <OMI>1</OMI> </OMA> </OMATTR> </OMA></OMOBJ>

  19. OpenMath and MathML Organizations • W3 Math working group (chaired by A. Diaz and P. Ion) • NAOMI • OpenMath Society • OpenMath Esprit project

  20. NAOMI • North American OpenMath Initiative • Started by S. Braham (SFU) and R. Sutor (IBM) • Partner organizations include FSU, NCS, Drexel, UC Berkeley

  21. OpenMath Society • Registered international society in Helsinki • President: A. Cohen (Eindhoven, The Netherlands) • Executive committee: A. Cohen, G. Gonnet, M. Seppälä, S. Watt, S. Braham, M. Dewar, M. Gaetano • openmath.org hosted by FSU

  22. OpenMath Esprit project • Coordinated by M. Dewar (NAG, Oxford) • Funding over 3 M$ for 1997-2000 • Included several academic and industrial partners in Europe • Produced the OM standard, phrasebooks and tools to create and edit OM objects

  23. Industrial partners of the OpenMath projects • IBM (techexplorer group) • Waterloo Maple • Springer Verlag • Other European partners • North American partners

  24. Example of a next generation OM application Cellular telephone as a scientific calculator(following slides provided by mofile.com, inc.)

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