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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

Mathematics in the internet

Mika Seppälä

University of Helsinki and

Florida State University

we need to be able to
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
standard encoding of mathematics
Standard encoding of mathematics

Needed for proper educational web material used for a virtual university

openmath and mathml
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)
openmath solution
OpenMath solution

Maple

Translation between OM and proprietary presentations by phrasebooks

Mathem.

OpenMath language as defined by CD’s

Editor

Database

Browser

preamble of an openmath cd
Preamble of an OpenMath CD

OpenMath Content Dictionary: arith1

preamble of an openmath cd1
Preamble of an OpenMath CD

OpenMath Content Dictionary: arith1Canonical URL: http://www.openmath.org/cd/arith1.ocd

preamble of an openmath cd2
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

preamble of an openmath cd3
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

preamble of an openmath cd4
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

preamble of an openmath cd5
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

openmath cd definitions
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)

openmath cd definitions1
OpenMath CD definitions

Formal Mathematical property (FMP): eq (lcm ( a, b) , divide (times ( a, b) , gcd ( a, b) ) )

om definition of sin x 2 1
OM definition of sin(x2+1)

x2

………. 2……….

om definition of sin x 2 11
OM definition of sin(x2+1)

x2+1

………. 2 1 ……….

om definition of sin x 2 12
OM definition of sin(x2+1)

(x2+1)

…… ( ) 2 1

om definition of sin x 2 13
OM definition of sin(x2+1)

sin(x2+1)

( ) 2 1

openmath and mathml organizations
OpenMath and MathML Organizations
  • W3 Math working group (chaired by A. Diaz and P. Ion)
  • NAOMI
  • OpenMath Society
  • OpenMath Esprit project
naomi
NAOMI
  • North American OpenMath Initiative
  • Started by S. Braham (SFU) and R. Sutor (IBM)
  • Partner organizations include FSU, NCS, Drexel, UC Berkeley
openmath society
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
openmath esprit project
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
industrial partners of the openmath projects
Industrial partners of the OpenMath projects
  • IBM (techexplorer group)
  • Waterloo Maple
  • Springer Verlag
  • Other European partners
  • North American partners
example of a next generation om application
Example of a next generation OM application

Cellular telephone as a scientific calculator(following slides provided by mofile.com, inc.)

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