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thesaurus.maths: Connecting Mathematics

thesaurus.maths.org: Connecting Mathematics. Mike Pearson University of Cambridge, England Igor Podlubny Tech Univ of Kosice, Slovakia Vera Ol á h J . Bolyai Math Soc, Hungary. Mathematics in Distance and E-Learning.

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thesaurus.maths: Connecting Mathematics

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  1. thesaurus.maths.org:Connecting Mathematics Mike Pearson University of Cambridge, England Igor Podlubny Tech Univ of Kosice,Slovakia Vera OláhJ. Bolyai Math Soc, Hungary

  2. Mathematics in Distance and E-Learning • “In any particular theory, there is only as much real science as there is mathematics” (Immanuel Kant, 1786) • If e-learning technologies are to succeed, they must be able to communicate mathematics with ease. • We are not quite there yet. Immanuel Kant (1724-1804)

  3. We need… • A common format for mathematical language which can be • written and understood by learners and teachers, • written and understood by machines, • copied and pasted without special handling • embedded in documents cleanly • edited and displayed in all web browsers • edited and displayed by all word processors.

  4. …and we need • Editing to include both text and visual modes • Content cleanly separated from presentation • Long-term solution, which is easy to maintain and develop • Multilingual text, too!

  5. …but we have to work with this:

  6. What is so difficult? • Symbols – where are they? • Formulae – how to construct them? • Equations – how to organise them? • Organising layout • Doing all this in an email or a web form.

  7. If Fermat were alive today… Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caperat. ( I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain. ) Pierre de Fermat (1601 - 1665)

  8. …the excuse would be different. Cuius rei demonstrationem mirabilem sane detexi hanc fenestrarum exiguitas non caperat ( I have discovered a truly marvelous demonstration of this proposition that this window is too narrow to contain. ) Andrew Wiles(1953 - )Proof of Fermat’s theorem in: Ann. Math. 141 (1995), 443-572

  9. Some editing options

  10. Visual editing Bill Gates (1955 - )

  11. Text editing • a_{i j} = \left ( \begin{array}{ccc} a_{1 1} & a_{1 2} & a_{1 3}\\ a_{2 1} & a_{2 2} & a_{2 3}\\ a_{3 1} & a_{3 2} & a_{3 3} \end{array} \right ) Donald Knuth(1938 - ),author of TeX Leslie Lamport(1940 - ),author of LaTeX

  12. Some publishing options

  13. XHTML + MathML = the accessible solution • Standards compliant - future proof • Browser independence • Screen resolution independence • Supports various accessibility schemes • User can control colours and styles • Screen readers will work • Highlighting parts of an expression • Formulae can be hyperlinks in whole or in part

  14. GIFs are accessible – but awful !

  15. Publishing – in MathML

  16. International mathematics Building an e-learning system to support multilingual mathematics demands more: • Unicode support is essential • Native keyboard input is essential • Local alphabets and character glyphs should display properly using fonts – not GIFs. With this extra constraint our options are fewer:

  17. Publishing maths on the web: our solution + ucs package

  18. Multilingual publishing and MathML

  19. Various kinds of illustrations Java3D Live3D Cinderella Shockwave VRML PNGs Flash

  20. Connecting Mathematics notions

  21. M-Button: Connecting maths on web (1) Find at least 9 differences between these two pictures !

  22. M-Button: Connecting maths on web (2) http://thesaurus.maths.org/mmkb/entry.html?action=entryById&id=804

  23. On-lineEditing Interface

  24. Download everything!

  25. User settings

  26. User Forums

  27. Popularity: Links to our thesaurus

  28. Popularity: Usage Statistics http://thesaurus.maths.org/logs/

  29. Our contribution to e-learning: • We solved the problem of publishing mathematics in accordance with long-term standards • Standard compliant (XHTML, MathML, CSS2, …) • Browser independent, browsing device independent • OS platform independent • User friendly • Accessible to people with disabilities • An (open source) engine for supporting e-learning in science and engineering • True multilingual solution (Unicode based) • M-buttons service • Numerous illustrations and demos

  30. This is abstract algebra: Evarist Galois (1811 – 1832)

  31. ... and this is the End ... Thank you!

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