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

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 ( )

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.

…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!

…but we have to work with this:

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 or a web form.

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 ( )

…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 ( ) Proof of Fermat’s theorem in: Ann. Math. 141 (1995),

Some editing options

Visual editing Bill Gates ( )

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 ( ), author of TeX Leslie Lamport ( ), author of LaTeX

Some publishing options

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

GIFs are accessible – but awful !

Publishing – in MathML

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:

Publishing maths on the web: our solution + ucs package

Multilingual publishing and MathML

Various kinds of illustrations PNGs Flash Cinderella Live3D Java3D Shockwave VRML

Connecting Mathematics notions

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

M-Button: Connecting maths on web (2)

On-line Editing Interface

Download everything!

User settings

User Forums

Popularity: Links to our thesaurus

Popularity: Usage Statistics

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

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

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