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

12÷ 3 = 4?

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)

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 email 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 (1601 - 1665)

…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

Some editing options

Visual editing

Bill Gates (1955 - )

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

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)

http://thesaurus.maths.org/mmkb/entry.html?action=entryById&id=804

On-line Editing Interface

Download everything!

User settings

User Forums

Popularity: Links to our thesaurus

Popularity: Usage Statistics

http://thesaurus.maths.org/logs/

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!