Re: [Axiom-developer] Raising the bar (again)

[Martin Baker]

> It is vital that we make the strong connection between group theory
> and Spad completely transparent. People need to have a presentation
> that makes it easy to move between group theory and Spad.

There is a book, which I like, called 'Visual Group Theory' [Nathen 
Carter, 2009]. This looks at the various ways to start learning about 
group theory: Cayley diagrams, multiplication tables and so on and a 
very graphical way. I think that this combination of looking at a 
subject from multiple viewpoints and in a visual way is very powerful. 
This would be even more powerful if both of these things could be done 
in an interactive way using Axiom.

Unfortunately the nature of Axiom seems to be against these things. 
First Axiom only defines groups in one way, as permutations, this makes 
sense if we want to make our definition as scalable as possible but it 
does mean that Axiom is not a tool for learning about mathematics.

Secondly, although Axiom has some graphics, it is clunky and does not 
produce the sort of graphics shown in the book above. It seems to me, 
that for discrete mathematics, a command line interface is very 
unhelpful. What is needed is an interactive graphical interface.

I realise that what you are interested in is teaching people about 
Axiom, not teaching people about mathematics (using Axiom). However 
perhaps there is some link between these. Personally I might question if 
concentrating on teaching mathematics using Axiom rather than just 
teaching Axiom might be a more successful approach?

Martin