
From:  Martin Baker 
Subject:  Re: [Axiomdeveloper] Raising the bar (again) 
Date:  Fri, 06 Mar 2015 08:27:05 +0000 
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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
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