Re: [Axiom-developer] SAGE, Axiom, and usage

[C Y]

--- Gabriel Dos Reis <address@hidden> wrote:

> For my own courses, I've been preparing materials for using Axiom as
> my main vehicle for introducing students to symbolic computation.
> Yesterday, I had to reconsider that decision given the many whoops to
> jump through and unfavorable impression when comparedn to recent
> versions of Maple or Mathematica.  Now, I'm thinking about switching
> to Maple alright for this fall.  

I hate to say this, but I think Bill made a good point about Axiom
probably not being the best way to introduce folks to computer algebra.
 I myself came to Axiom only through 1st Mathematica and then Maxima. 
Looking back on it, the benefits of Axiom become more apparent when you
start to reach the limits of what other systems are easily able to
accomplish (I didn't necessarily reach mathematical limits, but
certainly units in Maxima brought up some issues that made me think
about things differently.)

I'm not a teacher (only done a few labs over the years and a bit of
tutoring) but if I were to offer a suggestion (just what you needed ;-)
I would say this:

1.  Start by introducing either Maxima using the wxMaxima interface or
perhaps Yacas.  Either of those will probably be less intimidating to
students up front, and their limitations will not be readily apparent. 
Their prior experience with calculators will map to either of these
systems reasonably well - they will most likely be less intimidated if
they don't need to comprehend what a "type" is or why it matters up
front.

2.  Develop the students by gradually exploring more of the potential
of the first system, and take them to some problems that "symbolic
computation" doesn't handle so well.  I.e., show them both the utility
of symbolic computation (which the commercial success of Mathematica
and Maple prove is considerable) and its limitations.  This is good
both for showing the limitations of the approach and also why computers
can't substitute for an educated brain.

3.  Then, later on in the course, introduce them to a more formal
approach that avoids these limitations.  Most will probably not be real
excited about this because it will look harder (being precise is always
hard work ;-) but most will probably remember and if, in the future,
they begin to do work that would benefit from Axiom's more rigorous
approach they will know both about Axiom and why it might be better.

Of course, that was easy to say and hard to do.  Just a thought, for
whatever it may be worth.

Cheers,
CY

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