Re: Second TI-Nspire report
- From: Michael Kuyumcu <info@xxxxxxxxxxxx>
- Date: 8 May 2007 05:59:45 -0700
On May 7, 10:17 pm, pari...@xxxxxxxxxxxxxx wrote:
Michael Kuyumcu wrote:
I have published a second report on the TI-Nspire (with a few
comparisons with the hp49g+ as to strengths and weaknesses of
algorithms), focusing on students' and parents' observations and
feedback to working with the handheld calculator. The report is
available (in German) at
http://www.noemanetz.de/folgeseiten/artikel/CIMS-SH_Nspire.html
Regards,
Michael Kuyumcu
Fairly interesting report from what I could understand,
it would be nice to have it translated in English!
On your CAS algorithms remarks, I can give you a few hypothesis
* there is most probably nobody at TI working on improving
the maths algorithms. My guess is that they have
concluded the CAS is good enough for the nspire, and
they are most probably right. Competition will not come
until PC CAS will be widely available on handhelds.
The math soft of the nspire is therefore most probably exactly
the same as the latest TI89/V200 AMS versions, just recompiled
(with a few improvements in the non math areas).
* Points 1, 2, 3 of your Qualitat der Algorithm are not
math-related improvements.
* point 4 is because the size of an integer in base 2^8 is coded
on 8 bits: try 256*log(256.)
* point 5 would require something like MPFR on PC
* point 6 is because they use the Taylor formula instead of
arithmetic operations on expansion. That's what I find
the main weakness of the TI, but it's not apparent before
student are at the University, hence TI does not care
(same for arithmetic functions on polynomial or Bezout
identity for integers).
* point 10 is because it's hard to know exactly if a combination
of square roots is not 0. If you compute with sqrt of
2,3,5,6,7 and -1, you must work in an extension of degree
2^5=32 and most importantly you must check at each step
that it does not reduce further.
As for the comparison with the 49g, the CAS software is not
15 years old, 10 (or even less) would be more correct.
Thanks for the feedback. Right now I have too much school-related work
to do and can't come up with a translation, though I agree It would be
nice to have one. Thanks for your hypotheses:
1) I think that if you can't use more than 614 digits for integers,
this very well constitues a weakness of the underlying software
architecture, and in turn of the algorithms. 614 digits may be enough
for most school purposes, but if a student wants to experiment
further, s/he will run into a wall pretty soon, and this can well be
attributed to algorithm design (as the algorithm is tightly
interrelated with the underlying data structures like integer
numbers). On the hp, you have really long integers, up to 524288
digits, if I am correct, at least in theory, and equally long floating
point approximations to real numbers (as an in-built data type!). And
all of this with a pretty old software!
6) Yes, this was Konan Yao's idea, too. I think it will become
apparent already in grade 13 (which we teach at German "Gymnasium"s
when we will be dealing with Taylor developments.
10) I don't agree. Mathematica doesn't need a single second to print
the correct answer. It must be a matter of (non-existent!)
algorithmic quality.
Thanks for the correction of the software age.
Regards,
Michael Kuyumcu
.
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