Re: Programming skills required by mathematicians?

In article
<84498550-6584-4d29-8703-d737ffe2ebcb@[EMAIL PROTECTED]
>,
aruzinsky  <aruzinsky@[EMAIL PROTECTED]
> wrote:
>On Jun 25, 2:40=A0am, rAgAv <ragav.pa...@[EMAIL PROTECTED]
> wrote:
>> Hello,

			.....................

>> PS - At the moment, I know only the basics of C++.

>Beats me.  What would a "pure mathematician" do with computer
>programming?  As an EE grad student, my thesis adviser was from the
>math department and taught a graduate class on numerical analysis.  He
>authored papers mostly on finite element analysis of fluid flow.  I
>always thought of him as an applied mathematician.  The other math
>professors that I knew only used a computer for word processing.

Computers have been used in number theory, algebraic geometry,
computational problems which are more abstract than concrete,
as well as more "practical" problems.  My technical re****ts,
available from the Purdue Statistics Department, are a combination
of an odd type of numerical analysis, and involve using Boolean
operations on the bit patter of floats, something which is not
in any HLL to my knowledge.

Efficient random number procedures can be mainly done in HLL, 
but not with full efficiency.  And I doubt that anyone can 
get a full accuracy efficient procedure to generate 
f(x) = x - ln(1+x) to full machine precision without using
the hardware structure.  Also, on most machines, multiple 
precision (I consider what is called "double" to be single)
arithmetic is a mess because of the forced normalization of
floats and the hidden bit.  The factor may be higher than 10.
This is partly due to the HLLs, which have discounted fixed
point arithmetic.

>If you were an "applied mathematician," I would recommend Fortran and
>Algol only because there are many legacy programs written in these
>languages.  In particular, the Collected Algorithms from ACM Vol I to
>III are mostly in Algol and Fortran.

At that time, those were the only moderately well known HLLs.
Machine independence is fine, but one must take into account
the machine to get efficiency.
-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@[EMAIL PROTECTED]
         Phone: (765)494-6054   FAX: (765)494-0558