Re: Programming skills required by mathematicians?

On Jul 1, 10:16=A0am, hru...@[EMAIL PROTECTED]
 (Herman Rubin) wrote:
> In article
<84498550-6584-4d29-8703-d737ffe2e...@[EMAIL PROTECTED]
>,
>
> aruzinsky =A0<aruzin...@[EMAIL PROTECTED]
> wrote:
> >On Jun 25, 2:40=3DA0am, rAgAv <ragav.pa...@[EMAIL PROTECTED]
> wrote:
> >> Hello,
>
> =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 .....................
>
> >> PS - At the moment, I know only the basics of C++.
> >Beats me. =A0What would a "pure mathematician" do with computer
> >programming? =A0As an EE grad student, my thesis adviser was from the
> >math department and taught a graduate class on numerical analysis.
=A0He
> >authored papers mostly on finite element analysis of fluid flow. =A0I
> >always thought of him as an applied mathematician. =A0The 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. =A0My 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. =A0And I doubt that anyone can
> get a full accuracy efficient procedure to generate
> f(x) =3D x - ln(1+x) to full machine precision without using
> the hardware structure. =A0Also, 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. =A0The 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. =A0In 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. =A0I do not claim that these views
> are those of the Statistics Department or of Purdue University.
> Herman Rubin, Department of Statistics, Purdue University
> hru...@[EMAIL PROTECTED]
 =A0 =A0 =A0 =A0 Phone: (765)494-6054 =A0 FAX:
(765)=
494-0558

With modern compilers, one can easily mix a HLL with assembly
language.  For example, Visual C++ object code can be disassembled
into assembly language, modified, and then recompiled back to object
code.

For mental exercise and development, I recommend learning Forth which
uses Reverse Polish Notation (RPN), i.e. operands precede operators,
as in reality.  Forth and RPN foster efficient programming and
utilization of RAM. Standard Forth does not use floating point, but
Forth can be modified to do anything because it is easily extensible.
Some modified versions directly use the PC FPU stack very efficiently.