Industrial and Applied Mathematics
Quoted without permission from "
Graduate Studies
in Industrial Mathematics " (May 1996):
The concept of
Industrial Mathematics is not new.
An extensive article published in the American Mathematical Monthly
(1941), entitled "Industrial Mathematics", by T.C. Fry, details the qualities
and challenges of mathematicians in industry. This article, of course,
anticipated extensive involvment of mathematicians in goverment and industry
during the war.
ITW, being an abbreviation for
"Industriële en en Toegepaste Wiskunde", is the Dutch organization for
Industrial and Applied Mathematics. Professor R. Timman has been one of
the early promotors of ITW at the Delft
University of Technology. For the sake of underpinning this statement,
his "Intreerede" (Dutch) has been OCR-ed
and made on-line.
But there are many other places in the world where
Applied rules the roast nowadays, even more as
it is the case in Delft.
It cannot be denied, though, that there exists links to the World of Pure
Mathematics. Most pure mathematicians in the
Netherlands are a member of the so called
Wiskundig Genootschap. The most important mathematical institute here is
the CWI (Centrum voor Wiskunde en Informatica).
I don't know if he is still alive, but there is one more person I want to
mention explicitly in this context. His name is
Preston C. Hammer
He has been
a professor at the Pennsylvania State University. Several of his articles
and books have had great influence on my thoughts concerning mathematics.
Here are two manuscripts from him which have never been published. (They
were sent to me as a part of a private communication.) If you read these
articles, you will easily understand why it's so difficult to find
a publisher:
Well, a remedy in such cases is simply not to find a publisher and
"publish" a book (Dutch) entirely by yourself.
I guess that's where the Internet and the World Wide Web are for!
The book contains a chapter about Constructivism, which has been translated into English.
(Not difficult, because the former is a litteral translation from an
English text
into Dutch, so I just had to scan and OCR the original.)
Interesting Links
Snippets of Pure Applicable Mathematics
Industrial and Applied Mathematics is focussing on "demanding applications",
rather than to occupy itself with developing even more general & abstract
Theories.
So far so good. But ..
I have the uneasy feeling that some of these
industrial generalists tend to be so busy with generating "significant results"
that they sometimes have overlooked the fact that they are still dealing with
a profession called Mathematics. Those who want to be players in the
game should continue to obey some classical Rules in the first place.
Numerical Analysis
As far as the program sources are concerned, please note the following:
The languages I have employed for writing my programs are the following:
FORTRAN
BASIC
FORTH
PASCAL
/ DELPHI
If your (numerical) method is structured,
then your program may be structured,
regardless of the programming language. The reverse is not true. (HdB)
With other words: structured thinking cannot be replaced by Object Oriented
Programming.
SUNA
SUNA is abbreviation for: "Series on Unified Numerical Approximations".
The whole thing
comprises 221 KB. The Series was published in the
sci.math.num-analysis
newsgroup (1993 - 1994) on the Internet.
Here is the contents of the Series. There are
a few Basic and Fortran
programs associated with it. (I have been in the process of translating some of
these into Turbo Pascal: see below).
Disclaimer:
the articles in the Series are very much outdated now and then (: see the
HTML document for details). They are incidentally
being replaced by articles in LaTeX and PDF.
BETON
Once upon a time, I developed a couple of
Fortran
programs for a person who wanted to calculate the distribution of the
electrical potential in a piece of corroding re-enforced concrete.
A standard 2-D finite element method has been implemented for this
purpose. Perhaps the code and accompanying documents can be useful as kind
of a blueprint for
developing FEA programs of your own. The program has been
rewritten in Turbo Pascal and
Delphi.
BASBOEK
A number of Basic programs is associated with the following (Dutch)
chapter in my
book,
known (to me at last) as
Labrujère's Problem.
Some(what outdated) English renditions of
this document can
be unzipped from SUNA.
Check out here for the relevant parts.
Programs have been rewritten in Turbo Pascal
and Delphi.
ZONWIND
The following is about a collaboration which lasted for 3 years and
finally resulted in a publication by
Horst Fichtner, Han de Bruijn (= myself) and S. Ranga Sreenivasan.
The paper is titled:
Longitudinal gradients of the distribution
of anomalous cosmic rays in the outer heliosphere
How comes that someone who is working at a
Computing Centre of a Technical
University is going to collaborate with an astronomer? Well, that's bit
of a strange story indeed!
I have decided to distribute the computer programs and accompanying
documentation, with exception of the "coeffs" suroutine (containing all
of the Physics and developed by Horst Fichtner himself), as public domain
source code.
It might serve as a (somewhat obsoleted) blueprint for describing anisotropic
Convection & Diffusion within a hemisphere. The mathematics of Convection
& Diffusion should better be replaced by a proper translation from my newer
Delphi Pascal version.
Also available are LaTeX sources of the accompanying
PDF
document, with a somewhat obsolete description of Convection.
(Note: 'ps2pdf' files yield a blurry appearance on the screen with old Acrobat
Reader versions. This doesn't harm printing, which is pretty good. Preferably
use instead Adobe Reader > version 6.0)
Here are some visualizations of the results
obtained by Horst Fichtner.
I was in the opportunity to present a lecture about the numerics of the
matter at the "Woudschoten 1996 conference" on September 26th, Thursday,
12.15 - 12.45, Zeist (the Netherlands). Title of the presentation:
"On solving a Cosmic Ray equation".
A (necessarely incomplete: partly hand-written) collection of accompanying
overhead sheets was processed for inclusion in this
Homepage.
I have been successful in porting a full blown version of the 3-D ZONWIND code
to PC's, using Turbo Pascal and Delphi.
MISCELLANEOUS
For an excellent description of Iterative Methods for Large Sparse Systems of
Equations
unzip and print the Templates PS
document (mirrorred from netlib or GAMS).
The performance of Skew Upwinding has been somewhat disappointing, despite of
my theoretical and
programming effort spent on the subject.
Attempts to generalize the idea to multiple dimensions (say 3 + 1 = space
plus time) seem to be even more discouraging. There exist 58 tetrahedra which
share their corner points with those of one cube in 3-D. (This strategy differs
from the one which was outlined in previous work
and which should be characterized now as rather incomplete).
In 4-D there exist 3008 such pentahedra, however, as has been found by
running another little program. Imagine what
calculation time would be involved with just one of these space-time elements!
Statistics
Here are some of my Turbo Pascal programs I developed while studying a little
bit of Statistics
(though I'm particulary bad in this area):
(Note: these programs will not work without the Borland
BGI stuff, which must be placed in
the C:\TP\BGI directory.)
The first two programs are characterized by the use of
recursion.
Computational Geometry
There's a wealth of computer programs available via Internet, which cover
precisely this area of interest. One can find quite interesting
links in the Directory
of Computational Geometry Software, which in turn can be accessed via
netlib. The latter is an indispensable
resource of mathematical programs of all sorts!
In order to understand subsequent work, you should familiarize yourself
with Delaunay triangulations and Voronoi regions. Maybe a good start is
to download bits of software. For 2-D
as well as for 3-D there exists some
excellent public domain stuff.
There exist two articles in SUNA, the Series on
Unified Numerical Approximations, which are not truly Numerical in nature.
I think they rather belong to the area of Computational Geometry:
The Fortran programs in these two chapters have been zipped into one (16 KB)
file for convenience.
The following is perhaps more closely related to the area of Computer Graphics.
Here is a (Turbo Pascal) program for rendering
an arbitrary (wire-framed, alas!) cylinder, which is rotated into space with
help of
Quaternions. (Note: this program will not work without the Borland
BGI stuff, which must be placed in
the C:\TP\BGI directory.)
Another interesting place may be:
And how about a program which actually does the automatic coloring of
BitMapPed Country
Maps, with a minimal number of colors? Such a program does exist now!
One of the problems associated with the (in)famous
Four Colour Problem is solved herewith.
As part of a larger project (? I think) comes a tiny Delphi (visual Pascal)
program and its
executable
which does (say) the ultimate anti-aliasing of straight lines, according
to the theory in my (Dutch) book.
Another
program
and its
executable
does the anti-aliasing of black and white bit maps (B/W BMP files),
by convolution with a Gaussian distribution.
Puzzles
Or rather: programming them . . . What's useful then is a good
understanding of some algorithms for
Sorting and Searching.
LogiKwiz
It will be explained here, in Dutch,
how so called "LogiKwiz" puzzles are solved by computer programming.
Better skip this section if you prefer to solve them by hand!
Soma Cubes
It will be explained here how
Soma Cube
and Bedlam Cube
puzzles can be solved by computer programming.
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