FREE Software Packages for Computational Algebra

From time to time we will give you information about special purpose
software packages which have gained popularity among users worldwide
and are available free. Here are two of those for Computational Algebra:

Fermat:
Fermat is a Mac, Windows and Linux algebra package, strongly optimised
for polynomial and matrix algebra, over the rationals and finite fields. It
does arithmetic of arbitrarily long integers and fractions, symbolic
calculations, matrices over polynomial rings, graphics, etc.
It does not consume much memory and is very fast. It was developed
by Robert Lewis of Fordham University, NY and is available here:
http://bway.net/~lewis/ At this site you can also look at some
interesting papers based on research projects in which Fermat was used.

FELIX:
Felix was developed by the Computer algebra Group at Leipzig
University, Germany and is Available at http://felix.hgb-leipzig.de
Felix is used for computation in commutative and non-commutative
rings and modules. Versions for Windows, Linux and Solaris systems are
available at that site.

Maple : The powerful mathematical engine

The widely acclaimed "Maple" software package originated as project of
the Symbolic Computation group at the University of Waterloo, Ontario,
Canada. Maple's traditional strengths are in symbolic manipulation and
pure-mathematics works regularly used in universities. It has a million
plus user base swelled by licensed Maple symbolics engines behind the
scenes in "Mathcad", "Matlab" and "Scientific Workplace".

There is a strong user base in top-notch universities like Caltech, MIT,
Stanford and Cambridge as well as Industries - like Boeing, Raytheon,
Nortel ... We know some General Relativists who just love using Maple
for doing their tedious calculations of tensor algebra or differential forms.

Maplesoft provides strong online support. The Application Center
provides thousands of free worksheets, including larger "PowerTools"
application packages for researchers and Mathematics educators. There
is also a Student Centre and MaplePrimes, a commercial fast-track
support site for subscribers to the Maple Extended Maintenance Plan.

Math Education:
Maple has a student edition available to accredited students.
MapleNet is an online platform for web-based distance learning.
MapleTA is another online product for "testing and assessment" for
creating and administering online mathematical tests.

Maple 9.5 runs in all post-98 Windows, Linux, Unix and Mac OS X.
We will cover various aspects of Maple products in our future postings.

FEMLAB: Modeling with Partial Differential Equations

Femlab is a powerful solver of Partial Differential Equations (PDEs)
that underlie most science and engineering applications (e.g. fluid
flow, heat transfer, ...). It is a product of the Swedish company
Comsol (www.comsol.com).

Femlab offers an interactive environment to model single and coupled
physical systems based on PDEs. It has a Java-based front end which
can generate 3-D images taht can be rotated in any direction.

Usually it is used in Engineering and Physics research but recently
it has made its way into the laboratories of life sciences as well.
Big drugmakers like Pfizer and Merck are using it in their laboratories.

By the way Femlab can also be used in conjunction with Matlab and
so allows the users to make use of Simulink's powerful modelling
features or utilizing his/her already-developed library of models
in Simulink.

Robert Walker passed away

Robert Walker, the coauthor of the celebrated textbook "Mathematical
Methods of Physics" (by Jon Mathews and Robert Walker) and retired
professor of Physics at Caltech died on January 4th in New Mexico. He
was 85.

Walker's specialization was in experimental high energy physics. He was
a popular teacher and his research spanning 30 years at Caltech
synchrotron was also useful in his longtime colleague Richard Feynman's
theoretical studies of elementary particles.

After retiring from Caltech in 1981, Walker spent his time building
harpsichords at his home in Santa Fe.

Simulink Models

In the past the trend in simulation and modeling of a physical
system that uses a series of, say, partial differential equations was
this: You develop all these functions in C++. But writing hundreds
of lines of new code for each algorithm proved to be time-consuming
and impractical - even the object-oriented modular approach of
C++ coding did not provide much advantage. Maintenance of such
codes in this ever-changing world of software development turned
out to be taking time away from your first objective that you
started with - to understand that "physical system"!

The general trend nowadays is to use Simulink package of Matlab.
Simulink allows the users to write the algorithm quickly and
efficiently in a modular way. The various sections of the model and
the underlying equations are represented as functional blocks in
the software and can be easily manipulated by simply connecting
and arranging the blocks as required. It is also possible to create a
library of such models and then to easily combine them with some
newly developed ones and create a more complicated simulation
model.

"Publicon": Wolfram's new software for preparing documents

Publicon, the new software from Wolfram Research (who gave the
world - Mathematica software introduced in our postings a few
days back. www.wolfram.com) for composing technical documents,
incorporates intuitive maths typesetting technology with additional
templates for putting chemical equations, special characters and
symbols to prepare publication quality documents quickly and easily.

Well ... aren't there a number of such softwares available like
Latex, Tex etc which are widely used by Physics and Mathematics
community? So, what is new?

The best thing we like about Publicon is that the mathematical
equations from documents prepared in Publicon can be copied
and pasted for computation in Mathematica notebook or any other
interface. This dynamic interaction of Mathematica with a
'beautifully' presentable form of the text seemed to be the nicest
feature to hardcore users of Mathematica like us.

Publicon offers a good quality and very user-friendly graphical
user interface and produces platform-independent files that can
be exported to HTML, XML, and yes ...LaTex or custom formats
of Publicon itself.

We get the feeling that Publicon will quickly become a choice for
document preparation by people from a wide variety of fields -
Math, Physics, Engineering, Chemistry and Biotechnology.

Mathematics of Mapping

"The act of mapping is as profound as the invention of a number
system ... The combination of the reduction of reality and the
construction of an analogical space is an attainment in abstract
thinking of a very high order indeed ..."
- Arthur Robinson, "Early Thematic Mapping in the History of
Cartography"

In 1569, the Flemish Cartographer Gerardus Mercator first tried
to create a map of the world on a flat surface, as opposed to a globe
and the mathematical challenge he faced seemed to be
unsurmountable: How can a curved surface be accurately
represented on a flat surface?

In the end he came up with equations of projection which enabled
cartographers to create charts which sailors could easily navigate.
With that huge benefit of those years came the very uncomfortable
feeling of visual distortion. Mercator's projection method showed,
for example, Greenland to be larger than South America, when, in
fact, it is approximately of the size of Mexico.

After about 400 years a renowned cartographer named Arthur
Robinson first took up that challenge of bringing some sense of truth
in that totally mathematical representation of Mercator. In his
procedure of projection he followed a reverse direction - He started
with a sketch of a map that, in both shape and size, appeared to be
more accurately representing the world than that coming out of
Mercator's method. Thereafter he calculated the mathematical
representation of this map.

The poles appeared to be much less distorted in Robinson's map.
His projection method is used by maps from the company Rand
McNally (www.randmcnally.com) who commissioned Robinson to
work on this problem in 1963.

Robinson died on October 10th, 2004 at the age of 89.

The Best Book to Learn the MATLAB Software

"Mastering MATLAB 7" - D. Hanselman & B. Littlefield
(2005 Publisher: Pretice Hall, NJ)

As we introduced earlier, MATLAB ( www.mathworks.com ) is
an almost essential tool for Scientists and Engineers. It stores
all data in Matrix form [so, a scalar quantity or a single number
like 2.3 or 5 is also treated as a matrix, a 1 X 1 matrix] and does
all calculations through matrix manipulations. Matlab succedded
both as a programming language and data visualization tool.

It is an excellent software and can be used even by Middle school
students. There are so many features that its manual, available
in both hard copy and electronic form, exceeds 5000 pages of
information. This is overwhelming if you are starting on your own.

The book we introduce in this posting solves this problem in the
best possible way. We have been fans of this book since its first
edition for MATLAB 5.0 came out in 1998.

Mathworks inc. released MATLAB version 7.0 a few months back
and this book's new edition also came up - with more pages and
more examples and tutorials.

Book: Biography of Ramanujan

[Category: Popular]

The Man Who Knew Infinity: A Life of the Genius Ramanujan"
- Robert Kanigel
[1992 ed. Publisher: Washington Square Press Publication, NY]

This is a biography that everybody we know loved to finish and
we guess our readers too.

The amazing life of the genius Indian Mathematician Srinivasa
Ramanujan Iyengar is told in the best possible way with great
authenticity.

This book is so good that we do not feel like writing about it -
because we see that we start telling the book itself chapter by
chapter without skipping any line.

Is not that frustrating as a reviewer? So, just read ...

NUMB3RS : CBS show solves Crime with Math

Last night was the 4th episode of the new CBS crime drama:
NUMB3RS www.cbs.com/primetime/numb3rs/

A brief and quick description of the show: It is about an FBI
special agent (Don) and his genius mathematician brother
(Charlie) who, at 30, is a faculty of a prestigious institute like
Caltech in Pasadena. Don unwillingly (initially) takes his
brother's help to solve one mystery after another.

How much of the mathematics shown and discussed in the show
is real? Big Mathematicians say - Yes. For most of the part it
is real. Gary Lorden, a Caltech Professor of Mathematics, whose
main expertise is in the vast field of "Probability and Statistics"
and specifically in Sequence theory is a consultant to the show.

In fact the formula used in the first episode (for capturing a
serial rapist turned a killer) was derived by a Canadian
Mathematician who successfully used it to locate the point of
origin of a serial killer in Louisianna.

As they say, Math controls everything in this unverse.
Even its crimes and criminals!

Software and Mathematics

Over the years a number of fantastic softwares have got into the
desktops and laptops of Mathematicians, Scientists and Engineers
and are helping them in a spectacular way.

Considering the progress made in almost all fields in last century
or so, it is natural that such progress was on line for Mathematical
Softwares. After all, the whole civilization depends on how correctly
we use our Mathematics

Two softwares just come first in this list: Mathematica and Matlab.

The speciality of Mathematica is in Symbolic manipulation. It's just
wonderful. If you type a simple command like
> Expand[(a+b)^2 ]
it gives answer
> a^2 + 2 a b + b^2
In 1970s perhaps no one imagined it would be possible to do such
things. Mathematica is brain child of Stefan Wolfram, that genius
graduate student from Caltech who later wrote that great book
"A New Kind of science" .

Matlab, on the other hand, came out of the brain of Jack Little who
was an undergraduate at MIT. Matlab is based on matrix
manipulation techniques and comes to be very handy tool for all
kinds of Technology-related studies.

For details about Mathematica go to www.wolfram.com
and for Matlab www.mathworks.com

Mathematics: The fun and stories and information

We'll post a lot of things about Math here ...
Watch out ...