45 / 2012 FOSS for mathematics

I have added a detailed report on FOSS tools for those who use mathematics.

The report is downloadable from ::
http://www.freewebs.com/profpartha/publications/fossmath5.pdf

partha

112/2011 Saluting a mathematical genius

India celebrates 125 years of Srinivasa Ramanujan (1887-1920). . It is so gratifying to note the way we are celebrating this gift India gave to mathematics.

THE HINDU, India's most respected newspaper, carries a full supplement of 8 pages dedicated to Ramanujan. It also carries a whole page interview with Robert Kanigel, author of Ramanujan's biography "The man who knew infinity". The year 2012 has been nominated as the year of Mathematics. 22 Dec.(his day of birth) will be declared as the "National Mathematics day". The Prime Minister of India will inaugurate the year-long celebrations. A movie on Ramanujan's life has been planned.

I can't help comparing this expression of celebrating mathematics, with the less than lukewarm attention this same newspaper gave to ICM 2010, a world class conference on mathematics, held in 2010 in Hyderabad.

In my own little way, I have added two books on mathematics/Ramanujan to
the Professor's bookshelf

Let us hope all this will inspire our future mathematicians, and bring us at least one more Ramanujan.

partha

Interesting property of Fibonacci series

When we take a look at Fibonacci series, through modulo arithmetic, we get some interesting observations :

http://www.math.temple.edu/~renault/fibonacci/fib.html
http://en.wikipedia.org/wiki/Pisano_period

Maths is interesting, because there is so much beauty to discover.

partha

PS: This was a question in my exam for Kathmandu Uiniversity students.

YARMB

Yet another remarkable mathematics blog YARMB

Take a look ::
http://divisbyzero.com/

partha

Well said...Prof. Einstein

(About mathematics) :: Why does this magnificent applied science, which saves work
and makes life easier, bring us so little happiness? The simple
answer runs: Because we have not yet learned to make sensible
use of it.
Albert Einstein

Hyderabad Professor honoured again.

Prof C R Rao, eminent statistician and mathematician, is currently emeritus Professor at Hyderabad Ubiversity.
http://en.wikipedia.org/wiki/Calyampudi_Radhakrishna_Rao.
In addition to many awards and honours he has earned, he was recently honoured with he Royal Statistical Society’s Guy Gold medal.

Prof. C.R. Rao, is the first Asian to receive the Royal Statistical Society’s (TRSS) Guy Gold medal, the highest honour in statistics in the United Kingdom. TRRS ::

http://en.wikipedia.org/wiki/Royal_Statistical_Society

Prof. Rao is the prime mover for CR Rao Advanced Institute of Mathematics, Statistics and Computer Science (aka AIMSCS), located at the University of Hyderabad.


http://en.wikipedia.org/wiki/CR_Rao_Advanced_Institute_of_
Mathematics,_Statistics_and_Computer_Science


Congrats to you Sir. We are blessed to have you with us.

partha

Graph colouring (coloring)

Graph colouring is an interesting and computationally hard problem in graph theory. It has applications in a wide variety of areas. Although the problem is very simple to state, the underlying principles are often very hard to understand. Solving the graph colouring problem is a challenging exercise.
The only general solution to finding an optimal graph
coloring is exhaustive search. This strategy can become prohibitively expensive, as the graph size increases.
It is alo very difficult to get good material which one can read, and approach graph colouring problems.

I found a good starting point for the exploration of graph colouring. This overview of graph colouring, created by two Professors of the Danish institute IMADA (belonging to the University of Southern Denmark )

http://www.sdu.dk/Om_SDU/Institutter_centre/Imada_matematik_og_datalogi?sc_lang=en, gives an exhaustiv overview of graph colouring.

You can find the overview at ::

http://www.imada.sdu.dk/~btoft/Graphcol/overview.html


partha

One more source for graph theory

A very well done paper on graph thoery, mostly on the applications of graph theory ::


http://www.dharwadker.org/pirzada/applications/

Take a look.

partha

For lovers of mathematics

Lovers of mathematics will

love this.

Take a look.

partha

I now have an entry in the Electronic World Directory of Mathematicians (EWDM) maintained by the International mathematical Union.

Visit ::

http://www.mathunion.org/ewdm/search.php

and search for "partha"


partha

Intl. Math. Union (IMU) Newsletter

IMU recently conducted the ICM2010 Conference in Hyderabad. Unfortunately, teachers like me, do not have the money to pay for the registration expenses. But there is some hope for us. We can keep ourselves informed, by subscribing to the FREE (gratis) newsletter of IMU:: IMU-Net.

There are two ways of subscribing to IMU-Net:

1. Click on http://www.mathunion.org/IMU-Net with a Web browser and go
to the "Subscribe" button to subscribe to IMU-Net online.

2. Send an e-mail to imu-net-request@mathunion.org with the Subject-line:
Subject: subscribe

In both cases you will get an e-mail to confirm your subscription so
that misuse will be minimized. IMU will not use the list of IMU-Net
addresses for any purpose other than sending IMU-Net, and will not
make it available to others.

Previous issues can be seen at:
http://www.mathunion.org/imu-net/archive/


The IMU General Assembly, at its
meeting in Bangalore, prior to the ICM, decided that Seoul, the
capital of the Republic of Korea, will host the ICM in 2014. This
congress will take place from August 13 to 21, 2014.

partha

Maths awards

One of the biggest events in the International Congress of mathematicians 2010, now on at Hyderabad, india, is the announcement of the world's topmost awards in mathematics. We will get to know the people who made amazing contributions to mathematics.

The awards are listed at ::
http://www.icm2010.org.in/imu-prizes

This year's award winners are listed at ::
http://www.icm2010.org.in/imu-prizes/prize-winners-2010

You can see the names, affiliations and a brief bio sketch of the awardees. You can also get to know the citation of the award.

Take look.

Try harder. Maybe you will find your name in the next list.

partha

Mathematical writing

"Mathematical Writing" by Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts

This is a report based on a course given at Stanford University in 1987.

I stumbled on a pdf version of this classic by D E Knuth. Gives you many rules of clean and clear mathematical writing. It borrows many ideas from the classic book of style by Struk and White. This is a must-read for all those who (like me) use maths for making a living. Wish my maths teachers had read this book before teaching me maths.

partha

**************

Mathematics made difficult ..... and fun

Mathematics made difficult
[by] Carl E. Linderholm. (207 pages | 1972 | ISBN: 0529045524 | DJVU/PDF )

This is a remarkable book with a remarkably innovative title. It is usual for books to claim that they make a given subject simple, or uncomplicated (whereas, in fact, they complicate the subject beyond any hope). This book starts with an unusual claim. It may or may not have made maths difficult, but it certainly makes maths real fun to explore and discover. Each problem, and the discussion that follows, is a bundle of very hilarious and often subtle humour. The author however, manages to retain the rigour and precision of maths.

Thankfully, this book is available for download from the w-w-web. There are actually many sources from where you can download.

Download the book, read it, enjoy the wisdom, and become a better maths teacher.

partha

P=NP

My last post was about the recent achievement by an Indian mathematician to solve the P=NP? riddle. I did a Google search which threw up 30 results. Of these almost a dozen were from Germany (or in German), a few in Russian, and a few were newspaper reports. Of course, there was none from any mathematical research institute from India. This explains why Mr. Deolalikar lives in USA.

Mr. Vinay Deolalikar, if you are reading this blog, please be convinced that there are some Indians (although very few), living in India, who recognise and appreciate your efforts. Congrats to you Sir. We salute you.


partha

An Indian in America ... does it again

A mathematician of Indian origin (Vinay Deolalikar), settled, as expected in the USofA, has done something extraordinary. The P=NP ? conundrum has vexed mathematicians ever since it was introiduced. It was introduced in 1971 by Stephen Cook in his paper "The complexity of theorem proving procedures", and is considered by many to be the most important problem in the field of mathematics. The problem definition/statement itself is not easy to grasp. And now, a young Indian, breaks this mystery and comes with the answer (a NO).

I did a Google search "P=NP Deolalikar" and got 30 results. You can read about this achievement at::

http://www.livemint.com/2010/08/10230113/Indian-scientist-offers-proof.html?h=E

The paper still needs to be published in a major refereed journal and then be “generally accepted” by the mathematical community within two years of publication for Deolalikar to collect his Clay prize.

But experts have agreed, after preliminary readings, that his paper is an effort worthy of study.

Stephen Cook, who has written the official description of the P=NP problem for the Clay Institute, has called it “a relatively serious claim to have solved P vs NP”.

There is also a wiki page at http://en.wikipedia.org/wiki/P_versus_NP_problem whih explains the P=NP problem.

Take a look.

partha

PS:: The "International Congress of Mathematicians 2010", the world's biggest maths conference will be held in Hyderabad next week. See :: http://www.icm2010.org.in/

*********

Method of invariants

I read an excellent article on the "method of invariants", a less known but powerful tool for mathematical problem solving. The article, by Rajaram Bhat, appeared in the July 2010 issue of RESONANCE. This journal, RESONANCE, is another remarkable journal, and is published in India, by the Indian Academy of Sciences. You can browse this journal and back issues from their website ::
www.ias.ac.in/resonance/.

partha

The randomness of randomness

The randomness of randomness

GOD does not play dice .... Albert Einstein.

It all started with a rather innocent looking question on the Internet. Here is how it ran: Given a number (only one), we can answer certain questions about it e.g. is it a prime ? is it an even number ? etc. Now, given a number (only one) can we say if it is a random number ? Why not ?

I posted the above question on the net, and got some replies, all of which gave rise to more questions.

Some of the responders were statisticians in the traditional sense. And predictably, they took examples of their pet random process: tossing a coin, or casting a die. Yes, given no other information, such experiments may be considered to give random outcomes (will it be a head ? will be a tail ? will the die yield an even number ? will the next child be a boy ? ...). But, there is a catch somewhere deep within this premise. A physicist friend of mine argued that there could be no such thing as a random number generated by such devices (die, coin). After all, the outcome of a toss is bound by strict laws of physics. It is a different thing that we cannot measure exactly the various parameters influencing the outcome e.g. the force exerted by the thumb when tossing a coin, the velocity of air, temperature gradients, ballisttics etc. etc. All of these are important, to determine the exact trajectory of the coin, and hence the exact outcome of this experiment. If we could measure (and control) all these, there will be no such thing as a random toss. We can put forth such arguments for all such so-called random phenomena when they involve physical devices and objects.

We will stop tossing coins in the air, or throwing dice on the table, and look for some non-physical phenomenon, for generating random numbers. Let us look at the last digit of the first n (assume n=20 for this case) prime numbers [1]. Here is what we get:
2 3 5 7 1 3 7 9 3 9 1 7 1 3 7 3 9 1 7 1
Looks like a perfect chain of random numbers (perhaps generated
by a ten-faced die). Wrong again -- we can predict exactly the
21st digit which follows the last one above: 3 (the 21st prime
is 73) . Look at this from another viewpoint. Suppose we decide
to write these random numbers in a binary notation. And now, we
look at the last digit only (in this case we must call it a bit).
Here is what we will get:
0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ....... ad infinitum.
Nothing could be more predictable than this series !

Now, let us look at the first n (n=20) primes themselves ( The first 1000 primes :: http://www.utm.edu/research/primes ):
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71.... ??

If we know the magic potion which was used for generating the above numbers, then we can predict exactly the number which must follow (the 21st prime number in the series). If we ignore for a moment the monotonically increasing magnitudes, and if we hide the common phenomenon behind these numbers (the fact that they are all primes), we probably have a good candidate for random numbers. Suddenly, the same 21st number becomes random and unpredictable !

The conclusion is simple, there is no such thing as a true random number ! It is just whether we are or we are not able to formalise the underlying generating phenomenon that makes all the difference. Some people prefer to use a more explicit term: non-deterministic phenomenon , to refer to such processes.

Let us go back and look at the question which started all this. The answer is a big NO, because: .... we let the reader work out the arguments. (They rightly say so ...By just looking at the tracks, you can't say which way the train went.)

PS :: If you wish to comment on this, please send me a direct mail : drpartha AT gmail DOT com

* * * *

Astrology, myth, or reality ?

Just received the book -- Astrology -- believe it or not ? (S Balchandra Rao, Pub. : Navakarnataka Publishers). The author, a reputed mathematician, examines astrology in an impartial and rational sense. His study is rigorous, based on clear mathematical concepts, and demonstrates how mathematical concepts are distorted, to form a pseudo science called astrology. People confuse the fuzzy pseudo-science of astrology with the precise science of astronomy (a branch of mathematics), and intersperse their arguments using names of great sages like Varahmihira or Parshara or Jaimini. By juxtaposing these names with their own terminology, they create a certain euphoria which has still not been proven conlusively. This book is just the kind one has to read, to know the true worth (or otherwise) of astrology.

It is a pity I have no way to contact the author, to congratulate him and thank him.

I thank my friend Natarajan, who could procure this book for me.

partha

PS : I located this book, based on a review I read in RESONANCE (a brilliant journal produced by the Indian Academy of Science)

Dig for gold

I located one more amazing gold mine for info on mathematics:

http://www.numbertheory.org/ntw/gateways.html

All those who love maths, or want to learn maths, should visit this site and dig out the gold which is hidden here.

partha