Monthly Archives: March 2015

Jab We Met!!

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The Mathematician.....

           The Mathematician…..

31-March-2015 is one of the few mathematically memorable days of my life. This was different from my routine. Today I bunked all my theory classes as well as practical class at NISER. I walked in streets along with SSN (my batch-mate) searching for an address in hot-baked-afternoon. That address was of Prof. Swadhin Pattanayak. We interacted for about 2 hrs. We discussed various topics of analysis like: diverging series, summability, double sums, differential equations,….. He also shared his fascination of “how log tables were formed”, “how square-roots were calculated”, “beautification of electrodynamics by calculus”, “methods to calculate value of \pi”…… He has become too old, he takes time to write but still his love and passion for mathematics is young. Still he has mathematics research papers surrounding him and full of energy to learn and teach. At the end we shook hands, and I felt like shaking hands with some Super Star.

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Mathematician & Integrated Masters of Science

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It is nearly one year since I enrolled in “Integrated Masters of Science” course at National Institute of Science Education and Research (NISER), Bhubaneswar. I joined NISER with motive of becoming a mathematician and teacher. We are taught many subjects (physics, chemistry, biology, mathematics, economics, sociology, technical communication, psychology, programming).
Think about it this way:

Learning a small number of chords will enable you to  play quite a few songs on a guitar. It won’t make you the world’s best guitar player, but it will enrich your life. In this course you will learn the chords of modern science, which have been hidden from you. And this has potential to  enrich your life.

[Book Review] What is Mathematics?

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image This mid-sem recess I read : What is mathematics? by Balkrishna Shetty.

As many of you may know and have read the old classic by same title What is mathematics? by Richard Courant and Herbert Robbins. But both have completely different genre. One starling difference between these books is that Courant & Robbins have arranged their book in chapters as in a textbook where as Shetty has arranged his book on popular math topics. Though both books requires high school mathematics as prerequisite. I am not going to comment o the classic by Courant & Robbins.

Shetty has his focus on modern inter disciplinary aspects of mathematics. Shetty has written in a story telling form. A kind of Panchtantras genre. More of philosophical treatment of mathematics by drawing analogies which I don’t understand. There are mythological stories (Indian as well as western) at beginning of each section but I didn’t find much relation between the mathematical concept being explained and the story being told as a motivation for that concept. Shetty has tried to prove to common man that we all are mathematicians since mathematics is all around us. The book also consists the “Life Blood of Mathematics” i.e. Problems & Puzzles in form of Notes towards end of the book. Almost all famous recreational problems have been touched in form of notes in this book.

Shetty is not an active researcher. Actually he is a retired Indian diplomat who served as India’s Ambassador to Sweden, Latvia, Bahrain, Senegal and Mali. But before becoming a diplomat he was a researcher in Mathematics at the Tata Institute of Fundamental Research, Mumbai, he joined the Indian Statistical Service in 1973 and was Assistant Director, dealing with Industries and Trade Statistics in Central Statistical Organisation, Government of India, New Delhi.  Thus his style of writing may not at all appeal a person like me who is interested in pure & abstract beauty of mathematics. People like me don’t care much about physical existence of object to describe its beauty. But Shetty has tried to describe mathematics by attaching a physical meaning to it. Towards end of his book he discussed applications of mathematics in various fields (which is source for funding of abstract ideas of mathematicians).

Nested Radicals & Limit

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This is further continuation of stream of thoughts from my blog post: Nested Radical Sequences?

Just another idea against  representation of nested radical sequences came to my mind:

I know that, \sqrt{1+\sqrt{1+\sqrt{\ldots}}}=\phi where \phi is our famous golden ratio. But there is a theorem concerning series:

If \sum_{n=1}^\infty a_n converges then \lim_{n \to \infty} a_n = 0

But to be able to check validity of this theorem I should be able to find a_n which seems to be non-existent for nested radical sequences.

Nested Radical Sequences?

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I ended up with a task at the end of my post last month: Resting with ‘Nested Radicals’

I have figured out that \sqrt{1- \sqrt{1+ \sqrt{1- \sqrt{\ldots } }}} is a diverging series. But now I am struck with another problem:

What is the corresponding sequence for nested radical series?

In general, I am given a sequence and I write the corresponding series and check its convergence/divergence. But what if I am given a series without a general term (though wrong in many cases, as a given pattern of finite terms may be written as many different general terms.). For nested radicals I believe that there is only one general term and without this general term I will not be able to write terms of corresponding sequence (as in case of nested radicals I simply get partial sums). So I have a bigger question to ask:

Does there exists a sequence corresponding to any given series?

G.H. Hardy contributes to Biology !!!

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g-h-hardy  dd

Last month I appeared for my Biology mid-sem exam. I discovered Hardy-Weinberg Equation, which states that:

The Hardy-Weinberg equation is a mathematical equation that can be used to calculate the genetic variation of a population at equilibrium. The Hardy-Weinberg equation is expressed as: p^2 +2pq+q^2=1

You can understand this equation here:

Now the interesting point for me here was that Hardy preferred his work to be considered pure mathematics, perhaps because of his detestation of war and the military uses to which mathematics had been applied. He made several statements similar to that in his autobiography (A Mathematician’s Apology):

“I have never done anything ‘useful’. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.”