Pie Mathematics Association

Website: www.piemathassociation.com

The legacy of Ramanujan

Tribute to Ramanujan on his rd Remembrance Day

22 12 18 87

26 04 -40 149

19 20 155

-55

72

103 06 -42

95 91 96 92 97 93 98 94 99 ...

Ramanujan’s Birth Home

Ramanujan’s Horoscope and Family Deity

Ramanujan’s Home at Kumbakonam

Ramanujan’s Family Tree

Meritorius Schooling of Ramanujan

Ramanujan’s F.A. Mark Sheet

Ramanujan Lost and Found

Ramanujan’s Legacy

Ramanujan’s Legacy

Collected Papers of Ramanujan

Collected Papers of Ramanujan

Collected Papers of Ramanujan

Ramanujan’s Achievement

Ramanujan’s Achievement

Ramanujan’s Film

Ramanujan’s Film

Ramanujan’s Jottings

3 1 1 2 1 3 1 4 1 &c

4 1 6 2 7 3 8 4 9 &c

Ramanujan and Pi

Ramanujan’s InfluenceRamanujan's work on partitions:1 ; P(1) = 12 = 1+1 ; P(2) = 23 = 2+1 = 1+1+1 ; P(3) = 34 = 3+1 = 2+2 = 2+1+1= 1+1+1+1 ; P(4) = 5P(5)=7, P(6)=11, P(7)=15,. . .Ramanujan's congruencesP(5n+4) is a multiple of 5P(7n+5) is a multiple of 7P(11n+6) is a multiple of 11

P(25n+24) is a multiple of 25P(49n+47) is a multiple of 49P(121n+116) is a multiple of 121Ramanujan conjecture:If m = 5a7b11c

and 24l - 1 is a multiple of m,thenP(mn+l) is a multiple of m for all n.This has led to a great deal of work.

1( )

4 3k nP n e asn

n

2

3wherek

The study of the asymptotic behaviour of P(n) led Ramanujan and Hardy to develop Circle Method. This method helped to solve: Large Sieve, Ternary Goldbach Conjecture, Progress on binary Goldbach Conjecture and Waring's problem. All these problems looked beyond reach before the birth of Circle method. The Circle method is one of the most efficient tools in Analytic Number theory even today!

Applications

Ramanujan did mathematics for its own sake, for the fun of discovering new relationships between objects which look unrelated. Some of the applications from his works are: 1. Ramanujan's work has some applications in particle physics. 2. In computing pi up to a very large number of decimal places. 3. The work on Riemann zeta-function has applications to pyrometry, the investigation of the temperature of furnaces. 4. The work on p(n): has applications in new fuels and fabric like nylon. 5. Ramanujan’s Formulas are applied in statistical Mechanics 6. It is believed that some of Ramanujan’s formulas are applied in treating certain special types of cancer. 7. American Mathematician Ken Ono recently suggested that Ramanujan’s last work “Mock Theta Functions” help theoritical physicists to understand String Theory and Black Hole swhich are key for understanding the structure and behaviour of the Universe

MESSAGE FROM BRUCE BERNDT

Professor Bruce Berndt

Illinois University, USA

Expert on Ramanujan’s Notebooks.

Mathematics is a beautiful subject with lots of elegance, surprises, and ingenuity.  Please venture into the world of Ramanujan, where you will find an abundance of these features

MESSAGE FROM GEORGE ANDREWS

I happily send my greetings and best wishes to you and all the participants in the Workshop and Exhibition being held at the Krishnammal College.  Ramanujan's discoveries in mathematics have been a great gift to the entire world and have dramatically changed the lives of many especially me.  Perhaps an even greater gift is the example of his life.  Born in poverty and facing many obstacles he rose in his lifetime to be one of the most important mathematicians of the twentieth century.  It is wonderful that he is being remembered this workshop and exhibition.  I wish everyone attending all the best.

George E. AndrewsPast President, American Mathematical Society

Thank You!