Pie Mathematics Association Website: www.piemathassociation.com The legacy of Ramanujan.

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1 Pie Mathematics Association Website: www.piemathassociation.com The legacy of Ramanujan

2 Tribute to Ramanujan on his rd Remembrance Day 2212 1887 2604-40149 1920155-55 7210306-42

3 Ramanujan’s Birth Home

4 Ramanujan’s Horoscope and Family Deity

5 Ramanujan’s Home at Kumbakonam

6 Ramanujan’s Family Tree

7 Meritorius Schooling of Ramanujan

8 Ramanujan’s F.A. Mark Sheet

9 Ramanujan Lost and Found

10 Ramanujan’s Legacy

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12 Collected Papers of Ramanujan

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15 Ramanujan’s Achievement

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17 Ramanujan’s Film

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19 Ramanujan’s Jottings

20 Ramanujan and Pi

21 Ramanujan’s Influence Ramanujan's work on partitions: 1 ; P(1) = 1 2 = 1+1 ; P(2) = 2 3 = 2+1 = 1+1+1 ; P(3) = 3 4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1 ; P(4) = 5 P(5)=7, P(6)=11, P(7)=15,... Ramanujan's congruences P(5n+4) is a multiple of 5 P(7n+5) is a multiple of 7 P(11n+6) is a multiple of 11 P(25n+24) is a multiple of 25 P(49n+47) is a multiple of 49 P(121n+116) is a multiple of 121 Ramanujan conjecture: If m = 5 a 7 b 11 c and 24l - 1 is a multiple of m, then P(mn+l) is a multiple of m for all n. This has led to a great deal of work. 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!

22 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

23 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

24 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. Andrews Past President, American Mathematical Society

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