the legacy of ramanujan psgr college coimbatore
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Pie Mathematics Association
Website: www.piemathassociation.com
The legacy of Ramanujan
Tribute to Ramanujan on his rd Remembrance Day
2212 1887 2604-40149 1920155-55 72 10306-42
Ramanujans Birth Home
Ramanujans Horoscope and Family Deity
Ramanujans Home at Kumbakonam
Ramanujans Family Tree
Meritorius Schooling of Ramanujan
Ramanujans F.A. Mark Sheet
Ramanujan Lost and Found
Ramanujans Legacy
Ramanujans Legacy
Collected Papers of Ramanujan
Collected Papers of Ramanujan
Collected Papers of Ramanujan
Ramanujans Achievement
Ramanujans Achievement
Ramanujans Film
Ramanujans Film
Ramanujans Jottings
Ramanujan and Pi
Ramanujans Influence
Ramanujan'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 11P(25n+24) is a multiple of 25P(49n+47) is a multiple of 49P(121n+116) is a multiple of 121Ramanujan conjecture:If m = 5a7b11cand 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.
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. Ramanujans Formulas are applied in statistical Mechanics 6. It is believed that some of Ramanujans formulas are applied in treating certain special types of cancer. 7. American Mathematician Ken Ono recently suggested that Ramanujans 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 UniverseMessage from bruce berndtProfessor Bruce BerndtIllinois University, USAExpert on Ramanujans 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!