SHRINIVASA

RAMANUJAM

E.PARKAVI,II B.SC MATHEMATICS.

• BORN : 22 December 1887

Erode, Madras Presidency.

• DIED : 26 April 1920,

Chetput, Madras presidency..

BASIC INTRODUCTION OF RAMANNUJAM

BASIC INTRODUCTION

Father: Kuppuswamy Srinivasa Iyengar,

Clerical Assistant to a cloth Merchant.

Mother: Komalathammal, Homemaker.

Spouse: Janaki Ammal.

Residence: Kumbakonam.

Alma Matter: Government arts college,

Pachaiyappa college.

Advisors: G.H. Hardy, J.E. Littlewood

CHILD HOOD• Ramanujam exhausted maths of two college students by age 11 . Also ,he

mastered trigonometry book written by S.S. Lonely by age 13.

• When he graduated in 1904, he was awarded K. Ranganatha Rao prize for mathematics by school’s head master.

• He received a scholarship to study at Government Arts College, but failed to receive scholarship due to his poor performance in other subjects, except maths.

• Again he enrolled in Pachaiyappa’s college in Madras. But he failed in fellow of arts in 1906 and again a year later. He went on to individual research in maths.

Adult hood• He got a temporary job in Madras Accountant General’s

office,after that he was accepted as a clerk in Chief Accountant of the Madras Port Trust. He did easily what he was given and he spent his spare time with mathematical research,which his boss encouraged him about.

• Since he has showed his supernatural talent by himself,again people around him tried to connect him with big English matematicians .About Ramanujan G.H. Hardy thought at first it could be fraud because most of Ramanujan’s works were impossible to believe.But eventually,they were convinced and interested in his talent

Ramanujam Relation With God

His Best Known Results

Relation with Hardy

• G. H. Hardy , J.E. Littlewood who were great mathematicians of that time invited Ramanujam to England.

• Hardy, together with Littlewood, studied the long list of unproved theorems which Ramanujan enclosed with his letter. On 8 February he replied to Ramanujan.

Reply to Ramanujam

• I was exceedingly interested by your letter and by the theorems which you state. You will however understand that, before I can judge properly of the value of what you have done, it is essential that I should see proofs of some of your assertions

Little Woods Difficulty

• Littlewood was asked to help teach Ramanujan rigorous mathematical methods. However he said

• ... that it was extremely difficult because every time some matter, which it was thought that Ramanujan needed to know, was mentioned, Ramanujan's response was an avalanche of original ideas which made it almost impossible for Littlewood to persist in his original intention.

1729 Man

RAMANUJAM’S MAGIC SQUARE

Ramanujam’s Prime Number Theorem

• Suppose that in some neighborhood of ,

• for some function (say analytic or integrable) . Then

PRIME NUMBER THEOREM

• These functions form a forward/inverse transform pair. For example, taking for all give

• and

• which is simply the usual integral formula for the gamma function.

• Ramanujan used this theorem to generate amazing identities by substituting particular values for

OTHER WORKS OF RAMANUJAM

• In 1900, he worked on his own math summing zgeometric and arithmetic series.

• He solved cubic equations. (1902) ax3 + bx2 + cx + d = 0 • He went on finding his own method of solving quartic equation. ax4 + bx3 + cx2 + dx + e = 0

• He also worked on hyper geometric series.

• He also, Investigated the relation between series and integrals.

• Despite many brilliant results, some of his theorems on primes were completely wrong.

GETTING DEGREE IN ENGLAND

RETURN TO INDIA

• Ramanujam Always Suffered From Health Problems Due To Stress, Lack Of Vegetarian Food And Cimate In England.

• Ramanujam returned to India in 1919 and died despite medical treatment in 1920.

Birthday celebration of India

• 22 december celebrated as state IT day in Tamilnadu for his achievements.

Stamp released for him to mark his 75th birthday

Recognition By Indian Governemnt

• 2012 is celebrated as mathematical year to mark his 125th year birth anniversary.