History of Ramanujam And His Contributions

History Of Ramanujan And

His Contributions

Basic Introduction

Born 22 December 1887 Erode,  Madras

Presidency

Died 26 April 1920 (aged 32) Chetput,Madras

Presidency

Basic Introduction

o Father : Kuppuswamy Srinivasa Iyengar, a clerical assistant (Gumastha) to a cloth merchant

o Mother: Komalatammal, was a housewife

Basic Introductiono Spouse : Janaki Ammal

o Residence Kumbakonam

o Nationality Indian

o Fields Mathematics

o Alma mater Government Arts College Pachaiyappa's College

o Academic advisors G. H. Hardy J. E. Littlewood

o Signature

Best Known For

Landau–Ramanujan constant Mock theta functions Ramanujan conjecture Ramanujan prime Ramanujan–Soldner constant Ramanujan theta function Ramanujan's sum Rogers–Ramanujan identities Ramanujan's master theorem

Childhood• By age 12,he mastered an advanced

trigonometry book written by S.L. Loney by himself.

• After his graduation from high school,he could not get a degree from both colleges he entered at different times(Government College,Pachaiyappa’s College) due to his unwillingness about subjects except mathematics and he could not enter any university

• He has become seriously ill from time to time and they took so much time to be recovered.

ADULTHOOD

• He was married with a nine year old girl named Janaki Annal when he was 22 but he did not live with his wife till she was 12.

• Despite the fact that he was not educated well, he was known to the university mathematicians by his works and growing fame in

Madras.

• Ramanujan has been publishing his works with the help of people who admired his talent in Journal of Indian Mathematical Society

ADULTHOOD

• 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.

TO ENGLAND

He was invited England to improve his works by G.H. Hardy

and J.E. Littlewood,who were two of big mathematicans at this

time. G.H.Hardy J.E.Littlewood

Life in England

He was elected to

the London

Mathematical

Society and he

became a Fellow of

the Royal Society.

What he did???

He worked on…

Elliptic Functions :

f (z) and f (w + z) is same thing.

Continued fraction:

Infinite series

What he did???

But he continued developing math skills, the new ideas of math without any help other than Carr’s book.

In 1900, he worked on his own math summing geometric 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 failed to solve a quintic equation.

ax5 + bx4 + cx3 + dx2 + ex + f = 0

What he did???

He also investigated the series ∑(1/n) and calculated constant into 15 decimal places.

He began to study the Bernoulli’s (it was his own independent discovery )

(Bernoulli equation) x/(ex - 1) = (Bnxn)/n

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.

BACK TO INDİA

His entire life was with

health problems but his

health has been worse in

England due to stress,lack of

vegetarian food and being

far away from home.

Ramanujan returned India in

1919 and after a short while

he died in India despite

medical treatment.

About him…

He was a religious man.He often said,

“An equation for me has no meaning, unless it

represents a thought of God.”

People said that he also had an obsession about

vegetarian food.

About him..

Hardy and Littlewood had so many

troubles while they have been

educating him.Once Littlewood said

about it, “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.”

RECOGNITION Ramanujan's home state of  Tamil Nadu celebrates 22

December (Ramanujan's birthday) as 'State IT Day', memorializing both the man and his achievements, as a native of Tamil Nadu.

A stamp picturing Ramanujan was released by the Government of India in 1962 – the 75th anniversary of Ramanujan's birth – commemorating his achievements in the field of number theory, and a new design was issued on December 26, 2011, by the India Post

RECOGNITION On the 125th anniversary of his birth, the

Government of India declared that Ramanujan's birthday (22 December) should be celebrated every year as NATIONAL MATHEMATICS DAY, and also declared 2012 the NATIONAL MATHEMATICAL YEAR.

Presentation By

Vamshi TGC BhupenderJulian Jacob

Mirza Jameel BaigBala Praveen