Srinivasa Ramanujan

Srinivasa
Ramanujan

BIOGRAPHY

FULL NAME

Srinivasa Ramanujan
Aiyangar

Ramanujan BORN

December 22, 1887,
Erode, India

DIED

April 26, 1920,
Kumbakonam, India

CITIZENSHIP FIELDS

British Raj Mathematics

EDUCATION THESIS

~Government Arts College Highly Composite

(no degree) Numbers (1916)

~Pachaiyappa's College

(no degree) INSTITUTIONS
~Trinity College, Cambridge
Trinity College,
(Bachelor of Arts by
Cambridge
Research, 1916)

FAMILY & LIFE

SPOUSE Janakiammal

Janakiammal HOME
(m. 1909–1920)
Ramanujan's home on
MOTHER Sarangapani Sannidhi
Street, Kumbakonam
Komalatammal, who
earned a small amount of
money each month as a
singer at the local temple.

FATHER

K. Srinivasa Iyengar,
accounting clerk for a

clothing merchant.

BIRTHPLACE

18 Alahiri Street, Erode,

now in Tamil Nadu

TIMELINE

1887 1903

Born In Erode, Tamil Passes Matriculation
Nadu, on December 22 examination from Town
High School, Kumbakonam
1904

Joins Government Arts
College, Kumbakonam

1905

Drops out of

Kumbakonam college

1906

Joins Pachaiyappa’s College,
Madras, only to leave without
completing his studies

1911

Publishes first paper on

Bernoulli Numbers

1912

Gets a job at the Madras Port Trust
Ramanujan is introduced to G.H.
Hardy’s tract on ‘Orders of Infinity.’
He provides an answer to one of the problems posed by Hardy

TIMELINE

1913

Ramanujan writes his first letter to Hardy
Hardy recognises Ramanujan as ‘a mathematician of the highest
class', and tries to organise a visit by Ramanujan to England

1914

E.H. Neville, a Fellow of Trinity College, Cambridge meets
Ramanujan in Madras and convinces him to go to Cambridge
Neville writes to University of Madras to support Ramanujan
University of Madras offers Ramanujan scholarship
On March 17, leaves for England

1916

Gets B.A. degree by research from Cambridge University

1917

Periodically hospitalised for treatment

1918

Becomes Fellow of the Royal Society
Elected to Trinity College Fellowship

1919

Returns to India

1920

Health deteriorates
Dies on April 26, 1920 due to hepatic amoebiasis

1927

Collected papers of Ramanujan were edited by P.V. Seshu Aiyar,
G.H. Hardy and B.M. Wilson
Thereupon, was published by Cambridge University Press

CONTRIBUTIONS

Partition Functions

In number theory, the partition function p(n) represents the number of possible
partitions of a non-negative integer n. For instance, p(4) = 5 because the
integer 4 has the five partitions 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 3, 2 + 2, and 4.

Mock modular Form

In mathematics, a mock modular form is the holomorphic part of a
harmonic weak Maass form, and a mock theta function is essentially

a mock modular form of weight 1/2.

Ramanujan Conjuncture

Ramanujan's tau function given by the Fourier coefficients τ(n) of the cusp form
Δ(z) of weight 12

where , satisfies

when p is a prime number

Landau-Ramanujan Constant

The constant of proportionality (approximately 0.7642) in the
relationship between the number of positive integers less than x that
are the sum of two square numbers, for large x, and the expression.

Ramanujan Prime

A prime number that satisfies a result proven by Srinivasa

Ramanujan relating to the prime-counting function.

Ramanujan's Master Theorem

Ramanujan's master theorem is a technique that provides an

analytic expression for the Mellin transform of an analytic function.

CONTRIBUTIONS

Ramanujan-Soldner constant

A mathematical constant defined as the
unique positive zero of the logarithmic

integral function.

Ramanujan's sum

Ramanujan's sum, usually denoted , is a function of two positive
integer variables q and n defined by the formula:

where (a, q) = 1 means that a only takes on values coprime to q.

Rogers-Ramanujan Identities

The Rogers–Ramanujan identities are two identities related to basic
hypergeometric series and integer partitions.

Ramanujan-Sato series

A Ramanujan–Sato series generalizes Ramanujan’s pi formulas such as,

to the form

by using other well-defined sequences of integers s(k) obeying a certain
recurrence relation, sequences which may be expressed in terms of

binomial coefficients and A,B,C employing modular forms of higher
levels.

1729

The number 1729 is known as the Hardy–Ramanujan
number after a famous visit by Hardy to see Ramanujan at a
hospital. In Hardy's words:
“I remember once going to see him when he was ill at Putney. I had
ridden in taxi cab number 1729 and remarked that the number seemed
to me rather a dull one, and that I hoped it was not an unfavourable
omen. "No", he replied, "It is a very interesting number; it is the smallest

number expressible as the sum of two cubes in two different ways."

Immediately before this anecdote, Hardy quoted Littlewood as saying,
"Every positive integer was one of Ramanujan's personal friends."

Generalisations of this idea have created the
notion of "taxicab numbers".

1729, the Hardy-Ramanujan Number, is the smallest number
which can be expressed as the sum of two different cubes in
two different ways. 1729 is the sum of the cubes of 10 and 9 -

cube of 10 is 1000 and cube of 9 is 729; adding the two
numbers results in 1729.

ACADEMIC ADVISORS

FULL NAME FULL NAME

Godfrey Harold John Edensor
Hardy Littlewood

BORN BORN

7 February 1877 7th June 1885

DIED DIED

1st December 1947 6th September 1977

ACHIEVEMETS ACHIEVMENTS

Numer theory Smith's Prize (1908)
Mathematical Royal Medal (1929)
De Morgan Medal (1938)
analysis. Sylvester Medal (1943)
Copley Medal (1958)
Senior Berwick Prize (1960)

LOST NOTEBOOK

Ramanujan's lost notebook is the
manuscript in which Srinivasa Ramanujan
recorded the mathematical discoveries
of the last year (1919–1920) of his life. Its
whereabouts were unknown to all but a

few mathematicians until it was
rediscovered by George Andrews in
1976, in a box of effects of G. N. Watson
stored at the Wren Library at Trinity
College, Cambridge. The "notebook" is
not a book, but consists of loose and
unordered sheets of paper, more than
one hundred pages written on 138 sides
in Ramanujan's distinctive handwriting.
The sheets contained over six hundred

mathematical formulas listed
consecutively without proofs.

Ramanujan (centre) and his colleague G. H. Hardy (extreme
right), with other scientists, outside the Senate House,
Cambridge

PREPARED BY:

ANIS BATRISYIA
SANJALEE AARTI
KHALIQ ZAHYRAH
FARAH NUR RANIA

~ 2 BELIAN ~