A TRUE FRIEND OF NUMBERS

A GROUP POWERPOiNT PRESENTATiON

ON A MATHEMATiCiAN:

SRINIVASA RAMANUJAN

By the group:

Members of Mathematics Lions:

Rajkamal.s

Jagadeesh.h

Vignesh.k

Prasath.S

Rakesh.v

INTRODUCTION:1.Srinivasa ramanujan was one of India’s

Greatest mathematical geniuses

2.He made Substantial contributions to the analyticalTheroy of numbers and worked on elliptic Functions, continued fractions, and infiniteSeries.

Born : 22 December 1887 Erode, Madras Presidency (now in Tamil Nadu)

Died : 26 April 1920 (aged 32) Chetput, Madras, Madras Presidency (now Tamil Nadu)

Residence : Kumbakonam, Tamil Nadu

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

Known for : Landau–Ramanujan constat Ramanujan conjecture

Ramanujan prime Ramanujan–Soldner constant Ramanujan theta function

Influences : G. H. Hardy

Signature :

BRIEF INTRODUCTION:

History of Ramanujan:

Ramanujan's home on Sarangapani Street, Kumbakonam

Ramanujan was born on 22 December 1887 in Erode,Madras(nowpalipalayam, erode, Tamil Nadu),

His father, K. Srinivasa Iyengar, worked as a clerk in a sari shop and hailed from the district of tanjavur.

His mother, Komalatammal, was a housewifeand also sang at a local temple.They lived in Sarangapani Street in a traditional home in the town of Kumbakonam.

The family home is now a museum. When Ramanujan was a year and a half old, his mother gave birth to a son named Sadagopan, who died less than three months later. In December 1889, Ramanujan had smallpox and recovered, unlike thousands in the tanjavur. who died from the disease that year.

ATTENTiON TOWARDS MATHEMATiCS:

Ramanujan met deputy collector V. Ramaswamy Aiyer, who had recently founded the Indian Mathematical Society.

Ramanujan, wishing for a job at the revenue department where Ramaswamy Aiyer worked, showed him his mathematics notebooks. As Ramaswamy Aiyer later recalled:

I was struck by the extraordinary mathematical results contained in it [the notebooks]. I had no mind to smother his genius by an appointment in the lowest rungs of the revenue department

CONTACTING ENGLISH MATHEMATICIANS:

Rao and E.W.Middlemast tried to present

Ramanujan's work to British mathematicians.

One mathematician, M. J. M. Hill ofUniversity College

London, commented that Ramanujan's papers

were riddled with holes.  He said that although Ramanujan had "a

taste for mathematics, and some ability",

he lacked the educational background and

foundation needed to be accepted by

mathematician. In the spring of 1913, Narayana Iyer, Ramachandra

One of the theorems Hardy found scarcely possible to believe was on the bottom of page three (valid for 0 < a < b + 1/2):

LIFE IN ENGLAND

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

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

Hardy and Ramanujan had two opposite personalities.As Hardy

was an atheist and believes mathematical proof and

analysis,Ramanujan was a deeply religious guy and

he believed in his trustworthy intuition.Hardy had hard

times on his education without giving any damage on

hisself confidence and his values.

He was elected to the London Mathematical Society

and he became a Fellow of the Royal Society.Ramanujan (centre) with other

scientists at Trinity College

BACK TO INDIA Plagued by health problems throughout his life, living in a country

far away from home, and obsessively involved with his mathematics, Ramanujan's health worsened in England, perhaps exacerbated by stress and by the scarcity of vegetarian food during the First World War. He was diagnosed with tuberculosis and a severe vitamin deficiency and was confined to a sanatorium.

Ramanujan returned to Kumbakonam, Madras Presidency in 1919 and died soon thereafter at the age of 32 in 1920. His widow, S. Janaki Ammal, moved to Mumbai, but returned to Chennai (formerly Madras) in 1950, where she lived until her death at age 94 in 1994.[28]

A 1994 analysis of Ramanujan's medical records and symptoms by Dr. D.A.B. Young concluded that it was much more likely he had hepatic amoebiasis, a parasitic infection of the liver widespread in Madras, where Ramanujan had spent time. He had two episodes of dysentery before he left India. When not properly treated, dysentery can lie dormant for years and lead to hepatic amoebiasis,[76] a difficult disease to diagnose, but once diagnosed readily cured.[76]

ABOUT HIM: Ramanujan has left a number of theorems and his notebooks

which have still been being worked on.

Ramanujan found the mistery in the number,1729,while he was in his bed when he was sick. Hardy was asked about 1729 what he thought about it and he said it has nothing interesting.Then Ramanujan stated that 1729 is the smallest number which could be represented as in two different ways as a sum of two cubes. After that,1729 have been called “Ramanujan-Hardy number”.

According to the big mathematicians and specialists lived in that time,Ramanujan’s talent was reminded them Gauss,Jacobi,Euler.

In memoriam of Ramanujan,books have been written and movies were made since he died.An example could be the movie named The Man Who Knew Infinity: A Life of the Genius Ramanujan based on the book.

In mathematics, there is a distinction between having an insight and having a proof. Ramanujan's talent suggested a plethora of formulae that could then be investigated in depth later. It is said by G. H. Hardy that Ramanujan's discoveries are unusually rich. Examples of the most interesting of these formulae include the intriguing infinite series for π, is given below

MATHEMATICAL ACHIEVEMENTS

OTHER VIEWS ABOUT RAMANUJAN:

Hardy said : “Ramanujan combined a power of generalization, a

feeling for form, and a capacity for rapid modification of his hypotheses, that were often really startling, and made him, in his own peculiar field, without a rival in his day. The limitations of his knowledge were as startling as its profundity. Here was a man who could work out modular equations and theorems... to orders unheard of, whose mastery of continued fractions was... beyond that of any mathematician in the world, who had found for himself the functional equation of the zeta function and the dominant terms of many of the most famous problems in the analytic theory of numbers; and yet he had never heard of a doubly periodic function or ofCauchy's theorem, and had indeed but the vaguest idea of what a function of a complex variable was...".

Ramanujan's home state of Tamil Nadu celebrates 22 December (Ramanujan's birthday) as 'State IT Day', memorialising 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 number theory,[94] and a new design was issued on 26 December 2011, by the India Post

Government’s Honour forSrinivasa Ramanujan

Bust of Ramanujan in the garden of

Birla Industrial & Technological Museum

One of the problems he posed in the journal was:

ANS:

On page 105 of his first notebook, he formulated an equation that could be usedto solve the infinitely nested radicals problem as:

:

Problems he possed in the journal was:

1.

A.

B.

Hardy was also impressed by some of Ramanujan's other work relating to infinite series of the following:

C.

Ramanujan Notebook’s

The first notebook has 351 pages with 16 somewhat organised chapters and some unorganised material.

The second notebook has 256 pages in 21 chapters and 100 unorganised pages

The third notebook containing 33 unorganised pages. The results in his notebooks inspired numerous papers by later mathematicians trying to prove what he had found. Hardy himself created papers exploring material from Ramanujan's work as did G. N. Watson, B. M. Wilson, and Bruce Berndt. 

A fourth notebook with 87 unorganised pages, the so-called "lost notebook", was rediscovered in 1976 byGeorge Andrews.

Ramanujan Notebook:

An interesting example:

Ramanujan theta function:In mathematics, particularly q-analog theory, the Ramanujan theta function generalizes the form of the Jacobi theta functions, while capturing their general properties. In particular, the Jacobi triple product takes on a particularly elegant form when written in terms of the Ramanujan theta. The function is named after Srinivasa Ramanujan.

The Ramanujan theta function is used to determine the critical dimensions in Bosonic String Theory, Superstring Theoryand M-theory.

Definition:The Ramanujan theta function is defined as:

For |ab| < 1. The  Jacobi tripleproduct  identitythen takes the form

Page from Ramanujan's notebook stating his Master theorem.

In mathematics, Ramanujan's master theorem(named after mathematicianSrinivasa Ramanujan)is a techniquethat provides an analytic expression for the Mellin transform of a function.The result is stated as follows:

Assume function  has an expansion of the form”

Then Mellin transform of  is given by:

where  is the  Gamma function.

Ramanujan's master theorem

Famous quotes on G.H.Hardy

Famous quotes on Srinivasa Ramanujan

  I had never seen anything in the least like them before. A single look at them is enough to show that they could only be written by a mathematician of the highest class. They must be true because, if they were not true, no one would have the imagination to invent them.

-Srinivasa Ramanujan

GENiUSQUESTiO

N CORNER?

Question.1:

What’s sointeresting from

The following magic square?

Do you know?

Time up!Therefore the

answer is!

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