Math ppt

1. Contributions Of Great Mathemati
cian
S.RAMANUJAN
‫رامانجن‬ ‫ايس‬

3. History Of S.RAMANUJAN-
 Born on December 22 , 1887.
 In a village in Madras State, at Erode, in Tanjore District.
 In a poor HINDU BRAHMIN family.
 Full name is “SRINIVAS RAMANUJAN AYYANGER”.
 Son of Srinivas Iyenger.
 Accountant to a cloth merchant at KUMBHAKONAM. Daughter of petty
official ( Amin ) in District Munsif’s court at Erode.
 Daughter of petty official ( Amin ) in District Munsif’s court at Erode.
 First went to school at the age of 7.

4. --------------------------------------------
 His famous history was :- One day a primary S
chool teacher of 3rd form was telling to his studen
ts ‘If three fruits are divided among three persons,
each would get one , even would get one , even if
1000 fruits are divided among 1000 persons each
would get one ‘. Thus , generalized that any num
ber divided by itself was unity . This Made a child
of that class jump and ask- ‘ is zero divided by zer
o also unity?’ If no fruits are divided nobody , wi
ll each get one? This little boy was none other tha
n RAMANUJAN .

5.  So intelligent that as students of class 3rd or primary
school.
 Solved all problems of Looney’s Trigonometry mean
t for degree classes.
 At the age of seven , he was transferred to Town Hig
h School at Kumbhakonam.
 He held scholarship.
 Stood first in class.
 Popular in mathematics.

6. -------------------------------------------
 At the age of 12, he was declared “CHILD MATHEMA
TICIAN” by his teachers.
 Entertain his friends with theorem and formulas.
 Recitation of complete list of Sanskrit roots and repeatin
g value of ∏ and square root of 2, to any number of dec
imal places.
 In 1903 , at the age of 15, in VI form he got a book , “Ca
rr’s Synopsis”.
 “Pure and Applied Mathematics”

7.  Gained first class in matriculation in December 1903
.
 Secured Subramanian’s scholarship.
 Joined first examination in Arts (F.A).
 Tried thrice for F.A.
 In 1909, he got married to Janaki ammal.
 Got job as clerk.
 Office of Madras port trust.
Born 4 November 1897
Tellicherry,Kerala
Died February 1984 (aged 87)
Nationality Indian
Fields Botany, Cytology
Institutions University Botany,,Laboratory
Madras
Alma mater University of Michigan

8.  Published his work in “Journal of Indian Mathe
matical Society”.
 In 1911, at 23 , wrote a long article on some pro
perties of “Bernoullis Numbers”.
 Correspondence with Prof.J.H Hardy.
 Attached 120 theorems to the first letter.

9. In 1912, Mr. Walker, held high post under
the Government.
Obtained, scholarship of Rs. 75/- per mont
h.
In 1914, invited to Cambridge University,
and in 1916, got Hon. B.A. Degree of Uni
versity of Cambridge

10. His Achievements-
1) Divergent Series:- When Dr. Hardy examined his in
vestigation – “I had never seen anything the least like
them before. A single look at them is enough to show
that this could only be written by Mathematician of h
ighest class”.
2) Hyper Geometric series and continued Fraction:
He was compared with Euler and Jacobi.
3) Definite Integrals

11. -----------------
4)Elliptic Functions
5)Partition functions
6)Fractional Differentiation: He gave a meaning to Euleri
an second integral for all values of n .He proved x ⁿ−‫ا‬ e
−ͯ = Gamma is true for all Gamma.
7)Theory of Numbers: The modern theory of numbers is
most difficult branch of mathematician .It has many u
nsolved problems. Good Example is of Gold Bach’s Th
eorem which states that every even number is sum of t
wo prime numbers. Ramanujan discovered Reimann’s s
eries , concerning prime numbers . For him every integ
er was one of his personal friend.

12. ------
He detected congruence, symmetries and relations
hips and different wonderful properties.Taxi cab No
was an interesting number to him.
1729 = 1³+12³ = 9³ + 10³
8. Partition of whole numbers: Take case of 3. It can
be written as…
3+0,1+2,1+1+1
He developed a formula
, for partition of any number
which can be made to yield the
required result by a series of
successive approximation.

13. 9). Highly Composite Numbers : Highly composite num
ber is opposite of prime numbers. Prime number has two
divisions, itself and unity . A highly composite number h
as more divisions than any preceding number like: 2,4,6,
12,24,36,48,60,120,etc.He studied the structure ,distribu
tion and special forms of highly composite numbers. Har
dy says – “Elementary analysis of highly composite num
bers is most remarkable and shows very clearly Ramanu
jan’s extra-ordinary mastery over algebra of inequalities
”.

14.  Greatest masters in the field of higher geometric th
eories and continued fractions.
 He could work out modular equation, work out theo
rems of complex multiplication, mastery of continu
ed fraction.
 Found for him self functional equation of zeta funct
ion.
 Mathematician whom only first class mathematicia
ns follow.

15.  England honoured by Royal Society and Trinity
fellowship.
 Did not receive any honour from India.
 In spring of 1917, he first appeared tobe unwell.
 Active work for Royal Society and Trinity Fello
wship.
 Due to TB, he left for India and died in chetpet ,
Madras .
 On April 26, 1920 at the age of 33.

16. Made by :-
Yash Prakash
Karjekar,
Std-8th, Div-B,
Roll.No-35.