Contribution of Great Mathematician S.ramanujan in Mathematics

8/16/2019 Contribution of Great Mathematician S.ramanujan in Mathematics

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Contributions Of GreatContributions Of GreatMathematicianMathematician

S.RAMANUJANS.RAMANU

JAN

يسرمان يسرمان


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History Of S.RAMANUJAN-History Of S.RAMANUJAN- Born on December 22 , 1887.

In a village in Madras State, at Erode, in Tanjore District. In a poor I!D" B#$MI! %amil&.

'(ll name is )S#I!I*$S #$M$!"+$! $$!-E# .

Son o% Srinivas I&enger.

$cco(ntant to a clot/ merc/ant at 0"MB$0!$M. Da(g/ter o% pett&o%%icial $min 3 in District M(nsi%4s co(rt at Erode.

Da(g/ter o% pett& o%%icial $min 3 in District M(nsi%4s co(rt at Erode.

'irst 5ent to sc/ool at t/e age o% 7.


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------His famous history was :- ne da& a

primar& Sc/ool teac/er o% 6rd %orm 5as telling to

/is st(dents I% t/ree %r(its are divided among

t/ree persons, eac/ 5o(ld get one , even 5o(ld

get one , even i% 1 %r(its are divided among

1 persons eac/ 5o(ld get one . T/(s ,

generali9ed t/at an& n(mber divided b& itsel%

5as (nit& . T/is Made a c/ild o% t/at class j(mpand as:; is 9ero divided b& 9ero also (nit&


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So intelligent t/at as st(dents o% class 6rd or primar&

sc/ool.

Solved all problems o% =oone&4s Trigonometr&meant %or degree classes.

$t t/e age o% seven , /e 5as trans%erred to To5n

ig/ Sc/ool at 0(mb/a:onam.e /eld sc/olars/ip.

Stood %irst in class.

>op(lar in mat/ematics.


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---- $t t/e age o% 12, /e 5as declared )?I=D

M$TEM$TI?I$! b& /is teac/ers.

Entertain /is %riends 5it/ t/eorem and %orm(las.

#ecitation o% complete list o% Sans:rit roots and

repeating val(e o% @ and sA(are root o% 2, to an&n(mber o% decimal places.

In 16 , at t/e age o% 1C, in *I %orm /e got a boo: ,

)?arr4s S&nopsis.

)>(re and $pplied Mat/ematics


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-ained %irst class in matric(lation in December

16.

Sec(red S(bramanian4s sc/olars/ip.

+oined %irst eamination in $rts '.$3.

Tried t/rice %or '.$.

In 1, /e got married to +ana:i ammal.

-ot job as cler:.

%%ice o% Madras port tr(st.Born 4 November 1897

Tellicherry,Kerala

DiedFebruary 1984 (aged 87)

Nationality Indian

Fields Boany, !yology

Institutions "niver#iy Boany,,$aboraor

y %adra#

Alma mater "niver#iy o& %ichigan

http://en.wikipedia.org/w/index.php?title=University_Botany_Laboratory&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=University_Botany_Laboratory&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=University_Botany_Laboratory&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=University_Botany_Laboratory&action=edit&redlink=1


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>(blis/ed /is 5or: in )+o(rnal o% IndianMat/ematical Societ&.

In 111, at 26 , 5rote a long article on some

properties o% )Berno(llis !(mbers.?orrespondence 5it/ >ro%.+. ard&.

$ttac/ed 12 t/eorems to t/e %irst letter.


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In 112, Mr. al:er, /eld /ig/ post (ndert/e -overnment.

btained, sc/olars/ip o% #s. 7CF; per

mont/.In 11G, invited to ?ambridge "niversit&,

and in 11H, got on. B.$. Degree o%

"niversit& o% ?ambridge


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His Achieements-His Achieements-

1) Divergent Series; /en Dr. ard& eamined /isinvestigation J )I /ad never seen an&t/ing t/e least

li:e t/em be%ore. $ single loo: at t/em is eno(g/ to

s/o5 t/at t/is co(ld onl& be 5ritten b&

Mat/ematician o% /ig/est class.

2) Hyper Geometric series and continued Fraction

e 5as compared 5it/ E(ler and +acobi.

3) Definite Integrals


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4)Elliptic Functions

)!artition functions

")Fractional Differentiation e gave a meaning to

E(lerian second integral %or all val(es o% n .e proved

KL e N -amma is tr(e %or all -amma.−

#)$%eory of &um'ers T/e modern t/eor& o% n(mbers is

most di%%ic(lt branc/ o% mat/ematician .It /as man&

(nsolved problems. -ood Eample is o% -old Bac/4s

T/eorem 5/ic/ states t/at ever& even n(mber is s(mo% t5o prime n(mbers. #aman(jan discovered

#eimann4s series , concerning prime n(mbers . 'or /im

ever& integer 5as one o% /is personal %riend.


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--------------------------------------------------------------- e detected congr(ence, s&mmetries and

relations/ips and di%%erent 5onder%(l properties.Tai

cab !o5as an interesting n(mber to /im.

172 N 1OP12O N O P 1O

8( !artition of %ole num'ers Ta:e case o% 6. It can

be 5ritten asQ

6P,1P2,1P1P1

e developed a %orm(la

, %or partition o% an& n(mber 5/ic/ can be made to &ield t/e

reA(ired res(lt b& a series o%

s(ccessive approimation.


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3. Hig%ly *omposite &um'ers ig/l& compositen(mber is opposite o% prime n(mbers. >rime n(mber /as

t5o divisions, itsel% and (nit& . $ /ig/l& composite

n(mber /as more divisions t/an an& preceding n(mber

li:e 2,G,H,12,2G,6H,G8,H,12,etc.e st(died t/estr(ct(re ,distrib(tion and special %orms o% /ig/l&

composite n(mbers. ard& sa&s J )Elementar& anal&sis

o% /ig/l& composite n(mbers is most remar:able and

s/o5s ver& clearl& #aman(jan4s etra;ordinar& master&

over algebra o% ineA(alities.


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-reatest masters in t/e %ield o% /ig/er geometric

t/eories and contin(ed %ractions.

e co(ld 5or: o(t mod(lar eA(ation, 5or: o(tt/eorems o% comple m(ltiplication, master& o%

contin(ed %raction.

'o(nd %or /im sel% %(nctional eA(ation o% 9eta

%(nction.

Mat/ematician 5/om onl& %irst class

mat/ematicians %ollo5.


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England /ono(red b& #o&al Societ& and Trinit&%ello5s/ip.

Did not receive an& /ono(r %rom India.

In spring o% 117, /e %irst appeared tobe (n5ell.$ctive 5or: %or #o&al Societ& and Trinit&

'ello5s/ip.

D(e to TB, /e le%t %or India and died in c/etpet ,

Madras .

n $pril 2H, 12 at t/e age o% 66.

Contribution of Great Mathematician S.ramanujan in Mathematics

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