Language of Maths in Management

8/9/2019 Language of Maths in Management

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Plj Mceizcij an Ocpljocpkbr kePlj Mceizcij an Ocpljocpkbr keHzrkejrr OcecijojepHzrkejrr Ocecijojep


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Vxan X E Hlcppcblcx{c

Yl{ Ocpljocpkbr1Yl{ Ocpljocpkbr1

Ke ce cij ylje plj rpz`{ an plj ljc~jer `aokecpj` rbkjepknkb plazilp-

Icmkmja rck`- Plj ixjcp haad an ecpzxj bce hj xjc` aem{ h{ plarj ylaPlj ixjcp haad an ecpzxj bce hj xjc` aem{ h{ plarj yladeay plj mceizcij ke ylkbl kp ycr yxkppje% Ce` plkr mceizcij krdeay plj mceizcij ke ylkbl kp ycr yxkppje% Ce` plkr mceizcij krocpljocpkbrocpljocpkbr%%

Rpxkdkei c rkokmcx eapj ke c ozbl mcpjx jxc- ylje plj rpz`{ an plj keejxyaxdkeir an plj cpao lc` abbzvkj` plj oke`r an oce{ rbkjepkrpr nax cijejxcpkae- plj Bcohxk`ij vl{rkbkrp Gale Vamdkelaxej yxapj- ke 3;-Ocpljocpkbr kr plj chrpxcbp dj{ ylkbl pzxer plj mabd an plj vl{rkbcmOcpljocpkbr kr plj chrpxcbp dj{ ylkbl pzxer plj mabd an plj vl{rkbcm

zek~jxrj%zek~jxrj%

OCECIJOJEP RBKJEBJ kr plj rpz`{ an vxahmjor crchrpxcbpkaer ce` plj cvvmkbcpkae an plj xjrzmpkeipljax{ pa vxcbpkbcm rkpzcpkaer% Kpr pya nze`cojepcm`krbkvmkejr cxj hjlc~kaxcm rbkjebj ce` szcepkpcpk~jszcepkpcpk~j

ojpla`rojpla`r%


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Yl{ Ocpljocpkbr1Yl{ Ocpljocpkbr1

Yj zrj pljMceizcij an Ocpljocpkbr ke azx Hzrkejrr

Vxahmjor% Yj naxozmcpj vxahmjor zrkei pljocpljocpkbcm r{ohamrocpljocpkbcm r{ohamr ce` crrjrrjr pljvarrkhmj baerjszjebj an cmpjxecpk~j bazxrj ancbpkae- ra plcp kenaxoj` ce` jnnjbpk~j `jbkrkaer

bce hj pcdje% Ke Ocecijojep rpz`kjr- yj baebjepxcpj aem{ ae

rzbl cxjcr an ocpljocpkbr ylkbl yazm`rzbl cxjcr an ocpljocpkbr ylkbl yazm`

ljmv zr ram~j azx hzrkejrr vxahmjor%ljmv zr ram~j azx hzrkejrr vxahmjor%

Anpje yj lc~j pa kepjxvxjp bammjbpj` `cpc ,kevxa`zbpkae- ocxdjpkei- szcmkp{ baepxam- jpb%+% Yjzrj ~cxkazr paamr an Rpcpkrpkbrpaamr an Rpcpkrpkbr pa vjxnaxo rzbl

cecm{rkr%


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Ocpljocpkbr kr NZEOcpljocpkbr kr NZE


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Plj Cocwkei Ezohjx 3-6


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Plj Cocwkei Ezohjx 3-6


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Plj Je`mjrr MaavPlj Je`mjrr Maav

3%3% Rjmjbp c nazx/`kikp ezohjx ,j|bjvp aej plcp lcr cmm `kikprRjmjbp c nazx/`kikp ezohjx ,j|bjvp aej plcp lcr cmm `kikprplj rcoj+%plj rcoj+%

8%8% Xjcxxceij plj `kikpr an plj ezohjx ra plcp plj{ naxoXjcxxceij plj `kikpr an plj ezohjx ra plcp plj{ naxo

plj mcxijrp ezohjx varrkhmj%plj mcxijrp ezohjx varrkhmj%

2%2% Plje xjcxxceij plj `kikpr an plj ezohjx ra plcp plj{Plje xjcxxceij plj `kikpr an plj ezohjx ra plcp plj{

naxo plj rocmmjrp ezohjx varrkhmj%naxo plj rocmmjrp ezohjx varrkhmj%

0%0% Rzhpxcbp pljrj pya ezohjxr ,ah~kazrm{- plj rocmmjxRzhpxcbp pljrj pya ezohjxr ,ah~kazrm{- plj rocmmjx

nxao plj mcxijx+%nxao plj mcxijx+%:%:% Pcdj plkr `knnjxjebj ce` baepkezj plj vxabjrr nxao rpjvPcdj plkr `knnjxjebj ce` baepkezj plj vxabjrr nxao rpjv

8- a~jx ce` a~jx ce` a~jx- zepkm {az eapkbj raojplkei8- a~jx ce` a~jx ce` a~jx- zepkm {az eapkbj raojplkei

kepjxjrpkei kr lcvvjekei% @aep ik~j zv hjnaxjkepjxjrpkei kr lcvvjekei% @aep ik~j zv hjnaxj

raojplkei zezrzcm lcvvjer%raojplkei zezrzcm lcvvjer%


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Plj Je`mjrr MaavPlj Je`mjrr MaavJ~jepzcmm{- {az ykmm cxxk~j cp plj ezohjx >-390- vjxlcvr cnpjx aejJ~jepzcmm{- {az ykmm cxxk~j cp plj ezohjx >-390- vjxlcvr cnpjx aej

rzhpxcbpkae ax cnpjx rj~jxcm rzhpxcbpkaer% Ylje {az `a- {az ykmm nke`rzhpxcbpkae ax cnpjx rj~jxcm rzhpxcbpkaer% Ylje {az `a- {az ykmm nke`

{azxrjmn ke ce je`mjrr maav%{azxrjmn ke ce je`mjrr maav%

J\COVMJJ\COVMJ77

rjmjbp plj ezohjx 2-862% Plj mcxijrp ezohjx naxoj` ykpl pljrjrjmjbp plj ezohjx 2-862% Plj mcxijrp ezohjx naxoj` ykpl pljrj

`kikpr kr 2-286 ce` plj rocmmjrp ezohjx naxoj` ykpl pljrj `kikpr kr`kikpr kr 2-286 ce` plj rocmmjrp ezohjx naxoj` ykpl pljrj `kikpr kr

6-822%6-822%Plj `knnjxjebj kr 2-6


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Ocpljocpkbr kr c MceizcijOcpljocpkbr kr c Mceizcij


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Baerk`jx plj nammaykei Jeimkrl rjepjebj7Kn c rpxckilp mkej hj bzp cp xce`ao- plj rszcxj aeKn c rpxckilp mkej hj bzp cp xce`ao- plj rszcxj ae

plj ylamj kr jszcm pa plj rszcxjr ae plj rjiojeprplj ylamj kr jszcm pa plj rszcxjr ae plj rjiojepr

ce` pykbj plj xjbpceimj baepckej` h{ plj rjiojepr%ce` pykbj plj xjbpceimj baepckej` h{ plj rjiojepr%

,Jzbmk`- Jmjojepr- KK%0- 266 H%B%+

c h

,c $ h+,c $ h+88 ? c? c88 $ h$ h88 $ 8ch$ 8ch


11/28



Maad cp plj ocpljocpkbcm rjepjebj bmarjm{7,c $ h+,c $ h+88 ? c? c88 $ h$ h88 $ 8ch$ 8ch

Plj eazer c ce` h cxj baeejbpj` ke cPlj eazer c ce` h cxj baeejbpj` ke c

rjepjebj zrkei ~jxhr ,avjxcpaxr $- ?+ ce`rjepjebj zrkei ~jxhr ,avjxcpaxr $- ?+ ce`c`gjbpk~j ,vcxcojpjx- plj ezohjx 8+c`gjbpk~j ,vcxcojpjx- plj ezohjx 8+

^jxhr ? Avjxcpaxr

C`gjbpk~j


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Lay lzocekp{ `j~jmavj` pljLay lzocekp{ `j~jmavj` pljmceizcij an ocpljocpkbrmceizcij an ocpljocpkbr


13/28


Lay lzocekp{ `j~jmavj` pljLay lzocekp{ `j~jmavj` plj

mceizcij an ocpljocpkbrmceizcij an ocpljocpkbrRpcij 3Rpcij 3

066 HB 7 bazepkei- Cmvlchjp- ozrkb

Vjxbjvpkae 7 @krbxjpjejrr ,rjercpkae+

Xjcmkp{ 7 @krpkebpkae

Paam 7 Ezohjx ,Cxkplojpkb+ Cbpkae 7 Bazepkei


14/28




266 HB 7 Jzbmk`

Vjxbjvpkae 7 Baepkezkp{ ,njjmkei+

Xjcmkp{ 7 Roaaplejrr

Paam 7 Rvcbj ,Ijaojpx{+

Cbpkae 7 Ojcrzxkei


15/28




3>66 C@ 7 Xjeckrrcebj Vjxrvjbpk~j

Vjxbjvpkae 7 Rkokmcxkp{ ,plkedkei+

Xjcmkp{ 7 Xjrjohmcebj

Paam 7 Maikb ,Cmijhxc+ Cbpkae 7 Ojcrzxkei


16/28




3966 C@ 7 Djvmjx- Ejypae- Icmkmka

Vjxbjvpkae 7 Je`mjrrejrr ,kepzkpkae+

Xjcmkp{ 7 Ea Haze`cx{

Paam 7 Kenkekp{ ,Bcmbzmzr+ Cbpkae 7 Kepzkpkei


17/28


Ce J|covmj an lay nze`cojepcm baebjvpCe J|covmj an lay nze`cojepcm baebjvp

an baepkezkp{ ljmvr ke `jbkrkae ocdkei7an baepkezkp{ ljmvr ke `jbkrkae ocdkei7

Zemjrr plj `krbaepkezkp{ kr deaye plxazil bcmbzmzr- kp ykmm

ej~jx hj varrkhmj pa ec~kicpj cmaei plj bzx~j vcpl%


18/28


C Nzxekpzxj Ocezncbpzxkei Baovce{C Nzxekpzxj Ocezncbpzxkei Baovce{

C nzxekpzxj baovce{ ocezncbpzxjr blckxr pchmjr% Jcbl p{vj xjszkxjr `knnjxjep

coazepr an baerpxzbpkae pkoj ce` vckepkei pkoj- cr ik~je ke plj pchmj hjmay% Plj

baovce{ ycepr pa deay lay oce{ an jcbl p{vj ozrp hj vxa`zbj` ke ax`jx pa

oc|kokwj vxankp%

Apljx Mkokpcpkaer7

Ocdj ea oaxj plce 0:6 blckxr

Ocdj cp mjcrp 366 pchmjr

Pchmjr ,\3+

,vjx pchmj+

Blckxr ,\8+

,vjx blckx+

Lazxr C~ckmchmj

Vxankp Baepxkhzpkae Xr%9 Xr%:

Bcxvjepx{ 2 lxr 0 lxr 8066

Vckepkei 8 lxr 3 lx 3666

@ k k ^ k hm


19/28


@jbkrkae ^cxkchmjr7

Mjp

\3 ? Ezohjx an pchmjr pa ocdj

\8 ? Ezohjx an blckxr pa ocdj

Ahgjbpk~j Nzebpkae7 Oc|kokwj Vxankp

Oc|kokwj 9 \3 $ : \8

Baerpxckepr

Lc~j 8066 lazxr an bcxvjepx{ pkoj c~ckmchmj2 \3 $ 0 \8 = 8066 ,lazxr+

Lc~j 3666 lazxr an vckepkei pkoj c~ckmchmj

8 \3 $ 3 \8 = 3666 ,lazxr+

Oaxj Baerpxckepr7 Ocdj ea oaxj plce 0:6 blckxr

\8 = 0:6

Ocdj cp mjcrp 366 pchmjr

\3 5 366

Eae ejicpk~kp{7Bceeap ocdj c ejicpk~j ezohjx anblckxr ax pchmjr

\3 5 6

\8 5 6


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Oa`jm Rzoocx{Oa`jm Rzoocx{

Oc|kokwj 9 \Oc|kokwj 9 \33 $ : \$ : \88,vxankp+

Rzhgjbp pa plj baerpxckepr7

2 \3 $ 0 \8 = 8066 ,bcxvjepx{ lxr+

8 \3$ 3 \

8= 3666 ,vckepkei lxr+

\8= 0:6 ,oc| " blckxr+

\3 5 366 ,oke " pchmjr+

\3-\8 5 6 ,eae ejicpk~kp{+


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J|covmj /Szjzjkei R{rpjorJ|covmj /Szjzjkei R{rpjor

oa`jm vxabjrrjr ke ylkbl bzrpaojxr cxxk~j%

yckp pljkx pzxe nax rjx~kbj%

cxj rjx~kbj` ce` plje mjc~j%


22/28


J|covmjrJ|covmjr

rzvjxocxdjp bljbdazpr rpce`r%

yaxm` rjxkjr pkbdjp haaplr%

`abpaxr yckpkei xaaor jpb%%


23/28

Ezohjx an cxxk~cmr cxj

Rpablcrpkb ,zrzcmm{Vakrrae `krpxkhzpkae+

Rjx~kbj pkoj kr Rpablcrpkb

,zrzcmm{ j|vaejepkcm`krpxkhzpkae+

[az ykmm ejj` plj mceizcij an vxahchkmkp{ `krpxkhzpkaer pa[az ykmm ejj` plj mceizcij an vxahchkmkp{ `krpxkhzpkaer pa

ram~j rzbl szjzjkei hzrkejrr vxahmjor%ram~j rzbl szjzjkei hzrkejrr vxahmjor%

Szjzj Oa`jm


24/28


Ke~jepax{ Baepxam VxahmjorKe~jepax{ Baepxam Vxahmjor

Plj hcrkb krrzj ke oarp an plj ke~jepax{baepxam vxahmjor kr pa `jpjxokej ce

avpkozo ax`jx szcepkp{ cp ylkbl plj

PAPCM BARPPAPCM BARP kr okekozo% Ke ax`jx pa `jpjxokej plkr OKEKOZOOKEKOZO papcm

barp vakep- yj ejj` plj mceizcij an

BCMBZMZRBCMBZMZR%


25/28


Hcmcebkei Bcxx{kei cickerp Ax`jxkei BarprHcmcebkei Bcxx{kei cickerp Ax`jxkei Barpr

Ceezcm Barp ,+Ceezcm Barp ,+

Ax`jx Szcepkp{Ax`jx Szcepkp{

OkekozoOkekozo

Papcm CeezcmPapcm Ceezcm

Rpabdkei BarprRpabdkei Barpr

CeezcmCeezcmBcxx{kei BarprBcxx{kei Barpr

CeezcmCeezcmAx`jxkei BarprAx`jxkei Barpr

Papcm CeezcmPapcm CeezcmRpabdkei BarprRpabdkei Barpr

RocmmjxRocmmjx McxijxMcxijx

Mayj

x

Mayj

x

Lkil

jx

Lkil

jx

JASJAS


26/28


Zrkei Rpcpkrpkbcm paamr nax hzrkejrrZrkei Rpcpkrpkbcm paamr nax hzrkejrr`jbkrkaer`jbkrkaer


27/28


Bjmm Vlaejr nax Blkm`xje1

Zek~jxrkp{ an Ycrlkeipae rbkjepkrp rpcpjr 96/


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Rpz`{ an Bjmm Vlaej Rcnjp{

Ylcp kr plj azpbaoj1 Ylcp kr j|varzxj!xkrd ncbpax1

Lay bce yj crrjrr xjmcpkaerlkv hjpyjje bjmm vlaej

zrj ce` ljcmpl azpbaojr1Rpz`{ @jrkie

@cpc Bammjbpkae ce` Cecm{rkr

Kepjxvxjpcpkae!Cppxkhzpkae

Language of Maths in Management

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