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The Value of Mathematics in

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c Fischer Black Myron Scholes Robert Merton 1973 ... Many Body Model, ... PowerPoint Presentation ... – PowerPoint PPT presentation

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Title: The Value of Mathematics in


1
The Value of Mathematics in
Todays Society
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2
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3
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4
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5
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6
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7
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????,??????(?????),DNA??,????,????,???,????,??????
,???
??????????
Radon Transform, Diffusion Equation, Knot Theory,
Gauge Theory, Mathematics Computation on Quantum
Mechanics, Many Body Model, Inverse Problems
8
????Labor Dept. ?????????????
Other (non-mathematics) occupations that require
extensive knowledge of mathematics include
actuary, statistician, computer programmer,
system analyst, system engineer, operation
research analyst. A strong background in
mathematics also facilitates employment in
engineering, economics, finance, and physics.
9
????Labor Dept. ?????????????
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10
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11
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Si A ?????
A
Di A ?????
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14
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15
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  • ?? ???? Di

16
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???? 16 ???
A 1, 2, 3, 4, 5, 6, 7, 8, 8, 7, 6, 5, 4, 3, 2,
1
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S1 3, 7, 11, 15, 15, 11, 7, 3
????
D1 ?1, ?1, ?1, ?1, 1, 1, 1, 1
A S1 ? D1
17
?S1??????? S2 10, 26, 26, 10 D2 ?4, ?4,
4, 4
S1 S2 ? D2
?S2??????? S3 36, 36 D3 ?16, 16
S2 S3 ? D3
??,??? S4 72,D4 0
S3 S4 ? D4
18
?? A S4 ? D1 ? D2 ? D3 ? D4
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19
JPEG (Fourier) ? JPEG 2000 (??)
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20
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21
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?? 256 ?????
22
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23
RSA ????
  • ????????????????????????
  • ??????????? Rivest, Shamir, Adleman ?1978???
  • ??????????? ( ???????????????? )
  • ???????????????

24
RSA ???????
  • ?????????? Fermat ??
  • ?? RSA ?????????????????????
  • ??????????????????????,????,???????????????

25
????
????? e 1193?
n 63,978,486,879,527,143,858,831,415,041
26
?????84????
2305000118050021140405180001 202001031100120121140
3080020 0805001309191909120500141523
27
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C1 1060546943595003247867569919 C2
2485275951856773770355929250 C3
13101173280250715817550140912
  • ??? n ?????? p ? q ???
  • ????????? p ? q,?????????

28
n 63,978,486,879,527,143,858,831,415,041 p
? q 440,334,654,777,631?145,295,143,558,111
? r (p-1) ? (q-1) 63,978,486,879,526,558,
229,033,679,300
29
  • ??? e ?????? d ??
  • e ? d 1 (mod r) , 1 ? d ? r
  • d 30,568,095,156,186,201,333,234,581,057
  • ????
  • Cd (Me)d M (mod n)

??
30
RSA ? 1977 ????
n RSA-129 114381625757888867669235779976146612
01021829672124236256256184293570693524573389783059
7123563958705058989075147599290026879543541
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32769132993266709549961988190834461413177642967992
942539798288533
34905295108476509491478496199038981334177646384933
87843990820577
?
31
?2002?,???????,Agrawal, Kayak ? Saxena
????????????????????????????????? RSA
????????????????
32
? p ?????,? a ???? p ???????,? p
??????????? (x-a)p xp - a (mod p)
33
?????????????????????????????? r,?? (x-a)p xp -
a (mod xr-1, p) ????????,???? r2 log p ???????
34
?????
??
35
???????
  • ??????? (CEPA, 92)
  • JIT ???????
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36
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37
?????
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38
??? (Queuing Theory)
??????????????
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39
?? (Graph Theory)
  • ??????????
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40
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5
7
8
3
4
4
1
1
2
3
1
5
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1
1
7
2
2
2
1
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41
??????????F. Thomson Leighton
  • ?????????????
  • Akamai Technologies Incorporate (?????????) ????
  • ??????????


42
Akamai ?????
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  • Akamai ????
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  • ?????????????????,Akamai ????????????????????
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43
????????????????????
Akamai ??????? 54 ???
44
?????
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45
????
  • ????? (Risk)?
  • ????,??????????????
  • ?????
  • 911 ?? (??)
  • SARS
  • ??

46
???????????????????,???????????????? (Standard
Deviation) ??????????????? (Objective Risk) ?????
47
??,????????? 1000 ??????,??? 5 ??????????????????
?? 1 2 3 4 5
?? 1 7 11 10 9 13
?? 2 16 4 10 12 8
48
??????,???? 10,???????? 10/1000
0.01,??????????????????,??????? 2,??????? 4?
49
???? (Normal Distribution) ?????????????
50
?????????????????????
51
??????????????????? ????,?????? 10 ?????
2? ????,?????? 10 ????? 4?
52
??,????,????????????? 10 2 x 2 6, 14
??? ????,?? 10 2 x 4 2, 18
??? ???????,???????? 8 ??
?????,????????16??
53
????
??????????????????????,????????? 8/2 x 1/10
0.4,????? 16/2 x 1/10 0.8,????????????????????
54
?????????????,??????????,????????? 100 x 10
1000? ???????????? ?????????????
55
??,????,??????? 1,000 2 x 20 960, 1040
??,??????? 0.04? ????,??? 1,000 2 x 40 920,
1080 ??,?????? 0.08? ????????,????????,?? Law
of Large Number ?????
56
???
?????????????????????? ??????,?????????????????,?
????????? ??????? Law of Large Number
?????,??????????????????,????????????
57
????????? ???????????????????,??????????????????
??????,????? Black-Scholes ??????
58
????
???????????,?????? ??????????, ?? T ??????,??? K
????????
59
?? T ???,???? ST ,????????? c max (0, ST -
K),????? ST ????????,??????????????????,???????
(Brownian motion process)?
60
???? c ????????,??Fischer Black?Myron Scholes ?
Robert Merton ? 1973 ??????? ???? ??E???????,???
?Weiner?Ito ??????????
61
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62
?? Data mining ??????????????????????????????,????
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63
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?,???????????????????
64
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