The Value of Mathematics in

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The Value of Mathematics in
Todays Society
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Radon Transform, Diffusion Equation, Knot Theory,
Gauge Theory, Mathematics Computation on Quantum
Mechanics, Many Body Model, Inverse Problems
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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.
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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
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D1 ?1, ?1, ?1, ?1, 1, 1, 1, 1
A S1 ? D1
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?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
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?? A S4 ? D1 ? D2 ? D3 ? D4
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JPEG (Fourier) ? JPEG 2000 (??)
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RSA ????

• ????????????????????????
• ??????????? Rivest, Shamir, Adleman ?1978???
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RSA ???????

• ?????????? Fermat ??
• ?? RSA ?????????????????????
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????? e 1193?
n 63,978,486,879,527,143,858,831,415,041
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2305000118050021140405180001 202001031100120121140
3080020 0805001309191909120500141523
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C1 1060546943595003247867569919 C2
2485275951856773770355929250 C3
13101173280250715817550140912

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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
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• ??? 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)

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RSA ? 1977 ????
n RSA-129 114381625757888867669235779976146612
01021829672124236256256184293570693524573389783059
7123563958705058989075147599290026879543541
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32769132993266709549961988190834461413177642967992
942539798288533
34905295108476509491478496199038981334177646384933
87843990820577
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?2002?,???????,Agrawal, Kayak ? Saxena
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? p ?????,? a ???? p ???????,? p
??????????? (x-a)p xp - a (mod p)
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?????????????????????????????? r,?? (x-a)p xp -
a (mod xr-1, p) ????????,???? r2 log p ???????
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??? (Queuing Theory)
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?? (Graph Theory)

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??????????F. Thomson Leighton

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• Akamai Technologies Incorporate (?????????) ????
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Akamai ?????

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Akamai ??????? 54 ???
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???????????????????,???????????????? (Standard
Deviation) ??????????????? (Objective Risk) ?????
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??,????????? 1000 ??????,??? 5 ??????????????????
?? 1 2 3 4 5
?? 1 7 11 10 9 13
?? 2 16 4 10 12 8
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??????,???? 10,???????? 10/1000
0.01,??????????????????,??????? 2,??????? 4?
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???? (Normal Distribution) ?????????????
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??????????????????? ????,?????? 10 ?????
2? ????,?????? 10 ????? 4?
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??,????,????????????? 10 2 x 2 6, 14
??? ????,?? 10 2 x 4 2, 18
??? ???????,???????? 8 ??
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??????????????????????,????????? 8/2 x 1/10
0.4,????? 16/2 x 1/10 0.8,????????????????????
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?????????????,??????????,????????? 100 x 10
1000? ???????????? ?????????????
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??,????,??????? 1,000 2 x 20 960, 1040
??,??????? 0.04? ????,??? 1,000 2 x 40 920,
1080 ??,?????? 0.08? ????????,????????,?? Law
of Large Number ?????
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????????? ??????? Law of Large Number
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????????? ???????????????????,??????????????????
??????,????? Black-Scholes ??????
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?? T ???,???? ST ,????????? c max (0, ST -
K),????? ST ????????,??????????????????,???????
(Brownian motion process)?
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???? c ????????,??Fischer Black?Myron Scholes ?
Robert Merton ? 1973 ??????? ???? ??E???????,???
?Weiner?Ito ??????????
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