Mathematica for Financial Applications Mathematica에 대한 소개와 응용 사례

Yu-Sung Chang Wolfram Research, Inc.

How Are We: About Wolfram Research

Founded by Stephen Wolfram and Theodore Gray Wolfram Research, Inc. Champaign, IL

What is Mathematica? 2 Korea2009FinancialPublic_for_PUBLIC.nb

What Is Mathematica?

Number of Built-in Functions: From 557 to 2500

Features of Mathematica

Basic Mathematica Tutorial Korea2009FinancialPublic_for_PUBLIC.nb 3

Basic Arithmetic + 3.27 5.32 ê 3.12

4.97513

1 2 + 3 7 13

100 !

93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976 156518286253697920827223758251185210916864 000 000 000 000 000 000 000 000

2 2 3 a = 1 + + 7 4 471

196

N@a, 30 D

2.40306122448979591836734693878

+ x y ê z y x + z

Linear Algebra

2.0 3.1 −1.1 A = 0.2 −0.29 3.3 −1.5 4.2 4.7

Transpose @AD

882., 0.2, −1.5 <, 83.1, −0.29, 4.2 <, 8−1.1, 3.3, 4.7 <<

Inverse @AD

880.309722, 0.390433, −0.201646 <, 80.119836, −0.157679, 0.138757 <, 8−0.00824, 0.265511, 0.0244148 <<

3.8 0.8 0.1 B = 2.6 3.2 1.7 4 5 4.1

A.B

8811.26, 6.02, 0.96 <, 813.206, 15.732, 13.057 <, 824.02, 35.74, 26.26 <<

Clear @a, b, c, d, e, f, g, h, i, x, y, zD;

a b c A = d e f g h i

Transpose @AD êê MatrixForm 4 Korea2009FinancialPublic_for_PUBLIC.nb

a d g b e h c f i

Inverse @AD êê MatrixForm

−f h+e i c h−b i −c e+b f −c e g+b f g+c d h−a f h−b d i+a e i −c e g+b f g+c d h−a f h−b d i+a e i −c e g+b f g+c d h−a f h−b d i+a e i f g−d i −c g+a i c d−a f −c e g+b f g+c d h−a f h−b d i+a e i −c e g+b f g+c d h−a f h−b d i+a e i −c e g+b f g+c d h−a f h−b d i+a e i −e g+d h b g−a h −b d+a e −c e g+b f g+c d h−a f h−b d i+a e i −c e g+b f g+c d h−a f h−b d i+a e i −c e g+b f g+c d h−a f h−b d i+a e i

A.B êê MatrixForm

3.8 a + 2.6 b + 4 c 0.8 a + 3.2 b + 5 c 0.1 a + 1.7 b + 4.1 c 3.8 d + 2.6 e + 4 f 0.8 d + 3.2 e + 5 f 0.1 d + 1.7 e + 4.1 f 3.8 g + 2.6 h + 4 i 0.8 g + 3.2 h + 5 i 0.1 g + 1.7 h + 4.1 i

Linear Solve

2.0 3.1 −1.1 A = 0.2 −0.29 3.3 −1.5 4.2 4.7

−1 B = 2.2 0.5

= X LinearSolve @A,BD

880.448408 <, 8−0.397351 <, 80.604572 <<

A.X êê MatrixForm

−1. 2.2 0.5

Clear @a, b, c, d, e, f, g, h, i, x, y, zD;

a b c A = d e f ; g h i = B 88x<, 8y<, 8z<<;

LinearSolve @A,BD

−f h x + e i x + c h y − b i y − c e z + b f z :: >, −c e g + b f g + c d h − a f h − b d i + a e i −f g x + d i x + c g y − a i y − c d z + a f z −e g x + d h x + b g y − a h y − b d z + a e z : >, : >> c e g − b f g − c d h + a f h + b d i − a e i −c e g + b f g + c d h − a f h − b d i + a e i Korea2009FinancialPublic_for_PUBLIC.nb 5

Guide: Matrices and Linear Algebra

Basic Calculus

Derivatives

f = x3 + 3 x2 + x + 2

D@f, xD

1 + 6 x + 3 x2

∂x f

1 + 6 x + 3 x2

D@f, 8x, 2

6 + 6 x

= n + + + f x Log @x aD c

D@f, xD

1 n x−1+n + a + x

2 + 2 DAx y , 88x, y<

82 x, 2 y<

∂ x2 + y2 88x,y<< I M

82 x, 2 y<

Integration

3 Integrate Ax , xE

x3 x ‡

n + n−1 Integrate Ax a x , xE a x xn + n 1 + n

1 x ‡ x4 − a4

x ArcTan − + + A a E Log @ a xD Log @a xD − + − 2 a3 4 a3 4 a3

3 − Integrate Ax , 8x, 1, 2

4 6 Korea2009FinancialPublic_for_PUBLIC.nb

2 x3 x ‡−1 15

3 − → Plot Ax , 8x, 1, 2<, Filling 0E

3 Integrate Ax , 8x, a, b

Basic Statistics

Statistical measures

= data RandomReal @1, 810

80.496091, 0.149269, 0.35607, 0.471387, 0.460904, 0.383276, 0.419492, 0.111618, 0.92457, 0.914342 <

Mean @data D

0.468702

Median @data D

0.440198

Variance @data D

0.0732423

StandardDeviation @data D

0.270633

Skewness @data D

0.608371

Kurtosis @data D

2.52045

MovingAverage @data, 3D

80.33381, 0.325575, 0.429454, 0.438522, 0.421224, 0.304795, 0.485227, 0.650177 <

Quantile @data, .9 D

0.914342 Korea2009FinancialPublic_for_PUBLIC.nb 7

Correlations = In[114]:= data RandomReal @1, 810

Out[114]= 80.80533, 0.721439, 0.28599, 0.362672, 0.455081, 0.868824, 0.612958, 0.838698, 0.193259, 0.400555 <

= In[115]:= data2 RandomReal @10, 810

Out[115]= 88.74986, 9.32905, 0.834222, 8.39764, 3.59373, 6.81173, 5.84848, 4.52274, 3.92227, 5.2548 <

In[116]:= 8Covariance @data, data2 D, Correlation @data, data2 D<

Out[116]= 80.344837, 0.525245 <

DateListPlot @CountryData @"SouthKorea", 8"GDP", 81970, 2007 <

8 µ 10 11

6 µ 10 11

4 µ 10 11

2 µ 10 11

0 1970 1980 1990 2000

CountryData @"US", "Properties"D êê Short

8AdultPopulation, AgriculturalProducts, 220 , WaterArea, WaterwayLength <

? *Data

8AlgebraicRulesData, GraphicsData, AstronomicalData, ImageData, BoxData, IsotopeData, ButtonData, KnotData, CellGroupData, LatticeData, ChartElementData, OLEData, ChemicalData, OutputFormData, CityData, ParticleData, ColorData, PolyhedronData, CompressedData, ProteinData, ControllerInformationData, RawData, CountryData, SeriesData, ElementData, StyleData, ExampleData, SystemInformationData, FinancialData, TextData, FiniteGroupData, ValuesData, GenomeData, VectorGlyphData, GeodesyData, VirtualGroupData, GeoProjectionData, WeatherData, GraphData, WordData <

Real examples 1: Correlation between GDP per capita and life expectancy

= @ data Cases A8CountryData @ , "GDPPerCapita"D, CountryData @ , "LifeExpectancy"D< & ê CountryData @D, 9_ ? NumberQ, _ ?NumberQ =E;

ListPlot @data D

10 000 20 000 30 000 40 000 50 000 60 000

= gdp data @@All, 1DD; = life data @@All, 2DD;

Correlation @Log @10, gdp D, life D

0.743374 8 Korea2009FinancialPublic_for_PUBLIC.nb

Real examples 2: Dow Jones Index and S & P 500

= dowjones FinancialData @"^DJI", "Price", 82004, 1, 1<, "Value"D;

= sandp FinancialData @"^GSPC", "Price", 82004, 1, 1<, "Value"D;

Row @8ListPlot @dowjones D, ListPlot @sandp D

14 000 1400 12 000 1200 10 000 1000

200 400 600 800 1000 1200 1400 200 400 600 800 1000 1200 1400

ListPlot @Transpose @8dowjones, sandp

1400

1200

1000

8000 9000 10 000 11 000 12 000 13 000 14 000

Correlation @sandp, dowjones D

0.98451

Fitting

General fit

= data 880, 1<, 81, 0<, 83, 2<, 85, 4<<;

= line Fit @data, 81, x<, xD

0.186441 + 0.694915 x

= 2 parabola Fit Adata, 91, x, x =, xE

0.678392 − 0.266332 x + 0.190955 x2

→ Show @ListPlot @data, PlotStyle 8PointSize @Large D, Red

1 2 3 4 5 Korea2009FinancialPublic_for_PUBLIC.nb 9

Model fit

= data 880, 1<, 81, 0<, 83, 2<, 85, 4<<;

= lm LinearModelFit @data, x, xD

FittedModel B 0.186441 + 0.694915 x F

lm @"Data"D

880, 1<, 81, 0<, 83, 2<, 85, 4<<

lm @"DesignMatrix"D

881., 0. <, 81., 1. <, 81., 3. <, 81., 5. <<

lm @"ANOVATable"D DF SS MS F Statistic P-Value x 1 7.12288 7.12288 8.75521 0.0977564 Error 2 1.62712 0.813559 Total 3 8.75

= + + nlm NonlinearModelFit @data, a x ^ 2 b x c, 8a, b, c<, xD

2 FittedModel B 0.678392 - 0.266332 x + 0.190955 x F

nlm @"Properties"D êê Short

8AdjustedRSquared, AIC, ANOVATable, 44 , StandardizedResiduals, StudentizedResiduals <

= data 880, 1<, 81, 0<, 83, 2<, 85, 4<, 86, 4<, 87, 5<<;

= + nlm NonlinearModelFit @data, Log @a b x ^ 2D, 8a, b<, xD

Log 1.50632 + 1.42633 x2 FittedModel B B F F

Normal @nlm D

2 Log A1.50632 + 1.42633 x E

→ → Show @ListPlot @data, PlotStyle Red D, Plot @nlm @xD, 8x, 0, 7

0 0 1 2 3 4 5 6 7 10 Korea2009FinancialPublic_for_PUBLIC.nb

nlm @"FitResiduals"D

80.59033, −1.07591, −0.663282, 0.384644, 0.0324629, 0.731751 <

% → ListPlot @ , Filling Axis D

Real example 1

= data Transpose @8sandp, dowjones

ListPlot @data D

14 000

12 000

10 000

1000 1200 1400

= lm LinearModelFit @data, x, xD

FittedModel B 1134.22 + 8.04978 x F

Normal @lm D

1134.22 + 8.04978 x

→ → Show @ListPlot @data, PlotStyle 8PointSize @Tiny D, Red

14 000

12 000

10 000

1000 1200 1400

Real example 2

= data Transpose @8gdp, life

→ ListPlot @data, PlotRange All D Korea2009FinancialPublic_for_PUBLIC.nb 11

20 000 40 000 60 000 80 000 100 000

= + nlm NonlinearModelFit @data, a Log @xD b, 8a, b<, xD

FittedModel 28.2557 + 4.97588 Log x B @ D F

Normal @nlm D

28.2557 + 4.97588 Log @xD

→ → Show @ListPlot @data, PlotStyle Red D, Plot @nlm @xD, 8x, 0, 100000 <, PlotStyle Thick DD

20 000 40 000 60 000 80 000 100 000

Real example 3

= yahoo FinancialData @"F", "Price", 82007, 1, 1<, "Value"D;

= goog FinancialData @"TM", "Price", 82007, 1, 1<, "Value"D;

FinancialData @"^FVX", "Name"D

5 Year Treasury Note

= bond FinancialData @"^FVX", "Price", 82004, 1, 1<, "Value"D;

Length @bond D

1458

Length @dowjones D

1460

= − data Transpose @8bond, dowjones @@1 ;; 3DD

ListPlot @data D

14 000

12 000

10 000

3 4 5 12 Korea2009FinancialPublic_for_PUBLIC.nb

= + + + nlm NonlinearModelFit @data, a x b c ê Sin @d x eD, 8a, b, c, d, e<, xD

FittedModel 7264.07 + á19à x + 0.132641 Csc 5.61136 - 4.11568 x B @ D F

Normal @nlm D

7264.07 + 1012.17 x + 0.132641 Csc @5.61136 − 4.11568 xD

Plot @nlm @xD, 8x, 0, 5

12 000

11 000

10 000

9000

1 2 3 4 5

Optimization

Symbolic

2 − + Minimize A2 x 3 x 5, xE 31 3 : , :x → >> 8 4

Symbolic constrained

− 2 + 2 ≤ Maximize A9x 2 y, x y 1=, 8x, y> 5 5

= 2 + 2 ≤ − − g RegionPlot Ax y 1, 8x, 2, 2<, 8y, 2, 2

− Solve @x 2 y c, yD

1 ::y → H−c + xL>> 2

− + − → − → Manipulate @Show @g, Plot @1 ê 2 H c xL, 8x, 2, 2

Conditions

+ + Maximize @a x ^ 2 b x c, xD

c b 0 && a 0 b 0 && a < 0 H L »» H L 0 Hb 0 && a 0L »» Hb 0 && a < 0L b2−4 a c b − b > 0 && a < 0 b < 0 && a < 0 , x → − b > 0 && a < 0 b < 0 && a < 0 : 4 a H L »» H L : 2 a H L »» H L >> ∞ True Indeterminate True

Numerical

= 2 − + Clear @f, xD; fAx_ E : 2 x 3 x 5; NMinimize @f@xD, xD

83.875, 8x → 0.75 <<

= pts First @Last @Reap @NMinimize @f@xD, x, EvaluationMonitor Sow @xDDDDD;

− → Animate @Show @Plot @f@xD, 8x, .5, 2<, ImageSize 140 D, Graphics @8Red, PointSize @Medium D, Point @8pts @@iDD, f@pts @@iDDD

7.0 6.5 6.0 5.5 5.0 4.5

-0.5 0.5 1.0 1.5 2.0

Distribution = n NormalDistribution @0, 1D;

PDF @nD

12 − 2 & 2 π

− − Row @8Plot @PDF @nD@xD, 8x, 4, 4

0.4 1.0

0.3 0.8 0.6 0.2 0.4 0.1 0.2

-4 -2 2 4-4 -2 2 4

− Integrate @PDF @nD@xD, 8x, Infinity, Infinity

∞ PDF n x x ‡−∞ @ D@ D 1

= µ σ n NormalDistribution @ , D; PDF @nD@xD

x−µ 2 − H L 2 σ2

2 π σ

= ν = s StudentTDistribution @ D; s StudentTDistribution @1D

− − Plot3D @PDF @sD@uD PDF @sD@vD, 8u, 3, 3<, 8v, 3, 3

− → → Row @8Graphics @Point @RandomReal @8 1, 1<, 810 000, 2

0.5 0.5

0.0 0.0

-0.5 -0.5

-1.0 -1.0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 Korea2009FinancialPublic_for_PUBLIC.nb 15

Advanced Mathematica Topics

Data Processing

• 수많은 자료 화일 포멧에 대한 완벽한 통합 • 수학, 물리, 화학, 금융, 지리등 광범위한 분야에 관한 Load-on-demand 데이터 제공 (Curated Data).

Import and export of various formats

Import @"http:êêexampledata.wolfram.com êdinosaur.ply.gz"D

$ImportFormats êê Short

83DS, ACO, AIFF, ApacheLog, AU, AVI, Base64, Binary, Bit, BMP, Byte, BYU, BZIP2, CDED, CDF, 103 , USGSDEM, UUE, VCF, WAV, Wave64, WDX, XBM, XHTML, XHTMLMathML, XLS, XML, XPORT, XYZ, ZIP <

$ExportFormats êê Short

83DS, ACO, AIFF, AU, AVI, Base64, Binary, Bit, BMP, Byte, BYU, BZIP2, CDF, Character16, Character8, 86 , UUE, VRML, WAV, Wave64, WDX, WMF, X3D, XBM, XHTML, XHTMLMathML, XLS, XML, XYZ, ZIP, ZPR <

Import @"ExampleData êelements.xls", "Data"D êê Short

888AtomicNumber, Abbreviation, Name, AtomicWeight <, 110 , 8111., Rg, Roentgenium, 272. <<<

Curated data

Column @8Row @ 8ChemicalData @"Caffein"D, ChemicalData @"Caffein", "MoleculePlot"D, PolyhedronData @"Dodecahedron"D

N N

N O N 16 Korea2009FinancialPublic_for_PUBLIC.nb

Dynamic Interactivity

• 빠르고 손쉬운 인터페이스 제작. • 인터페이스를 통한 그래픽, 수식, 테이블, 문서의 동적인 조작

Manipulate: Instant interface generation

+ 5 Expand AHx yL E

x5 + 5 x4 y + 10 x3 y2 + 10 x2 y3 + 5 x y4 + y5

+ n Manipulate AExpand AHx yL E, 8n, 1, 100, 1

x + y

N@Pi, 30 D

3.14159265358979323846264338328

Manipulate @N@Pi, nD, 8n, 1, 30000, 1

Interactive graphics

Manipulate @Plot @Sin @a xD, 8x, 0, 2 Pi

1.0

0.5

1 2 3 4 5 6 -0.5

-1.0 Korea2009FinancialPublic_for_PUBLIC.nb 17

+ − − → Manipulate @Plot3D @Sin @a Sqrt @x ^ 2 y ^ 2DD, 8x, Pi, Pi <, 8y, Pi, Pi <, ImageSize 150 D, 8a, .1, 3

−1.1 0.9 A = ; −1.4 0.3 @ → → Manipulate @ParametricPlot @Evaluate @MatrixExp @A t, D & ê pt D, 8t, 0, 10 <, PlotRange 5, ImageSize 180 D, − → 88pt, 882, 0<, 80, 1<, 8 3, 0<<<, Locator <, SaveDefinitions True D

-4 -2 2 4

-2

-4

= Manipulate @Block @8f<, f LinearModelFit @pts, x, xD; → → Plot @f@xD, 8x, 1, 10 <, PlotRange 8All, 80, 6<<, ImageSize 160 DD, 88pts, Table @8i, RandomReal @81, 5

6 5 4 3 2 1

2 4 6 8 10 18 Korea2009FinancialPublic_for_PUBLIC.nb

Graphics and Charting

• 함수와 자료에 관한 2 차원 및 3 차원 고급 그래픽, 동영상의 자동 제작 • 시스템 인터페이스와 배포 (deployment): 데이터베이스, 스프래드 시트, C와 Fortran 코드, 웹 서비스, 자바, .NET등과의 유동적 연결

High quality graphics for publication

+ + + + ParametricPlot3D @8Cos @vD 0.3 Sin @3 uD 0.04 Sin @20 vD, u, Sin @vD 0.3 Cos @3 uD 0.04 Sin @20 vD<, −π π −π π → → 8u, , <, 8v, , <, PlotPoints 200, MaxRecursion 0, → → → → PlotStyle 8Orange, Specularity @White, 10 D<, Axes None, Mesh None, RotationAction "Clip"D

Animation creation for web publishing

Animate BWith B π π = θ = θ :q Quotient B , F, m Mod B , F>, 2 2 − + Graphics @8EdgeForm @Black D, LightGray, Rotate @Rectangle @8q, 0

0 1 2 3 4 5

% Export @"square.swf", D

square.swf Korea2009FinancialPublic_for_PUBLIC.nb 19

Charting

→ → Grid @88BarChart @RandomReal @1, 83, 3

From Simple Ideas To Real World Application

Just Beautiful...

Manipulate @ = − = − Module @8m1 8Reverse @pt1 D, 8 1, 1< pt1 <, m2 8Reverse @pt2 D, 8 1, 1< pt2 <<, Graphics @Map @Line, NestList @ + − + − Flatten @Map @88 @@2DD, @@2DD m1.H @@2DD @@1DDL<, 8 @@2DD, @@2DD m2.H @@2DD @@1DDL<< &, D, − → → − − 1D &, 8880, 1<, 80, 0<<<, nDD, ImageSize 200, PlotRange 88 3, 3<, 8 1, 5<

generation 1

Credit: Theodore Gray, Wolfram Research, Inc.

먹이 사슬 = → → → → foodchain 8"Fox" "Bird", "Fox" "Rodent", "Fox" "Snake", "Fox" "Rabbit", "Fox" → "Salamander", "Wolf" → "Rodent", "Wolf" → "Skunk", "Wolf" → "Deer", "Wolf" → "Rabbit", "Snake" → "Rodent", "Snake" → "Insect", "Snake" → "Toad", "Wildcat" → "Bird", "Wildcat" → "Rodent", "Racoon" → "Bird", "Racoon" → "Insect", "Bear" → "Rodent", "Bear" → "Plant", "Bear" → "Deer", "Skunk" → "Rodent", "Skunk" → "Insect", "Toad" → "Insect", "Rabbit" → "Plant", → → → → "Salamander" "Insect", "Bird" "Plant", "Deer" "Plant", "Insect" "Plant"<; → → → LayeredGraphPlot @foodchain, VertexLabeling True, AspectRatio .5, ImageSize 550 D

Fox

Wolf Snake

Wildcat Racoon Bear Skunk Salamander Toad Rabbit

Bird Rodent Deer Insect

Plant Korea2009FinancialPublic_for_PUBLIC.nb 21

먹이 사슬 2

picfoodchain =

→ → → → −> foodchain ê. :"Fox" , "Bird" , "Rodent" , "Snake" , "Rabbit" ,

"Salamander" → , "Wolf" → , "Skunk" → , "Deer" → , "Insect" → ,

→ → → −> → "Toad" , "Wildcat" , "Racoon" , "Bear" , "Plant" >;

→ → → LayeredGraphPlot @picfoodchain, VertexLabeling True, AspectRatio .5, ImageSize 550 D

나라별 통계자료간의 상관 관계

ü 문문문맹문맹맹맹률률률률

Graphics @8EdgeForm @Black D, = With @8r CountryData @ , "LiteracyFraction"D<, 8If @NumberQ @rD, ColorData @"SolarColors"D@rD, White D, @ → Tooltip @CountryData @ , "SchematicPolygon"D, Column @8 , r

ü GDP

DateListPlot @CountryData @"SouthKorea", 8"GDP", 81970, 2005 <

8 µ 10 11

6 µ 10 11

4 µ 10 11

2 µ 10 11

0 1970 1980 1990 2000

→ → TabView @Map @Tooltip @Show @CountryData @ , "Shape"D, ImageSize 40 D, D DateListPlot @CountryData @ , 88"GDP"<, 81970, 2005 <

1 µ 10 12

8 µ 10 11

6 µ 10 11

4 µ 10 11

2 µ 10 11

0 1970 1980 1990 2000 Korea2009FinancialPublic_for_PUBLIC.nb 23

ü 평균수명과 국민소득

Graphics A99With A8 = pt 8CountryData @ , "LifeExpectancy"D, Log @10, CountryData @ , "GDPPerCapita"DD<, = r Rescale @CountryData @ , "Population"D, 810^1.65, 10^9.11

벽돌 쌓기

ü 단순한 벽돌 쌓기를 넘어서 로보틱스를 활용한 신신신 건축 기술 : Link

ü Mathematica 를를를 이용한 실험 (Credit: Chris Carlson, Wolfram Research, Inc.) : Link

친친친 환경적 건축

ü The Ghirkin : Link (http://en.wikipedia.org/wiki/30_St_Mary_Axe) 24 Korea2009FinancialPublic_for_PUBLIC.nb

ü Mathematica 를를를 이용한 예제 (Credit: Chris Carlson, Wolfram Research, Inc.)

• Lofting (건축이나 선박제조 기술)

= Loft Acontours_ E : Module @ = = 8nc Length @contours D, n Length @First @contours DD<, @@ GraphicsComplex @Join contours, Polygon @Flatten @Table @Table @ + + + + 1 8j Mod @i, nD, j Mod @i 1, nD, + + + + + j n Mod @i 1, nD, j n Mod @i, nD<, − − 8i, 0, n 1

= pts 8880, 0, 0<, 80, 1, 0<, 81, 1, 0<, 81, 0, 0<<, 880, 0, 1<, 80, 1, 1<, 81, 1, 1<, 81, 0, 1<<<; @ Row @8Graphics3D @Point ê pts D, Graphics3D @Loft @pts DD

= pts Table @Table @8Sqrt @jD Cos @2 Pi i ê 6D, Sqrt @jD Sin @2 Pi i ê 6D, j<, 8i, 0, 5

• Manipulating the lofting

Manipulate @ Graphics3D @8Specularity @White, 50 D, Opacity @.7 D, Loft @Table @Table @ + + π π π 8Cos @bD Cos @a tw bD, Cos @bD Sin @a tw bD, h Sin @bD<, 8a, ê np, 2 , 2 ê np

contours 16

points 35

height 2.22

twist 0.83

Around The World In 80 Days

최단 경로 검색

= SC A9lat_, lon_ =E : r 9Cos Alon °E Cos Alat °E, Sin Alon °E Cos Alat °E, Sin Alat °E=;

r = 6378.7; = places CountryData @"Countries"D; = centers Map @CountryData @ , "CenterCoordinates"D &, places D; = distfun A9lat1_, lon1_ =, 9lat2_, lon2_ =E : VectorAngle @SC @8lat1, lon1

Graphics @8LightBlue, EdgeForm @Opacity @.5, Black DD, @ CountryData @ , "SchematicPolygon"D & ê CountryData @D, Red, Point @Reverse @centers, 2DD

= → 8dist, route < FindShortestTour @centers, DistanceFunction distfun D;

= surfaceCenters Map @SC, centers @@route DDD;

= GreatCircleArc A9lat1_, lon1_ =, 9lat2_, lon2_ =E : = = = Module @8u SC @8lat1, lon1

Graphics3D @8Sphere @80, 0, 0<, 0.99 rD, Map @ − Line @Map @SC, CountryData @ , "SchematicCoordinates"D, 8 2

From Simple Ideas To Real World Application

2004 Indian Ocean Tsunami

Shallow Water Equation

1 swe = ∂t h λ, φ, t + : @ D φ R Cos @ D ∂ λ φ λ φ − λ φ + ∂ λ φ λ φ − λ φ φ H λ Hu@ , , tDHh@ , , tD b@ , DLL φ Hv@ , , tDHh@ , , tD b@ , DL Cos @ DLL 0, ∂ u λ, φ, t v λ, φ, t ∂ λ φ λ φ ∂ λ φ φ @ D @ D g λ h@ , , tD u@ , , tD λ u@ , , tD + + ∂t u λ, φ, t + f v λ, φ, t , φ @ D φ @ D R R Cos @ D R Cos @ D ∂ v λ, φ, t v λ, φ, t g ∂ h λ, φ, t λ φ ∂ λ φ φ @ D @ D φ @ D u@ , , tD λ v@ , , tD + + ∂t v λ, φ, t + −f u λ, φ, t ; @ D φ @ D> R R R Cos @ D

From Simple Ideas To Real World Application

Some Videos... Korea2009FinancialPublic_for_PUBLIC.nb 27

What Is Wolfram|Alpha?

Wolfram Research와와와 Stephen Wolfram의의의 최신 Project

ü http://www.wolframalpha.com ü 2009년년년 5월월월 18일일일 서비스 시작

ü 시작 3일동안 5천만건의 입력 처리

지식 연산 엔진 (Computational Knowledge Engine)

체계가능한 지식 (Curatable Data) 에 대한 즉각적인 계산 (Computation) 과 이를 모든 사람이 이용가능한 형태로 제공 (Presentation)

= 사용자 입력 언어 분석 데이터 검색 알고리즘 적용 프리젠테이션 labels 9" ", " ", " ", " ", " "=; → → → → → → GraphPlot @81 2, 2 3, 3 4, 4 5<, DirectedEdges True, VertexRenderingFunction → → HText @Style @Framed @labels @@ 2DDD, 9D, 1, Background White D &L, ImageSize 400 D

사용자 입력 언어 분석 데이터 검색 알고리즘 적용 프리젠테이션

Four Essential Components of Wolfram|Alpha

방대한 양의 데이터 컬렉션 (Data Curation Pipeline)

• 다양한 분야의 내용을 고루 망라한 데이터 컬렉션 • 전문 Data Curators: 각 분야의 방대한 데이터에 대한 분석, 정리, 컴퓨터가 처리를 쉽게 할수 있는 데이터로 변경 • Crowd sourcing (Community effort): Volunteers

알고리듬 계산 시스템 (Algorithmic Computation System)

• 사용자들의 입력에서 저장된 계산가능한 데이터들 검색 • 수천수만가지의 알고리즘중 필요한 것들을 적용하여 새로운 결과를 제공

언어 프로세싱 시스템 (Linguistic Processing System)

• 지속적인 사용자 입력 패턴 연구 • 사용자들의 일상적 언어에 가까운 질문과 여러분야의 용어를 더 잘 이해할수 있도록 노력

자동 프리젠테이션 시스템 (Automated Presentation System)

• 전문가들에 의한 유저인터페이스 디자인 • 사용자의 질문에 대한 답을 보다 정리된 형태로 출력하기 위한 끊임없는 연구 28 Korea2009FinancialPublic_for_PUBLIC.nb

Behind Technologies

ü Mathematica

ü webMathematica ü gridMathematica

ü Super computer clusters

Let's Try It: Wolfram Alpha Examples

Go Online... Mobile Application

Wolfram Web Resources

Wolfram|Alpha

http://www.wolframalpha.com

Wolfram Demonstration Project

http://demonstrations.wolfram.com

MathWorld etc...

http://www.mathworld.com http://functions.wolfram.com http://www.wolfram.com/solutions

The End

감감감사감사사사합합합합니니니니다다다다!