DIMACS Workshop On Algorithmic Mathematical Art:
DIMACS Workshop onAlgorithmic Mathematical Art:Special Cases and TheirApplicationsMay 11 - 13, 2009DIMACS Center, CoRE Building, Rutgers UniversityJean-Marie DendonckerDimacs Algorithmic Mathematical Art1
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math0. A picture of the contextA primary school with 100% of the children who don’t speak Dutch at home65 % of the children are underprivileged45% are refugees“How can we help these children?”Dimacs Algorithmic Mathematical Art2
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.1 Arithmetic algorithm: tables of multiplicationDimacs Algorithmic Mathematical Art3
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art4
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art5
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art6
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art7
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art8
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art9
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art10
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art11
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art12
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art13
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art14
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationWhat if the basic curve is an ellipseinstead of a circle?Dimacs Algorithmic Mathematical Art15
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art16
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art17
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art18
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art19
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art20
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationDimacs Algorithmic Mathematical Art21
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.2 Geometric algortihm: wavefronts in a two dimensional representationSolution:Evolute ellipseTetracuspidcurveDimacs Algorithmic Mathematical Art22
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3 Geometric algortihm in a three dimensional representationA further generalization is tovisualize curves in space1.3.1 Wavefront surface1.3.2 Cardioid and nephroid1.3.3 Hyperbolic paraboloid1.3.4 Conoid1.3.5 Surface of Scherk1.3.6 Elliptic surfaceDimacs Algorithmic Mathematical Art23
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.1 Wavefronts in a three dimensional representationDimacs Algorithmic Mathematical Art24
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.1 Wavefronts in a three dimensional representationSome properties of the wavefront surfaceDimacs Algorithmic Mathematical Art25
elliptic ridgePoint ofcurvatureof thebasicellipsefocal point of thebasic ellipseDimacs Algorithmic Mathematical Art26
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.2 Cardioid and nephroid in a three dimensional representationDimacs Algorithmic Mathematical Art27
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.2 Cardioid and nephroid in a three dimensional representationDimacs Algorithmic Mathematical Art28
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.3 Hyperbolic paraboloidUsing the same way of curvestitching to visualise aparabola it’s possible to dothe same in space.Dimacs Algorithmic Mathematical Art29
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.3 Hyperbolic paraboloidDimacs Algorithmic Mathematical Art30
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.3 Hyperbolic paraboloid ?I have a little problem:‘ There’s a hole in my bucket ‘by Harry Belafonte(and my mother)Dimacs Algorithmic Mathematical Art31
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.3 Hyperbolic paraboloid , NODimacs Algorithmic Mathematical Art32
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.4 ConoidDimacs Algorithmic Mathematical Art33
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1. Projects : IT’S MATHEMAGIC1.3.5 Surface of ScherkThe hyperbolic paraboloid should not be confused with the surface of Scherk(1798-1885). This surface is the only non trivial minimal translation surface. Itcan be given, with disregard of a translation and homothetic transformation,by the equation .z lncos ycos xIt is formed by shifting in perpendicular planes without losing contact witheach other the two curves ,1g ( x) ln cos(cx c0 ) c1c1h( x) ln cos(cx d 0 ) d1cwith integration constants c0 , c1 , d 0 , d1Dimacs Algorithmic Mathematical Art34
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.5 Surface of Scherkas a translation surfaceas a minimal surfaceDimacs Algorithmic Mathematical Art35
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.6 Elliptic surfaceO1 A1 11O1 B1 , O2 B2 O2 A233B1Oˆ 1Q1 A2 Oˆ 2 Q2Dimacs Algorithmic Mathematical Art36
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.6 Elliptic surfaceDimacs Algorithmic Mathematical Art37
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICJ-M DendonckerMay 11 - 13, 2009- Van Maat tot Math1.3.6 Elliptic surfaceSome properties of the elliptic surface1.Contour lineson¼- ½- ¾of thedistencebetween thetwo ellipses .Dimacs Algorithmic Mathematical Art2.The angle between therulings and the plane ofthe ellipses is constant.3.The length between twoconnected points P1 andP2 is constant.38
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.7 Two experiments : the Euler characteristicFind the mystery of EulerExercise 1Exercise 2Exercise 3Only after making the real models, more children understood the generalcalculating method.Dimacs Algorithmic Mathematical Art39
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.7 Two experiments : the mobile hyperboloidLet ‘s tryDimacs Algorithmic Mathematical Art40
DIMACS Algorithmic Mathematical Art1. Projects : IT’S MATHEMAGICMay 11 - 13, 2009J-M Dendoncker- Van Maat tot Math1.3.7 Two experiments : conclusionI can conclude as Prof. Eisenberg of the University of Coloradodescribes in his paper ‘Mathematical Crafts for children: BeyondScissors and Glue’, that mathematical crafts have to be seen as astrong element of mathematical education.It’s clear that the use of algorithms gives to youngunderprivileged children a better structure not only in the use ofmathematics but also in their lives.Dimacs Algorithmic Mathematical Art41
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker2. Higher degree mathematics IT’S MATHEMAGIC2.1 Finite geometryA second type of examples of a practice of algorithms inmathematics is the use of graph theory.The goal of this project was to make some representationsof models that occur in a finite space.Dimacs Algorithmic Mathematical Art42
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker2. Higher degree mathematics IT’S MATHEMAGIC2.1 Fano configuration (7,7,3)This problem has no concrete solutions.Instead of using lines as real lines, we represented them aspoints. Lines are then nothing else then a sequence ofthree points.After numbering the points respectively 1, 2, 3, 7, it ispossible to find the lines as{1, 2, 3}, {1, 4, 5}, {1, 6, 7}, {2, 4, 6}, {2, 5, 7}, {3, 4, 7}, {3, 5, 6}Dimacs Algorithmic Mathematical Art43
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker2. Higher degree mathematics IT’S MATHEMAGIC2.1 Fano configurationDimacs Algorithmic Mathematical Art44
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker2. Higher degree mathematics IT’S MATHEMAGIC2.2 Desargues configuration (10,10,3)To make a realizable spatial configuration, you number thepoints as 12, 13, 14, 15 23, 24, 25 34, 35 and 45Solution:The lines are formed by three points with only threedifferent digits. Doing this you obtain:{12, 13, 23}, {12, 14, 24}, {12, 15, 25}, {13, 14, 34},{13, 15, 35}, {14, 15, 45}, {23, 24, 34}, {23, 25, 35},{24, 25, 45} and {34, 35, 45}Dimacs Algorithmic Mathematical Art45
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker2. Higher degree mathematics IT’S MATHEMAGIC2.2 Desargues configurationDimacs Algorithmic Mathematical Art46
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker2. Higher degree mathematics IT’S MATHEMAGIC2.3 (15,15,3) Tutte configuration (15,15,3)For this purpose the points are numbered as12, 13, 14, 15, 16 23, 24, 25, 26 34, 35, 36 45, 46 56 .Solution:Three points form a line if their numbers containall the digits from 1 to 6{12, 34, 56}, {12, 35, 46}, {12, 36, 45}, {13, 24, 56}, {13, 25,46}, {13, 26, 45}, {14, 23, 56}, {14, 25, 36}, {14, 26, 35},{15, 23, 46}, {15, 24, 36}, {15, 26, 34}, {16, 23, 45}, {16, 24, 35}{16, 25, 34}.Dimacs Algorithmic Mathematical Art47
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker2. Higher degree mathematics IT’S MATHEMAGIC2.3 (15,15,3): GQ(2,2)Dimacs Algorithmic Mathematical Art48
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker2. Higher degree mathematics IT’S MATHEMAGIC2.4 (45,27,3): GQ(4,2)Dimacs Algorithmic Mathematical Art49
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker2. Higher degree mathematics IT’S MATHEMAGIC2.5 Exercise 1: a colorproblem on a torusHow many colors are at least needed to color an arbitrary mapon a torus so that each adjacent ‘country’ has another color?{1, 3, 4}{2, 4, 5}Solution:{3, 5, 6}{4, 6, 7}{5, 7, 1}{6, 1, 2}{7, 2, 3}i.e. the Fano configurationDimacs Algorithmic Mathematical Art50
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker2. Higher degree mathematics IT’S MATHEMAGIC2.5 Exercise 1: modelDimacs Algorithmic Mathematical Art51
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker2. Higher degree mathematics IT’S MATHEMAGIC2.5 Exercise 2: two new olympic disciplinesShot putDiscus throwDimacs Algorithmic Mathematical Art52
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker2. Higher degree mathematics IT’S MATHEMAGIC2.6 Other modelsDimacs Algorithmic Mathematical Art53
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009Dimacs Algorithmic Mathematical ArtJ-M Dendoncker54
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009Dimacs Algorithmic Mathematical ArtJ-M Dendoncker55
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic number He formulated his fundamental ideas inLe nombre plastiqueQuinze leçons sur l’ordonnance architectoniqueBrill Leiden 1960De Architectonische ruimteVijftien lessen over de dispositie van het menselijk verblijfBrill Leiden 1983Dimacs Algorithmic Mathematical Art56
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberSTEP 1: first experimentA sheet of paper of 50 cm torn in twoequal parts produced in his experimentwith 50 people lengths between 24.5cm or 25.5 cm so that they differ 1/25to each other.Dimacs Algorithmic Mathematical Art57
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberSTEP 2: second experimentDimacs Algorithmic Mathematical Art58
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberSTEP 3: classification of 36 squaresDimacs Algorithmic Mathematical Art59
DIMACS Algorithmic Mathematical ArtJ-M DendonckerMay 11 - 13, 20093. The architecture of Van der Laan and the use of the plastic numberSTEP 4: margin, type and order of sizeORDER OF SIZE40Type 6687115153526990120159547294125165Type VType VIType IIType IIIType IVDimacs Algorithmic Mathematical ArtMARGIN60
DIMACS Algorithmic Mathematical ArtJ-M DendonckerMay 11 - 13, 20093. The architecture of Van der Laan and the use of the plastic numberSTEP 5: the common ratio of the geometric sequenceTo establish the basic proportion of the real threedimensional quantity it’s necessary to know the sizeof the smallest different size.Dimension 1: I I IIDimension 2: I II IIIDimension 3: I II IVGolden numberPlastic numberDue to this last requirement, there exists a fixed common ratiobetween the threshold measures.Dimacs Algorithmic Mathematical Art61
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberSTEP 5: the common ratio of the geometric sequenceSo Van der Laan determined exactly the common ratio of thegeometric sequence of the different threshold values of the differenttypes of sizes.Dimacs Algorithmic Mathematical Art62
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberSTEP 6: the extent of the order of sizeAs I II IV than VI-V (III IV) - (II III) IV – II IDimacs Algorithmic Mathematical Art63
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberSTEP 7: a total system of eight measuresDimacs Algorithmic Mathematical Art64
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberCONCLUSION: a system of eight measuresTypeNameRatioPlastic ratioISmall element11IIGreat element4/31,3247 ΨIIISmall piece7/41,7548 Ψ2IVGreat piece7/32,3247 Ψ3VSmall part33,0795 Ψ4VIGreat part44,0795 Ψ5VIISmall ensemble5 1/35,4043 Ψ6VIIIGreat ensemble77,1591 Ψ7Dimacs Algorithmic Mathematical ArtI II IVΔ 1H(VIII, VII) 6,1591VIII – H(VIII,VII) 165
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberSTEP 8: morphic numbersA real number a is a morphic number if there exist two natural numbers kand l so thata 1 a kanda 1 a lΨ is a morphic number as I II IV and VI – I Vk 3Only Φ and Ψ are morphic numbers.l 4Kruijtzer, Aarts and Fokkink 2002Dimacs Algorithmic Mathematical Art66
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberSTEP 9: polynomiographyz 2 z 1Golden numberz3 z 1Plastic number: I II IVDimacs Algorithmic Mathematical Artz5 z4 1Plastic number: VI – I V67
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberNunnery WaasmunsterColors :Floor: tint 5Wall: 1Ceiling: 3Dimacs Algorithmic Mathematical Art68
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberDimacs Algorithmic Mathematical Art69
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberDimacs Algorithmic Mathematical Art70
DIMACS Algorithmic Mathematical ArtMay 11 - 13, 2009J-M Dendoncker3. The architecture of Van der Laan and the use of the plastic numberDimacs Algorithmic Mathematical Art71
DIMACS Algorithmic Mathematical Art May 11 - 13, 2009 J-M Dendoncker 1. Projects : IT’S MATHEMAGIC - Van Maat tot Math 1.3.5 Surface of Scherk Dimacs Algorithmic Mathematical Art 34 The hyperbolic paraboloid shoul
XSEDE HPC Monthly Workshop Schedule January 21 HPC Monthly Workshop: OpenMP February 19-20 HPC Monthly Workshop: Big Data March 3 HPC Monthly Workshop: OpenACC April 7-8 HPC Monthly Workshop: Big Data May 5-6 HPC Monthly Workshop: MPI June 2-5 Summer Boot Camp August 4-5 HPC Monthly Workshop: Big Data September 1-2 HPC Monthly Workshop: MPI October 6-7 HPC Monthly Workshop: Big Data
“algorithmic” from “software” has been also reflected in media studies. [2] “Drawing on contemporary media art practices and on studies of visual and algorithmic cultures, I would like to develop the idea of algorithmic superstructuring as a reading of aest
Algorithmic Trading Table: Proportions of trading volume contributed by di erent category of algorithmic and non-algorithmic traders in the NSE spot and equity derivatives segment (for the period Jan-Dec 2015) Custodian Proprietary NCNP Total Spot Market Algo 21.34% 13.18% 7.76% 42.28% Non-
aforementioned model. Thus, the Triangulation Algorithmic Model is provided and defined to aid in understanding the process of measurement instrument construction and research design. The Triangulation Algorithmic Model for the Tri-Squared Test The Algorithmic Model of Triangulation is of the form (Figure 2). Where,
In these notes we focus on algorithmic game theory, a relatively new field that lies in the intersection of game theory and computer science. The main objective of algorithmic game theory is to design effective algorithms in strategic environments. In the first part of these notes, we focus on algorithmic theory's earliest research goals—
What problems have beginners in learning algorithms/programming? Give some examples why algorithmic thinking is useful in other subjects/daily life Try to give a definition of Algorithmic Thinking : Title: Learning Algorithmic Thinking with Tangible Objects Eases Transition to Computer Programming
v. Who is doing algorithmic trading? Many algorithmic trading firms are market makers. This is a firm that stands ready to buy and sell a stock on a regular and continuous basis at a publicly quoted price. Customers use them to place large trades. Large quantitative funds (also called investment or hedge funds) and banks have an algorithmic .
Cambridge IGCSE Cambridge International O Level Cambridge International AS and A Level Cambridge International Project Qualification Cambridge ICE/AICE Diploma 21 February 22 February – 17 April 17 April 18 April onwards We recommend that you submit your entries at least two weeks before the final entry deadline. This will give you
