COMPACT COURSES CADGME 2007 János Karsai COMPACT COURSES ON COMPUTER-AIDED VISUALIZATION AND EXPERIMENTATION

COMPACT COURSESCOMPACT COURSES CADGME 2007

János KarsaiJános Karsai

COMPACT COURSES COMPACT COURSES

ON COMPUTER-AIDED VISUALIZATION ON COMPUTER-AIDED VISUALIZATION

AND EXPERIMENTATIONAND EXPERIMENTATION


Éva RáczSzéchenyi University, Győr

Angela Schwenk, Norbert KalusTechnische FachhochSchule Berlin

Árpád Takácsi, Djurdica TakácsiUniversity of Novi Sad

Lajos Szilassi, György Dombi, Zoltán Hantos, Béla Viskolcz, Krisztina BodaZoltán Kovács, Róbert Vajda, University of Szeged

… and Our Students who continuously help to improve our programs

Collaborations:


http://silver.szote.u-szeged.hu

Download (from next week) of demo course materials


The control of problem-solving (after The control of problem-solving (after Neumann)

ControlControl

The problem

The Mind

(Controller)Library

Solutions

Knowledge bases

.

.

.

.

.

.

Languages

Computerized

In mind


A C.A.S. system

Mathematical Programming Languages

+

Knowledge base


Problems

Computer system is an independent „person” with

•Own Language

• Own rules and working logic

•Sometimes unusual, strange work

•Sometimes works with Error


The formula:The formula: n1

1

2n

Visual descriptionVisual description

On the importance of the languageOn the importance of the language


Visual mathematical language

n1

1

2n

Sum[1/2^n, {n, 1, Infinity}]

For[n = 1; S = 0, n < 100, S = S + 1/2^n; n++];Print[S]

Non-mathematical programming language


Mathematical programming language


Advanced mathematical language

NestList#12&, 1, 1000. List Plus

ApplyPlus, NestList#12&, 1, 1000


{a,b,c} {a,b,c} {x,y,z}{x,y,z} ={a ={axx,b,byy,c,czz}}


Some questions and concerns

Singularities can disappear

The beauty of ideas can disappear or appear somewhere else.

Expanded calculatability

Wrong (or unusual) work

PlotSinxx,x, 7, 7;-6 -4 -2 2 4 6

-0.2

0.2

0.4

0.6

0.8

1

N33 0.721125 1.24902

Plotx3,x, 7, 7;

1 2 3 4 5 6 7

0.5

1

1.5

0

xx

2x

12 Erfx

Erf'x2 x2

k1

12k

1

2k 1

122 Log4

k1

1

2k 1

1

2k

Log42


What are missedWhat are missed

• Deductive methodsDeductive methods

• Theoretical basis Theoretical basis

• Proofs (?)Proofs (?)

• Singular casesSingular cases

• Heuristic methods (?)Heuristic methods (?)

• Intuition (?)Intuition (?)

The computerized knowledge basesThe computerized knowledge bases

(Programming) language + knowledge formulated in the language (Programming) language + knowledge formulated in the language

Computerized knowledge basesComputerized knowledge bases

Typical formulations, methodsTypical formulations, methods

• Constructive methodsConstructive methods

• Can be given → Give itCan be given → Give it

• Exists → DO itExists → DO it

• For all … → ???For all … → ???

• VisualizeVisualize

• ExperimentsExperiments


Computing methods in the Curriculum:Computing methods in the Curriculum:A possible solutionA possible solution

The flowThe flow

Basic course 1

Basic course 2

Basic course n

Advanced course 1

Advanced course 2

Advanced course n

Time

Basic course 2

Semester 1 Semester k

Basic (Parallel) Computer

course

Advanced(Compact) Computer

course

High level(Compact) Computer

course

Resarch


• Joint or built in another course with extra classes• Students learn new computer tools after understaning the theory

• Theory: • Only computer illustrations: advanced graphics, 3D scenes, animations etc.• Students should not learn computer techniques, language. • No time for improvisation in the classroom, every material is well-prepared.

• Computer Lab• Main topics: Fit the joint theoretical course + additional topics• Learn and apply the computer languages, tools• Visualization, constructive methods, experimental methods practical applications

are emphasized and preferred to the formal mathematical methods (vs. theoretical class!)

• Well-prepared modeling schemes• Students learn to perform mathematical concepts and procedures by computer.• Students investigate problems with the help of computerized procedures.• The instructor and the students work on computers simultaneously.• Teaching experiment: A teacher and an instructor lead the work together.

Basic (Parallel) Computer courses


• Form: Compact course between semesters• Assumes theoretical and computing knownedge• Results should be applied in advanced theoretical courses.• Problem-oriented treatment, topics from different fields are considered• Theoretical background is summarized. • Perform theoretical concepts and procedures by computer.• Practical problems with the help of computerized mathematical procedures.• Visualization, constructive methods, experimental methods are emphasized

and preferred to the formal mathematical methods• Models arising from their professional experience.• Complete set of well-prepared modeling schemes• The instructor and the students work on computers simultaneously.• Teaching experiment: A teacher and an instructor lead the work together.

Advanced (Compact) Computer course


A joint work: TFH Berlin, Computational engineering:

Computer algebra I-II (one week long courses at the beginning of semesters 1 and 2

Some versions

University of Szeged, PhD. Course, accepted by Budapest Technical University and University of Debrecen:

Computer-aided study of dynamical systems (one week long courses in the spring semester

Technical University of Prague, Babes - Bolyai University of Kolozsvár:

Mathematical programming in Mathematica


• Compact course-series after the (independent of) graduate school system• Gives introduction to different fields• Small number of classes. Assumes an intensive individual work• Results are used directly in the research.• Problem-oriented treatment• Theoretical background is summarized. • Perform theoretical concepts and procedures by computer.• Practical problems with the help of computerized mathematical procedures.• Problems taken from the professional experience.• Complete set of well-prepared schemes• The instructor and the students work on computers simultaneously.• Teaching experiment: A teacher and an instructor lead the work together.

High level interdisciplinary course-series


A new interregional project granted by EU

Computer-aided Modeling and Simulation in Natural Sciences

•University of Szeged – University of Novi Sad

•Two interdisciplinary compact schools at the parties.

Szeged, Novi Sad, 2008 spring

•Directions:

•Mathematics – Physics and Life sciences

•Researchers and Teachers

•Participants:

•High school and univerrsity teachers

•Researchers

•Phd (or talented graduate) students


Program of the schools

Direction Direction

Szeged Math -Phys

Life Sci. Novi Sad Math -Phys

Life Sci.

R T R T R T R T

Math. and Visual. packages (Mathematica)

8 8 4 4 Math. and Visual. packages (MATLAB, Anylogic...)

8+4

8+4

Computer-aided modeling: Continuous and discrete models in time

8 8 4 4 Computer-aided modeling: Cont. and discr. statio-temporal models

8 8 8 8

Intelligent

Test & Measurement 4 4 8 8 Oscillation and waves,

signals, Fourier analysis8 8 8 8

Statistical packages, biostatistics

4 4 4+4

4+4

Computer-aided analysis of mathematical models

Computer-modeling of 3D geometric structures

8 8 4 4 Dynamical geometry, spacegeometry

8 8

Molekula design and quantumchemistry

4+2

4+2

4+4

4+4

Chemical Informatics 8 8

Molecule – modeling, Interact. in biol. Systems

4 4 Chemistry models in environment protection

8 8


ExamplesExamples


ILLUSTRATIONS TO ILLUSTRATIONS TO

THEORETICAL COURSESTHEORETICAL COURSES


Introductory Examples

These are all tan(x)

-3 -2 -1 1 2 3

-40

-20

20

40

-3 -2 -1 1 2 3

-3

-2

-1

1

2

3

-3 -2 -1 1 2 3

2

4

6

8

10

12


Tangent line, derivative


Find minimum

-4 -2 2 4

-2

-1

1

2


Examples from Examples from modeling coursesmodeling courses


G(a_) → F(a)G(a_) → F(a)

-1

-0.5

0

0.5

-0.5

0

0.5

1

-1

-0.5

0

0.5

1

-1

-0.5

0

0.5

-0.5

0

0.5

1

Replace everything by everythingReplace everything by everything

Setting, substitutions, patternsSetting, substitutions, patterns


LinesLines

Kísérletek

Binary treesBinary trees


LinesLines

Koch curvesKoch curves


Polygons; Sierpinsky trianglesPolygons; Sierpinsky triangles



Rotating, midpoint, …Rotating, midpoint, …

)(:},...,,{},,...,{ 11111 XShiftxxxxxxX nnnn

))((5.0)( 1 XShiftXXMid )(XMidX


-1-0.5

0

0.5

1

-1

-0.5

0

0.5

1

-1

-0.5

0

0.5

1

-1-0.5

0

0.5

1

-1

-0.5

0

0.5

1

-1-0.5

0

0.5

1

-1

-0.5

0

0.5

1

-1

-0.5

0

0.5

1

-1-0.5

0

0.5

1

-1

-0.5

0

0.5

1

)(XMidX

Rotating, midpoint, …Rotating, midpoint, …


Applications: Kasner polygonsApplications: Kasner polygons


SmoothingSmoothing

20 40 60 80

-1

-0.5

0.5

1

20 40 60 80

-0.5

0.5

1

…… xxk-1 k-1 xxk k xxk+1k+1 …… xxkk →→ w w-1-1xxk-1 k-1 + + ww00xxk k + + ww11 xxk+1k+1

)}(),(),(}.{,,{ 101101 XShiftXShiftXShiftwwwX


Heat transferHeat transfer


Rotation on the planeRotation on the plane

XXk,lk,l XXk,l+1k,l+1

XXk+1,lk+1,l

XXk-1,lk-1,l

XXk,l-1k,l-1


HeatHeat

1

1,,, )(

jijiji XShiftwX


WaveWave


Parity rule:Parity rule:

Cellular AutomataCellular Automata


EcologyEcology


Image processingImage processing


Something else: vectorsSomething else: vectors


Something else: tetrahedraSomething else: tetrahedra


Something else: tetrahedraSomething else: tetrahedra

Documents

COMPACT COURSES CADGME 2007 János Karsai COMPACT COURSES ON COMPUTER-AIDED VISUALIZATION AND EXPERIMENTATION