COMPACT COURSES CADGME 2007 János Karsai COMPACT COURSES ON COMPUTER-AIDED VISUALIZATION AND...
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Transcript of COMPACT COURSES CADGME 2007 János Karsai COMPACT COURSES ON COMPUTER-AIDED VISUALIZATION AND...
COMPACT COURSESCOMPACT COURSES CADGME 2007
János KarsaiJános Karsai
COMPACT COURSES COMPACT COURSES
ON COMPUTER-AIDED VISUALIZATION ON COMPUTER-AIDED VISUALIZATION
AND EXPERIMENTATIONAND EXPERIMENTATION
COMPACT COURSESCOMPACT COURSES CADGME 2007
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:
COMPACT COURSESCOMPACT COURSES CADGME 2007
http://silver.szote.u-szeged.hu
Download (from next week) of demo course materials
COMPACT COURSESCOMPACT COURSES CADGME 2007
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
COMPACT COURSESCOMPACT COURSES CADGME 2007
A C.A.S. system
Mathematical Programming Languages
+
Knowledge base
COMPACT COURSESCOMPACT COURSES CADGME 2007
Problems
Computer system is an independent „person” with
•Own Language
• Own rules and working logic
•Sometimes unusual, strange work
•Sometimes works with Error
COMPACT COURSESCOMPACT COURSES CADGME 2007
The formula:The formula: n1
1
2n
Visual descriptionVisual description
On the importance of the languageOn the importance of the language
COMPACT COURSESCOMPACT COURSES CADGME 2007
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
On the importance of the languageOn the importance of the language
Mathematical programming language
COMPACT COURSESCOMPACT COURSES CADGME 2007
Advanced mathematical language
NestList#12&, 1, 1000. List Plus
ApplyPlus, NestList#12&, 1, 1000
On the importance of the languageOn the importance of the language
{a,b,c} {a,b,c} {x,y,z}{x,y,z} ={a ={axx,b,byy,c,czz}}
COMPACT COURSESCOMPACT COURSES CADGME 2007
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
COMPACT COURSESCOMPACT COURSES CADGME 2007
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
COMPACT COURSESCOMPACT COURSES CADGME 2007
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
COMPACT COURSESCOMPACT COURSES CADGME 2007
• 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
COMPACT COURSESCOMPACT COURSES CADGME 2007
• 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
COMPACT COURSESCOMPACT COURSES CADGME 2007
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 COURSESCOMPACT COURSES CADGME 2007
• 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
COMPACT COURSESCOMPACT COURSES CADGME 2007
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
COMPACT COURSESCOMPACT COURSES CADGME 2007
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
COMPACT COURSESCOMPACT COURSES CADGME 2007
ExamplesExamples
COMPACT COURSESCOMPACT COURSES CADGME 2007
ILLUSTRATIONS TO ILLUSTRATIONS TO
THEORETICAL COURSESTHEORETICAL COURSES
COMPACT COURSESCOMPACT COURSES CADGME 2007
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
COMPACT COURSESCOMPACT COURSES CADGME 2007
Tangent line, derivative
COMPACT COURSESCOMPACT COURSES CADGME 2007
Find minimum
-4 -2 2 4
-2
-1
1
2
COMPACT COURSESCOMPACT COURSES CADGME 2007
Examples from Examples from modeling coursesmodeling courses
COMPACT COURSESCOMPACT COURSES CADGME 2007
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
COMPACT COURSESCOMPACT COURSES CADGME 2007
LinesLines
Kísérletek
Binary treesBinary trees
COMPACT COURSESCOMPACT COURSES CADGME 2007
LinesLines
Koch curvesKoch curves
COMPACT COURSESCOMPACT COURSES CADGME 2007
Polygons; Sierpinsky trianglesPolygons; Sierpinsky triangles
COMPACT COURSESCOMPACT COURSES CADGME 2007
COMPACT COURSESCOMPACT COURSES CADGME 2007
Rotating, midpoint, …Rotating, midpoint, …
)(:},...,,{},,...,{ 11111 XShiftxxxxxxX nnnn
))((5.0)( 1 XShiftXXMid )(XMidX
COMPACT COURSESCOMPACT COURSES CADGME 2007
-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, …
COMPACT COURSESCOMPACT COURSES CADGME 2007
Applications: Kasner polygonsApplications: Kasner polygons
COMPACT COURSESCOMPACT COURSES CADGME 2007
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
COMPACT COURSESCOMPACT COURSES CADGME 2007
Heat transferHeat transfer
COMPACT COURSESCOMPACT COURSES CADGME 2007
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
COMPACT COURSESCOMPACT COURSES CADGME 2007
HeatHeat
1
1,,, )(
jijiji XShiftwX
COMPACT COURSESCOMPACT COURSES CADGME 2007
WaveWave
COMPACT COURSESCOMPACT COURSES CADGME 2007
Parity rule:Parity rule:
Cellular AutomataCellular Automata
COMPACT COURSESCOMPACT COURSES CADGME 2007
EcologyEcology
COMPACT COURSESCOMPACT COURSES CADGME 2007
Image processingImage processing
COMPACT COURSESCOMPACT COURSES CADGME 2007
Something else: vectorsSomething else: vectors
COMPACT COURSESCOMPACT COURSES CADGME 2007
Something else: tetrahedraSomething else: tetrahedra
COMPACT COURSESCOMPACT COURSES CADGME 2007
Something else: tetrahedraSomething else: tetrahedra