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

2. COMPACT COURSES CADGME 2007 Éva Rácz Széchenyi University, Győr Angela Schwenk, Norbert Kalus Technische FachhochSchule Berlin Árpád Takácsi, Djurdica Takácsi University of Novi Sad Lajos Szilassi, György Dombi, Zoltán Hantos, Béla Viskolcz, Krisztina Boda Zoltán Kovács, Róbert Vajda, University of Szeged … and Our Students who continuously help to improve our programs Collaborations:

3. COMPACT COURSES CADGME 2007 http://silver.szote.u-szeged.hu Download (from next week) of demo course materials

4. COMPACT COURSES CADGME 2007 The control of problem-solving (after The control of problem-solving (after Neumann) Control The problem The Mind (Controller) Library Solutions Knowledge bases............ Languages Computerized In mind

5. COMPACT COURSES CADGME 2007 A C.A.S. system Mathematical Programming Languages + Knowledge base

6. COMPACT 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

7. COMPACT COURSES CADGME 2007 The formula: Visual description On the importance of the language

8. COMPACT COURSES CADGME 2007 Visual mathematical language Non-mathematical programming language On the importance of the language Mathematical programming language

9. COMPACT COURSES CADGME 2007 Advanced mathematical language On the importance of the language {a,b,c} {x,y,z} ={a x,b y,c z }

10. COMPACT 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

11. COMPACT COURSES CADGME 2007 What are missed Deductive methodsDeductive methods Theoretical basisTheoretical basis Proofs (?)Proofs (?) Singular casesSingular cases Heuristic methods (?)Heuristic methods (?) Intuition (?)Intuition (?) The computerized knowledge bases (Programming) language + knowledge formulated in the language Computerized knowledge bases Typical 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

12. COMPACT COURSES CADGME 2007 Computing methods in the Curriculum: A possible solution The 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

13. COMPACT 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

14. COMPACT 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

15. COMPACT 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

16. COMPACT 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

17. COMPACT 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

18. COMPACT COURSES CADGME 2007 Program of the schools Direction Szeged Math - Phys Life Sci. Novi Sad Math - Phys Life Sci. RTRTRTRT Math. and Visual. packages (Mathematica) 8844Math. and Visual. packages (MATLAB, Anylogic...) 8+ 4 Computer-aided modeling: Continuous and discrete models in time 8844Computer-aided modeling: Cont. and discr. statio- temporal models 8888 Intelligent Test & Measurement 4488Oscillation and waves, signals, Fourier analysis 8888 Statistical packages, biostatistics 444+ 4 Computer-aided analysis of mathematical models Computer-modeling of 3D geometric structures 8844Dynamical geometry, spacegeometry 88 Molekula design and quantumchemistry 4+ 2 4+ 4 Chemical Informatics88 Molecule – modeling, Interact. in biol. Systems 44Chemistry models in environment protection 88

19. COMPACT COURSES CADGME 2007 Examples

20. COMPACT COURSES CADGME 2007 ILLUSTRATIONS TO THEORETICAL COURSES

21. COMPACT COURSES CADGME 2007 Introductory Examples These are all tan(x)

22. COMPACT COURSES CADGME 2007 Tangent line, derivative

23. COMPACT COURSES CADGME 2007 Find minimum

24. COMPACT COURSES CADGME 2007 Examples from modeling courses

25. COMPACT COURSES CADGME 2007 G(a_) → F(a) Replace everything by everything Setting, substitutions, patterns

26. COMPACT COURSES CADGME 2007Lines Kísérletek Binary trees

27. COMPACT COURSES CADGME 2007Lines Koch curves

28. COMPACT COURSES CADGME 2007 Polygons; Sierpinsky triangles

29. COMPACT COURSES CADGME 2007

30. COMPACT COURSES CADGME 2007 Rotating, midpoint, …

31. COMPACT COURSES CADGME 2007 Rotating, midpoint, …

32. COMPACT COURSES CADGME 2007 Applications: Kasner polygons

33. COMPACT COURSES CADGME 2007Smoothing …x k-1 x k x k+1 … x k → w -1 x k-1 + w 0 x k + w 1 x k+1 x k → w -1 x k-1 + w 0 x k + w 1 x k+1

34. COMPACT COURSES CADGME 2007 Heat transfer

35. COMPACT COURSES CADGME 2007 Rotation on the plane X k,l X k,l+1 X k+1,l X k-1,l X k,l-1

36. COMPACT COURSES CADGME 2007Heat

37. COMPACT COURSES CADGME 2007Wave

38. COMPACT COURSES CADGME 2007 Parity rule: Cellular Automata

39. COMPACT COURSES CADGME 2007 Ecology

40. COMPACT COURSES CADGME 2007 Image processing

41. COMPACT COURSES CADGME 2007 Something else: vectors

42. COMPACT COURSES CADGME 2007 Something else: tetrahedra

43. COMPACT COURSES CADGME 2007 Something else: tetrahedra