Multimedia Technology for Mathematics and Computer Science Education Srdjan Vukmirovic Faculty of Mathematics Belgrade

Multimedia Technology for Mathematics and Computer Science Education (MTMCSE) In the beginning (2001): Technical University Berlin Faculty of Mathematics, Belgrade Mathematical Institute of SANU, Belgrade Nowadays (2008): Frei Universität Berlin Faculty of Mathematics, Belgrade Mathematical Institute of SANU, Belgrade Faculty of Electronic Engineering of the University of Niš Faculty of Mathematics and Informatics of the University of Sofia Department of Mathematics of Budapest University of Technology and Economics Faculty of Electrical Engineering and Information Technologies of the University Ss. Cyril and Methodius, Skopje Faculty of Civil Engineering of the University of Zagreb Fachinformationszentrum Karlsruhe

Aims of the Project MTMCSE Knowledge transfer in the field of multimedia technology in education and research in the fields of mathematics and computer science. Establishing of local competence centers in multimedia technology and their cross linking in a network. Development and use of new multimedia content and software for mathematics and computer science education. Project website: http://geom.mi.fu-berlin.de/projects/daad/index.html http://www.matf.bg.ac.yu/~daad/ (Belgrade)

Some activities of the project (Belgrade) VIVE MATH - Niš, Yugoslavia, 2001 Workshops (2004, 2005, 2006, 2007) in Belgrade Visits of people from Berlin to Belgrade (lectures for students) Visits of people from Belgrade to TU Berlin 15 students from Belgrade participated to Spring School Geometry and Visualization, Berlin 2006

Some results of the project (Belgrade) Geometrical visualization Computer aided teaching Computer aided research Development of regional mathematical information infrastructure

Geometrical visualization - the main tools JavaView (www.javaview.de) (K. Polthier and others) 3D geometry viewer and a mathematical visualization software allows interactive display of 3D geometries in any HTML document on the internet. WinGCLC (http://www.matf.bg.ac.yu/~janicic/gclc/) (P. Janicic) tool for visualizing and teaching geometry, and for producing mathematical illustrations Support for many geometrical constructions, isometric transformations, conics, and parametric curves GCLC constructions are formal procedures, rather than drawings

Computer aided teaching Online textbooks: Textbook in Analytical Geometry (JavaView, Wafl, DB2) (N. Bokan, S. Malkov, N. Mitic, Z. Rakic, students) Problem book in Descriptive Geometry (JavaView, AutoCAD) (S. Vukmirovic, students) Textbook in Descriptive geometry (JavaView) (N. Bokan, M. Ljucovic, S. Vukirovic) Euclid’s Elements (html version of the famous book, Serbian) (Z. Lucic, studenti) Ten Problems of Apollonius (WinGCLC, html) (Z. Lucic, studenti)

Computer aided teaching (continued) Using WinGCLC in Teaching Geometry (WinGCLC) (M. Antic, M. Djoric, B. Zivkovic) Isometries of Euclidean Plane, Polygons (C++ language) (S. Vukmirovic, students) Numerical Modelling (C++ language, Java) (D. Radunovic, F. Maric, A. Samardzic, students) Example: wavelets applet (by student Goran Predovic) Solar Eclipses Visualized (C++ language) (C++, DirectX) (P. Glisovic, S. Segan, I. Stojanovic) Root System of Simple Lie Algebras (Mathematica, JavaView) (Lj. Boskovic, B. Radusinovic, S. Vukmirovic)

Computer aided teaching (continued) Geometry for elementary school (JavaView) (B. Radusinovic)

Computer aided research Knot theory program - LinKnot (Mathematica) (S. Jablan, R. Sazdanovic) Playing with homology (C++) (P. Blagojevic, A. D. Blagojevic, M. Milosevic) Geodesic on sphere with respect to a non-standard connection (Z. Stanic) Discrete geometry of polyhedral surfaces (Z. Stanic) Graph theory: Star Complement Technique (C++) (Z. Stanic)

Development of regional mathematical information infrastructure Mirrors of EMIS and Zentralblatt MATH Database of electronic editions of mathematical journals published in Serbia Digitization of mathematical heritage in Serbia