ESTABLISHING COMPUTATIONAL SCIENCE AND ENGINEERING IN BULGARIA AND MACEDONIA

SCOPES Project 7 IP 65642 : An Institutional Partnership Project supported by the SCOPES Program of the Swiss NSF, January 2002 - June 2004

PROGRESS REPORT

of the activities taken at the Institute of Informatics, Faculty of Mathematics and Natural Sciences, “Ss. Cyril and Methodius” University, Skopje, Republic of Macedonia

The activities taken at the Institute of Informatics in the scope of CSE can be divided into two parts, educational and scientific. The educational activities are established by building suitable curricula for the education of computer science engineers, by preparing suitable teaching materials and by involving into the teaching process new computational technologies, like Mathematica and Mathlab packages. The scientific activities are made for solving different kinds of scientific and application problems.

1. CSE in the educational process at the Institute of Informatics. Three years ago a new curricula was established at the Institute of Informatics, and the education was divided into two major subjects: programming engineering and industrial mathematics (or informatics). While the subject of programming engineering was based on what today is known as computer sciences, the subject of industrial mathematics was quite new for our experience. According to our staff capacity and the best of our knowledge, we introduced several new courses. Also, we changed the studying programs of some of the traditional mathematical courses, by using mainly the package Mathematica as an educational tool.

Up to now, the following courses were held by using the package Mathematica as an educational tool or by using a lot of computing power: Calculus (divided in two parts, differential calculus and integral calculus), Vectors and matrices, Functions of several variables, Mathematical analysis, Numerical computations, Finite mathematics and Statistics (where statistical packages are used).

In the following examples we illustrate what calculus student are able to compute.

Example 1.

Example 2.

Example 3.

Also, some of the undergraduate and graduate students obtained some special tasks or small scientific problem to be solved by using Mathematica, like this one: 1. Draw the graphic of an implicit function by using small tangent line approximation. 2. Numerically solve a definite integral by using polynomial function approximations of order 3, 4, 5, ... Compare the obtained results with Tangent and Simpson rule. 3. Generate the Mandelbrot set, Julia sets, and other fractal pictures. 4. Draw the graphic of equation and of inequality with two unknowns where only the function of addition, subtraction, scalar multiplication and absolute values are used.

For the other courses the students were trained to solve problems of similar kind for the corresponding subjects.

2. CSE in science and applications at the Institute of Informatics. There are several fields where a lot of computations and usage of computers were needed for obtaining research results.

In Chaos theory, control in multidimensional chaotic systems by small perturbations and a method for secure communication by time targeting of the trajectories of chaotic systems were investigated by Dr. Danilo Gligoroski.

Optimizations of a hydro-thermal electrical power system were considered by Dr. Vanco Kusakatov. It is a very complex dynamical optimization problem since several sets of cascaded hydro-power plants with variable heats should be optimally scheduled within a hydro-thermal system. Various mathematical methods can be applied, and one of that is the method of minimum norm.

A research group on cryptography problems, consisting of Dr. Smile Markovski as a leader, Dr. Danilo Gligoroski, Dr. Vanco Kusakatov, Dr. Verica Bakeva and others, used a lot of computing and computer power in their investigations of using quasigroup transformations for producing different kind of cryptographic tools, like symmetric stream ciphers, hash functions, pseudo-random number generators. Sometimes, for obtaining relevant results, twenty Pentium II computers for two months were in use.

3. Meetings. The very first meeting where the ideas of CSE were presented before the people of the Institute of Informatics was the Second CiiT (conference of informatics and information technologies) in Molika, Bitola, in December 2001. There Prof. S. Markov and Prof. E. Popova from the IMI of BAS gave talks and introduce the aim of the present project. At the first kick-off meeting of the project in Sofia, the lectures given from Prof. W. Gander and Prof. P. Arbenz showed clearly what results CSE can give. At that meeting Prof. S. Markovski and Dr. V. Bakeva from our institute gave talks as well.

4. The next steps. This year and the year after this one new courses will be established, where the students should be trained for using computation on several subjects: Probability models and applications, Modeling, simulation and visualization, Information theory, Operational researches, Cryptography and computer systems security, Pattern recognition. In all of these courses CSE is contained in smaller or larger extent and suitable effort is needed for their proper positioning. We expect that the experience of the ETH Zurich in CSE will be very useful for us. We find that the major benefit of the overall project will be just in improving this part of the educational process in the Institute of Informatics.

In the next period the research activities mentioned in 2 should continue. An interest is shown among younger researchers from our Institute for topics like image processing, signal processing and their applications, where we have not enough experience, and we expect to be helped from ETH Zurich as well.

Coordinator of the Project for

the Institute of Informatics,

Prof. Dr. Smile Markovski