In last 15 years my research interests concentrate on the three interconnected areas:

1. Developing computer technology for mathematics
2. Using computer technology in teaching mathematics and scientific computing
3. Visualization of mathematical objects.

Developing computer technology for mathematics

For years I am involved in development and testing some software tools for mathematics - Scientific Notebook from MacKichan Inc, MuPAD Pro from SciFace GmBH, JavaView from TU in Berlin and Geometry Expressions from Saltire Software. I am part of MuPAD development. MuPAD is the youngest Computer Algebra System developed at the University of Paderborn and SciFace GmBH company. While being part of this development I gained a significant knowledge about the structure of MuPAD and its functionality. This knowledge was a fundamental base for my books about MuPAD. I have been developing also a number of various MuPAD programs for different topics in mathematics. There are still more to come. I guess, my collection of MuPAD programs needs some cleaning and organizing before I will be able to give away the whole collection. However, some of my notebooks are available on the web site for my books at majewski.wordpress.com..

Recently I developed a Polish version of Geometry Expressions. This is a new Dynamic Geometry tool that can also serve as a geometry interface for MuPAD. More abut it at www.geometryexpressions.com.

Using computer technology in teaching mathematics and scientific computing

Teaching mathematics with a computer is a very popular trend. However, it is important to use computer technology in such a way that students will really benefit from it. Most of my papers in last 15 years addresses various issues in teaching mathematics with a computer software. The most important is to find a good methodology for teaching maths with a highly intelligent software like Computer Algebra Systems or Symbolic Geometry tool. This will be the main objective of my works in next few years.

For a few years I was the editor of mathPAD Online a journal that publishes papers related to MuPAD and various aspects of teaching with MuPAD.

For a number of years I am running the MathPAD Conference - a conference for mathematics teachers who use or wish to use computer technology in their mathematics classes. The very first coonference took place in 2002 in Akademia Świętokrzyska in Piotrków. Later the conference moved to the Mathematics and Computer Science Faculty of the Nicholas Copernicus University in Toruń. The conference web site is at mathcas.wordpress.com.

Visualization of mathematical objects

Long time ago I did my M. Sc. and Ph.D. in topics related to geometry. For this reason, even now, many years after completing these two major steps in my education I am still interested in geometry and in particular in visualization of mathematical objects. At mjv.50webs.com there is published large collection of experiments with online visualization. The published there material, called Virtual Models, is an outcome of many years of cooperation with Prof. Konrad Pothier from Zuse Institute and Free University in Berlin, and Klaus Derscher from SciFace GmBH in Paderborn, in Germany.

Finally on www.mathpad.org/2006/ there are published results of my works on visualizing Waterman polyhedrons with MuPAD. My code for visualizing Waterman polyhedrons was implemented as part of the MuPAD 4.0 graphics library.

I always considered mathematics as a form of art and I am always looking for mathematics in artistic creations. I am spending quite a lot of time exploring ethnic geometric patterns and I model them using MuPAD. This topic fascinates me and I treat it rather as a hobby than a serious work. It is possible that as the time goes I may go into a more serious involvement in mathematics and art. For instance, quite often I investigate Chinese lattice patterns, I extract from them algorithms used to create these patterns, generalize these algorithms and write a MuPAD procedures implementing these algorithms. With my friend Prof. Jiyan Wang, from East China Normal University in Shanghai, we wrote a few papers on Chinese lattice patterns.

I am also thinking about writing a book on mathematical art with computer technology. This book could be a nice blend of art, algorithms, and mathematics. Who knows, perhaps it will be my next book or one of my next books?