Mathematical problem solving environments for education and research

The simulation of complex problems demands a Lot of mathematical know-how. For this reason students (especially of applied sciences) get a profound education in applied higher mathematics. Help was always necessary and welcome. In former times we used slide rules, then pocket computers. Today, students can use powerful computers on which numerical software can be developed or simply used as problem Solving Environments (PSEs). Some time ago, the main application of such environments was number crunching and visualisation. But today's machines are so powerful that complex symbolic problems can be tackled by special PSEs called Computer Algebra Systems, even on small desktop computers. This is very helpful, particularly for learning mathematics. Using PSEs in teaching and learning does not replace the knowledge of mathematical rules and methods. The student can achieve a deeper understanding by experiencing mathematics and get automatically an idea of applicability and limitations of mathematical algorithms.