There is a big difference between teaching undergraduate students having no idea why mathematics is included in their curriculum and what they can do with it, and teaching more specialised mathematical topics to graduate students who already know why they have included these topics in their curriculum and who have mastered the basic mathematical skills. Thus, for most teachers, the latter form a much more pleasant audience to teach. Service teaching to undergraduates has its own particular problems, both with respect to mathematical contents and to didactics.

In this contribution I will combine my own opinions with respect to content, presentation and developments in the near future with some of the points of view found in the contributed papers.

The starting point of the discussion document [4] for the ICMI-study is that mathematics is taught as a service subject in response to a need. It then concentrates on three questions:

1. - Why do we teach mathematics to students of discipline X?

2. - What mathematics should be taught to these students?

3. - How should this mathematics be taught?

I would like to start with considering these questions for service teaching to undergraduates, thereby describing the situation at this moment at many places. Next I propose to discuss whether the present situation gives a satisfactory answer to these questions in the light of the changing demands of the disciplines and the increasing availability of computer hard- and software.