In this paper we will examine some of the problems and difficulties in modern university teaching and how these difficulties were overcome and the problems were solved. Because the syllabus in Danish (and other European) high schools has been substantially weakened over the last decade and especially since 2002, the university students have experienced new serious problems in their first year learning. This has had the consequence that many students dropped out of their studies and that many others failed at their first year exams. This was not acceptable and therefore something had to be done. In this paper we will only deal with the first year courses in mathematics for economists at The University of Copenhagen, and it is told how the teaching in mathematics was changed during the last two years such that the rate of failure dropped considerably. Many resources were spent to reach this aim, and it was very important to engage and activate the students and to give them more personal excitement, such that they also obtained higher ability for studies on their own hand. The result of the new way of teaching was remarkable and the aim of a much lower rate of failure was reached. Furthermore the students saw mathematics not only as a scientific tool useful in modern economic theory but also as a cultural and academic discipline with a long and interesting historical development. The students got much more knowledge and they obtained a personal attitude to their mathematical education. Both for the students and for the Department of Economics this was a success.