At the University of Helsinki, special effort has been put to help beginning math students to get started with their studies. This involves new ways of teaching a lecture course and new ways of giving peer support to the students. The results have been promising: the number of students passing certain important courses has been at least doubled compared to the earlier prevailing level. The present article describes the work done in connection to a lecture course and the thinking that lies behind it. A paper on peer support is planned. (Contains 1 figure and 2 tables.)