Following the official guidelines for Degree Classes in Mathematical Science, the degree programme combines the teaching reform measures already being implemented within this degree programme in mathematics, the expectations of the working world as experienced by Bologna University maths graduates, and the material and human resources that our University possesses. The proposal is to seize the opportunity of the present organizational changes to bring in a reform of maths teaching, serving two educational needs: to train young researchers, future teachers (after completion of a teacher-training programme and passing the selection processes as per current law) and popular science writers; and to meet the demand for personnel possessing a solid grounding in mathematics which is increasingly being expressed by public and private research institutes, industry, banks, insurance and finance firms, and more generally the high-tech service sector.