The 2nd cycle Degree Course in Mathematics is the natural continuation of the 1st cycle course with the same name. It provides for educational activities completing and deepening the acquired mathematical competences. At the same time, it is structured in a way to permit attendance also to students coming from other, similar, 1st cycle courses and wishing to develop their studies with a strong mathematical emphasis. The course aims at educating graduates with advanced knowledge of the scientific method and a sound theoretical, methodological and applicative background in the principal mathematical areas. The course develops analysis and synthesis capabilities, as well as the capability of translating into a mathematical language interdisciplinary issues and of identifying solutions for complex problems. The course might be articulated in different curricula, depending on the cultural interests of individual students and/or on professional opportunities. For instance, it may privilege one or more areas of pure mathematics, also in the perspective of further studies, such as a PhD, or core mathematics and teaching methodologies. The cultural and methodological training will enable in any case the placement of graduates in areas which are not strictly scientific, requiring planning and managerial capabilities. The preferred teaching tool consists of lectures, practice sessions and integrative seminars. Practice can be proposed to be carried out independently, through which students are encouraged to explore the limits of their abilities. Students can receive handouts of the lessons (also available online) or have one or more reference texts. Examinations are carried out through the evaluation of a written paper and/or an oral interview. The final examination consists of a dissertation, consistent with the training, in which the student, under the guidance of a supervisor, must demonstrate independence and originality.