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. It is designed 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 training graduates with advanced knowledge of the scientific method and sound theoretical, methodological and applicative groundings in the principal mathematical areas. The course develops analysis and synthesis capabilities, as well as the capability of translating interdisciplinary issues into a mathematical language 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 applied mathematics 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 course consists of lectures, practice sessions and integrative seminars. Independent practice encourages students 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 typically consist of written tests and/or an oral interviews. The final examination consists of a dissertation, consistent with the course outline, in which the student, under the guidance of a supervisor, must demonstrate independence and originality.