The main objectives of the PhD programme are:

• to consolidate the doctoral candidate’s foundational skills in modelling, data analysis, and data processing, with further development in systems for efficient information management and/or numerical methods for large-scale problems;
• to enhance proficiency in advanced techniques specific to the chosen thesis research topic;
• to increase autonomy and the ability to develop innovative ideas in a structured manner, by comparing proposed solutions with existing approaches;
• to foster critical and analytical thinking skills, enabling the interpretation of research results and, where necessary, the refinement and improvement of the initial research idea in order to achieve the expected outcomes;
• to develop the ability to work in teams and collaborate with both senior researchers, such as the thesis supervisor, and peers, as well as within heterogeneous groups composed of researchers with potentially diverse scientific backgrounds.

Research activities are structured across several areas, including:

• Models for Applied Sciences: web and social network analysis, statistical models, computer graphics, image reconstruction, and modelling for monument degradation and related interventions;
• Numerical Methods: approximation of integro-differential and fractional operators; constructive approximation, spectral analysis, and computation for matrices and operators; iterative solvers for large-scale linear (and non-linear) systems; numerical optimization;
• Analytical and Geometric Methods: variational methods in nonlinear analysis; geometric analysis methods; operator theory; linear and nonlinear Schrödinger equations; metric and symplectic aspects on manifolds; non-integrable geometries;
• Innovative Information Management Systems (IoT, Social Networks, Blockchain): supporting models and architectures, as well as processes for information management;
• Data Analysis: machine learning, image processing, natural language processing, deep learning, and big data as a service;
• Data Security and Privacy: models and mechanisms for selective data sharing, risk and trust management, user privacy management models, and processing of encrypted data;
• Network Security Protocols: definition of distributed, security- and privacy-aware network architectures and policy enforcement mechanisms to ensure reliable data transmission;
• Empirical Software Engineering: evaluation of software quality and development processes, development of predictive models, definition of quality metrics for models, Artificial Intelligence for Software Engineering, and Software Engineering for Artificial Intelligence.

In addition to providing access to academic careers, the PhD in Computer Science and Computational Mathematics offers opportunities to pursue technical and managerial positions within the broad and diverse field of Information and Communication Technology (ICT). At both international and, in particular, European and Italian levels, there has long been a recognized shortage of highly specialized professionals as well as experts with interdisciplinary competencies.
Based on past experience with related doctoral programmes at the University of Insubria, graduates have demonstrated strong employment outcomes across universities, research centres, banks, and national and international companies. Many former students of the programme are currently employed in academic and industrial research centres, including institutions of outstanding excellence such as the University of Cambridge, Google Research, IBM Dublin, KTH Royal Institute of Technology (Sweden), the Italian Institute of Technology (IIT), the National Institute for Astrophysics (INAF), and several Italian universities (e.g., University of Pisa, Sapienza University of Rome, University of Rome Tor Vergata, University of Cagliari).
Some alumni have also founded highly successful start-ups focused on developing innovative solutions to prevent security attacks on industrial control systems.

PhD students are required to attend and successfully complete at least four doctoral-level courses during the three-year program.
These courses may be selected from the offerings at the University of Insubria or from other accredited institutions, such as other national or international universities or ational and international doctoral schools.

In accordance with the organization of educational activities proposed by the Doctoral School, the PhD program requires students to obtain the following credits over the three-year period:

• 8 CFU of core curricular activities;
• 3 CFU of soft skills (cross-curricular activities);
• 1 CFU of elective activities, chosen by the student.

Each year, the PhD Faculty Board offers several 2 CFU courses (16 hours each) within the curricular framework. Students may select the courses most relevant to their research path, with the option to supplement them with courses offered by other Italian or international universities and/or summer/winter schools, subject to the approval of their tutor and the PhD Coordinator.