# Ph.D. programme in Mathematics and Computer Science

## Course information

### Overview

The Doctoral Degree in Mathematics and Computer Science is aimed at the training of highly qualified researchers and professional people in informatics and mathematical disciplines. Research graduates should acquire a deepened knowledge of the essential tools in informatics and mathematical disciplines, distinguishing themselves as researchers in a university context or in public and private research institutions, or as individuals with a high profile industrial-type professional expertise in private companies involved in the cooperative information systems, knowledge management, logistics, and artificial intelligence sector. During the Doctor’s Degree, students follow courses and other highly specialised training activities, aimed both at the consolidation and deepening of basic knowledge and at the launching of research. Training periods are provided for at foreign Universities, Institutes and/or Research Structures (Italian or foreign) with a duration of no longer than18 months. Work experience is provided for at Institutes and/or Research Structures (Italian or foreign) and at private structures, in accordance with the arrangements already stipulated or in the process of being stipulated.

### Topics of interest

- Artificial Intelligence, Knowledge Representation and Reasoning, Answer Set Programming, Logic Programming, Constraint Satisfaction Problems.
- Databases, Data and Knowledge Integration, Database Theory, Data and Text-Mining, Knowledge Management.
- Theoretical Computer Science, Game theory, Decidability and Complexity Theory.
- Grid Computing, Computational Science, Cellular Automata.
- Optimization Models and Methods for solving problems in Transport and Logistics.
- Combinatorics
- Study of canonical models of surfaces of general type. Algebraic curves and their moduli spaces, Groups and Graphs.
- Relationships between algebra and geometry, and geometry and mathematical physics in modern and contemporary art. Historical developments of the theory of decisions. History of mathematics in education. Mathematics Education with particular reference to the role and use of technology in teaching and learning
- "Calculus of variations, Variationals methods in Nonlinear Analysis, Critical points Theory and applications to nonlinear partial differential equations, Geometry of Banach spaces. Ordinary differential equations, Differential problems with local and non-local conditions, Implicit and explicit approximation methods, Minimum point problems and projections, Equilibrium problems of mixed or generalized type, Uniform distribution and discrepancy, Almost Monte Carlo integration methods."
- Random processes and fields, namely: percolation, statistical mechanics, interacting particle systems, dynamical systems, quantitative finance, stochastic simulation and mathematical statistics.
- Problems of Quantum Theory. Group-theoretic approach to the theory of the interaction. Semiclassical models and quantum for the transport of current and heat in semiconductors. Problems coupling devices-electrical networks.
- Sequences of Sheffer polynomials and approximation of operators involved. Numerical approximation of solutions of partial differential equations of high order and with boundary conditions that initial. Approximations for Scattered Data Interpolation and rational. Applications of mathematics to engineering problems and statistics.

## Overall Organization

### Courses

The Doctor’s Degree courses are chosen among the specialised courses offered in the University and courses held by members of the scientific board and by national and international experts and professors, qualified in the disciplines belonging or related to the scientific areas referred to for the Doctor’s Degree Course. The courses can take the following forms: standard-type courses, courses structured as seminars, and project courses. Each course will be associated with the corresponding number of Credits. Students must achieve a minimim of 24 Credits over 3 years. Of these, a minimum of 18 Credits must be completed as part of the specialised teaching of their doctorate and a minimum of 6 Credits as cross-curricular or not strictly related teaching provided within the University Catalogue. Participation is obligatory and the assessment of the profit will take place according to the modalities decided by the scientific board, bearing in mind that each activity provides for a final test with assessment. Students must submit a study plan, which may be revised periodically (approximately every three months), in order to adequate them to possible changes in the course list, or to needs motivated by the development of their PhD career.

### Seminars

The seminars, which are an integral part of the training activities to be assigned to the doctoral students, are chosen among specialised seminars offered in the University and seminars held by members of the scientific board and by national and international experts and professors, qualified in the disciplines belonging or related to the scientific areas referred to for the Doctor’s Degree Course. Laboratory activities are provided for in the structures. An updated list of seminars is available **here**.

### Research Activities

Students are encouraged to begin research activities connected with the doctorate thesis in the second year. Regarding the mathematical area, students will be able to decide their inclusion in advanced research choosing from a wide range of curricular possibilities in the sectors of mathematical analysis, geometry, history of mathematics, physics-mathematics, numerical analysis, and applied mathematics. The informatics area, in its turn, will offer the possibility of harmoniously combining informatics and applied mathematics skills, with the objective of training as an innovative professional figure, orientated to problem-solving, with deepened knowledge in the field of theoretical informatics, computational sciences and informatics systems.

## Employment

### Possibilities

The PhD in Mathematics and Computer Science is designed to train both researchers and highly skilled professionals in disciplines concerning Computer Science and Mathematics. The Doctors of Philosophy in these disciplines can work as researchers in universities or in public and private research institutions, or as experts with relevant skills in industrial sectors which are engaged in private companies working on cooperative information systems, knowledge management, logistics, and artificial intelligence. In particular, the training programs aim to enable postdocs to rapidly enter the job market, which nowadays is increasingly looking for professionals with skills in Computer Science, that are able to combine expertise with a solid background in Mathematics.

### Employment 3 years after Ph.D

All the Doctors of Philosophy in Mathematics and Computer Science are currently working. A bit more than 80% of them have a postdoctoral position or work as researchers (assistant professor, or lecturer) in national or international universities. The remaining 20% of them work as experts with relevant skills in industrial sectors or in private companies involved in the field of information systems. From the data of the Statistical Office of UNICAL it emerges that all of our postdocs have found employment within 3 years after the final examination, and that 80% of them already in a few months.