## 31 Results in Mathematics

**Degrees**

**Location**

**Study type**

**Pace**

Nowadays, science and technology are rapidly developing with an ever-increasing impetus and a substantial part of knowledge is comprised of quantitative data. The analysi ... [+]

Nowadays, science and technology are rapidly developing with an ever-increasing impetus and a substantial part of knowledge is comprised of quantitative data. The analysis and interpretation of this data require the use of mathematical and statistical methods. The Applied Mathematics and Statistics doctorate program practiced by the Department of Mathematics enables the students to conduct advanced research for application in the fields of Engineering, Medicine, Physics, Biology, Computer Sciences under the supervision of advisors. The academic staff comprises dynamic lecturers who are capable of conducting efficient scientific research and publishing them in internationally recognized journals.... [-]

The Ph.D. program in Geometry and Mathematical Physics focuses on the study of analytic and geometric aspects of physical phenomena that are of fundamental interest in bo ... [+]

The Ph.D. program in Geometry and Mathematical Physics focuses on the study of analytic and geometric aspects of physical phenomena that are of fundamental interest in both pure and applied sciences and covers a wide spectrum of topics in modern algebraic and differential geometry and their applications.

Research Topics Integrable systems in relation to differential, algebraic and symplectic geometry, as well as with the theory of random matrices, special functions and nonlinear waves, Frobenius manifolds Deformation theory and virtual classes moduli spaces of sheaves and of curves, in relation to supersymmetric gauge theories, strings, Gromov-Witten invariants, orbifolds and automorphisms Quantum groups, noncommutative Riemannian and spin geometry, applications to models in mathematical physics Mathematical methods of quantum mechanics Mathematical aspects of Quantum Field Theory and String Theory Symplectic geometry, sub-Riemannian geometry Geometry of quantum fields and strings Seminar on Hodge theory ... [-]The aim of the Ph.D. Course in Mathematical Analysis, Modelling, and Applications is to educate graduate students in the fields of mathematical analysis and mathematical ... [+]

The aim of the Ph.D. Course in Mathematical Analysis, Modelling, and Applications is to educate graduate students in the fields of mathematical analysis and mathematical modeling, and in the applications of mathematical and numerical analysis to science and technology. The goal is to enable PhDs to work as high-level researchers in these fields in universities, research institutes, and private companies.

Research TopicsThe activity in Mathematical Analysis is mainly focused on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry and reduced order modeling are also developed.... [-]

The Department offers programs towards the Master of Science, Master of Science in Teaching, and the Doctor of Philosophy in Mathematical Sciences. There are two areas of ... [+]

The Department offers programs towards the Master of Science, Master of Science in Teaching, and the Doctor of Philosophy in Mathematical Sciences. There are two areas of concentration: pure mathematics and applied mathematics. The programs emphasize the interaction between these two areas and the common role of scientific computation. Students can take courses common to both areas, enabling them to gain an appreciation of the mathematical techniques and the connections between theory and applications.

Department research interests include classical analysis, harmonic analysis, Fourier analysis, approximation theory, algebra, number theory, graph theory, combinatorics, fluid mechanics, biomathematics, differential equations, numerical analysis, and modeling.... [-]

The PhD curriculum in Mathematics of Natural, Social and Life Sciences at Gran Sasso Science Institute will lead the students to deal not only with the more traditional a ... [+]

The PhD curriculum in Mathematics of Natural, Social and Life Sciences at Gran Sasso Science Institute will lead the students to deal not only with the more traditional aspects of this discipline, such as Pure Mathematics, Partial Differential Equations and Mathematical Physics, but also with entirely new problems, requiring the development of the most appropriate tools to deal with the complexity, such as stochastic analysis and computational mathematics.

The curriculum consists of 4 years of study and research. During the first year, after initial training classes, students will be offered three main courses and a wide number of short courses, covering a large spectrum of topics. By the beginning of the second year students select a research project under the supervision of one (or more) of the mathematicians affiliated to GSSI.... [-]

The PhD Program in Mathematical Methods and Numerical Simulation in Engineering and Applied Sciences is an official university degree, imparted jointly by the three Galic ... [+]

The Programme Doctoral Degree in Mathematical Methods and Numerical Simulation in Engineering and Applied Sciences Is an official university degree, taught jointly by the three Galician universities, which forms researchers in the field of mathematical modeling and numerical resolution of problems that arise in different industrial and business areas. In addition to the participating doctors from the three universities, it has the collaboration through an agreement of 27 companies and technological centers, which propose research topics of great relevance and topicality.

Why study the degreeAt present, with the rapid evolution of engineering and applied sciences, it is evident the need to train specialists at the doctoral level in the modeling and numerical simulation of processes that come from the industrial or business scope, so that Impel from the university the transfer of knowledge and the incorporation of doctors to the R & D & I departments. These doctors will have training in mathematical modeling and simulation aimed at optimizing processes, reducing costs, improving product quality, designing technologies, increasing safety, reducing environmental pollution, valuing products, investments and financial risks, etc.... [-]

The graduate of the Ph.D. studies in mathematics education is prepared to deal with both theoretical and application problems in the mathematical education of children an ... [+]

Candidates for doctoral studies in Didactics of Mathematics are expected to:

show interest in mathematics education in general (for example, by taking part in scientific conferences and conferences for teachers), have an overview of the most important scientific journals and books related to mathematics education, have an idea of the area of mathematics education they are willing to focus on in their studies and be able to specify it in a written project of up to 10 pages (including tentative research questions, methodology, and theoretical background and a list of references).Program without specialization

Description of verification and evaluation criteria ... [-]This proposal proposes an interdisciplinary doctorate whose itineraries in specific areas of specialization allow the formation of PhD students in different areas of know ... [+]

This proposal proposes an interdisciplinary doctorate whose itineraries in specific areas of specialization allow the formation of PhD students in different areas of knowledge (Fundamental Mathematics, Applied Mathematics, Statistics, Mathematical Transfer, Information Technologies, among others). In these moments, the scientific production and the formative capacity of the researchers of the different groups in the field of the Scientific Computing, Mathematical, Mathematical Models and Statistical Techniques advises the creation of a specific doctorate program, with its own identity, that allows the consolidation of the research and transfer activity in this area.

Justification of the title... [-]The study program provides advanced theoretical and practical knowledge of computational mathematics, which deals with the solution of mathematical problems describing ph ... [+]

The study program provides advanced theoretical and practical knowledge of computational mathematics, which deals with the solution of mathematical problems describing phenomena in natural, technical and social sciences. The study is focused on the understanding of problems in a wider context.

The study includes the theoretical aspects of the methods of computational mathematics as well as a computer solution of the mathematical tasks motivated by practical problems. The students are prepared for the development of the field itself as well as to employ the achieved knowledge in solving mathematical problems in natural and applied sciences.

The program does not contain specializations.... [-]

Computational linguistics is an interdisciplinary scientific field involving mathematics (including topics such as discrete mathematics, statistics, and probability), com ... [+]

Computational linguistics is an interdisciplinary scientific field involving mathematics (including topics such as discrete mathematics, statistics, and probability), computer science (e.g. algorithmization, machine learning, artificial intelligence) and classical linguistics (e.g. morphology, syntax, language typology). Computational linguistics investigates language from a formal point of view, and it aims at developing methods that could be used in software applications in the field of Natural Language Processing, in which languages in their spoken or written form are handled.

The program does not contain specializations.

Description of verification and evaluation criteriaAdmission for studies... [-]

It is an interdisciplinary study program which connects classical physics (particularly continuum mechanics and thermodynamics) with mathematical analysis and numerical m ... [+]

It is an interdisciplinary study program which connects classical physics (particularly continuum mechanics and thermodynamics) with mathematical analysis and numerical mathematics. The student should go through the construction or understanding of the physical model, its mathematical analysis up to its numerical solution.

Due to the complexity of problems studied both in the research and in the praxis a closed collaboration among specialist from different areas is needed. Typically, the physicists and engineers construct the models and mathematicians study the mathematical properties of the models and solve the models numerically. These specialists often use different languages to describe the same problem. The graduates of this program should be able to communicate with all of them and are therefore prepared to lead such groups. Moreover, they should also be prepared to solve simpler problems by themselves: from the construction of the model through its analysis up to its numerical solution.... [-]

The program "Geometry, Topology, and Global Analysis" offers to students a broad and deep knowledge in the selected areas. The aim is to train the students to be able to ... [+]

The program "Geometry, Topology, and Global Analysis" offers to students a broad and deep knowledge in the selected areas. The aim is to train the students to be able to learn and use new scientific achievements, mathematical methods and theories, independently develop and apply them, and present the results at international conferences and meetings. The program prepares students to pursue an academic career at universities, scientific institutes, and also in companies and firms having applied research and development branches.

The program does not contain specializations.

Description of verification and evaluation criteriaAdmission for studies

Admission for studies will be granted to the applicants, who:... [-]

The doctoral program primarily aims at graduates from teacher preparation programs in mathematics and computer science, enabling them to deepen their knowledge from maste ... [+]

The doctoral program primarily aims at graduates from teacher preparation programs in mathematics and computer science, enabling them to deepen their knowledge from master's programs and take part in ongoing research. The program focuses on elementary mathematics and computer science, their history, as well as teaching. In elementary mathematics and computer science, the emphasis is placed on topics that connect and extend both high-school and university curricula. In history, attention is paid especially to the 19th and 20th centuries, Czech mathematics and computer science. History is also closely related to problems of teaching, as the progress of science depends on the transfer of knowledge from teachers to students, which is supported by textbooks.... [-]

The study field of mathematical analysis is focused on the studium of basic and advanced parts of the mathematical analysis. It is a subdiscipline of mathematics whose pr ... [+]

The study field of mathematical analysis is focused on the studium of basic and advanced parts of the mathematical analysis. It is a subdiscipline of mathematics whose primary goal is the description of natural or social processes which involve a certain form of dynamic progress, mostly a motion or a change. The basic principles of mathematical analysis consist of all forms of limiting processes. The top education in mathematical analysis consists of the ability to solve differential equations of all types.

The program does not contain specializations.

Description of verification and evaluation criteriaAdmission for studies

Admission for studies will be granted to the applicants, who:... [-]

The study program "Algebra, Number Theory, and Mathematical Logic" offers students an advanced education in a selected area. The education allows the program graduates to ... [+]

The study program "Algebra, Number Theory, and Mathematical Logic" offers students an advanced education in a selected area. The education allows the program graduates to follow contemporary research. It teaches them the basics of independent scientific work and how to approach various abstract problems.

The program does not contain specializations.

Description of verification and evaluation criteriaAdmission for studies

Admission for studies will be granted to the applicants, who:

submitted a complete application form together with all obligatory attachments before the deadline, they were granted an entrance examination waiver or they successfully passed the entrance examination, they successfully passed the language examination or they got a waiver of it. ... [-]