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Master's Degree, I.I. Vorovich Institute of Mathematics, Mechanics and Computer Science

01.04.00 Mathematics and Mechanics

Program length: 2 years

Language of study: Russian

Place of study: Rostov-on-Don

Purpose of this educational program

Fundamental Mathematics is the main toolkit for Mechanics, Applied Mathematics and Mathematical modeling. The apparatus of differential and integral equations is the basis for solving contact problems of mechanics, diffraction and wave propagation in aeroacoustics and dynamic theory of elasticity. Various sections of mathematical and functional analysis, integral transformations form the basis of methods for solving inverse problems in mathematical physics and other branches of mechanics. And the list of relevant mathematical methods can be easily continued. Thus, without in-depth knowledge of fundamental mathematics, it is impossible to solve urgent problems of modern mechanics.

Methods of mathematical modeling and general technologies of numerical methods based on them ; FEM (finite element method), MD (finite difference method), MGE (boundary element method), MKO (finite volume method) and others, represent the foundations of effective methods for solving a large class of problems of modern science and technology. These methods have been particularly widely applied in problems of mechanics, since during observation of these problems mostly often only a qualitative study of the problem is not enough, and a correct description of mechanical systems requires an accurate quantitative assessment of the corresponding physical parameters, which is achieved by mathematical modeling methods.

Applied mathematics provides tools for algorithmic representation of mathematical formulation of mechanical problems. Before the advent of computers, “Mechanics" was called “Applied mathematics", and it was only with the advent of computers that these two names began to be used as independent ones. Methods and algorithms of applied mathematics ; such as discretization of processes continuous in time and space; iterative algorithms; collocation methods; methods of computational mathematics; other methods of applied mathematics ; are effectively used in various fields of modern applied science and technology. However, it is in mechanics that they have a special specificity of their applications, since applied mathematics actually came out of mechanics, transferring it to the language of computer algorithms and discrete methods.

On the other hand, the internal logical development of mathematics leads to the creation of new modern sections, the practical significance of which sometimes remains questionable. The experience of recent years shows that many new branches of mathematics quickly and successfully find their applications in mechanics.

The main purpose of this program is to train highly qualified personnel in the field of Mathematics, Mechanics and Mathematical Modeling, the use of fundamental and Applied Mathematics methods in Modeling mechanical processes in solids, liquids and gases. Fundamental mathematical modeling methods will be aimed at solving problems in the following fields of knowledge:

• Stability, deformation and dynamic processes in solids, liquids and gases,
• inverse problems of the theory of elasticity and hydroacoustics,
• mechanics of coupled fields, mechanics of destruction, mechanics of contact interactions,
• biomechanics,
• Atmospheric dynamics,
• interaction of elastic elements of aircraft with air flows,
• reduction of noise generated by aircraft,
• Aerodynamics and aeroacoustics of wind power plants,

The difference of this Masters program is the training of professional scientists and practitioners in the field of fundamental mathematics, mechanics and mathematical modeling.

Logistical support is provided in the classrooms of the building of the I.I. Vorovich Institute of Mathematics, Mechanics and Computer Sciences of the Southern Federal University at 8a Milchakova Str. Classes are fully provided with computer and multimedia equipment, as well as the necessary licensed software. There is access to supercomputer clusters located in the IMM and KN. There is the necessary material support and laboratory complexes, three laboratory classes with the necessary equipment and measuring instruments for conducting experimental research.

Core curriculum

Advantages of this study program:

• The uniqueness of the educational program is explained by the academic traditions of the scientific school of Mathematics and Mechanics in Rostov-on-Don. The School of Mechanics of Deformable Bodies and Media was founded by Joseph Israelevich Vorovich, Doctor of Physical and Mathematical Sciences, Academician of the Russian Academy of Sciences, and is now the main training center for specialists in the field of mechanics. At the same time, the founder of the school, Academician I.I. Vorovich, focused on rigorous mathematical methods of research and modeling of mechanical processes.
• Graduates work as teachers of fundamental and applied mathematics, theoretical mechanics and resistance of materials, mathematical modeling, and Research Institute staff. The scientific and pedagogical school of scientists, created by I.I. Vorovich, enjoys great authority in Russia and abroad, among which there are more than 35 doctors and 160 candidates of sciences. Prominent scientists and educators, such as Academician of the Russian Academy of Sciences V.A. Babeshko (Kuban State University), as well as a number of other well-known specialists, have formed in her environment.
• The main feature of the program  is that it is a combined program of three areas of study 01.04.01, 01.04.02, 01.04.03, and provides classes for teachers of six departments of the Institute of Mathematics, Mechanics of Computer Science of the I.I.Vorovich SFedU: 1) Departments of Elasticity Theory; 2) Departments of Theoretical and Computer Hydroaerodynamics; 3) Departments of Mathematical Analysis; 4) Departments of Differential and Integral Equations; 5) Departments of Mathematical Modeling; 6) Departments of Computational Mathematics and Mathematical Physics.
• The profile of this master's program in the part of “Intelligent materials" corresponds to the Priority direction of scientific research of the SFedU “Information Technologies, nanotechnology, intelligent materials".
• Training practices are conducted at specialized departments, as well as at a partner company: Bastion Company (Rostov-on-Don), Southern scientific center of the Russian Academy of Sciences, Don State Technical University.

Prospects. Career & Employment

The employment of graduates is based on the long-standing scientific ties of the staff of the departments with large scientific centers in Russia and abroad, with various industrial enterprises, as well as with universities in other regions of Russia and abroad. Our graduates are prepared to improve the staff of research institutes, experimental design bureaus and enterprises in the field of Fundamental and Applied Mathematics, Mechanics and Mathematical modeling.

Graduates are ready for independent research work in research institutes and scientific production institutions. They are ready to continue their scientific work in postgraduate studies in the relevant specialties, as well as to continue working as teachers of universities of natural science and technical profile. There is an opportunity to teach mathematics, computer science and physics in schools with knowledge of the most modern achievements in the spheres of Mathematics and Mechanics. ​​​​​​​