Mathematics and Applied Mathematics

Mathematics can be called “the queen of knowledge”. Due to the close relationship between abstract theorems, principles and their physical counterparts in the material world, mathematics can be applied to different branches of science. It is vital in the study of mechanics, engineering, optics, astronomy, geodesy, electricity and other fields of knowledge.

Mathematics thrived and flourished with the growth of civilization as man’s quantitative needs increased. One might say that mathematics was born when the man began to count. The Greeks elevated mathematics to the field of abstract thinking. In its higher form, mathematics becomes a form of logic in which basic assumptions are laid down and results are then deduced within the framework of the system. The system itself is composed of a few elementary terms such as numbers, points and lines which are called primitives and rules that govern their operations.

Mathematics is a language of symbols that is understood in all civilized countries of the world. It can also be described as the study of patterns, where a pattern is any kind of regularity in the form of an idea. This study of patterns has been very important for science because pattern, regularity and symmetry occur quite often in nature. Light, sound, electric currents, waves of the sea, magnetism and even the flight of a bird or the shape of a snowflake and the mechanics of the atom can be classified by mathematics.

The main branches of mathematics are: geometry, trigonometry and calculus. Pure mathematics includes arithmetic – the science of numbers and computation; algebra – the language of symbols, operations and relations; geometry – the study of shapes, sizes and spaces; statistics – the study of interpreting data and graphs; calculus – the study of limits and infinity.

Today mathematics includes many newly developed branches for example, one of the leading departments at the Faculty of Mechanics and Mathematics – the Department of Algebra and Discrete Mathematics – is concerned not only with algebra. The game theory, the theory of analytical function, pseudodifferential operators, systematic programming and many other problems are studied there. One of the important areas of study in the department – the operators of a convolution type – is widely applied in the theory of random processes and mechanics.

Another field of research involves the study of approximate methods of solving equations with convolution operators. These methods are also applied in the theory of equations of mathematical physics and in the study of mapping and modelling.

Mathematical logic is also one of the main fields of algebra studied in this department, since mathematical logic is increasingly used in modern computers.

The invention of computers is one of the greatest achievements of mankind. They have greatly increased man’s ability to plan, analyse, compute and control. First electronic computers were installed at Rostov State University in the 1960s when the Department of Computational Mechanics started its work. The Computer Centre was founded at the same time, it helped to train the first computer programmers in the North Caucasus and Southern Russia. The Faculty of Mechanics and Applied Mathematics is a thriving centre of scientific study in our country. It has eleven departments, four of them belong to the Division of Applied Mathematics. They are the Operation Research Department, the Algebra Department, the Department of Computing Mathematics, and the Department of Software.

In their third year students of the faculty choose the field of mathematics, applied mathematics or mechanics and one of eleven departments to major in.

3.2 What new facts about mathematics and the Faculty of Mechanics and Applied Mathematics have you learnt from the text?

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