Acquaintance of pupils with elements of the theory of counts on facultative and after-hour employment
Astrakhan State University, Faculty of mathematics and information technology, algebra and geometry chair, Russia, 414156, Astrakhan, Tatischeva st., 20а, Tel.: 8(8512)610883, е-mail: email@example.com pp. (accepted)
There is a considerable quantity of the practical problems which consideration is reduced to studying of set of the objects which essential properties are described by communications between them. For example, on a card of airlines interest represents only between what cities there is a communication. At studying of electric chains on the foreground character of connections of its various elements acts. Organic molecules form the structures which characteristic properties are communications between atoms. Various economic relations, communications and human relations, events, conditions, and in general, between any objects can represent interest.
The first work under columns has been executed by Leonardom Euler in 1736 and devoted to the decision of the well-known problem about кенигсбергских bridges. The theory of counts is connected with names of many known mathematicians. So, A.Keli has applied the theory of counts to a problem раскраски cards, and U. Gamilton investigated one interesting class of the counts named subsequently гамильтоновыми columns. In the beginning of the XX-th century the theory of counts was issued in the form of independent mathematical discipline. There were important practical appendices of counts, many of which demanded thin mathematical methods. So, Kirhgof has applied columns to the analysis of electric chains, and Keli investigated the important class of counts for studying of the sated hydrocarbons.
Now the theory of counts became very popular among teachers, schoolboys and students. It is connected by that in language of the theory of counts of a condition of problems get presentation, and decisions, unlike decisions other methods, do not contain tiresome calculations. However the theory of counts is not included into curricula of mathematical specialities of universities and in programs of mathematical schools. The exception is made by technical and economic high schools where students are compelled to get acquainted fluently with columns by consideration of some appendices.
Acquaintance to separate sections of the theory of counts becomes possible already in an elementary school at the decision of every possible logic problems and puzzles. The further acquaintance to columns helps with the basic school at studying of many mathematical sections and serves as good help at the decision difficult олимпиадных problems.
In work acquaintance of pupils with elements of the theory of counts on facultative and after-hour employment at schools of different level and a profile is offered.