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Conference publications

Abstracts

XIX conference

Teaching of the single mathematics: logical and evolutional approaches

Serovajsky S.Ya.

Kazakhstan, 050078, Almaty, al-Farabi av., 71

1 pp. (accepted)

The standard theory of the mathematical education includes separate basic mathematical courses in schools (arithmetic, geometry, algebra) and universities (mathematical analysis, algebra, differential equations, etc.). Each course is really self-reliant. The relation between courses is “upright” essentially. For example, the functional analysis is the logical continuation of the classical mathematical analysis, and the theory of mathematical physics equations is the continuation of the theory of ordinary differential equations.

This system of teaching is natural enough. However the formation of the integral conception of mathematics is to a large degree unsatisfactory. This serious shortcoming is shown up in the learning as professional mathematicians and users of mathematics. Professional mathematicians are as a rule extremely narrow specialists. Users (physicists, engineers, economists, and others) apprehend mathematics as the collection tools for various applications. They could be improve their professional level, if had a holistic view of mathematics. But it could be possible, if this problem become one of the general aims of the mathematical education.

The solving of this problem is difficult enough by means of standard mathematical courses, which are limited as its subject, the program and the time of training. However it could be realized with using of two additional courses for the final stage of learning. Complementing each other, these courses are devoted to the logical and evolutionary views on mathematics. The aim of the course “Architecture of mathematics” is a logical structure of mathematics. It includes the mathematical logic and the sets theory; determinations of numbers and different (ordered, algebraic, topological, etc.) mathematical objects as extensions of sets of numbers; definitions of synthesis mathematical theories (universal algebras, structures, categories). The subject of the course “History of mathematics” is a characterization of the evolution of general mathematical conceptions, for example, the number, the equation, the limit, the integral, etc.

These courses are taught for master students of the Faculty of mechanics and mathematics of al-Farabi Kazakh national university.



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