Abstract
The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.
Highlights
“The book of nature is written by the mathematical language” [1]
This Galileis manifesto determined the methodology of natural science development on the basis of observations and experiments, the result of these observations and experiments are interpreted within the frames of corresponding mathematical model
The latter implicitly assumes the mechanism of science integration this methodology of development have been successfully realized during the last century beginning with famous Newton’s “Mathematical Priciples of Natural Philosophy” (1687) [2]
Summary
This Galileis manifesto determined the methodology of natural science development on the basis of observations and experiments, the result of these observations and experiments are interpreted within the frames of corresponding mathematical model The latter implicitly assumes the mechanism of science integration this methodology of development have been successfully realized during the last century beginning with famous Newton’s “Mathematical Priciples of Natural Philosophy” (1687) [2]. With the appearance of computers in the middle of the XX th century, a separate direction connected with the realization of intellectual systems (IS) has been formed in cybernetics [7,8] Accents in this case focused on learning of cognitive processes. Optimal control by cognitive processes is carried out, including creative search and interdisciplinary learning
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