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.
KeywordsThe Cybernetic ConceptionOptimization of ControlQuantitative And Qualitative Information MeasuresModellingIntellectual SystemsNeural NetworkMathematical EducationThe Control of Pedagogical ProcessesCreative PedagogicsCognitive And Creative ProcessesInformal Axiomatic TherySemantic Net
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Net Optimization Parameters
The Topology of Semantic Net
Metrization
The System of Coverings
Stochastic Model of Creative Processes At The Formation of Mathematical Knowledge
Branching Markovian Process
Great Main Points Strategy (GMP-Strategy) of The Creative Processes Control
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