Semantic model and optimization of creative processes at mathematical knowledge formation

Author(s)
Victor Egorovitch Firstov

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.

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.

Cite this paper

Firstov, V. (2010) Semantic model and optimization of creative processes at mathematical knowledge formation.*Natural Science*, **2**, 915-922. doi: 10.4236/ns.2010.28113.

Firstov, V. (2010) Semantic model and optimization of creative processes at mathematical knowledge formation.

References

[1] Galilei, G. (1964) Il Saggiatore. Opere. Salani, Firenze.

[2] Newton, I. (1946) Mathematical Principles of Natural Philosophy. The Universitet of California Press, Berkley.

[3] Boltzmann, L. (1909) Wissenschaftliche abhandlungen. Leipzig.

[4] Wiener, N. (1961) Cybernetics (or control and communication in the animal and machine). The MIT Press, New York.

[5] Shannon, C.E. (1948) A mathematical theory of communication. Bell System Technical Journal, 27(3), 379-423.

[6] Henry, P. and Lazarsfeld, N.W. (1966) Readings in mathematical social science. In: P. F. Lazarsfeld and N. W. Henry Eds., A Collection of Articles, Science Research Associates, Chicago.

[7] Rosenblatt, F. (1958) The perception: A probabilistic model for information storage and organization in the brain. Psychological Review, 65(6), 386-408.

[8] Feigenbaum, E.A. (1963) Computers and thought. In: E. A. Feigenbaum and J. Feldman Eds., A Collection of Articles, McGraw-Hill Book Co., New York, 477-523

[9] Anderson, J.R. (1983) The architecture of cognition. Harvard University Press, Cambridge, Massachusetts, USA.

[10] Hopfild, J.J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of USA, 79(8), 2554-2558.

[11] Brusilovsky, P. (1996) An intelligent tutoring system onWorld-Wide Web. Proceedings of the 3th International WWW Conference, Fraunhofer Institute for Computer Grafics, Darmstagt, 42-45.

[12] Firstov, V.E. (2006) The semantic model and optimization trough mathematical knowledge formation and propagation. Vestnik Saratov State Technical University, 3(14), 34-43.

[13] Rashevsky, N. (1955) Live, information theory and topology. The Bulletin of Mathematical Biophysics, 17(3), 25-78.

[14] Kolmogorov, A.N. [in Russian: Колмогоров А. Н. (1965) Три подхода к определению понятия “количество информации”. Проблмы передачи информации. Т.1, вып.1, сс.3-11].

[15] Firstov, V.E. (2006) The stochastic model by the information space of deductive theory formation and optimization of the research work in mathematics. Vestnik Saratov State Technical University, 4(17), 13-21.

[16] Harris, T.E. (1963) The theory of branching processes. Springer-Verlag, Berlin-G?ttingen-Heidelberg.

[17] Glaser, R. (1984) Education and thinking: The role of knowledge. American Psychologist, 39(2), 93-104.

[18] Hilbert, D. (1900) Mathematische probleme. Nachr. Ges. Wiss. G?ttingen, 253-297.

[19] Moulin, H. (1988) Axioms of cooperative decision making. Cambridge University Press, Cambridge-New York- New Rochelle-Melbourne-Sydney.

[20] M?bius, A.F. (1885) Der barycentrische calcul. Bd. 1, Gesammelte Werke, Leipzig.

[21] Hardy, G.H. (1908) Mendelian proportions in a mixed population. Science, 28(706), 49-50.

[22] Weinberg, W. (1908) über den Nachwies der Vererbung beim Menschen. Jahreshefte des Vereins for Vater- landische Naturkunde in Würtemberg, 64, 368-382.

[23] Crow, J.F. and Kimura, M. (1970) An introduction in Population Genetics Theory. Harper and Row, New York.

[24] Arnheim, R. (1988) The power of the center. A study of composition in the visual arts. University of California Press, Berkeley.

[25] Firstov, V.V., Firstov, V.E. and Voloshinov, A.V. (2005) Conception of colorimetric barycenter in painting analysis. Proceedings of the International Congress on Aesthetics, Creativity and Psychology of the Arts, Moscow, 2005, 258-260.

[26] Firstov, V.V., Firstov, V.E. and Voloshinov, A.V. (2006) The concept of colorimetric barycenter in group analysis of painting. Culture and Communication: Proceedings of the XIX Congress International Association of Empirical Aesthetics, Avignon, France, 2006, 439-443.

[27] Firstov, V. V., Firstov, V. E., Voloshinov, A. V. and Locher, P. (2007) The Colorimetric Barycenter of Paintings. Empirical Studies of the Arts, 25(2), 209-217.

[28] Firstov, V.E., Firstov, V.V. and Voloshinov, A.V. (2008) The concept of colorimetric barycenter and visual perception of the color balance center in painting. Proceedings of the XX Biennial Congress of the International Association of Empirical Aesthetics, Chicago, USA, 2008, 273-277.

[29] Firstov, V.E. (2009) About teaching math in humanitarian specializations and occupations in IHE. Higher Education Today, 2, 82-84.

[30] Firstov, V.E. (2009) Cybernetic concept of current educational process. Higher Education Today, 3, 66-68.

[31] Firstov, V.E. (2007) Dialogue education: Cybernetic aspect. Vestnik Saratov State Technical University, 4(28), 135-145.

[32] Firstov, V.E. (2008) Informational conception of optimization of group cooperation in teaching. Vestnik Saratov State Technical University, 3(34), 105-109.

[33] Firstov, V.E. (2008) The concept of defeveloping training of L.S. Vygotsky, pedagogics of cooperation and cybernetics. Yaroslavl Pedagogical Bulletin, 3(56), 98- 104.

[34] Firstov, V.E. (2009) Expert systems and information conception in developing training. Yaroslavl Pedagogical Bulletin, 1(58), 69-73.

[35] Firstov, V.E. (2008) A special matrix trasformation semigroup of primitive pairs and the genealogy of pythagorean triples. Mathematical Notes, 84(2), 263-279.

[1] Galilei, G. (1964) Il Saggiatore. Opere. Salani, Firenze.

[2] Newton, I. (1946) Mathematical Principles of Natural Philosophy. The Universitet of California Press, Berkley.

[3] Boltzmann, L. (1909) Wissenschaftliche abhandlungen. Leipzig.

[4] Wiener, N. (1961) Cybernetics (or control and communication in the animal and machine). The MIT Press, New York.

[5] Shannon, C.E. (1948) A mathematical theory of communication. Bell System Technical Journal, 27(3), 379-423.

[6] Henry, P. and Lazarsfeld, N.W. (1966) Readings in mathematical social science. In: P. F. Lazarsfeld and N. W. Henry Eds., A Collection of Articles, Science Research Associates, Chicago.

[7] Rosenblatt, F. (1958) The perception: A probabilistic model for information storage and organization in the brain. Psychological Review, 65(6), 386-408.

[8] Feigenbaum, E.A. (1963) Computers and thought. In: E. A. Feigenbaum and J. Feldman Eds., A Collection of Articles, McGraw-Hill Book Co., New York, 477-523

[9] Anderson, J.R. (1983) The architecture of cognition. Harvard University Press, Cambridge, Massachusetts, USA.

[10] Hopfild, J.J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of USA, 79(8), 2554-2558.

[11] Brusilovsky, P. (1996) An intelligent tutoring system onWorld-Wide Web. Proceedings of the 3th International WWW Conference, Fraunhofer Institute for Computer Grafics, Darmstagt, 42-45.

[12] Firstov, V.E. (2006) The semantic model and optimization trough mathematical knowledge formation and propagation. Vestnik Saratov State Technical University, 3(14), 34-43.

[13] Rashevsky, N. (1955) Live, information theory and topology. The Bulletin of Mathematical Biophysics, 17(3), 25-78.

[14] Kolmogorov, A.N. [in Russian: Колмогоров А. Н. (1965) Три подхода к определению понятия “количество информации”. Проблмы передачи информации. Т.1, вып.1, сс.3-11].

[15] Firstov, V.E. (2006) The stochastic model by the information space of deductive theory formation and optimization of the research work in mathematics. Vestnik Saratov State Technical University, 4(17), 13-21.

[16] Harris, T.E. (1963) The theory of branching processes. Springer-Verlag, Berlin-G?ttingen-Heidelberg.

[17] Glaser, R. (1984) Education and thinking: The role of knowledge. American Psychologist, 39(2), 93-104.

[18] Hilbert, D. (1900) Mathematische probleme. Nachr. Ges. Wiss. G?ttingen, 253-297.

[19] Moulin, H. (1988) Axioms of cooperative decision making. Cambridge University Press, Cambridge-New York- New Rochelle-Melbourne-Sydney.

[20] M?bius, A.F. (1885) Der barycentrische calcul. Bd. 1, Gesammelte Werke, Leipzig.

[21] Hardy, G.H. (1908) Mendelian proportions in a mixed population. Science, 28(706), 49-50.

[22] Weinberg, W. (1908) über den Nachwies der Vererbung beim Menschen. Jahreshefte des Vereins for Vater- landische Naturkunde in Würtemberg, 64, 368-382.

[23] Crow, J.F. and Kimura, M. (1970) An introduction in Population Genetics Theory. Harper and Row, New York.

[24] Arnheim, R. (1988) The power of the center. A study of composition in the visual arts. University of California Press, Berkeley.

[25] Firstov, V.V., Firstov, V.E. and Voloshinov, A.V. (2005) Conception of colorimetric barycenter in painting analysis. Proceedings of the International Congress on Aesthetics, Creativity and Psychology of the Arts, Moscow, 2005, 258-260.

[26] Firstov, V.V., Firstov, V.E. and Voloshinov, A.V. (2006) The concept of colorimetric barycenter in group analysis of painting. Culture and Communication: Proceedings of the XIX Congress International Association of Empirical Aesthetics, Avignon, France, 2006, 439-443.

[27] Firstov, V. V., Firstov, V. E., Voloshinov, A. V. and Locher, P. (2007) The Colorimetric Barycenter of Paintings. Empirical Studies of the Arts, 25(2), 209-217.

[28] Firstov, V.E., Firstov, V.V. and Voloshinov, A.V. (2008) The concept of colorimetric barycenter and visual perception of the color balance center in painting. Proceedings of the XX Biennial Congress of the International Association of Empirical Aesthetics, Chicago, USA, 2008, 273-277.

[29] Firstov, V.E. (2009) About teaching math in humanitarian specializations and occupations in IHE. Higher Education Today, 2, 82-84.

[30] Firstov, V.E. (2009) Cybernetic concept of current educational process. Higher Education Today, 3, 66-68.

[31] Firstov, V.E. (2007) Dialogue education: Cybernetic aspect. Vestnik Saratov State Technical University, 4(28), 135-145.

[32] Firstov, V.E. (2008) Informational conception of optimization of group cooperation in teaching. Vestnik Saratov State Technical University, 3(34), 105-109.

[33] Firstov, V.E. (2008) The concept of defeveloping training of L.S. Vygotsky, pedagogics of cooperation and cybernetics. Yaroslavl Pedagogical Bulletin, 3(56), 98- 104.

[34] Firstov, V.E. (2009) Expert systems and information conception in developing training. Yaroslavl Pedagogical Bulletin, 1(58), 69-73.

[35] Firstov, V.E. (2008) A special matrix trasformation semigroup of primitive pairs and the genealogy of pythagorean triples. Mathematical Notes, 84(2), 263-279.