Introducing Discrete Dynamic Systems in Algebra Teaching Process

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ABSTRACT

The aim of this work is to present a university classroom experience where the concepts of discrete dynamic systems are introduced in Algebra and Analytical Geometry subject with the purpose of using simulations where matrices are involved, in this case cellular automaton models are used as a dynamical system with discrete values in space, time and state. In this experience, computer scientists and mathematicians work together to carry out interdisciplinary projects which present discrete data management to first-year engineering students. Taking into account the fact that cellular automata have been used in different disciplines successfully, the authors of this paper consider introducing its concepts and applications in engineering teaching process.

KEYWORDS

Discrete dynamic systems, cellular automata, computational mathematics

REFERENCES

[1] G. Merino, Use of a Cellular Automaton to Create a Diffusion Model of Pollutants in a Soil-Water System. Journal of Mathematics: Theory and Applications, Vol.18, Nro.1, 2011, pp. 63-76.

[2] A. Ilachinski, Cellular Automata: A Discrete Universe, World Scientific, 2001, pp. 175-185.

[3] J. Quartieri, N. Mastorakis, G. Iannone, C. Guarnacci, A Cellular Automata Model for Fire Spreading Prediction, Proceedings of 3rd WSEAS International Conference on Urban Planning and Transportation, 2010, pp. 173-179.

[4] M. Dascalu, G. Stefan, A. Zafiu, A. Plavitu, Applications of Multilevel Cellular Automata in Epidemiology, Proceedings of the 13th WSEAS international conference on Automatic control, modelling & simulation, 2011, pp. 439-444,.

[5] R. Gaylor, P. Wellin, Computer Simulations with Mathematica: explorations in complex physical and biological systems. Springer-Verlag, 1995.

[6] M. Resnick, Turtles, Termites, and Traffic Jams, MIT Press, 1994.

[7] S. Wolfram, Cellular automata as Model of Complexity. Nature, Vol.311, 1984, pp. 419- 424.

[8] R. Gaylor, K. Nishidate, Modeling Nature: Cellular Automata Simulations with Mathematica, Springer-Verlag, 1996.

[9] J. Muñoz, Autómatas Celulares y Física Digital, Memorias del Primer Congreso Colombiano de Neuro Computación. Academia Colombiana de Ciencias Exactas, Físicas y Naturales, Bogotá, 1996.

[10] A. Tinnirello, E. Gago, M. Dádamo, M. Valentini, Design, Simulation and Analysis of a Fluid Flow System through Multiphysics Platform, Proceedings of 7th International Conference of Education, Research and Innovation, 2014, pp. 5847-5855.

[11] T. Ostoma, M. Trushyk, Cellular Automata: Theory and Physics. A New Paradigm for the Unification of Physics, Cornell University Library, 1999.

[12] S. Wolfram, Computer Software in Science and Mathematics, Scientific American, Vol.251, 1984.

Cite this paper

Paola Szekieta, Alicia Tinnirello, Eduardo Gago. (2017) Introducing Discrete Dynamic Systems in Algebra Teaching Process. International Journal of Education and Learning Systems, 2, 395-400