The inclusion and exclusion principle in view of number theory
DOI:
https://doi.org/10.23755/rm.v36i1.465Keywords:
inclusion, exclusion, number theory, combinatorics, MatlabAbstract
The inclusion and exclusion (connection and disconnection) principle is mainly known from combinatorics in solving the combinatorial problem of calculating all permutations of a finite set or other combinatorial problems. Finite sets and Venn diagrams are the standard method of teaching this principle. The paper presents an alternative approach to teaching the inclusion and exclusion principle from the number theory point of view, while presenting several selected application tasks and possible principle implementation into the Matlab computing environment.References
J. Sedláček. Faktoriály a kombinační čísla. Praha, Mladá fronta, 1964.
A. Vrba. Kombinatorika. Praha: Mladá fronta, 1980.
Š. Znám. Teória čísel. Bratislava, SPN, 1975.
M.T. Keller, W.T. Trotter. Applied Combinatorics. American Institute of Mathematics, 2017.
M. Škoviera. Úvod do diskrétnej matematiky. Bratislava, Katedra informatiky FMFI UK, 2007.
K. H. Rosen. Discrete mathematics and its applications. 4th ed., WCB/McGraw Hill, Boston, 1999.
M.J. Erickson. Introduction to Combinatorics. John Wiley & Sons, New York, ISBN: 0-471-15408-3, 1996.
Š. Hošková-Mayerová, Z. Rosická. Programmed learning. In: Procedia - Social and Behavioral Sciences, Vol. 31, p. 782-787, 2012 DOI: 10.1016/j.sbspro.2011.12.141.
Mathworks. Online documentation. 2019. Available at: https://www.mathworks.com/help/matlab/set-operations.html, Accessed 15th of April 2019.
E. Fechová. Application of mathematical software in solving the problems of electricity. In: RATIO MATHEMATICA - JOURNAL OF MATHEMATICS, STATISTICS, AND APPLICATIONS, vol. 29, p. 41-52, 2015, ISSN: 1592-7415, DOI: 10.23755/rm.v29i1.21.
D. Gonda: The Elements of Substitution Thinking and Its Impact On the Level of Mathematical Thinking. In: IEJME — MATHEMATICS EDUCATION, vol. 11, no. 7, p. 2402-2417, Look Academic Publishers, 2016.
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