The Maple Computer Algebra System in Teaching the Basics of Set Theory

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Authors: А. А. Olenev, K. A. Kirichek and E. V. Potechina
Page Range: 215-242
Published in: International Journal of Mathematics, Game Theory, and Algebra, 30#4
ISSN: 1060-9881

Table of Contents

ABSTRACT

The paper presents the identified capabilities of the Maple computer algebra system for: specifying sets in various ways (using a worksheet (listing elements of a set, specifying a characteristic property of a set), using Maplet); controlling knowledge of performing operations on numerical and textual sets; demonstrating the validity of the laws (properties) of sets (using a table of occurrences; based on the expression of operations on sets through logical operations); solving textual problems in set theory; constructing Euler diagrams. The identification of the presented possibilities was carried out in order to determine and implement the directions of using Maple in teaching set theory. The approbation of the presented materials was carried out within the framework of teaching the discipline “Abstract and computer Algebra” to students of the training direction “Pedagogical Education”, profiles “Mathematics” and “Computer Science”, “Primary Education” and “Computer Science” of the Stavropol State Pedagogical Institute (Stavropol, Russian Federation). The results of the study of the use of Maple in teaching set theory give an idea of ways to improve the learning process by visualizing educational material, freeing time from routine calculations, giving the study a research character. The results also showed that the computer algebra system tends to increase the cognitive interest of students in the study of mathematics, computer science and the level of understanding and mastering of the studied issues, contributes to the development of ICT competence of students.

Keywords: set theory, operations on sets, Euler diagrams, computer algebra system, Maple, Maplet

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