Studying elements of set theory using the computer mathematics system Mathematica

Abstract

One of the most popular and powerful computer mathematics systems is Mathematica. It is used both by professional researchers for their studies and by educators and students in the learning process. Being a universal tool, Mathematica can be applied across various fields. There are many general publications about using different computer mathematics systems, including Mathematica, to solve mathematical problems. However, less attention is given to specific methodologies for studying individual sections of mathematical analysis. This paper proposes a methodology for studying elements of set theory using Mathematica. It demonstrates that this system enables users to: 1) define sets of various types, including lists and regions in  and ; 2) verify element membership in sets and set inclusions; 3) perform operations such as union, intersection, complement, and subtraction; 4) graphically represent sets and draw Euler circles; 5) verify the correctness of formulas involving set operations; and 6) check the validity of logical statements. The procedure for performing these actions is described, and illustrative examples are provided. In our view, a tool like Mathematica does not eliminate the need to understand the theory and solve problems independently. On the contrary, it stimulates more profound knowledge, experimentation, and exploration. It also enhances computer literacy, algorithmic thinking, and programming skills. The significance of these results lies in the following: 1) increased accuracy and reliability of problem-solving; 2) improved efficiency through rapid idea generation and verification of individual steps; 3) better comprehension of material through visualization; 4) development of algorithmic thinking and programming skills; and 5) greater engagement in studying the material.