Computer Tools in Education

Solving multicriteria problems of rating alternatives based on pairwise comparisons

Nikolai Krivulin — 2024-08-29

Well-known examples of multicriteria problems of evaluating alternatives based on paired comparisons are considered. Numerical solutions to these problems are presented, obtained using the method of analytic hierarchy process, the method of weighted geometric means, and also a method based on the log-Chebyshev approximation of pairwise comparison matrices. When solving problems using log-Chebyshev approximation, models and methods of tropical mathematics are used, which studies the theory and applications of algebraic systems with idempotent operations.

Cubic equations with 2 Roots in the interval [-1, 1]

Helmut Ruhland — 2024-08-30

The conditions for cubic equations, to have 3 real roots and 2 of the roots lie in the closed interval [-1, 1] are given. These conditions are visualized. This question arises in physics e.g. the theory of tops.

Development of a System for Evaluating the Performance of Computer Algebra Algorithms in Finding Grobner Bases

Yury Blinkov — 2024-08-30

This work presents the development of a specialized system for evaluating the performance of computer algebra algorithms in finding Gr¨obner bases. To verify the functionality and evaluate the performance of the improved GInv 2.0 version, a special automated testing tool has been developed. This tool allows loading test data sets in JSON format, calculating Gr¨obner bases using various algorithms, and visualizing test results. The modules for data import, basis calculation, and test result output are described in detail. GInv 2.0 was tested on a set of systems of equations of varying complexity. The test results are presented, including time characteristics of calculations for each test.

Software Implementation for Construction of an Earth Satellite Orbit

Victoria Aldokhina — 2024-08-30

The work is devoted to the creation of a program that visualizes the dependence of the orbit of an artificial Earth satellite in near-Earth space on the values of its elements.T he process of unperturbed motion of the satellite is simulated. For greater clarity of the model, additional constructions are provided such as lines of apses, lines of nodes, equatorial plane, directions to the vernal equinox point. The influence of the nonsphericity of the Earth on the movement of an object is shown. The program is intended for use by students and teachers in full-time and remote modes.

A Software Module for Working with Context-Free Grammars

Mikhail Zhegalin — 2024-08-30

The article presents the development of an educational software module to support the initial stage of learning formal grammars. The developed module allows the student or teacher to describe a given language through context-free grammar. In the process of completing a grammar assignment, the module provides an interactive response to the differences between the constructed grammar and the reference one. The main technical problem that the authors solved is related to the fact that there is no algorithm for determining the equivalence of two context-free grammars. Therefore, the module must generate in real time a sufficiently large number of words of a language of different lengths in order to detect differences between the proposed grammar and the reference one with a high probability. In the work, several word generation algorithms were analyzed, after which the algorithm most appropriate to the conditions of use of the module was selected. The developed module can be used for conducting Olympiads in discrete mathematics and computer science for schoolchildren and students, as well as to support students’ independent work on the topic "Formal languages and grammars".

Implementation of machine learning algorithms by means of relational database management systems

Natalia Grafeeva — 2024-08-30

The article discusses the problems of integrating machine learning algorithms into relational database management systems. The author conducted a review and comparative analysis of the current technical capabilities of relational database management systems like Oracle, PostgreSQL, SQL Server, DB2 and MySQL, which were adapted to data mining. Based on the obtained results, conclusions about the level of readiness of modern database management systems to solve the problem of data analysis have been drawn.

Directions for using generative artificial intelligence in initial programming training at universities

Michael Dolinsky — 2024-08-28

This paper provides a review of the literature on the use of generative artificial intelligence (GenAI) in initial programming education at universities. The main areas of application of generative artificial intelligence are given: specialized narrow-topic developments, integration into online learning platforms and testing solutions, students working with GenAI without restrictions, guiding systems for interaction of students with GenAI (without providing solutions), teacher assistance, tools for developing intelligent teaching systems It also contains a review of works that analyze the results achieved and unresolved problems.