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Latex system in distance learning of the probability theory
(2023-11-20) Hubal, Halyna
Article discusses the main issues for writing interactive mathematical tests in the LaTeX system. The LaTeX system is convenient to use for writing interactive mathematical tests in distance learning. We use the eqExam package, the AcroTeX eDucation Bundle package, the turnthepage package in order to write interactive mathematical tests, for example tests on the probability theory. For this, we create (tasks) of the “True/False” type, the “Short Answer” type, the “Essay” type (“Specifying a Definition”, “Justification of a Theoretical Hypothesis”) and the “Multiple Choice” type.
Analysis of approaches to the study of limits of sequences and functions and the use of information technologies
(2024-01-25) Hubal, Halyna
Article analyzes approaches to the study of limits of sequences and functions and the use of information technologies. The theorem on the limit of an intermediate sequence is of great importance when investigating the convergence of sequences and when calculating the limits of sequences. It is developed an algorithm for applying this theorem that is illustrated with examples. An example of calculating the limit of a function with a geometric interpretation of the obtained result is considered. The possibility of completing the calculation of limits at infinity, using the program code written by the author in the LaTeX programming language, is considered.
Digital technologies as a powerful toolkit for improving the quality of students' mathematical training
(Kraków, 2025) Hubal, Halyna
The article considers the application and impact of digital technologies on improving the quality of students’ mathematical training. It is shown the advantages of using digital technologies. It is described the features of deepening students’ knowledge through digital technologies.
Improvement of references and footnotes in mathematical and other texts by creating macros in the LaTeX programming language
(2023-09-01) Hubal, Halyna
The LaTeX programming language considered in this article is used to represent mathematical and other texts in scientific research. Many LaTeX packages provide advanced code-formatting features. Expanding the LaTeX programming language with macros automates the performance of a large number of tasks. In this research, the author programs in the LaTeX system when creating new macros. New macros created by the author improve adding references to everything that can be numbered and improve adding different types of footnotes in texts. Source codes of these new macros are given in this article. These macros can be embodied in a LaTeX style file, and they expand the capabilities of LaTeX.
Information technologies in teaching probability theory to foreign students in English in higher education institutions
(Oxford, 2025) Hubal, Halyna
The article presents some features of teaching probability theory to foreign students in English in higher education institutions in Ukraine. The article emphasizes the importance of using information technologies both for teaching probability theory and for understanding this discipline by foreign students. Examples of using the LaTeX system in creating educational materials and test tasks are given.
Automation of the creation of problems in mathematical analysis
(2026) Hubal, Halyna
In order to automatically create mathematical expressions for mathematical analysis, in particular mathematical expressions for the theory of limits, it is advisable to use the LaTeX programming language. In this article, the functionality of the LaTeX system was expanded to automatically create mathematical expressions for the theory of limits of mathematical analysis through programming methods using the LaTeX programming language. New commands were created. The created new commands accelerate the creation and updating of mathematical documents and provide flexibility in changing parameters. The created new commands can be used to prepare scientific publications and educational materials on mathematical analys.

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