Keyword: «symbiosis of ideas»

A school as an ecosystem is a dynamically developing educational environment that creates a symbiosis of ideas/conceptions about objects, processes and phenomena. But often, this symbiosis is completely unobvious to students. The role of the subject being studied in the formation of skills and abilities necessary for related subjects is not always correctly assessed. This article, using the example of models of three objects, demonstrates the possibility of synchronizing the meanings of various professional fields and school subjects of the physics and mathematics cycle.

This article examines the synergy of computer science and mathematics through the prism of an interdisciplinary approach to studying Cauchy sequences and describes how the interaction of mathematical theories and algorithmic practices allows us to create more efficient and robust algorithms for solving complex problems. The article analyzes the use of Cauchy sequences in various areas of computer science, such as numerical computing, data processing and machine learning, and emphasizes the importance of a mathematical foundation for the development of algorithmic thinking. Conversely, examples of the practical application of an interdisciplinary approach are analyzed, demonstrating how the synergy of the two sciences can lead to new discoveries and innovations. But this is possible only if there is a developed skill of independent problem solving, using a variety of tools. Thus, the article talks not so much about an interdisciplinary approach, but about the formation of universal literacy of students through the synthesis of mathematics and computer science. This article explores the interaction between the mathematical concept of the Cauchy sequence and its application in computer science, especially in the context of algorithmic thinking. At the same time, both mathematics and computer science are considered in the dominant format, that is, the role of each of the subjects is not reduced to the level of a tool. That is, on the one hand, the article reveals mathematical principles that help to form clear and effective algorithmic solutions in programming and data analysis. On the other hand, machine learning and optimization algorithms help to improve mathematical calculations in data processing. Thus, the article includes examples of the application of Cauchy sequences in various areas of computer science, such as numerical methods, machine learning and data processing. The main approaches to teaching algorithmic thinking are also discussed, with an emphasis on the importance of a mathematical foundation. This article presents the mutual penetration of two disciplines, with an attempt to maintain a balance between them, without translating into a tool format.