This article discusses mental arithmetic, the benefits and origins of mental arithmetic. Some examples and problems related to mental arithmetic are explored.

This article explores methods of teaching math topics to children who are undergoing long-term treatment. This will ultimately help improve learning outcomes that meet specific learning objectives. In addition, he learns that each subject should be regularly linked not only to life, but also to other subjects.

Socio-economic relations in the country, changes in the public education system, as reflected in the Law "On Education" and the "National Training Program" an important task is set before the primary school teacher. These tasks allow to distinguish the specific links for primary education, which are connected with the introduction of education in different curricula, curricula, textbooks, as well as a network in the methodological system. can form. When we say the methodological-mathematical training of a primary school teacher, we mean the preparation of the methodology of teaching mathematics on the basis of a scientific worldview in an integral connection with the general pedagogical-psychological and mathematical training. The task of such preparation is to acquire certain knowledge and skills in mathematics in the field of primary education, as well as to master the upbringing of children through teaching

Looking back at the history of civilization, we can see that in ancient times, our ancestors used various tools to educate and educate the younger generation.  Various stones, bones or fruit seeds were used for teaching arithmetic, waxed boards for teaching writing, and a stick with a sharp metal blade attached to the end known as a "stylo".  Today, the state education standard, curriculum and textbook are the main tools of English language teaching.

This article discusses the importance of mathematics in the work of experts in the field, given the growing role of psychologists in any field, and measures to increase their knowledge in the use of mathematical operations in research processes. The article also provides valuable information needed to develop the mathematical skills of industry professionals. Experts in the field who do not have the ability to perform mathematical operations are given information on the further development of mental thinking in relation to mathematical operations, arithmetic, taking into account the importance of mathematical ability in the analysis of psychological tests.

This article discusses the importance of mathematics in the work of experts in the field, given the growing role of psychologists in any field, and measures to increase their knowledge in the use of mathematical operations in research processes. The article also provides valuable information needed to develop the mathematical skills of industry professionals. Experts in the field who do not have the ability to perform mathematical operations are given information on the further development of mental thinking in relation to mathematical operations, arithmetic, taking into account the importance of mathematical ability in the analysis of psychological tests.

This article is dedicated to studying the deep and multifaceted connection between algebraic geometry and number theory. These two areas of mathematics, though initially appearing separate, have shown throughout history an ever-closer and mutually enriching relationship. The article examines the historical evolution from Diophantine equations to modern concepts such as elliptic curves, category theory, motives, the Langlands program, and Arakelov geometry. Furthermore, the significant role of these connections in modern mathematics is analyzed, including their importance in applications such as cryptography and future research directions. The aim of the research is to provide an overview of how geometric methods help solve arithmetic problems and, conversely, how ideas from number theory contribute to the understanding of geometric structures.

In spite of their practical importance, the connections between technology and mathematics have not received much scholarly attention. This article begins by outlining how the technology–mathematics relationship has developed, from the use of simple aide-mémoires for counting and arithmetic, via the use of mathematics in weaving, building and other trades, and the introduction of calculus to solve technological problems, to the modern use of computers to solve both technological and mathematical problems. Three important philosophical issues emerge from this historical résumé: how mathematical knowledge depends on technology, the definition of the hybrid concept of a (technological) computation, and the (perhaps surprising) usefulness of mathematics in technology.