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The purpose of this paper is to illustrate how the evaluation of the definite integral of real functions of real variables that exhibit particular symmetries can be simplified. The proposal will then be substantiated through some application rules. [ABSTRACT FROM AUTHOR]

The paper aims to illustrate the relationships between music, mathematics and architecture in the work of Iannis Xenakis through an in-depth study of three compositions: "Metastaseis" (1954), whose initial score was the inspiration for the construction of the Philips Pavilion; "Achorripsis" (1957) the result of probability calculus procedures; and "Herma" (1962), based on set theory. The intent is to demonstrate how the study of Xenakis's compositional thought can contribute to the construction of an overview of the humanities and mathematics. [ABSTRACT FROM AUTHOR]

The right to education in prison offers a chance for human growth in a complex and dehumanizing environment. However, the peculiarities of prison systems, together with past experiences of school failure, can constitute significant obstacles to knowledge access. To enhance accessibility, participation, and achievement, even within prisons, it is necessary to review teaching practices. This paper aids in the reconsideration of the teaching of mathematics for incarcerated adults or young adults. Drawing on Paulo Freire’s theories, we analyze the dialogues with and among prisoner students about mathematics. [ABSTRACT FROM AUTHOR]

The Mathematical Olympiad, or Mathematical Championships, is a major event for the Italian schools. The present paper aims to give the reader an overview of how they work, focusing on describing the main organization structure and analyzing them from the point of view of a teacher which is both a District Coordinator and a School representative. Finally, some thoughts on the impact of the project on the students and the whole school system will be set forth. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to suggest how to overcome the difficulties which arise when secondary school students have to deal with too formal and abstract proofs. In fact, such difficulties emerge very often in math classes. As a result, students do not achieve a real and deep comprehension of the proofs, but limit themselves to learn them by heart. On the other hand, the introduction of proofs based on concrete and visual elements greatly helps them to gain a clear understanding of the underlying mathematical concepts. An alternative way to prove the irrationality of the square root of two will exemplify how to make proofs less formal and more semantic. [ABSTRACT FROM AUTHOR]