University of Isfahan Mathematics and Society 2345-6493 1 3 2025 01 19 Children, mathematics, philosophy Children, mathematics, philosophy 1 5 6865 10.22108/msci.2016.6865 FA Masoud Ariannejad University of Zanjan Journal Article 1392 12 23 Review of Understanding and Teaching Mathematics in the Realm of Nurturing and Developing the Creativity of Children and Adolescents and its Connection with Another Field, Such as Philosophy and Philosophy Education, Alongside Possible Rules in the Context of these Fields, Centered on the Meanings and References of this Writing Review of Understanding and Teaching Mathematics in the Realm of Nurturing and Developing the Creativity of Children and Adolescents and its Connection with Another Field, Such as Philosophy and Philosophy Education, Alongside Possible Rules in the Context of these Fields, Centered on the Meanings and References of this Writing

https://math-sci.ui.ac.ir/article_6865_3f052c0486fbec40cd694fdc95982751.pdf

University of Isfahan Mathematics and Society 2345-6493 1 3 2016 11 21 What is a paraproduct? What is a paraproduct? 7 12 7546 10.22108/msci.2016.7546 FA Mozhdeh Shirani University of Isfahan Journal Article 2014 04 08 The concept of 'Paraproduct' emerged in the development of Paradifferential operators. This theory itself is a pivotal point in the theory of Beyond Pseudodifferential operators, with the Paraproduct expected to possess properties far beyond those of regular multiplication. Since their inception in 1965, Paraproducts have played a central role in the analysis and partial differential equations. These concepts are related to the theory of two-parameter Calderón-Zygmund theory and form the foundation for many other bilinear operators. Notable applications of these concepts include the well-known theorems such as T1 and Tb theorems, boundedness of Calderón commutator, the Hilbert bilinear transform, theories of pointwise multipliers in function spaces, the theory of corrected compressibility. The concept of 'Paraproduct' emerged in the development of Paradifferential operators. This theory itself is a pivotal point in the theory of Beyond Pseudodifferential operators, with the Paraproduct expected to possess properties far beyond those of regular multiplication. Since their inception in 1965, Paraproducts have played a central role in the analysis and partial differential equations. These concepts are related to the theory of two-parameter Calderón-Zygmund theory and form the foundation for many other bilinear operators. Notable applications of these concepts include the well-known theorems such as T1 and Tb theorems, boundedness of Calderón commutator, the Hilbert bilinear transform, theories of pointwise multipliers in function spaces, the theory of corrected compressibility.

https://math-sci.ui.ac.ir/article_7546_547b9407e09ece5c73111b511f320528.pdf

University of Isfahan Mathematics and Society 2345-6493 1 3 2016 11 21 The missing place of the number 'e' in secondary school books The missing place of the number 'e' in secondary school books 13 23 7547 10.22108/msci.2016.7547 FA Mehdi Hassani University of Zanjan Azizeh Ahmadi University of Zanjan Journal Article 2014 04 29 The limited information about the number $\mathrm{e}$ found in secondary school books prompted us to write this article in defense of the possibility of providing more comprehensive explanations about this number at the secondary education level. We begin with presenting a historical background of this number and then proceed to prove the inequality, $0<\mathrm{e}-\sum_{k=0}^{n}{1}/{k!}<{1}/{(n.n!)}$ which holds for every $n\geq 1$. By utilizing this inequality, we infer the enigmatic nature of $\mathrm{e}$ and calculate the sum of $\sum_{k=0}^{n} P(n,k)$. This sum leads us to the counting of distinct paths between two arbitrary vertices of a complete graph. Finally, we demonstrate the proof of the inequality involving arithmetic, geometric, and harmonic means based on the inequality Image. All the proofs and deductions are based on the materials covered in the final year of secondary education. The limited information about the number $\mathrm{e}$ found in secondary school books prompted us to write this article in defense of the possibility of providing more comprehensive explanations about this number at the secondary education level. We begin with presenting a historical background of this number and then proceed to prove the inequality, $0<\mathrm{e}-\sum_{k=0}^{n}{1}/{k!}<{1}/{(n.n!)}$ which holds for every $n\geq 1$. By utilizing this inequality, we infer the enigmatic nature of $\mathrm{e}$ and calculate the sum of $\sum_{k=0}^{n} P(n,k)$. This sum leads us to the counting of distinct paths between two arbitrary vertices of a complete graph. Finally, we demonstrate the proof of the inequality involving arithmetic, geometric, and harmonic means based on the inequality Image. All the proofs and deductions are based on the materials covered in the final year of secondary education.

https://math-sci.ui.ac.ir/article_7547_ff9daeffa9086b3eab13b6273d4697ab.pdf

University of Isfahan Mathematics and Society 2345-6493 1 3 2000 09 01 The derivative à la Carathéodory The derivative à la Carathéodory 25 29 7862 10.22108/msci.2016.7862 FA Mohammad Sal Moslehian Ferdowsi University of Mashhad Journal Article 1970 01 01 This paper is a translation of the the following paper into Persian: [Kuhn, Stephen, The derivative à la Carathéodory, Amer. Math. Monthly, 98 no. 1 (1991) 40--44]. Abstract Translator: According to Carathéodory, a function $f$ is differentiable at a point $a \in D_f$ if there exists a function $\varphi$ continuous at $a$ such that for each $x$ in an open interval $U$ containing $a$ it holds that $f(x)-f(a)=\varphi(x)(x-a)$. In this paper we investigate this definition, prove that it is equivalent to the usual notion of differentiability and show that it can be used to prove some elementary theorems in the topic of derivative in calculus. This paper is a translation of the the following paper into Persian: [Kuhn, Stephen, The derivative à la Carathéodory, Amer. Math. Monthly, 98 no. 1 (1991) 40--44]. Abstract Translator: According to Carathéodory, a function $f$ is differentiable at a point $a \in D_f$ if there exists a function $\varphi$ continuous at $a$ such that for each $x$ in an open interval $U$ containing $a$ it holds that $f(x)-f(a)=\varphi(x)(x-a)$. In this paper we investigate this definition, prove that it is equivalent to the usual notion of differentiability and show that it can be used to prove some elementary theorems in the topic of derivative in calculus.

https://math-sci.ui.ac.ir/article_7862_317b8f8c392fe54bb10aff4ce32a44eb.pdf

University of Isfahan Mathematics and Society 2345-6493 1 3 2016 11 21 Mathematics citation quotient Mathematics citation quotient 31 37 7726 10.22108/msci.2016.7726 FA Omidali Ghasem Shahed University Aidin Azari Shahed University Journal Article 2014 11 27 In today's fast-paced world, knowledge of various information sources and familiarity with electronic resources and their features is considered a crucial necessity for subject matter experts. The prominent characteristic of these information sources is the novelty of knowledge, the credibility of collected information, and awareness of the latest published research in emerging fields. Moreover, policymakers, planners, and research managers now more than ever prefer to make decisions based on solid scientific evidence. For instance, they aim to allocate more budget and research facilities to the most capable and deserving group of researchers and delegate more research tasks to them. After publication, they also evaluate and accredit the research based on achieving set objectives and even the impact it has on the scientific community. This article, using a review and library-based approach, focuses on introducing the American Mathematical Society (AMS) index and abstracts and the introduction of the Mathematics Citation Quotient (MCQ). Understanding these databases can be a guiding light for planners, research managers to achieve their desired objectives, and for bibliometric experts and information centers. In today's fast-paced world, knowledge of various information sources and familiarity with electronic resources and their features is considered a crucial necessity for subject matter experts. The prominent characteristic of these information sources is the novelty of knowledge, the credibility of collected information, and awareness of the latest published research in emerging fields. Moreover, policymakers, planners, and research managers now more than ever prefer to make decisions based on solid scientific evidence. For instance, they aim to allocate more budget and research facilities to the most capable and deserving group of researchers and delegate more research tasks to them. After publication, they also evaluate and accredit the research based on achieving set objectives and even the impact it has on the scientific community. This article, using a review and library-based approach, focuses on introducing the American Mathematical Society (AMS) index and abstracts and the introduction of the Mathematics Citation Quotient (MCQ). Understanding these databases can be a guiding light for planners, research managers to achieve their desired objectives, and for bibliometric experts and information centers.

https://math-sci.ui.ac.ir/article_7726_e02afe31a05bf6a048fc6543b0fe4a34.pdf

University of Isfahan Mathematics and Society 2345-6493 1 3 2000 03 23 What is a rauzy fractal? What is a rauzy fractal? 39 43 10023 10.22108/msci.2016.10023 FA Saeid Alikhani University of Yazd Ali Noroozi University of Yazd Journal Article 1970 01 01 This paper is a translation of the the following paper into Persian: [P. Arnoux and E. Harriss, What is a Rauzy fractal?, Notice of the AMS, 61 no. 7 (2014) 768-770.] According to an ancient tradition, it is possible to associate symbolic and infinite words with dynamical systems. Conversely, for infinite words generated by algebraic or combinatorial methods, it is possible to provide geometric representations, which can be a family of self-similar sets with fractal boundaries. As an example, in this article, we study fractals called Rauzy fractals. This paper is a translation of the the following paper into Persian: [P. Arnoux and E. Harriss, What is a Rauzy fractal?, Notice of the AMS, 61 no. 7 (2014) 768-770.] According to an ancient tradition, it is possible to associate symbolic and infinite words with dynamical systems. Conversely, for infinite words generated by algebraic or combinatorial methods, it is possible to provide geometric representations, which can be a family of self-similar sets with fractal boundaries. As an example, in this article, we study fractals called Rauzy fractals.

https://math-sci.ui.ac.ir/article_10023_fbaf67c5de68b311409e8dc1e51469e9.pdf