University of Isfahan Mathematics and Society 2345-6493 3 1 2018 05 22 The role of intuition in mathematics education The role of intuition in mathematics education 1 8 21616 10.22108/msci.2017.21616 FA Ali Parsian Tafresh University Journal Article 2016 05 27 According to the views of some scientists and historians of science, the intuition and insight of mathematicians play a crucial role in the exploration of their field. Examples of these perspectives can be found in the works of some great mathematicians. The aim of this article is to delve deeper into this topic by examining the works and statements of mathematicians and then exploring the role of intuition in mathematics education. According to the views of some scientists and historians of science, the intuition and insight of mathematicians play a crucial role in the exploration of their field. Examples of these perspectives can be found in the works of some great mathematicians. The aim of this article is to delve deeper into this topic by examining the works and statements of mathematicians and then exploring the role of intuition in mathematics education.

https://math-sci.ui.ac.ir/article_21616_e0de419b5fb16ace4eef9a3ecf1d8cbf.pdf

University of Isfahan Mathematics and Society 2345-6493 3 1 2018 05 22 Groups theory: origins and destiny Groups theory: origins and destiny 9 17 22117 10.22108/msci.2017.104332.1226 FA Seyyed Mohsen Qureshi Shahraki Chamran University of Ahvaz Journal Article 2017 05 24 The concept of groups emerged in the 19th century as a result of humanity's millennia-long quest to solve polynomial equations. Almost immediately, it was observed that groups appeared in other branches of mathematics, including number theory, geometry, differential equations, and physics. Discovering the applications of groups in various sciences emphasized the importance of studying them, and the classification of finite simple groups became one of the major goals of mathematicians. By the early 21st century, the classification of finite simple groups was completed. However, this achievement cast a shadow over the theory of groups, with some considering the classification the end of the road for this theory. This article briefly touches upon the formation of group theory, the theorem of classifying finite simple groups, and the challenges faced by group theorists after completing the classification. The concept of groups emerged in the 19th century as a result of humanity's millennia-long quest to solve polynomial equations. Almost immediately, it was observed that groups appeared in other branches of mathematics, including number theory, geometry, differential equations, and physics. Discovering the applications of groups in various sciences emphasized the importance of studying them, and the classification of finite simple groups became one of the major goals of mathematicians. By the early 21st century, the classification of finite simple groups was completed. However, this achievement cast a shadow over the theory of groups, with some considering the classification the end of the road for this theory. This article briefly touches upon the formation of group theory, the theorem of classifying finite simple groups, and the challenges faced by group theorists after completing the classification.

https://math-sci.ui.ac.ir/article_22117_734effaa4b92bb1abb34b807838fd084.pdf

University of Isfahan Mathematics and Society 2345-6493 3 1 2018 05 22 Did Brouwer really believe that? Did Brouwer really believe that? 19 24 22266 10.22108/msci.2017.106277.1247 FA Reza Sotoudeh Yasuj University Hamidreza Goudarzi Yasuj University Journal Article 2017 09 14 This paper is a translation of the the following paper into Persian: [Douglas S. Bridges, Did Brouwer Really Believe That?, 2007] This article is a commentary on remarks made in a recent book [ E.A. Ok, Real Analysis with Economic Applications, Princeton Univ. Press, Princeton, NJ, 2007. ] that perpetuate several myths about Brouwer and intuitionism. This paper is a translation of the the following paper into Persian: [Douglas S. Bridges, Did Brouwer Really Believe That?, 2007] This article is a commentary on remarks made in a recent book [ E.A. Ok, Real Analysis with Economic Applications, Princeton Univ. Press, Princeton, NJ, 2007. ] that perpetuate several myths about Brouwer and intuitionism. https://math-sci.ui.ac.ir/article_22266_18ec67979f82be61d64338cdc9181c6e.pdf

University of Isfahan Mathematics and Society 2345-6493 3 1 2018 05 22 Application of linear algebra in global positioning system (GPS) Application of linear algebra in global positioning system (GPS) 25 39 22265 10.22108/msci.2017.101224.1209 FA Sayyed Ghasem Ghasemzade Fasa University Salman Boroumand Fasa University Roghayeh Khosravi Fasa University Journal Article 2016 12 22 The Global Positioning System (GPS) is a navigation system consisting of a constellation of satellites orbiting the Earth. By receiving signals from at least three satellites, the system can calculate position, speed, and time information and display them in practical formats. Interestingly, relatively simple mathematical calculations are employed in this system. This article aims to familiarize young enthusiasms with the functioning of GPS and the equations used. Also, it specifically delves into algebraic issues in GPS. Firstly, the calculation of positions using the triangulation principle, the impact of time error and correction for the GPS receiver are discussed. Then, the concept of pseudo-range, solving pseudo-range equations, and extracting the estimation error of position and time are explained. Different types of errors in GPS are also examined. Finally, an interesting problem in GPS is presented and solved. The Global Positioning System (GPS) is a navigation system consisting of a constellation of satellites orbiting the Earth. By receiving signals from at least three satellites, the system can calculate position, speed, and time information and display them in practical formats. Interestingly, relatively simple mathematical calculations are employed in this system. This article aims to familiarize young enthusiasms with the functioning of GPS and the equations used. Also, it specifically delves into algebraic issues in GPS. Firstly, the calculation of positions using the triangulation principle, the impact of time error and correction for the GPS receiver are discussed. Then, the concept of pseudo-range, solving pseudo-range equations, and extracting the estimation error of position and time are explained. Different types of errors in GPS are also examined. Finally, an interesting problem in GPS is presented and solved.

https://math-sci.ui.ac.ir/article_22265_a985e5a4aa1a29c4f691f2fef3cf361b.pdf

University of Isfahan Mathematics and Society 2345-6493 3 1 2018 05 22 Application of curve fitting and least squares method for investigating the geometry of Iranian arches Application of curve fitting and least squares method for investigating the geometry of Iranian arches 41 53 22280 10.22108/msci.2018.24929.1130 FA Farzin Izadpanah Shahid Bahonar university of Kerman Journal Article 2015 03 01 There are different perspectives regarding the use of conic sections in the structures of historical domes. This debate is also prevalent in Iranian architecture, shaping part of the history of global architectural studies. Some argue for the use of catenary curves, which represent the most significant competitor to conic sections in the history of arch geometry studies. Part of the research into this hypothesis is a historical examination, while another part involves a mathematical analysis of the arch curves. In the architectural literature, the investigation of arch curves has been carried out by plotting curves on the arch and visually comparing them. However, the author seeks a more precise method for examining this issue. In this paper, curve fitting using a matrix method is employed for examination. To compare the error rates in the fitting of the desired curves, the least squares method is highlighted. For demonstration purposes, a selected arch from the Elam period is examined and compared with catenary and conic section curves.The author recommends this method as a suitable approach for studying historical graphical documents. There are different perspectives regarding the use of conic sections in the structures of historical domes. This debate is also prevalent in Iranian architecture, shaping part of the history of global architectural studies. Some argue for the use of catenary curves, which represent the most significant competitor to conic sections in the history of arch geometry studies. Part of the research into this hypothesis is a historical examination, while another part involves a mathematical analysis of the arch curves. In the architectural literature, the investigation of arch curves has been carried out by plotting curves on the arch and visually comparing them. However, the author seeks a more precise method for examining this issue. In this paper, curve fitting using a matrix method is employed for examination. To compare the error rates in the fitting of the desired curves, the least squares method is highlighted. For demonstration purposes, a selected arch from the Elam period is examined and compared with catenary and conic section curves.The author recommends this method as a suitable approach for studying historical graphical documents.

https://math-sci.ui.ac.ir/article_22280_60b86a6a15d25048a6ba9ee63e192ed2.pdf

University of Isfahan Mathematics and Society 2345-6493 3 1 2018 05 22 The kronecker product and its application The kronecker product and its application 45 57 22340 10.22108/msci.2018.104599.1227 FA Hamideh Afshari Arjmand University of Qom ٍEftat Golpar Rabuki University of Qom Journal Article 2017 05 26 The Kronecker product of two matrices, denoted by $ A\otimes B $, possesses interesting properties that have led to its extensive use in various fields such as signal processing, image processing, and quantum computations. This multiplication preserves properties such as invertibility, orthogonality, triangularity, symmetry, and many others. If $ A $‎ is a matrix of zeros and ones or an adjacency matrix of a graph, the powers of its Kronecker product result in the generation of fractals or Kronecker product graphs. Another highly practical application is in solving matrix equations like Sylvester equations $ AX+XB=C $‎ and Lyapunov equations $ AX+XA=H $. This article aims to familiarize the reader with some properties of the Kronecker product. Additionally, it briefly describes some of its applications in fast transforms, graphs, fractals, random self-avoiding walks, matrix equations, and matrix decompositions. The Kronecker product of two matrices, denoted by $ A\otimes B $, possesses interesting properties that have led to its extensive use in various fields such as signal processing, image processing, and quantum computations. This multiplication preserves properties such as invertibility, orthogonality, triangularity, symmetry, and many others. If $ A $‎ is a matrix of zeros and ones or an adjacency matrix of a graph, the powers of its Kronecker product result in the generation of fractals or Kronecker product graphs. Another highly practical application is in solving matrix equations like Sylvester equations $ AX+XB=C $‎ and Lyapunov equations $ AX+XA=H $. This article aims to familiarize the reader with some properties of the Kronecker product. Additionally, it briefly describes some of its applications in fast transforms, graphs, fractals, random self-avoiding walks, matrix equations, and matrix decompositions.

https://math-sci.ui.ac.ir/article_22340_143300c808b86cd9c99d08d4a16f3b73.pdf