University of IsfahanMathematics and Society2345-6493512020052126393FAJournal Article20220227https://math-sci.ui.ac.ir/article_26393_741f9f707e0590d23cdecbf2835e9ee5.pdfUniversity of IsfahanMathematics and Society2345-64935120200521Application of Taylor expansion in reducing the size of convolutional neural networks for classifying Impressionism and Miniature paintingsApplication of Taylor expansion in reducing the size of convolutional neural networks for classifying Impressionism and Miniature paintings1162535110.22108/msci.2021.124814.1387FAMahmoodAmintoosiFaculty of Mathematics and Computer Science, Hakim Sabzevari University, SabzevarJournal Article20200916Taylor expansion is one of the methods for approximating functions that are differentiable of any order. The main paradigm in neural networks learning is based on deriving from the objective function and using gradient descent to achieve optimal solutions. Convolutional neural networks are among the most important tools in the field of deep learning. Most of these networks involve models with large sizes, and reducing the volume of these models is a current research topic. The primary method of reducing the size of models is pruning the redundant connections of neural networks, which are usually based on the size of connection weights. One of these methods is using Taylor expansion of the objective function to prioritize connections for removal from the network. In this paper, this method is extensively discussed, and a new application of it in classifying paintings with impressionism and miniature styles is presented. The experimental results show that with the Taylor expansion-based method, 83% of the network connections can be selected and removed without compromising the accuracy of the model in this specific application.Taylor expansion is one of the methods for approximating functions that are differentiable of any order. The main paradigm in neural networks learning is based on deriving from the objective function and using gradient descent to achieve optimal solutions. Convolutional neural networks are among the most important tools in the field of deep learning. Most of these networks involve models with large sizes, and reducing the volume of these models is a current research topic. The primary method of reducing the size of models is pruning the redundant connections of neural networks, which are usually based on the size of connection weights. One of these methods is using Taylor expansion of the objective function to prioritize connections for removal from the network. In this paper, this method is extensively discussed, and a new application of it in classifying paintings with impressionism and miniature styles is presented. The experimental results show that with the Taylor expansion-based method, 83% of the network connections can be selected and removed without compromising the accuracy of the model in this specific application.https://math-sci.ui.ac.ir/article_25351_af3f8e0e53ca9364b729ae74ed0f229a.pdfUniversity of IsfahanMathematics and Society2345-64935120200521Chomsky hierarchy classification in computational theoryChomsky hierarchy classification in computational theory17352556310.22108/msci.2021.125480.1393FASomayyehTariDepartment of Mathematics, Faculty of Basic Sciences, Shahid Madani University of Azerbaijan, Tabriz, Iran0000-0001-5569-2380Journal Article20201018A comprehensive understanding of fundamental concepts and basics in any scientific field is necessary for its progress. The continuous growth of computer science topics, both from a descriptive mechanics and a formal descriptive perspective, also demands this. Therefore, this article provides a brief overview of one of the fundamental topics in the field of computational theory (Chomsky hierarchy classification).A comprehensive understanding of fundamental concepts and basics in any scientific field is necessary for its progress. The continuous growth of computer science topics, both from a descriptive mechanics and a formal descriptive perspective, also demands this. Therefore, this article provides a brief overview of one of the fundamental topics in the field of computational theory (Chomsky hierarchy classification).https://math-sci.ui.ac.ir/article_25563_e5f049577883d27a31a0c306db1cfe99.pdfUniversity of IsfahanMathematics and Society2345-64935120200521The problems and misconceptions that students have regarding the concept of negative numbersThe problems and misconceptions that students have regarding the concept of negative numbers37482567910.22108/msci.2021.124854.1383FANargesYaftianDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training
UniversityNegarMahdaviDepartment of Mathematics, Shahid Rajaee Teacher Training University, Tehran, IranBitaMehr AeeinDepartment of Mathematics, Shahid Rajaee Teacher Training University, Tehran, IranJournal Article20200912Negative numbers are a fundamental concept in mathematics, introduced to students in the sixth and seventh grades. Understanding this concept has always been challenging for students, and they face various misconceptions. Teachers' awareness of these misconceptions and changes in their teaching methods can contribute to a deeper understanding of negative numbers among students. The aim of this article is to introduce the problems and misconceptions that students encounter in learning and solving problems related to negative numbers based on relevant research. Awareness of these issues can be useful for teachers of relevant grades, textbook authors, and researchers.Negative numbers are a fundamental concept in mathematics, introduced to students in the sixth and seventh grades. Understanding this concept has always been challenging for students, and they face various misconceptions. Teachers' awareness of these misconceptions and changes in their teaching methods can contribute to a deeper understanding of negative numbers among students. The aim of this article is to introduce the problems and misconceptions that students encounter in learning and solving problems related to negative numbers based on relevant research. Awareness of these issues can be useful for teachers of relevant grades, textbook authors, and researchers.https://math-sci.ui.ac.ir/article_25679_ca612a7b0c304bc946412621f1855f56.pdfUniversity of IsfahanMathematics and Society2345-64935120200521SIAM education subcommittee report on undergraduate degree programs in applied mathematicsSIAM education subcommittee report on undergraduate degree programs in applied mathematics49542568010.22108/msci.2021.127375.1415FAHaniyehHajinezhadFaculty of Mathematical Sciences, Department of Mathematics, Payam Noor University, Tehran0000-0001-6360-7676Journal Article20210210This paper is a translation of the the following paper into Persian:<br />[R. Levy, E. Chow, B. Kwon and K. Socha, SIAM education subcommittee report on undergraduate degree programs in applied mathematics, <em>SIAM Review</em>, <strong>59 </strong>no. 1 (2017) 199-204.]<br /> <br />The SIAM Education Committee has released a report called Undergraduate Degree Programs in Applied Mathematics. The report describes the general and specific features of undergraduate education in applied mathematics, based on interviews with 12 diverse but representative programs, and offers commentary based on the experience of the committee. This article summarizes the key findings of the SIAM report, focusing on curricular requirements, the role of industry, undergraduate research, student recruitment, and starting a new program. The goal of the report and this article is to provide guidance to new programs, existing programs, and the development of policy.This paper is a translation of the the following paper into Persian:<br />[R. Levy, E. Chow, B. Kwon and K. Socha, SIAM education subcommittee report on undergraduate degree programs in applied mathematics, <em>SIAM Review</em>, <strong>59 </strong>no. 1 (2017) 199-204.]<br /> <br />The SIAM Education Committee has released a report called Undergraduate Degree Programs in Applied Mathematics. The report describes the general and specific features of undergraduate education in applied mathematics, based on interviews with 12 diverse but representative programs, and offers commentary based on the experience of the committee. This article summarizes the key findings of the SIAM report, focusing on curricular requirements, the role of industry, undergraduate research, student recruitment, and starting a new program. The goal of the report and this article is to provide guidance to new programs, existing programs, and the development of policy.https://math-sci.ui.ac.ir/article_25680_c6d0c8dd598e3da05db1c93786a82318.pdfUniversity of IsfahanMathematics and Society2345-64935120200521Fractal differential and integral calculus: from theory to applicationsFractal differential and integral calculus: from theory to applications55682568110.22108/msci.2021.125705.1402FAAmirPishkooPhysics and Accelerators Research Institute, Nuclear Science and Technology Research Institute, North Working End, TehranAlirezaKhalili GolmankhanehPhyric Department, Islamic Azad University, Urmia Branch, UrmiaJournal Article20201120In this article, we introduce the basic concepts of fractal differential and integral calculus and discuss their similarities and differences with classical and fractional calculus. We will see that fractal differential and integral calculus, as well as classical calculus, are local, while fractional calculus is non-local.In this article, we introduce the basic concepts of fractal differential and integral calculus and discuss their similarities and differences with classical and fractional calculus. We will see that fractal differential and integral calculus, as well as classical calculus, are local, while fractional calculus is non-local.https://math-sci.ui.ac.ir/article_25681_6d53764d332e58dce1cb16d41ceb50e1.pdfUniversity of IsfahanMathematics and Society2345-64935120200521The introduction of proximal bundle algorithm for solving nonsmooth optimization problemsThe introduction of proximal bundle algorithm for solving nonsmooth optimization problems69812568210.22108/msci.2021.126616.1409FANajmehHoseiniDepartment of Applied Mathematics and Computer Science - Faculty of Mathematics and Statistics - University of IsfahanJournal Article20201223Proximal Bundle Algorithm is one of the suitable algorithms for solving nonsmooth optimization problems. Initially introduced for solving unconstrained convex nonsmooth optimization problems, this algorithm has been extended over the years to solve various problems. The aim of this article is to introduce this algorithm and extend it to solve unconstrained nonconvex nonsmooth optimization problems. At the end of the article, we implement the Proximal Bundle algorithm for solving nonconvex optimization problems in the MatLab software and present the results of running the algorithm for several examples.Proximal Bundle Algorithm is one of the suitable algorithms for solving nonsmooth optimization problems. Initially introduced for solving unconstrained convex nonsmooth optimization problems, this algorithm has been extended over the years to solve various problems. The aim of this article is to introduce this algorithm and extend it to solve unconstrained nonconvex nonsmooth optimization problems. At the end of the article, we implement the Proximal Bundle algorithm for solving nonconvex optimization problems in the MatLab software and present the results of running the algorithm for several examples.https://math-sci.ui.ac.ir/article_25682_130e9fcfa2cb97526585871c916cca29.pdf