• Communications of Mathematical Education
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• v.30 no.4
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• pp.453-468
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• 2016

This study is a result of experiment to recognize geometric and spacial conceptions for early childhood. This researcher had built up Mandala figures which was an intermediary between consciousness and unconsciousness, and then have studied about early childhood's geometric and spatial concepts by using Mandala figures. In this paper, authors have studied fractal art activities of early childhood as a follow-up study, since the structure of fractal art is similar to Mandala. As a result, three years old young children have significant correlation in four areas(figure perception, visual discrimination, position-in space perception and visual memory), but five years old young children have significant in three areas(figure perception, position-in space perception and visual memory). For five years old group, there is some difference between boys and girls, also they had described for their art activities like real models.

• The Mathematical Education
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• v.50 no.1
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• pp.119-128
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• 2011

In this paper, we studied into a qualitative research to see mathematical understanding of preschool and kindergarten's teachers such as feeling attitude, parents' concern, difficulty of math teaching in kindergarten field, teacher's role, type of feed back, beauty of math, relationship of real life, and self philosophy of math education. We selected 10 teachers whose career was 7~10 years. Because this research way is qualitative, we can new aspect that teacher want to break their ignorance for math. Moreover, they would like to learn about math practicality, application, and beauty from art in professional training. Therefore we assert that fusion math lecture would support in the professional training for teacher, preschool or kindergarten's president training, and remuneration training.

• Smart Structures and Systems
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• v.17 no.2
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• pp.195-208
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• 2016

Seismic isolation systems are essentially designed to preserve structural safety, prevent occupants injury and properties damage. An active saturated LMI-based control design is proposed to attenuate seismic disturbances in base-isolated structures under saturation actuators. Using a mathematical model of an eight-storied building structure, an active control algorithm is designed. Performance evaluation of the controller is carried out in a simplified model version of a benchmark building system, which is recognized as a state-of-the-art model for numerical experiments of structures under seismic perturbations. Experimental results show that the proposed algorithm is robust with respect to model and seismic perturbations. Finally, the performance indices show that the proposed controller behaves satisfactorily and with a reasonable control effort.

• Journal for History of Mathematics
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• v.19 no.1
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• pp.43-54
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• 2006

The purpose of this paper, followed by 'Nature$\cdot$Human, and Golden Section I ', is to study aesthetic consciousness, mentality model and body proportion of human, and the golden section applied to architecture and hand axe of stone age. In particular, handaxes of one million years ago have shown that they had critical competency to the basis of art and mathematics in the future. Furthermore, without pen, paper and ruler, the existence of mentality model made fundamental conversion of mathematics possible. Different sizes of handaxes were made by maintaining the equal golden section. This was the first example in relation to the principle mentioned in 'Stoicheia' by Euclid which was published hundred thousands of years later.

• Journal for History of Mathematics
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• v.19 no.4
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• pp.81-96
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• 2006

This paper aims to review Leibniz's analytic ideas in his philosophy, logics, and mathematics. History of analysis in mathematics ascend its origin to Greek period. Analysis was used to prove geometrical theorems since Pythagoras. Pappus took foundation in analysis more systematically. Descartes tried to find the value of analysis as a heuristics and found analytic geometry. And Descartes and Leibniz thought that analysis was played most important role in investigating studies and inventing new truths including mathematics. Among these discussions about analysis, this paper investigate Leibniz's analysis focusing to his ideas over the whole of his studies.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.101-107
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• 2010

A module M is said to satisfy the $EC_{11}$ condition if every ec-submodule of M has a complement which is a direct summand. We show that for a multiplication module over a commutative ring the $EC_{11}$ and P-extending conditions are equivalent. It is shown that the $EC_{11}$ property is not inherited by direct summands. Moreover, we prove that if M is an $EC_{11}$-module where SocM is an ec-submodule, then it is a direct sum of a module with essential socle and a module with zero socle. An example is given to show that the reverse of the last result does not hold.

• Journal of the Korea Convergence Society
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• v.8 no.7
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• pp.331-339
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• 2017

Mathematics has kept the relationships with other studies constantly. However, there is not many researches about the integrated teaching-learning materials for mathematics. In this paper, we review the integrated learning theories and domestic research trends of the integrated learning for the mathematics. Through the literature review, we survey the integrated teaching-learning materials, which integrate the mathematics and other subjects for the secondary school. As a result, it can be seen that integrated teaching-learning materials of mathematics and science, social studies, arts, physical education, and korean literature have recently been developed to help raise awareness of the usefulness of mathematics. Further study on the revision and supplementation of these materials should be carried out based on this paper.

• East Asian mathematical journal
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• v.37 no.3
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• pp.333-354
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• 2021

A support vector machine (SVM) is a state-of-the-art machine learning model rooted in structural risk minimization. SVM is underestimated with regards to its application to real world problems because of the difficulties associated with its use. We aim at showing that the performance of SVM highly depends on which kernel function to use. To achieve these, after providing a summary of support vector machines and kernel function, we constructed experiments with various benchmark datasets to compare the performance of various kernel functions. For evaluating the performance of SVM, the F1-score and its Standard Deviation with 10-cross validation was used. Furthermore, we used taylor diagrams to reveal the difference between kernels. Finally, we provided Python codes for all our experiments to enable re-implementation of the experiments.

• School Mathematics
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• v.13 no.1
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• pp.1-17
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• 2011

This study investigated the Chinese national university entrance examination (Gaokao) in mathematics administered in 2009 and 2010 to draw out some implications on the College Scholastic Ability Test (CSAT) in mathematics of Korea. To evaluate the attainments of basic mathematical skills and multilateral abilities required for further studies in university, the Gaokao mathematics is set in two forms(Art/Science), based on the Chinese national mathematics curriculum. The types of items in the Gaokao mathematics are multiple-choice, single-answer, and write-out-answer. The mathematical abilities that the Gaokao mathematics evaluates are mathematical reasoning, operation, geometrical imagination, application, and creativity. As a result, some implications on the Korean CSAT are drawn out in terms of the level of difficulty, the types of items, the arrangements, and the scores of items.

• Journal for History of Mathematics
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• v.32 no.4
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• pp.159-173
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• 2019

In this paper, we examine the brief history of the ring of four almonds regarding Mesopotamian mathematics, and present reasons why the Omar Khayyam's triangle, a special right triangle in a ring of four almonds, was essential for artisans due to its unique pattern. We presume that the ring of four almonds originated from a point symmetry figure given two concentric squares used in the proto-Sumerian Jemdet Nasr period (approximately 3000 B.C.) and a square halfway between two given concentric squares used during the time of the Old Akkadian period (2340-2200 B.C.) and the Old Babylonian age (2000-1600 B.C.). Artisans tried to create a new intricate pattern as almonds and 6-pointed stars by subdividing right triangles in the pattern of the popular altered Old Akkadian square band at the time. Therefore, artisans needed the Omar Khayyam's triangle, whose hypotenuse equals the sum of the short side and the perpendicular to the hypotenuse. We presume that artisans asked mathematicians how to construct the Omar Khayyam's triangle at a meeting between artisans and mathematicians in Isfahan. The construction of Omar Khayyam's triangle requires solving an irreducible cubic polynomial. Omar Khayyam was the first to classify equations of integer polynomials of degree up to three and then proceeded to solve all types of cubic equations by means of intersections of conic sections. Omar Khayyam's triangle gave practical meaning to the type of cubic equation $x^3+bx=cx^2+a$. The work of Omar Khayyam was completed by Descartes in the 17th century.