• The Mathematical Education
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• v.43 no.4
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• pp.337-347
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• 2004

Korea and China have maintained close relationships since the ancient times along with Japan, which also shares the common Chinese culture. The three major players in Northeast Asia have been recognizing their increasing importance in politics, economy, society, and culture. Considering those relationships among the three countries, it's necessary to compare and investigate their mathematics terminology. The purpose of this study is to investigate the similarities and differences between the terminology of school mathematics in Korean, Chinese and Japanese. The mathematics terms included in the junior high school of Korea were selected, and the corresponding terms in Chinese and Japanese were identified. Among 133 Korean terms, 72 were shared by three countries, 9 Korean terms were common with China, and the remaining 52 Korean terms were the same as Japanese terms. Korea had more common terms with Japan than China, which can be explained by the influences of the Japanese education during its rule of Korea in the past. The survey with 14 terms which show the discrepancy among 3 countries were conducted for in-service teachers and pre-service teachers. According to the result of the survey, preferred mathematics terms are different from one group to the other, yet the Korean mathematics terms were more preferred in general. However some terms in Chinese and Japanese were favored in certain degree. This result may provide meaningful implications to revise the school mathematics terms in the future.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2149-2154
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• 2017

In this paper, we obtain a simple lower bound for the number of positive (resp. negative) crossings in oriented link diagrams in terms of the maximal (resp. minimal) degree of the Jones polynomial.

• Journal of the Korean Mathematical Society
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• v.23 no.2
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• pp.101-108
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• 1986

• The Mathematical Education
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• v.33 no.1
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• pp.103-114
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• 1994

• The Mathematical Education
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• v.42 no.1
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• pp.11-18
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• 2003

One of the terms that are most often used in mathematics classrooms by either teachers or students might be about 'understanding' of mathematical concepts. Although 'understanding' in mathematics teaching and learning has been highly emphasized by many people, there is no exact and undebatable definition of 'understanding' as of yet. This paper tries to contribute to unfolding the meaning and the structure of understanding in mathematics education along with various literature and finally enhance our understanding of 'understanding' in mathematics education.

• The Mathematical Education
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• v.58 no.2
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• pp.319-335
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• 2019

In this paper, we examine the effectiveness of calculation according to automation, which is one of Computational Thinking, by coding the conceptual process into Python language, focusing on the concept of divisibility in elementary school textbooks. The educational implications of these considerations are as follows. First, it is possible to make a field of learning that can revise the new mathematical concept through the opportunity to reinterpret the Conceptual Thinking learned in school mathematics from the perspective of Computational Thinking. Second, from the analysis of college students, it can be seen that many students do not have mathematical concepts in terms of efficiency of computation related to the divisibility. This phenomenon is a characteristic of the mathematics curriculum that emphasizes concepts. Therefore, it is necessary to study new mathematical concepts when considering the aspect of utilization. Third, all algorithms related to the concept of divisibility covered in elementary mathematics textbooks can be found to contain the notion of iteration in terms of automation, but little recursive activity can be found. Considering that recursive thinking is frequently used with repetitive thinking in terms of automation (in Computational Thinking), it is necessary to consider low level recursive activities at elementary school. Finally, it is necessary to think about mathematical Conceptual Thinking from the point of view of Computational Thinking, and conversely, to extract mathematical concepts from computer science's Computational Thinking.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.397-408
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• 2018

It is well-known that quasi-$Pr{\ddot{u}}fer$ domains are characterized as those domains D, such that every extension of D inside its quotient field is a primitive extension and that primitive extensions are characterized in terms of INC-extensions. Let $R={\bigoplus}_{{\alpha}{{\in}}{\Gamma}}$ $R_{\alpha}$ be a graded integral domain graded by an arbitrary torsionless grading monoid ${\Gamma}$ and ${\star}$ be a semistar operation on R. The main purpose of this paper is to give new characterizations of gr-${\star}$-quasi-$Pr{\ddot{u}}fer$ domains in terms of graded primitive and INC-extensions. Applications include new characterizations of UMt-domains.

• Journal of the Korean Mathematical Society
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• v.61 no.3
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• pp.565-602
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• 2024

We study the collective behaviors of two second-order nonlinear consensus models with a bonding force, namely the Kuramoto model and the Cucker-Smale model with inter-particle bonding force. The proposed models contain feedback control terms which induce collision avoidance and emergent consensus dynamics in a suitable framework. Through the cooperative interplays between feedback controls, initial state configuration tends to an ordered configuration asymptotically under suitable frameworks which are formulated in terms of system parameters and initial configurations. For a two-particle system on the real line, we show that the relative state tends to the preassigned value asymptotically, and we also provide several numerical examples to analyze the possible nonlinear dynamics of the proposed models, and compare them with analytical results.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.657-664
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• 2000

A new concept of stability that includes Lyapunov and orbital stabilities and leads to concepts in between them is discussed in terms of a given topology of the function space. The criteria for such new concepts to hold are investigted employing suitably Lyapunov-like functions and the comparison principle.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.965-976
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• 2012

We prove an $L^2$-estimate of Ricci curvature in terms of harmonic 1-forms on a closed oriented Riemannian 3-manifold admitting a solution of any rescaled Seiberg-Witten equations. We also give a necessary condition to be a monopole class on some special connected sums.