• 대한수학회보
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• 제60권6호
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• pp.1439-1451
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• 2023

This paper provides a constructive proof of the weak factorizations of the classical Hardy space H¹(ℝⁿ) in terms of multilinear fractional integral operator on the variable Lebesgue spaces, which the result is new even in the linear case. As a direct application, we obtain a new proof of the characterization of BMO(ℝⁿ) via the boundedness of commutators of the multilinear fractional integral operator on the variable Lebesgue spaces.

• 대한수학회지
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• 제61권1호
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• pp.149-160
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• 2024

In this paper, we study the unicorn's Landsberg problem from an intrinsic point of view. Precisely, we investigate a coordinate-free proof of Numata's theorem on Landsberg spaces of scalar curvature. In other words, following the pullback approach to Finsler geometry, we prove that all Landsberg spaces of dimension n ≥ 3 of non-zero scalar curvature are Riemannian spaces of constant curvature.

• 대한수학회보
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• 제61권3호
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• pp.779-784
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• 2024

Baker proved that any strongly quasi-positive fibered knot is minimal with respect to the ribbon concordance among fibered knots in the three-sphere. By applying Rapaport's conjecture, which has been solved by Kochloukova, we can check that any strongly quasi-positive fibered knot is minimal with respect to the ribbon concordance among all knots in the three-sphere. In this short note, we give an alternative proof for the fact by utilizing the knot Floer homology.

• 대한수학교육학회지:수학교육학연구
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• 제13권1호
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• pp.13-28
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• 2003

Practice of proof is considered in, the view of language and meta-mathematics, recognizing the role of proof that is the means of communication and development of mathematical understanding. Linguistic components in proof texts are symbol, verbal language and visual text, and contain the implicit knowledge in the meta-mathematics view. This study investigates the functions of linguistic elements according to Halliday's functional grammar and the rhetoric skills in proof texts in math textbook, teacher's note, and student's written text. We need to inquire into the aspects of language for mathematics learning process and the understanding and use of students' language.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제23권3호
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• pp.887-921
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• 2009

인류 문명의 발달과 함께 폭넓게 활용된 수학적 내용 중의 하나가 피타고라스 정리이다. 특히, 이집트, 메소포타미아, 중국과 같은 고대 문명의 발생지에서 발굴되는 많은 역사적 기록 속에서 피타고라스 정리에 대한 내용을 찾아 볼 수 있다. 피타고라스 정리는 중등학교 수학교육에서 매우 중요한 정리로써, 정리 내용 자체뿐만 아니라 다양한 증명 방법과 증명 과정에 내재된 수학적 아이디어는 수학 교육학적 측면에서 큰 의미를 가지고 있다. 이에 본 연구에서는 먼저 피타고라스 정리의 390여 가지의 알려진 증명 방법들을 중심으로 하여, 피타고라스 정리의 다양한 증명 방법들에 대한 분석을 한다. 분석된 결과를 바탕으로 각 증명 방법들에 대한 핵심 아이디어, 선수학습개념, 주요 아이디어들을 알아보고 내재된 수학교육학적 아이디어를 분석할 것이다.

• Kyungpook Mathematical Journal
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• 제11권2호
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• pp.185-188
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• 1971

• 한국수학교육학회지시리즈A:수학교육
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• 제52권4호
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• pp.549-565
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• 2013

To help students understand the deduction system in the proof, we analyzed the textbook on mathematics at first. As results, we could find that the textbook' system of deduction is similar with the Euclid' system of deduction. The starting point of deduction is different with each other. But the flow of deduction match with each other. Next, we searched for the example of circular argument and analyzed. As results, we classified the circular argument into two groups. The first is an internal circular argument which is a circular argument occurred in a theorem. The second is an external circular argument which is a circular argument occurred between many theorems. We could know that the flow of deduction system is consistent in internal-external dimension. Lastly, we proposed the desirable teaching direction to help students understand the deduction system in the proof.

• 대한수학회논문집
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• 제9권3호
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• pp.565-570
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• 1994

In this article we prove a version of the Perron-Frobenius Theorem in linear algebra using the Brouwer's Fixed Point Theorem in topology. We will mostly concentrate on he qualitative aspect of the Perron-Frobenius Theorem rather than quantitative formulas, which would be enough for theoretical investigations in ergodic theory. By the nature of the method of the proof, we do not expect to obtain a numerical estimate. But we may regard it worthwhile to see why a certain type of result should be true from a topological and geometrical viewpoint. However, a geometric argument alone would give us a sharp numerical bounds on the size of the eigenvalue as shown in Section 2. Eigenvectors of a matrix A will be fixed points of a certain mapping defined in terms of A. We shall modify an existing proof of Frobenius Theorem and that will do the trick for Perron-Frobenius Theorem.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제22권1호
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• pp.65-77
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• 2008

Haga 정리는 정사각형 색종이의 접기를 통해 얻어지는 선분들의 비를 수학화시킨 정리로, 종이접기에 관련된 수학적 내용의 탐구에서 폭넓게 활용된다. 본 연구에서는 과학고등학교의 수학 영재교육을 통해 얻어진 산출물인 Haga 정리의 새로운 증명 방법, Haga 제 2정리의 일반화로 발전된 정리를 제시하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제53권3호
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• pp.383-397
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• 2014

This study aims to explore secondary students' thinking while doing proof in geometry. Two secondary students were interviewed and the interview data were analyzed. The results of the analysis suggest that the two students similarly showed as follows: a) tendencies to use the rules of congruent and similar triangles to solve a given problem, b) being confused about the rules of similar and congruent triangles, and c) being confused about the definitions, partition and hierarchical classification of quadrilaterals. Also, the results revealed that a relatively low achieving student has tendency to rely on intuitive information such as visual representations.