• 한국수학교육학회지시리즈A:수학교육
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• 제42권1호
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• pp.57-67
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• 2003

In this paper we analyze educational aspects of a mathematical problem. As a result of the analysis, we extract five meaningful mathematical knowledge and ideas. Corresponding with these we suggest some chains of mathematical problems that are expected to activate student's self-oriented mathematical investigation.

• 호남수학학술지
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• 제40권2호
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• pp.355-366
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• 2018

Let R be a commutative ring with identity and let M be a finitely generated module over a Noetherian local ring R. Then it is well-known that M has a minimal projective resolution, which is unique up to isomorphisms of exact sequences. We provide a new proof of its uniqueness. Moreover, we deal with the cohomologies of (M, R/m).

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제20권4호
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• pp.621-634
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• 2006

In this study we describe the characteristics of solving geometry problems related with the ratio of segments using the principle of the lever and the center of gravity, compare and analyze this problem solving method with the traditional Euclidean proof method and the analytic method.

• 대한수학회논문집
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• 제16권3호
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• pp.399-404
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• 2001

We examine plane waves of the elastic reduced wave equation in the half-space, and show that linear combinations of them can cover all plane waves on the boundary. The proof is based on the complex analysis for the symbol in the (dual) variable in the normal direction to the boundary.

• 통합자연과학논문집
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• 제5권1호
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• pp.38-41
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• 2012

In this paper we show that for any triangle and any point on the circumcircle the envelope of the Wallace-Simson lines with signed angle ${\alpha}$ is a parabola. The proof is obtained naturally using polar coordinates. We also present the reparametrization of the envelope which is a linear normal curve.

• Korean Journal of Mathematics
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• 제26권4호
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• pp.747-756
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• 2018

We study a maximum principle for a uniformly elliptic second order differential operator in nondivergence form. We allow a bounded positive zeroth order coefficient in a certain type of unbounded domains. The results extend a result by J. Busca in a sense of domains, and we present a simple proof based on local maximum principle by Gilbarg and Trudinger with iterations.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권2호
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• pp.171-177
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• 2022

The aim of this note is to establish two known sums involving central binomial coefficients via a hypergeometric series approach. As an application, we discover two new closed-form evaluations of generalized hypergeometric function.

• 과학교육연구지
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• 제34권1호
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• pp.175-184
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• 2010

이 논문에서는 Hanna와 Jahnke의 수학적 증명에서의 물리적 논증의 사용에 대한 주장에 동의하면서, 그들의 논문에서 취급된 무게중심의 개념을 이용한 물리적 논증을 통해 삼각형의 무게중심에 대한 증명의 예를 분석하고 보다 현실적인 모델을 제시하였다. 전통적인 수학적 논증과 비교하여 물리적 논증에 있어서 물리적 개념과 모델의 역할을 명백히 드러내고, 또한 물리적 논증을 교실에서 학생들에게 제시하고 활용해야 할 필요성에 대하여 논하였다.

• 대한수학회지
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• 제54권4호
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• pp.1149-1161
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• 2017

An ($n_1,\;n_2,\;{\ldots},\;n_k$)-colored permutation is a permutation of $n_1+n_2+{\cdots}+n_k$ in which $1,\;2,\;{\ldots},\;n_1$ have color 1, and $n_1+1,\;n_1+2,\;{\ldots},\;n_1+n_2$ have color 2, and so on. We give a bijective proof of Steinhardt's result: the number of colored permutations with no monochromatic cycles is equal to the number of permutations with no fixed points after reordering the first $n_1$ elements, the next $n_2$ element, and so on, in ascending order. We then find the generating function for colored permutations with no monochromatic cycles. As an application we give a new proof of the well known generating function for colored permutations with no fixed colors, also known as multi-derangements.

• 대한수학회보
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• 제55권4호
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• pp.1209-1219
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• 2018

We provide a direct proof of the following theorem of Kalton, Hollenbeck, and Verbitsky [7]: let H be the Hilbert transform and let a, b be real constants. Then for 1 < p < ${\infty}$ the norm of the operator aI + bH from $L^p(\mathbb{R})$ to $L^p(\mathbb{R})$ is equal to $$\({\max_{x{\in}{\mathbb{R}}}}{\frac{{\mid}ax-b+(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}ax-b-(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p}{{\mid}x+{\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}x-{\tan}{\frac{\pi}{2p}}{\mid}^p}}\)^{\frac{1}{p}}$$. Our proof avoids passing through the analogous result for the conjugate function on the circle, as in [7], and is given directly on the line. We also provide new approximate extremals for aI + bH in the case p > 2.