• 대한수학교육학회지:수학교육학연구
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• 제8권1호
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• pp.291-298
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• 1998

This study deals with the problem of proof education in the middle school geometry bby examining van Hiele#s geometric thought level theory and Freudenthal#s mathematization teaching theory. The implications that have been revealed by examining the theory of van Hie이 and Freudenthal are as follows. First of all, the proof education at present that follows the order of #definition-theorem-proof#should be reconsidered. This order of proof-teaching may have the danger that fix the proof education poorly and formally by imposing the ready-made mathematics as the mere record of proof on students rather than suggesting the proof as the real thought activity. Hence we should encourage students in reinventing #proving#as the means of organization and mathematization. Second, proof-learning can not start by introducing the term of proof only. We should recognize proof-learning as a gradual process which forms with understanding the meaning of proof on the basic of the various activities, such as observation of geometric figures, analysis of the properties of geometric figures and construction of the relationship among those properties. Moreover students should be given this natural ground of proof.

• 한국컴퓨터정보학회논문지
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• 제27권7호
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• pp.35-48
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• 2022

본 연구에서는 멀티에이전트 환경에서 지식을 표현하고 추론함에 있어서 증명 이론적 방법을 제안한다. 이 방법은 논리적 결과를 기계적 방법으로 결정하므로 초기 인공지능 연구부터 핵심분야로 발전해 왔다. 하지만 임의의 닫힌 문장들의 집합에서 항상 명제가 증명할 수 있지 않기에 논리적 결과가 결정할 수 있어지려면 절 형식의 문장으로 그 표현 범위를 제한한다. 그리고 절 형식의 문장들에서만 적용 가능한, 단순하면서도 강력한 추론 규칙인 비교흡수 원리(Resolution principle)를 적용한다. 또한 증명이론을 메타술어로 표현할 수 있으므로 증명이론의 메타논리로 확장 가능하다. 메타논리가 모델 이론의 인식 논리(epistemic logic)보다 향상된 표현력을 기반으로 실용적인 면과 효율면에서 우월할 수 있다. 이를 입증하기 위해 인식 논리의 의미론과 증명이론의 메타논리 방식으로 각각 Muddy Children 문제에 적용한다. 그 결과 협력적 멀티에이전트 환경에서 메타논리를 사용하여 지식과 공통지식을 표현하고 추론한 방법이 더 효율적임을 증명한다.

• 대한수학회지
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• 제47권1호
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• pp.123-134
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• 2010

The aim of this paper is to provide a proof for a version of the Morse inequalities for manifolds with boundary. Our main results are certainly known to the experts on Morse theory, nevertheless it seems necessary to write down a complete proof for it. Our proof is analytic and is based on the J. Roe account of Witten's approach to Morse Theory.

• 대한수학교육학회지:수학교육학연구
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• 제11권2호
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• pp.385-402
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• 2001

The purpose of this study is to conceptualize 'proof' school mathematics. We based on the assumption the following. (a) There are several different roles of 'proof' : verification, explanation, systematization, discovery, communication (b) Accepted criteria for the validity and rigor of a mathematical 'proof' is decided by negotiation of school mathematics community. (c) There are dynamic relations between mathematical proof and empirical theory. We need to rethink the nature of mathematical proof and give appropriate consideration to the different types of proof related to the cognitive development of the notion of proof. 'proof' in school mathematics should be conceptualized in the broader, psychological sense of justification rather than in the narrow sense of deductive, formal proof 'proof' has not been taught in elementary mathematics, traditionally, Most students have had little exposure to the ideas of proof before the geometry. However, 'proof' cannot simply be taught in a single unit. Rather, proof must be a consistent part of students' mathematical experience in all grades, in all mathematics.

• 대한수학회지
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• 제40권3호
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• pp.423-434
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• 2003

We prove an approximation result, and we get a new proof of the main result in [7]. I hope that this new proof may be a step towards a generalization of the Poletsky theory of discs to the case of almost complex manifolds.

• 통상정보연구
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• 제8권4호
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• pp.159-175
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• 2006

This paper that explain exchange rate determination using Korea's economy data moment investigate whether each theory cause effect that is some on exchange rate showdown analyzing actual proof relation between foreign exchange fluctuation and financing part variance examine wish to. Because korea economic enters in the 1990s and the 2000s and the change is notable, foreign exchange fluctuation by such change is real condition that is changing. In this paper, I wish to enforce actual proof analysis if change such as him is grasped by form that is some about foreign exchange fluctuation. First, the second chapter investigates exchange rate decision theory that is used on actual proof interpretation, and executes actual proof Test in reply in subsequent the third chapter. And finally, the fourth chapter wishes to drive conclusion of this paper.

• 의료법학
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• 제9권1호
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• pp.9-56
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• 2008

The medical practice does not always get a satisfatory result since the disease progress of patients are depended on patients' physical constitution and the doctors cannot control the outcomes about patients' physiological and biological reaction after the treatment. Moreover, the medical practice may bring wrong result fatalistically because of the unpredictablility of life. To demand for compensation of the damage to the doctors about these wrong result, the patient side holds the burden of proof that is between medical practice and demage, and there is damage from doctor's malpractice according to the accepted theory about the fundamental principle of distribution of the burden of proof. This falls not only under the liability of Tort Law, but also liability of Contract Law. However, the patient may be in difficult situation to prove the malpractice of doctors since he or she cannot recognize the facts because he or she was in unconscious while the medical practice was conducted, or they cannot judge precisely even though they recognize the facts. Nevertheless, the lawsuits against medical malpractice are the field that never achieves the equality of arms since the most of the evidence belong to the doctor's side. Hence, to maintain the principle of the equality of arms under the constitution, the theory leads to alleviate the burden of proof that patients hold. However, the doctors cannot be asked for the burden of proof that they conduct medical practice without errors. Because the doctors may experience difficulty to prove their innocence as the patients because of the unique characteristic that medical practices have. Therefore, the methods of the alleviation of the patient's burden of proof should have the equality of arms and the equal opportunity between the patients and the doctors with the evaluation of the justifiable interest from both the patients and the doctors. As the methods of the alleviation of the burden of proof, the alleviation of the demands and the degree of the burden of proof or resolutely the conversion of the burden may be considered. However, Recognizing the exception from general principle with converting the burden of proof is not proper in principle because the doctors may experience difficulty of the proof as the patients may have. If the difficulty of proof can be resolved by alleviating of the demands and the degree of the burden of proof, it is more desirable resolution rather than converting the burden of proof.

• 대한수학회지
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• 제41권4호
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• pp.591-615
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• 2004

In this paper, we provide the algebraic foundations to the theory of relative $\ell$$_1$ homology. In particular, we prove that $\ell$$_1$ homology of topological spaces, both for the absolute case and for the relative case, depends only on their fundamental groups. We also provide a .proof of Gromov's Equivalence theorem for $\ell$$_1$ homology, stated by Gromov without proof [4].

• 한국수학교육학회지시리즈A:수학교육
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• 제50권4호
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• pp.441-466
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• 2011

In this article, we study on the teaching design, focused on the geometric methods, of 2-D isoperimetric problem for the elementary mathematically gifted students. For our teaching design, we discussed the ideals of Zenodorus's polygon proof, Steiner's four-hinge proof, Steiner's mean boundary proof, Steiner's snowball-packing proof, Edler's finite existence proof and Lawlor's dissection proof, and then the ideals achieved were modified with the theoretical backgrounds-the theory of Freudenthal's mathematisation, the method of analysis-synthesis. We expect that this article would contribute to the elementary mathematically gifted students to acquire and to improve spatial sense.

• 대한수학회보
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• 제45권2호
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• pp.273-275
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• 2008

We will give a short and elementary proof of the existence of infinitely many primes p such that a given positive integer a congruent 3 modulo 4 is a quadratic non-residue modulo p.