• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.05a
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• pp.261-264
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• 2002

이 논문에서는 구간 수의 값을 갖는 함수들의 쇼케이적분을 생각하고자 한다. 이러한 구간 수의 값을 갖는 함수들의 성질들을 조사하여 오토연속인 퍼지측도에 관련된 쇼케이적분에 대한 수렴성 정리를 증명한다.

• East Asian mathematical journal
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• v.24 no.5
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• pp.521-526
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• 2008

In this study, we'll check the proof of Morley's theorem that calculate the sides XY, YZ and ZX of Morley's triangle. We may now consider calculate area of Morley triangle and observation that, for example, in triangle ABC, length or sides XY, YZ and ZX are $8Rsin{\alpha}sin{\beta}sin{\gamma}$, respectively. Therefore, compare with the area of Morley's triangle XYZ and the area of triangle ABC.

• The Korean Journal of Applied Statistics
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• v.7 no.2
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• pp.323-333
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• 1994

In this paper we present some approximation theorems related to the problem of finding optimal densities with prescribed moments. The implementation of the approximation theorems is to be done in some examples.

• Proceedings of the Korean Information Science Society Conference
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• 2003.10a
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• pp.880-882
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• 2003

본 논문에서는 소프트웨어 공학에서 널리 사용되고 있는 정형기법을 보안 운영체제의 검증에 활용하기 위해 각 검증기법의 특성과 도구에 대해서 설명한다. 정리증명의 대표적인 도구인 PVS와 모델체킹의 대표적 도구인 SMV, 특수한 목적을 위해 개발된 NPA등에 대해서 알아보고, 각 방법을 비교, 분석하여 보안운영체제의 검증에 적합한 도구를 찾아본다.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.511-528
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• 2010

Students' intuition in formal proof should be expressed as symbols according to the deductive process. The symbol will play a role of the mediation between the intuition and the formal proof. This study examined the evolution process of intuition mediated by the symbol in geometry proof. According to the results first, symbol took the great roles when students had the non-formed intuition for the proposition. The signification of symbols could explain even the proof process of the proposition with the non-expectable intuition. And when students proved it by symbols, not by figure nor words, they could evolute the conclusive intuition about the proposition.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.59-76
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• 2011

Starting from a collection V as a model which satisfies the axioms of NBG, we call the elements of V as sets and the subcollections of V as classes. We reconstruct the G$\ddot{o}$del's proof of the consistency of GCH and AC with the axioms of Zermelo-Fraenkel set theory by using Mostowski-Shepherdson mapping theorem, reflection principles in Tarski-Vaught theorem and Montague-Levy theorem and the fact that NBG is a conservative extension of ZF.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.173-192
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• 2013

It may be replacement proofs with understanding and explaining geometrical properties that was a remarkable change in school geometry of 2009 revised national curriculum for mathematics. That comes from the difficulties which students have experienced in learning proofs. This study focuses on one of those difficulties which are caused by the forms of proofs: using letters for designating some sides or angles in writing proofs and understanding some long sentences of proofs. To overcome it, this study aims to investigate the applicability of Byrne's method which uses coloured diagrams instead of letters. For this purpose, the proofs of three geometrical properties were taught to middle school students by Byrne's visual method using the original source, dynamic representations, and the teacher's manual drawing, respectively. Consequently, the applicability of Byrne's method was discussed based on its strengths and its weaknesses by analysing the results of students' worksheets and interviews and their teacher's interview. This analysis shows that Byrne's method may be helpful for students' understanding of given geometrical proofs rather than writing proofs.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.299-314
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• 2008

The purposes of this study were to investigate what attitudes students have toward learning proofs and what difficulties they have in learning proofs, and to examine how the use of dynamic geometry software, the Geometer's Sketchpad, helps students' proof learning. The study involved 117 9th graders in 2 high schools. According to questionnaire data, over 50 percent of the total respondents(116) indicated negative attitudes toward learning proofs, on the other hand, only 16 percent of the total respondents indicated positive attitudes toward the learning. Memorizing and remembering many kinds of theorems, definitions, and postulates to use in proving statements was the most difficult part in learning proofs, which the largest proportion of the total respondents indicated. The study found that the use of the Geometer's Sketchpad played positive roles in developing students' understanding of proofs and stimulating students' interests in learning proofs.

• Journal for History of Mathematics
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• v.23 no.1
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• pp.79-88
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• 2010

G$\ddot{o}$del's proof attempts to establish the existence of God by the definition that God is a being having all positive properties. The proof uses here second order modal logic system $S_5$ with the axiom ${\diamondsuit}{\Box}p{\rightarrow}{\Box}p$. We review the G$\ddot{o}$del's own version and prove his ontological theorems.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.20 no.3
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• pp.3-8
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• 2010

There are some efficient brute force algorithm for factorization. Fermat's factorization is one of the way of brute force attack. Fermat's method works best when there is factor near the square-root. This paper shows that why Fermat's method is effective and verify that there are only one answer. Because there are only one answer, we can start Fermat's factorization anywhere. Also, we convert from factorization to finding square number.