• 대학교육
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• s.111
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• pp.78-81
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• 2001

• The Mathematical Education
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• v.13 no.3
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• pp.17-18
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• 1975

거리공간과 Normal countable compact의 위상적이 Normal이라는 것은 A.H. Stone에 의하여 이미 밝혀졌고, V.I. Malyhin은 space expX의 Cardrmal invariant와 공간 X 사이의 관계를 논하였다. 본 논문에서는 V.I. Malyin이 밝힌 tightness의 개념을 도입하여 countable tightness의 pracompact와 normal strongly countable compact 공간의 topological product가 Normal이라는 것을 증명하였다.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.93-102
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• 2005

In this paper, we introduce the history of dynamical systems and the notion of the H-shadowing property. And we study some relationships between the H-shadowing property and other dynamical properties such as expansivity and topological stability.

• Journal for History of Mathematics
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• v.18 no.2
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• pp.1-8
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• 2005

In this paper, we describe H. Hopf's life and works from the historical point of view. We have a very brief mention of history and results prior to Hopf. He raised the question of the topological implications of the sign of curvature. We discuss his contributions in the field of Riemannian geometry.

• Journal for History of Mathematics
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• v.24 no.1
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• pp.31-44
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• 2011

Partial differential equations on a Riemannain manifold is one of the most important areas in differential geometry. In this article, we survey the role of parabolic equations on some of the main results of differential geometry and topology, especially in the modern mathematical history. Also, we introduce some recent research in this area.

• Communications of Mathematical Education
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• v.27 no.2
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• pp.165-177
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• 2013

Mathematics teaching is often more effective when teachers connect the contents of mathematics with history, culture, and social events. In the history of mathematics, the 'paradigm' theory from Thomas Kuhn's scientific revolution is very effective to explain the revolutionary process of development in mathematics, and his theory has been widely quoted in the history of science and economics. However, it has not been appropriate to use his theory in the other fields. This is due to the fact that the scope of Kuhn's paradigm theory is limited to mathematics and science. In this study, this researcher introduced pan-paradigm as a general concept that encompasses all, since through any relation in the field of mathematics and architecture, Thomas Kuhn's theory of paradigm does not explain the phenomena. That is, at the root of various cultures there exist always a 'collective unconsciousness' and 'demands of the times,' and these two factors by synergism form values and controlling principles common to various parts of the culture, and this synergism leads the cultural activities, the process of which is a phenomenon called pan-paradigm.

• Journal for History of Mathematics
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• v.33 no.3
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• pp.135-154
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• 2020

This paper tries to show the formation of 'Kyungpook School' that is a nickname given to mathematicians of Kyungpook National University (KNU). In the early period, the role of professor Park Jung-gi was the most important drive to set the research tradition. He made Korea's first english journal in mathematics, Kyungpook Mathematical Journal KMJ which became a cornerstone for students to join the international academic community. Professor Ki U-hang published the most amount of papers in Korea in 1970s and became a role model for young scholars. In this background, KNU's Topology and Geometry Research Center at KNU was chosen as the only Science Research Center in mathematics in 1989, and KNU's mathematicians could get a long-period support for capable mathematics researchers' community.

• The Journal of the Korea Contents Association
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• v.20 no.7
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• pp.212-222
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• 2020

The purpose of this study is to understand the current status and trends of the research studies published by the Society for Industrial and Applied Mathematics which is a leader in the field of industrial mathematics around the world. To perform this purpose, titles and abstracts were collected from 6,255 research articles between 2016 and 2019, and the R program was used to analyze the topic modeling model with LDA techniques and a regression model. As the results of analyses, first, a variety of studies have been studied in the fields of industrial mathematics, such as algebra, discrete mathematics, geometry, topological mathematics, probability and statistics. Second, it was found that the ascending research subjects were fluid mechanics, graph theory, and stochastic differential equations, and the descending research subjects were computational theory and classical geometry. The results of the study, based on the understanding of the overall flows and changes of the intellectual structure in the fields of industrial mathematics, are expected to provide researchers in the field with implications of the future direction of research and how to build an industrial mathematics curriculum that reflects the zeitgeist in the field of education.

• Communications of Mathematical Education
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• v.15
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• pp.23-28
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• 2003

실수계와 n-차원 벡터 공간을 대수적 특성, 순서적 특성 그리고 위상적 특성을 중심으로 전개하고, 실변수 실가 함수와 n-차원 벡터 공간을 정의역으로 하는 실가함수를 연속성 (미분가능성), 단조성 그리고 볼록성을 중심으로 내용을 다룬다. 특히 실생활과 관련하여 이론을 전개하여 학습을 지도할 수 있는 교육과정을 개발하고, 직관적인 사고와 수리 논리적인 사고의 적절한 배합을 통해 학습자들이 적극적으로 학습에 임할 수 있는 교수 학습 방법을 개발하는 것을 목적으로 한다.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.189-205
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• 2002

본 요약논문에서는 리만다양체에서 정의되는 L$^2$조화미분 형식의 성질과 존재성에 대하여 알아보고 그 응용으로 유클리드 공간의 극소초평에서 L$^2$조화미분형식과 위상구조와의 관계를 살펴본다.