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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
> Journal Vol & Issue
Journal for History of Mathematics
Journal Basic Information
Journal DOI :
The Korean Society for History of Mathematics
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Volume & Issues
Volume 22, Issue 4 - Nov 2009
Volume 22, Issue 3 - Aug 2009
Volume 22, Issue 2 - May 2009
Volume 22, Issue 1 - Feb 2009
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Frege's Critiques of Cantor - Mathematical Practices and Applications of Mathematics
Park, Jun-Yong ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 1~30
Frege's logicism has been frequently regarded as a development in number theory which succeeded to the so called arithmetization of analysis in the late 19th century. But it is not easy for us to accept this opinion if we carefully examine his actual works on real analysis. So it has been often argued that his logicism was just a philosophical program which had not contact with any contemporary mathematical practices. In this paper I will show that these two opinions are all ill-founded ones which are due to the misunderstanding of the theoretical place of Frege's logicism in the context of contemporary mathematical practices. Firstly, I will carefully examine Cantorian definition of real numbers and Frege's critiques of it. On the basis of this, I will show that Frege's aim was to produce the purely logical definition of ratios of quantities. Secondly, I will consider the mathematical background of Frege's logicism. On the basis of this, I will show that his standpoint in real analysis was much subtler than what we used to expect. On the one hand, unlike Weierstrass and Cantor, Frege wanted to get such real analysis that could be universally applicable. On the other hand, unlike most mathematicians who insisted on the traditional conceptions, he would not depend upon any geometrical considerations in establishing real analysis. Thirdly, I will argue that Frege regarded these two aspects - the independence from geometry and the universal applicability - as those which characterized logic itself and, by logicism, arithmetic itself. And I will show that his conception of real numbers as ratios of quantities stemmed from his methodological maxim according to which the nature of numbers should be explained by the common roles they played in various contexts to which they applied, and that he thought that the universal applicability of numbers could not be adequately explicated without such an explanation.
The Mathematical Foundations of Cognitive Science
Hyun, Woo-Sik ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 31~44
Anyone wishing to understand cognitive science, a converging science, need to become familiar with three major mathematical landmarks: Turing machines, Neural networks, and
incompleteness theorems. The present paper aims to explore the mathematical foundations of cognitive science, focusing especially on these historical landmarks. We begin by considering cognitive science as a metamathematics. The following parts addresses two mathematical models for cognitive systems; Turing machines as the computer system and Neural networks as the brain system. The last part investigates
achievements in cognitive science and its implications for the future of cognitive science.
The heuristic function of mathematical signs in learning of mathematical concepts
Cheong, Kye-Seop ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 45~60
Mathematical thinking can be symbolized by the external signs, and these signs determine in reverse the form of mathematical thinking. Each symbol - a symbol in algebra, a symbol in analysis, and a diagram which verifies syllogism - reflects the diverse characteristic of cogitation in mathematics and perfirms a heuristic function.
History of mathematics in Chosun dynasty
Koh, Young-Mee ; Ree, Sang-Wook ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 61~78
We first of all emphasize the importance of the research on the history of Korean mathematics. We next make a survey of the brief history of Chosun mathematics as a seed knowledge for further research on Korean mathematics. We hope that our survey will serve researchers as a seed knowledge of their research.
Sang-Seol LEE: Father of Korean Modern Mathematics Education
Seol, Han-Guk ; Lee, Sang-Gu ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 79~102
Most who have heard of Sang-Seol Lee know him for his contribution to the Korean independence movement nearly a hundred years ago. This paper, however, will discuss Lee's other great contribution to his country; that of being "The father of modern mathematical education in Korea". Lee passed the rigorous government officer examination with the highest honor and became a teacher for the royal prince. Later he became the president of Sunkyunkwan, a national institute of higher learning since 1398, and eventually a well-known university bearing the same name. Lee was also a highly regarded Confucian scholar and well versed in foreign languages. He wanted Korea to become a modern country and felt that the areas of science and engineering were studies that needed improving in order to achieve modernization. While researching Western textbooks on the subjects he realized that Western mathematics would be especially important for Korea. With that, it became his mission to integrate Western mathematics into the Korean educational system. This paper will explain the importance of Sang-Seol Lee's contributions to mathematic education in Korea and how it helped Korea become the modern nation it is today.
Korean Mathematics in (the History of) the World
Ree, Sang-Wook ; Koh, Young-Mee ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 103~112
In this article, we look into the present status of Korean mathematics and stress the importance and the need of research on its history. Some researches on it have been done by Hong, though not known to the world. We search some of the ways of activating the research on Korean mathematics history and introducing it to the world.
Polanyi's Epistemology and the Tacit Dimension in Problem Solving
Nam, Jin-Young ; Hong, Jin-Kon ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 113~130
It can be said that the teaching and learning of mathematical problem solving has been greatly influenced by G. Polya. His heuristics shows down the explicit process of mathematical problem solving in detail. In contrast, Polanyi highlights the implicit dimension of the process. Polanyi's theory can play complementary role with Polya's theory. This study outlined the epistemology of Polanyi and his theory of problem solving. Regarding the knowledge and knowing as a work of the whole mind, Polanyi emphasizes devotion and absorption to the problem at work together with the intelligence and feeling. And the role of teachers are essential in a sense that students can learn implicit knowledge from them. However, our high school students do not seem to take enough time and effort to the problem solving. Nor do they request school teachers' help. According to Polanyi, this attitude can cause a serious problem in teaching and learning of mathematical problem solving.
A study on the relation between the real number system of Dedekind and the Eudoxus theory of proportion
Kang, Dae-Won ; Kim, Kwon-Wook ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 131~152
The Eudoxean theory of Proportion is correlated with 'Dedekind cut' with which Dedekind defined the real number system in modern usage. Dedekind established a firm foundation for the real number system by retracing some of Eudoxus' steps of over two thousand years earlier. Thus it should be quite worthy that we separate Greek inheritance from the definition of Dedekind, However, there is a fundamental difference between Eudoxean theory of proportion and Dedekind cut. Basically, it seems impossible for Greeks to distinguish between the distinction between number and magnitude. In this paper, we will consider how the Eudoxean theory of proportion was related to Dedekind cut introduced to prove the Dedekind's real number completion and how it influenced Dedekind cut by looking at the relation between Eudoxos's explication of the notion of ratio and Dedekind's well-known construction of the real numbers.
The life and scholastic career of a New Math campaigner, Zoltan P. Dienes
Kim, Soo-Mi ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 153~170
Zoltan, P. Dienes is a famous researcher and practitioner who has tried to teach mathematical structures to children for about 50 years. Even though his ideas of teaching mathematics and materials including MAB have been well known in Korea, they are only a part of his achievement he has developed for his whole life. So this article is designed for taking an overview of his whole life and achievement and getting some implications for today's mathematics education. In this article, his life story could be divided by five periods in terms of a scholastic career and his research achievement could be reorganized with respect to five theses: psychology of learning mathematics, mathematical curriculum, teacher education, games and material for mathematical learning. As a result, it is found that there is a deep connection between his personal life and his scholastic career.
The Study on the
Psychology in Invention
Lee, Dae-Hyun ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 171~186
is mathematician and the episodes in his mathematical invention process give suggestions to scholars who have interest in how mathematical invention happens. He emphasizes the value of unconscious activity. Furthermore,
points the complementary relation between unconscious activity and conscious activity. Also,
emphasizes the value of intuition and logic. In general, intuition is tool of invention and gives the clue of mathematical problem solving. But logic gives the certainty.
points the complementary relation between intuition and logic at the same reasons. In spite of the importance of relation between intuition and logic, school mathematics emphasized the logic. So students don't reveal and use the intuitive thinking in mathematical problem solving. So, we have to search the methods to use the complementary relation between intuition and logic in mathematics education.
The Study of the Extension of the Scale of Notation by Analogy and the Notation in History
Suh, Bo-Euk ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 187~206
On this study, the historical flow of the notation was briefly examined and the direction of mathematical investigation activity of the content of notation by analogy was explored and teaching learning materials were developed. Diverse mathematical facts were investigated on the basis of decimal system and binary system which are learned in middle school. First, the way of progressing analytic activity with algebraic material was examined. Second, on the basis of the notation which are learned in the first grade of middle school, the definition of the scale of a -notation, -a -notation,
-notation was extended by analogy. The result of this study will be expected to establish the curriculum of mathematics and provide teaching and learning with the meaningful current events.
Korean tertiary mathematics and curriculum in early 20th century
Lee, Sang-Gu ; Ham, Yoon-Mee ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 207~254
We would like to give an introduction about Korean Tertiary Mathematics and curriculum in the early 20th centuryan Ttails like, when tertiary mathematics was introduced in Korea, who adiated it, and how it appeared in curriculum for college education were presented. From the late 19th century, the royal circle of the dynasty, officers, socd. Felites, intellectu. sculum in tand many foreatn my mionaries, who entered Korea, began to establish educational ulstitutions begulnearlfrom the nt80s. Kearl GoJongtannounced thescript for general education icentur. Most of the new schoo scadiated western mathematics as tcompulsory course in their curriculumiese introduced tertiary mathematics in most of the curriculumurse end curriculum in, lfrom nt85 to 1960. Since then, tertiary mathematics was tautit at most of the new private and public schools of each level and in colleges. We have investigated the history of Korean tertiary mathematics with its curriculum from 1895 to 1960.
R. L. Moore's method and small group discover method
Choi, Eun-Mi ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 255~272
R. L. Moore's discovery methods are known to have been very effective with certain classes of students. However when the method was attempted by others at the undergraduate level, the results sometimes were disappointing. In this article we study the history of developing modified Moore methods with small group discovery method for the purpose of undergraduate education, and then we discuss some educational point of view in our universities.
The Controversy on the Conceptual Foundation of Space-Time Geometry
Yang, Kyoung-Eun ;
Journal for History of Mathematics, volume 22, issue 3, 2009, Pages 273~292
According to historical commentators such as Newton and Einstein, bodily behaviors are causally explained by the geometrical structure of space-time whose existence analogous to that of material substance. This essay challenges this conventional wisdom of interpreting space-time geometry within both Newtonian and Einsteinian physics. By tracing recent historical studies on the interpretation of space-time geometry, I defends that space-time structure is a by-product of a more fundamental fact, the laws of motion. From this perspective, I will argue that the causal properties of space-time cannot provide an adequate account of the theory-change from Newtoninan to Einsteinian physics.