• Journal for History of Mathematics
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• v.17 no.3
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• pp.61-72
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• 2004

In this paper, we investigate several values of the Nine Chapters on the Mathematical Art on mathematics educational viewpoint. We study them with four points of view: mathematical approach through problems of real life, algorithmization of concept and type, significance of affective domain and application of arithmetic. The result shows that the Nine Chapters on the Mathematical Art have great meaning of today's Korean mathematics education and possibility of application.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.87-100
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• 2004

There is great enthusiasm among many mathematics educators to seek to understand how mathematical history can be employed to emphasize the usefulness of mathematics and to make it even more useful. This study focused on reviewing the history of mathematics to provide a 'source of insight.' In this study, the reasons for including the history of mathematics in the mathematics curriculum were divided into three domains: cognitive, affective, and sociocultural. Each domain included the followings: mathematical thinking and understanding; development of a positive attitude and increase motivation; and last, humanistic facets and sociocultural experience. At the same time, we need to develope a pedagogical approach that allows educators to use history properly. Furthermore, we must integrate the historical topics into regular curricula including the syllabus historically-informed grounds.

• Honam Mathematical Journal
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• v.6 no.1
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• pp.1-12
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• 1984

Let(X, $\Im$) be a probabilistic metric space with a t-norm. Common fixed point theorems and convergence theorems generalizing the results of Ćirić, Fisher, Sehgal, Istrătescu-Săcuiu and others are proved for three mappings P,S,T on X satisfying $F_{Pu, Pv}(qx){\geq}min\left{F_{Su,Tv}(x),F_{Pu,Su}(x),F_{Pv,Tv}(x),F_{Pu,Tv}(2x),F_{Pv,Su}(2x)\right}$ for every $u, v {\in}X$, all x>0 and some $q{\in}(0, 1)$. One of the main results is extended to uniform spaces. Mathematics Subject Classification (1980): 54H25.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.705-717
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• 2013

In this paper, we study the geometry of half lightlike submanifolds M of a semi-Riemannian manifold $\tilde{M}$ with a semi-symmetric non-metric connection subject to the conditions; (1) the characteristic vector field of $\tilde{M}$ is tangent to M, the screen distribution on M is totally umbilical in M and the co-screen distribution on M is conformal Killing, or (2) the screen distribution is integrable and the local lightlike second fundamental form of M is parallel.

• Communications of Mathematical Education
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• v.22 no.2
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• pp.211-227
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• 2008

The method of being composed of small groups has a strong influence on mathematics and cooperative learning and therefore, the group classification should be made in a way of considering not only a learner's cognitive factor but also a affective factor in order to maximize the effects. In this research, we regarded personality as the important standard of the group classification for cooperative learning and tried to find out the influence on the mathematical attitude and achievement in mathematics by means of conducting mathematics and cooperative learning according to the personality types. In order to resolve this problem, we performed the cooperative learning of small group subject to the students at year 6 in an elementary school by making up a similar personality type of group and a different personality type of group through MMTIC examination, and also tried to find out any significant difference in terms of mathematical attitude and achievement in mathematics between two groups. The results obtained in this research are as follows; First, organizing groups in accordance with personality types did not affect on mathematical attitude. Although there were some positive opinions towards mathematics and cooperative learning, the both similar personality type of group and different personality type of group showed no significant difference in terms of mathematical attitude between two groups. Second, organizing groups in accordance with personality types showed positive effects on the achievement in mathematics. The similar personality type of group showed the better achievement in mathematics than the different personality type of group.

• Journal for History of Mathematics
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• v.17 no.2
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• pp.73-84
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• 2004

Stone introduced extremally disconnected spaces as the image of complete Boolean algebras under his famous duality between Bool and ZComp and they turn out to be projective objects in various categories of Hausdorff spaces and completely regular ones are exactly those X with Dedekind complete C(X, ). In the pointfree setting, extremally disconnected frame (= De Morgan frame) are those with De Morgan condition. In this paper, we investigate a historical aspect of De Morgan frame together with that of De Morgan.

• Journal of applied mathematics & informatics
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• v.3 no.1
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• pp.25-34
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• 1996

Many important large-scale linear programs with special structures lead to special computational procedures which are more ef-ficient than the ordinary procedure of the generalized methods. Prob-lems and their solvers taking advantage of multiple updatings of the basis in the dual simplex type method are presented. Computational results run by the efficient algorithm and a presented. Computational results run by the efficient algorithm and a standard code MINOS for the test problems are compared and analyzed. It is shown that the amount of work for the optimal solution for the prblem can be re-duced by the new algorithm.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.1-12
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• 2004

In the Analysis, there have been many cases of confusion on topological structure and uniform structure because they were dealt in metric spaces. The concept of metric spaces is generalized into that of topological spaces but its uniform aspect was much later generalized into the uniform structure by A. Weil. We first investigate Weil's life and his mathematical achievement and then study the history of the uniform structure and its development.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.23-32
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• 2004

In this paper, Ive investigated algebraic concepts which are contained in Euclid's Elements. In the Books II, V, and VII∼X of Elements, there are concepts of quadratic equation, ratio, irrational numbers, and so on. We also analyzed them for mathematical meaning with modem symbols and terms. From this, we can find the essence of the genesis of algebra, and the implications for students' mathematization through the experience of the situation where mathematics was made at first.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.101-122
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• 2004

It has been always the issue to discuss 'how we teach mathematics' for the mathematical learning. As for an answer to this, it was suggested to use the history of mathematics. The reason is simple that is, the education of mathematics requires to understand mathematics and to know the history of mathematics is effective for mathematical understanding. In particular, the history of algebra was discussed to some extent as an illustration. This study focuses on the history of geometry from this point of view. We review the history of geometry by comparison in terms of three criteria from the origin of geometry to modem differential geometry in the middle of the 20th century, which are backgrounds (inner or outer ones), characterizations (approach, method, object), influences to modem mathematics. As an application of such historical data to the education of mathematics, we pose the problem to determine the order of instruction in mathematics.