• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.89-98
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• 1995

This paper presents the interesting properties of a certain patterned matrix that plays an significant role in the multi-way balanced designs. The necessary and sufficient condition on the existence of the inverse of the patterned matrix and its determinant are described. In special cases of the pattermed matrix, explicit formulas for its inverse, determinant and the characteristic equation are obtained.

• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.30-35
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• 2013

Motivated by the emergency scheduling in a transportation network, this paper considers a transportation problem, in which, the truck times and transportation costs are assumed as uncertain variables. To meet the demand in the practical applications, two optimization objectives are considered, one is the total costs and another is the completion times. And then, a multi-objective optimization model is developed according to the situation in applications. Because there are commensurability and conflicting between the two objectives commonly, a solution does not necessarily exist that is best with respective to the two objectives. Therefore, the problem is reduced to a single objective model, which is an uncertain programming with a chance-constrain. After some analysis, its equivalent deterministic form is obtained, which is a nonlinear programming. Based on a stepwise optimization strategy, a solution method is developed to solve the problem. Finally, the computational results are provided to demonstrate the effectiveness of our model and algorithm.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.307-320
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• 2001

Traditionally, there are many inherent restrictions in highschool mathematics textbooks. They are restricted in its contents and inevitably resorted to reader's ability of intuition. So they are usually lacked logical precisions and have various differences in expressions. We are mainly concerned with the definite integral and its applications in current highschool mathematics II textbooks according to 6th curriculum. We choose 6 of them arbitrarily and survey by comparison to deduce some controversial topics among them as follows. 1) absurd metaphors in formula process 2) confusions in important notations and too much choices in terms and statements. 3) lack of precisions in - teaching hierarchy (between some contents of Physics and the applications of definite integral) - introducing a proof of theorem (fundamental theorem of Calculus I) - introducing the methods (integral substitutions 1, ll) 4) adopting small topics such as - mean value theorem of integral - integrals with variable limits. In coming 7th curriculum, highschool students in Korea are supposed to choose calculus as a whole, independent course. So we hope that the suggested controversial topics are to be referred by authors to improve the preceding Mathematics ll textbooks and for teachers to use them for better mathematics education.

• East Asian mathematical journal
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• v.13 no.1
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• pp.99-108
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• 1997

• Korean Journal of Mathematics
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• v.3 no.1
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• pp.135-142
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• 1995

• Communications of Mathematical Education
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• v.34 no.4
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• pp.545-561
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• 2020

The purpose of this study is to investigate the applications and possibilities of major programs that provide services using artificial intelligence in mathematics education. For this study, related papers, reports, and materials were collected and analyzed, focusing on materials mostly published within the last five years. The researcher searched the keywords of "artificial intelligence", "artificial intelligence", "AI" and "mathematics education" independently or in combination. As a result of the study, artificial intelligence for mathematics education was mostly supporting learners' personalized mathematics learning, defining it as an auxiliary role to support human mathematics teachers, and upgrading the technology of not only cognitive aspects but also affective aspects. As suggestions, the researcher argued that followings are necessary: Research for the establishment of an elaborate artificial intelligence mathematical system, discovery of artificial intelligence technology for appropriate use to support mathematics education, development of high quality of mathematics contents for artificial intelligence, and the establishment and operation of a cloud-based comprehensive system for mathematics education. The researcher proposed that continuous research to effectively help students study mathematics using artificial intelligence including students' emotional or empathetic abilities, and collaborative learning, which is only possible in offline environments. Also, the researcher suggested that more sophisticated materials should be developed for designing mathematics teaching and learning by using artificial intelligence.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.191-197
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• 1996

The purpose of this paper is to prove a new topological existence theorem by using the connectness property, and some applications are also given.

• School Mathematics
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• v.1 no.1
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• pp.157-185
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• 1999

Maple is introduced for school mathematics. Many applications of Maple to school mathematics are given in order for teachers to have ideas how to use it. Effects of computer softwares including Maple are also discussed. Some points which teachers have to consider are listed when they use softwares in school mathematics.

• East Asian mathematical journal
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• v.19 no.2
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• pp.221-232
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• 2003

An identity for n-time differentiable functions of a real variable in terms of multiple integrals and applications for Ostrowski type inequalities are given.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.117-136
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• 2001

A generalization of Ostrowski integral inequality for mappings whose derivatives are bounded and applications for general quadrature formulae are given.