• Journal of the Korea Society for Simulation
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• v.5 no.2
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• pp.85-93
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• 1996

Simulation is commonly used to find the best values of decision variables for problems which defy analytical solutions. This objective is similar to that of optimization problems and thus, mathematical programming techniques may be applied to simulation. However, the application of mathematical programming techniques, e.g., the gradient methods, to simulation is compounded by the random nature of simulation responses and by the complexity of the statistical issues involved. In this paper, therefore, we explain the Reverse-Simulation method to optimize a simulation model in a single simulation run. First, we point the problem of the previous Reverse-Simulation method. Secondly, we propose the new algorithm to solve the previous method and show the efficiency of the proposed algorithm.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.565-570
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• 1994

In this article we prove a version of the Perron-Frobenius Theorem in linear algebra using the Brouwer's Fixed Point Theorem in topology. We will mostly concentrate on he qualitative aspect of the Perron-Frobenius Theorem rather than quantitative formulas, which would be enough for theoretical investigations in ergodic theory. By the nature of the method of the proof, we do not expect to obtain a numerical estimate. But we may regard it worthwhile to see why a certain type of result should be true from a topological and geometrical viewpoint. However, a geometric argument alone would give us a sharp numerical bounds on the size of the eigenvalue as shown in Section 2. Eigenvectors of a matrix A will be fixed points of a certain mapping defined in terms of A. We shall modify an existing proof of Frobenius Theorem and that will do the trick for Perron-Frobenius Theorem.

• Journal of the Korean Mathematical Society
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• v.33 no.1
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• pp.25-29
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• 1996

The Debreu-Gale-Nikaido theorem [2] is a potential tool to prove the existence of a market equilibrium price. Walras' law is of a quantitative nature (i.e. it measures the value of the total excess demand), and it is interesting to note that the existence result holds true under some qualitative assumptions. In fact, the Debreu-Gale-Nikaido theorem states that the continuity of the excess demand function and Walras' law has the following implication : For some price and corresponding value of the excess demand function, it is not possible to respond with a new price system such that the value at the new price of every element in the value of the demand function associated with the old price system is strictly positive.

• East Asian mathematical journal
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• v.34 no.2
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• pp.191-201
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• 2018

The character education has been regarded as important in nature and purpose of mathematics education. A discussion about models for the teaching of character to a student has been. However, The character education of teachers has not gathered as much attention as that of students in mathematics education. How to educate morally and ethically sound mathematics teachers is an important research topic to be sincerely inquired in current. Little attention has been given to the way how we prepare a morally humane pre-mathematics teacher. This paper inquires into the issues of character education in pre-mathematics teacher education.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1353-1362
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• 2016

Using the notion of complete nonabelian exterior square $G\hat{\wedge}G$ of a pro-p-group G (p prime), we develop the theory of the exterior degree $\hat{d}(G)$ in the infinite case, focusing on its relations with the probability of commuting pairs d(G). Among the main results of this paper, we describe upper and lower bounds for $\hat{d}(G)$ with respect to d(G). Here the size of the second homology group $H_2(G,\mathbb{Z}_p)$ (over the p-adic integers $\mathbb{Z}_p$) plays a fundamental role. A further result of homological nature is placed at the end, in order to emphasize the influence of $H_2(G,\mathbb{Z}_p)$ both on G and $\hat{d}(G)$.

• Research in Mathematical Education
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• v.3 no.1
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• pp.1-8
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• 1999

The present study extends previous research in this area by investigating perceptions of change and reactions to reform efforts by pre-service and practicing secondary school mathematics teachers in the People's Republic of China (PRC) and the United States of America. Interviews were used to gather data about school experiences, teaching practices, and planned changes in mathematics programs. Analysis of the interview data supported earlier findings with respect to the well-planned nature of lessons by PRC teachers and the influence of mathematics contents and examination systems in the PRC. Findings also indicated a general agreement among teachers from both countries favoring less lecturing and more discussion and interactive activities. There were contrasts by nationality in descriptions of future teaching, ideal lessons, sources of teaching ideas, and preferences about school mathematics programs.

• The Mathematical Education
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• v.47 no.3
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• pp.353-371
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• 2008

This study contains three themes as follows concerning the state of mathematics education and the textbooks in east and west germany before unification and in unified germany. The first subject is the investigations of the organization of the school systems and of the syllabus of mathematics in east germany in those days. Second, we analyzed the process of preparation for integration before unification, the nature of integration policies and the convention for the unification. Finally, we compare and analyze the similarities and differences in east and west german mathematics textbooks for middle school students combining those in south and north Korea, and further we suggest tasks to be studied in future research.

• Journal for History of Mathematics
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• v.14 no.1
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• pp.47-60
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• 2001

The present study develops the given theme “Mathematics and Reality” along two lines. First, we explore the answers, in its various facets, to the following question: How is it possible that mathematics shows such wondrous efficiency when explaining nature\ulcorner In addition to a comparative analysis between empiricism and rationalism, constructivism as a function of idealism is compared with realism within the frame provided by rationalism. The second step involves limiting our discussion to realism. We attempt to explain the various stages of mathematical realism and their points of difficulty. Postulate of parallels, Godel's theorem, continuum hypothesis and choice axiom are typical examples used in demonstrating undecidable propositions. They clearly show that it is necessary to mitigate the mathematical realism which depends on bivalent logic based on an objective exterior world. Lowenheim-Skolem theorem, which states that reality is composed not of one block but rather of diverse domains, also reinforces this line of thought. As we can see the existence of undecidable propositions requires limiting the use of reductio ad absurdum proof which depends on the concept of excluded middle. Consequently, it becomes obvious that bivalent logic must inevitably cede to a trivalent logic since there are three values involved: true, false, and undecidable.

• East Asian mathematical journal
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• v.31 no.2
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• pp.189-210
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• 2015

Character means a person's nature and the mind and behavior to lead a desirable life personally and socially. Also character can be changed with education and environment. Therefore character education will be possible to do practice through various educational activities and life experiences in school. In other words, we think that students will get person's character required to lead a desirable life personally and socially beyond what they just learn knowledge and skill, enter the higher schools and succeed one's way. This study accepts merits of existing character education policy through subject(mathematics) education and focus on direction for character education through subject(mathematics) education for systematic and synthetic approach for practice of character education. For this, we will see applicability of the plan for character education in the whole subject education, in particular focusing on cases of character education in mathematics subject.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.61-71
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• 2017

In the present paper, we further study the generalized fractional differintegral (integral and differential) operators involving Appell's function $F_3$ introduced by Saigo-Maeda [9], and are applied to the K-Series defined by Gehlot and Ram [3]. On account of the general nature of our main results, a large number of results obtained earlier by several authors such as Ram et al. [7], Saxena et al. [14], Saxena and Saigo [15] and many more follow as special cases.