• 한국수학교육학회지시리즈A:수학교육
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• 제40권1호
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• pp.125-137
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• 2001

We review the mathematics education in Korea just after the 1595 Liberation and the first, second curriculum announced in 1955 and 1963, respectively. The 3rd curriculum announced in 1973 is influenced by “New Mathematics” in America. There were theoretical research about “New Mathematics”, but no experimental research about it in the school. So, there was not much effect of “New Mathematics” in mathematics education. After that we have the 4th, 5th and 6th curriculum which is improved by the result of experience in teaching. The 7th curriculum announced in 1997 emphasized practical mathematics. In this paper, we review the mathematics education and consider some problems in the 7th curriculum. We also consider some problems in mathematics textbook authorization under the 7th curriculum. To solve these problems, we suggest some facts. Especially, we need the philosophy about mathematics education and the enough knowledge about “Mathematics for Mathematics Teachers”.

• East Asian mathematical journal
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• 제40권2호
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• pp.209-229
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• 2024

In this study, we design a teaching unit that constructs Pascal graphs and extended Pascal triangles to explore number patterns inherent in them. This teaching unit is designed to consider the diachronic process of teaching-learning by combining Dörfler's theoretical generalization model with Wittmann's design science ideas, which are applied to the didactical practice of mathematization. In the teaching unit, considering the teaching-learning level of prospective teachers who studied discrete mathematics, we generalize the well-known Pascal triangle and its number patterns to extended Pascal triangles which have directed graphs(called Pascal graphs) as geometric models. In this process, the use of symbols and the introduction of variables are exhibited as important means of generalization. It provides practical experiences of mathematization to prospective teachers by going through various steps of the generalization process targeting symbols. This study reflects Wittmann's intention in that well-understood mathematics and the context of the first type of empirical research as structure-genetic didactical analysis are considered in the design of the learning environment.

• 한국초등수학교육학회지
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• 제11권1호
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• pp.61-80
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• 2007

한국과 일본은 인접국가로서 역사적으로 관계가 깊고, 문화나 교육적 환경이 비슷하다. 이 연구의 목적은 한국과 일본의 초등학교 5, 6학년 수학 교과서를 비교하는 데 있다. 먼저, 남한과 북한, 한국과 인도, 연변의 수학교과서를 비교한 것과 한국과 일본(분수, 평면도형)의 비교연구의 선행연구를 고찰하여 비교의 기준을 마련하였다. 이 기준을 토대로 한국과 일본의 초등학교 수학 교과서의 단원명과 단원체계를 비교하였다. 이어서 양국 5, 6학년 교과서의 영역별 세부내용을 비교하였다.

• Korean Journal of Mathematics
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• 제24권4호
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• pp.737-750
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• 2016

In this note we describe some classes of rings in relation to Abelian property of factorizations by nilradicals and Jacobson radical. The ring theoretical structures are investigated for various sorts of such factor rings which occur in the process.

• Journal of applied mathematics & informatics
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• 제8권1호
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• pp.71-80
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• 2001

The purpose of this paper is to give the classification of homogeneous integral table algebras of degree 5 containing a faithful real element of which 2. In fact, these algebras are classified to exact isomorphism, that is the sets of structure constants which arise from the given basis are completely determined. This is work towards classifying homogeneous integral table algebras of degree 5. AMS Mathematics Subject Classification : 20C05, 20C99.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.567-584
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• 2014

In this paper, we consider approximation of eigenelements of a two dimensional compact integral operator with a smooth kernel by discrete collocation and iterated discrete collocation methods. By choosing numerical quadrature appropriately, we obtain convergence rates for gap between the spectral subspaces, and also we obtain superconvergence rates for eigenvalues and iterated eigenvectors. We then apply Richardson extrapolation to obtain further improved error bounds for the eigenvalues. Numerical examples are presented to illustrate theoretical estimates.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1327-1335
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• 2011

This paper demonstrates that there is a unique exponentially stable equilibrium state of a class of impulsive cellular neural network with delays. The analysis exploits M-matrix theory and generalized comparison principle to derive some easily verifiable sufficient conditions for the global exponential stability of the equilibrium state. The results extend and improve earlier publications. An example with its simulation is given for illustration of theoretical results.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.105-121
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• 2009

In this paper we will be interested in characterizing and computing matrices $X\;{\in}\;C^{n{\times}n}$ that satisfy $e^X$ = A, that is logarithms of A. The study in this work goes through two lines. The first is concerned with a theoretical study of the solution set, S(A), of $e^X$ = A. Along the second line computational approaches are considered to compute the principal logarithm of A, LogA.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.769-784
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• 2013

We consider the modulus-based successive overrelaxation method for the linear complementarity problems from the discretization of Black-Scholes American options model. The $H_+$-matrix property of the system matrix discretized from American option pricing which guarantees the convergence of the proposed method for the linear complementarity problem is analyzed. Numerical experiments confirm the theoretical analysis, and further show that the modulus-based successive overrelaxation method is superior to the classical projected successive overrelaxation method with optimal parameter.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.853-867
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• 2013

In this paper a methodology is developed to solve a nonlinear fractional programming problem, whose objective function and constraints are interval valued functions. Interval valued convex fractional programming problem is studied. This model is transformed to a general convex programming problem and relation between the original problem and the transformed problem is established. These theoretical developments are illustrated through a numerical example.