• 한국수학교육학회지시리즈E:수학교육논문집
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• 제21권4호
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• pp.621-646
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• 2007

컴퓨터의 발전은 수학교육 특히 선형대수학 교수-학습 방법에 큰 개선 가능성을 보여준다. 수학 교육 및 연구용으로 많이 쓰이는 프로그램은 MATHEMATICA, MATLAB, MAPLE, Drive, LINPRAC 등 다양하다. 그 중 MATLAB(MATrix LABoratory)은 행렬 연산 속도가 뛰어나고 계산 수학 특히 수치적 선형대수학 연구와 교육에 잘 맞는 프로그램이다. 본 논문에서는 $R^n$의 부분공간 개념을 중심으로 선형대수학의 주요 개념을 시각적 이해를 통하여 효과적으로 전달하는 교수학습법을 MATLAB를 이용하여 소개한다.

• Nuclear Engineering and Technology
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• 제55권8호
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• pp.2864-2872
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• 2023

The criticality problem in this study is studied with the recently investigated the Anlı-Güngör scattering function. The scattering function depends on the Legendre polynomials as the Mika scattering function, but it includes only one scattering parameter, t, and its orders. Both Mika and Anlı-Güngör scattering are the same for only linear anisotropic scattering. The difference appears for the quadratic scattering and further. The analytical calculations are performed with the H_N method, and the numerical results are calculated with Wolfram Mathematica. Interpolation technique in Mathematica is also used to approximate the isotropic scattering results when t parameter goes to zero. Thus, the calculated results could be compared with the literature data for isotropic scattering.

• 충청수학회지
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• 제15권1호
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• pp.87-94
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• 2002

Trot(1999) considered how to calculate the expected area of a random triangle in the unit square $[0,1]{\times}[0,1]$. He used the Mathematica software package for the computational part. In this article, we study various aspects of the probability distribution of a triangle randomly chosen inside the circle of radius r. A simulation activity that can be conducted in statistics and probability classrooms is also considered.

• 정보보호학회논문지
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• 제7권4호
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• pp.73-80
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• 1997

유한체 위에서 다항식의 근을 구하는 문제는 수학의 오래된 문제중 하나이고 최근들어 암호학과 관련하여 유한체 위서의 다항식 연산과 성질등이 쓰이고 있다. 유한체 위에서 다항식의 최대공약수(greatest common divisor) 를 구하는데 많은 시간이 소요 된다. Rabin의 알고리즘에서 주어진 다항식의 근들의 곱(F(x), $x^{q}$ -x)를 구하는 과정을 c F(p), $f_{c}$ (x)=(F(x), $T_{r}$ (x)-c), de$gf_{c}$ (x)>0인 $f_{c}$(x) s로 대체한 효율적인 알고리즘 제안과 Mathematica를 이용한 프로그램의 실행 결과를 제시한다.

• 충청수학회지
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• 제19권2호
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• pp.133-139
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• 2006

By combining the classical Newton's method with the pseudo-secant method, pseudo-secant-Newton's method is constructed and its order and rate of convergence are investigated. Given a function $f:\mathbb{R}{\rightarrow}\mathbb{R}$ that has a simple real zero ${\alpha}$ and is sufficiently smooth in a small neighborhood of ${\alpha}$, the convergence behavior is analyzed near ${\alpha}$ for pseudo-secant-Newton's method. The order of convergence is shown to be cubic and the rate of convergence is proven to be $\(\frac{f^{{\prime}{\prime}}(\alpha)}{2f^{\prime}(\alpha)}\)^2$. Numerical experiments show the validity of the theory presented here and are confirmed via high-precision programming in Mathematica.

• 충청수학회지
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• 제22권2호
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• pp.217-227
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• 2009

Assuming that a given nonlinear function f : $\mathbf{R}{\rightarrow}\mathbf{R}$ has a zero $\alpha$with integer multiplicity $m{\geq}1$ and is sufficiently smooth in a small neighborhood of $\alpha$, we define extended leap-frogging Newton's method. We investigate the order of convergence and the asymptotic error constant of the proposed method as a function of multiplicity m. Numerical experiments for various test functions show a satisfactory agreement with the theory presented in this paper and are throughly verified via Mathematica programming with its high-precision computability.

• 충청수학회지
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• 제20권1호
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• pp.11-21
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• 2007

Given a nonlinear function f : $\mathbb{R}{\rightarrow}\mathbb{R}$ that has a simple real zero ${\alpha}$, a new numerical method to be called k-fold pseudo- Halley's method is proposed and it's error analysis is under investigation to confirm the convergence behavior near ${\alpha}$. Under the assumption that f is sufficiently smooth in a small neighborhood of ${\alpha}$, the order of convergence is found to be at least k+3. In addition, the corresponding asymptotic error constant is explicitly expressed in terms of k, ${\alpha}$ and f as well as the derivatives of f. A zero-finding algorithm is written and has been successfully implemented for numerous examples with Mathematica.

• Nuclear Engineering and Technology
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• 제49권6호
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• pp.1301-1309
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• 2017

The extinction probability of a branching process (a neutron chain in a multiplying medium) is calculated for a system randomly varying in time. The evolution of the first two moments of such a process was calculated previously by the authors in a system randomly shifting between two states of different multiplication properties. The same model is used here for the investigation of the extinction probability. It is seen that the determination of the extinction probability is significantly more complicated than that of the moments, and it can only be achieved by pure numerical methods. The numerical results indicate that for systems fluctuating between two subcritical or two supercritical states, the extinction probability behaves as expected, but for systems fluctuating between a supercritical and a subcritical state, there is a crucial and unexpected deviation from the predicted behaviour. The results bear some significance not only for neutron chains in a multiplying medium, but also for the evolution of biological populations in a time-varying environment.