• 대한수학교육학회지:수학교육학연구
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• 제12권4호
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• pp.557-579
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• 2002

The purpose of this study is to find out the problems which are caused when the limit concept of sequences is learned through an intuitive definition and to suggest a way of solving those problems. Students in Korea study the limit concept of sequences through an intuitive definition. They fail to apply the intuitive definition properly to the problems and they are apt to have misconception even though the Intuitive definition is applied properly. To solve these problems, this study examined the develop- mental process of the limit concept of sequences from the Intuitive definition to the formal definition, and looked into the way of students' internalization of the process through a field study. In this study, the levels of the limit concept of sequences possessed by the students at ZPD are as follows; level 0 : Students understand the limit concept of sequences through the intuitive definition. level 1 : Students understand the limit concept of sequences as 'The difference between $\alpha$$_{n}$ and $\alpha$ approaches 0' rather than 'The sequence approaches $\alpha$ infinitely.' level 2 : Students understand the limit concept of sequences through the formal definition. The levels of students' limit concept development were analysed by those criteria. Almost of the students who studied the limit concept of sequences through the intuitive defition stayed at level 0, whereas almost of the students who studied through the formal definition stayed at level 1. Through the study, I found that it was difficult for the students to develop the higher level of understanding for themselves but the teachers and peers could help the students to progress to the higher level. Students' learning ability was one of major factors that make the students progress to the higher level of understanding as the concept was developed hierarchically from Level 0 to Level 2. If you want to see your students get to the higher level of understanding in the limit concept, you need to facilitate them to fully develop understanding in lower levels through enough experiences so that they can be promoted to the highest level.

• 호남수학학술지
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• 제16권1호
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• pp.111-117
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• 1994

In this note we prove a functional central. limit theorem for LPQD sequences, statisfying some moment conditions. No stationarity is required. Our results imply an extension of Birkel's functional central limit theorem for associated processt'S to an LPQD sequence and an improvement of Birkel's functional central limit theorem for LPQD sequences.

• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.219-224
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• 1995

A central limit theorem with random indices is obtained for stattionary martingale difference sequences.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.541-552
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• 2023

In 2005, Patterson studied lacunary statistical convergence of double sequences of real numbers and, in 2009, Mursaleen introduced notion of lacunary statistical convergence of single sequences in intuitionistic fuzzy normed space. The current work intends to investigate the lacunary statistical convergence of double sequences and some significant conclusions on the algebra of the lacunary statistical limit of double sequences in intuitionistic fuzzy normed space. In addition, we have studied some examples to support the definitions.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.1017-1025
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• 2011

In this paper, we survey various notions and results related to statistical convergence of a sequence of fuzzy numbers, in which statistical convergence for fuzzy numbers was first introduced by Nuray and Savas in 1995. We will go over boundedness, convergence of sequences of fuzzy numbers, statistically convergence and statistically Cauchy sequences of fuzzy numbers, statistical limit and cluster point for sequences of fuzzy numbers, statistical mono-tonicity and boundedness of a sequence of fuzzy numbers and finally statistical limit inferior and limit inferior for the statistically bounded sequences of fuzzy numbers.

• 대한수학회논문집
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• 제10권4호
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• pp.963-974
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• 1995

We formulate central limit theorems for non-linear functionals of stationary Gaussian vector processes with long-range dependence.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제26권2호
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• pp.205-220
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• 2012

이 연구에서는 수렴하는 자연 수 수열의 사례를 구성하는 것을 목표로 특별한 패턴의 자연수 수열을 찾아 연구하였다. 자연수 수열의 수렴과 관련하여 다음 두 가지를 조사 분석하였다. 첫째, 극한에 대한 일상의 언어지만 수학적 의미를 내포한 고등학교 직관적 정의를 자연수 수열의 수렴성에 대한 이해의 토대가 되는 상수 수열을 포함한 기본적인 수열들에 어떻게 적용하는지를 수학교육전공의 대학생을 중심으로 살펴보았다. 둘째, 자명하지 않으며 특수한 패턴을 가진 수렴하는 자연수 수열의 사례로 전자항의 각 자릿수의 제곱의 합이 후자항을 결정하는 자연수 수열들에서 찾았다. 이 수열들의 탐구를 위해 꼬리의 개념을 사용하였고, 지필의 환경에서 이 수열들의 극한과 관련된 속성들이 쉽게 관찰되지 않아 원활한 탐색을 위해 스프레드시트를 활용하였다. 여기서 스프레드시트는 실험과 관찰을 도모하고 수학적 패턴의 발견을 도울 뿐 아니라 추론과 증명을 뒷받침하는 자료 추출의 도구가 될 수 있다는 시사점올 준다.

• Journal of the Korean Statistical Society
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• 제24권1호
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• pp.249-256
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• 1995

In this note we prove an invariance principle for strictly stationary linear positive quadrant dependent sequences, satifying some assumption on the covariance structure, $0 < \sum Cov(X_1,X_j) < \infty$. This result is an extension of Burton, Dabrowski and Dehlings' invariance principle for weakly associated sequences to LPQD sequences as well as an improvement of Newman's central limit theorem for LPQD sequences.

• 호남수학학술지
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• 제43권1호
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• pp.47-58
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• 2021

In this paper, we introduce rough statistical convergence of difference double sequences in normed linear spaces as an extension of rough convergence. We define the set of rough statistical limit points of a difference double sequence and analyze the results with proofs.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.417-425
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• 2008

For stationary m-dimensional martingale difference sequences we prove the random functional central limit theorems and propose an almost sure consistent estimator for the limiting covariance matrix.