• 한국전자거래학회지
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• 제6권2호
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• pp.167-178
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• 2001

Key is generally formed using the Random Number. How to make the Random Number is to cast coin or dice as classical method, to form the Real Random Number with Hardware and to make the Pseudo Random Number by means of utilizing mathematical algorithm. This thesis presented NRNG(New Random Number Generator) which put self-development Hardware to use as Key Generation Method and inspected to compare the Real Random Number with the Pseudo Random Number and special properties which PRNG(Pseudo-Random Number Generator) creates.

• East Asian mathematical journal
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• 제35권1호
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• pp.85-90
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• 2019

In this paper, we are interested in the evaluation of special values of the Dedekind zeta function of a totally real number field. In particular, we revisit Siegel method for values of the zeta function of a totally real number field at negative odd integers and explain how this method is applied to the case of non-normal totally real number field. As one of its applications, we give divisibility property for the values in the special case

• 한국학교수학회논문집
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• 제20권4호
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• pp.495-519
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• 2017

본 연구에서는 실수 e의 다양한 의미와 맥락을 살펴보고, 실수 e에 대한 예비교사들의 이해 정도를 조사하였다. 먼저 실수 e의 역사적 발생과 수학적 의미를 살펴보았으며, 이를 바탕으로 검사지를 개발하여 예비교사 28명에게 적용하고, 그 중 8명에게 반성 및 탐구 활동을 수행하였다. 실수 e에 대한 예비교사들의 이해를 분석한 결과는 다음과 같다. 상당수의 예비교사들이 실수 e의 형식적 정의와 그 표현과의 관계를 인식하지 못하였으며, 실수 e의 표현을 극한 표현에 편중되어 이해하고 있었다. 실수 e의 무리수 속성과 작도 불가능성에 대해서는 대체적으로 적절한 판단을 내렸으나, 그 근거에서는 다소 미흡한 면모를 드러내었다. 또한 실수 e의 연속 복리 맥락과 지수함수 맥락에는 높은 이해도를 나타낸 반면에, 기하적 맥락과 자연로그 맥락을 미흡하게 이해하고 있음을 확인하였다. 향후 예비교사 프로그램의 개선 방향으로, 예비교사들에게 실수 e의 다양한 표현과 속성, 맥락에 대한 학습기회를 제공하고, 실수 e의 다양한 측면이 잘 조직된 관계망 속에서 통합 지도될 필요가 있음을 제시하였다.

• 한국수학사학회지
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• 제18권3호
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• pp.55-66
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• 2005

현재 학교수학에서는 소수를 기초로 무리수와 실수를 지도한다. 이와 관련하여, 이 글에서는 역사적 분석을 통하여 무한소수에 의한 실수와 무리수 정의의 본질을 확인하였다. 역사적으로 실수의 형성은 모든 크기의 수치화, 무리수의 형성은 통약 불가능한 양의 수치화라는 의미를 가지고 있다. 이러한 역사적 분석에 기초하여 실수 개념에의 의미있는 접근을 기대할 수 있는 구체적 지도 방안을 제안하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제39권1호
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• pp.37-47
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• 2000

Number concept is basic in mathematics education. But it is very complex and is not easy to understand real number concept, because of its infinity. This study tried to show that what percents of secondary school mathematics teachers in Korea understood the properties of real number, such as cardinality, continuity, relation with real line, and infinity, which were written by verbal language.

• 충청수학회지
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• 제24권3호
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• pp.595-599
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• 2011

We prove that for any positive integer $g{\geq}3$, there are ${\gg}q^{\frac{l}{2g}}$ real cyclotomic function fields whose conductor has degree ${\leq}l$ and ideal class number is divisible by $\frac{g}{gcd(2,g)}$.

• 대한수학회논문집
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• 제28권4호
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• pp.735-740
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• 2013

In this paper, we will introduce the notion of the real quadratic function fields of minimal type, which is a function field analogue to Kawamoto and Tomita's notion of real quadratic fields of minimal type. As number field cases, we will show that there are exactly 6 real quadratic function fields of class number one that are not of minimal type.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제16권1호
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• pp.72-80
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• 2016

Re-auction happens when a bid winner defaults on the payment without making second in-line purchase declaration even after determining sales permission. This is a process of selling under the court's authority. Re-auctioning contract price of real estate is largely influenced by the real estate business, real estate value, and the number of bidders. This paper is designed to establish a statistical model that deals with the number of bidders participating especially in apartment re-auctioning. For these, diverse factors are taken into consideration, including ratio of minimum sales value from the point of selling to re-auctioning, number of bidders at the time of selling, investment value of the real estate, and so forth. As an attempt to consider ambiguous and vague factors, this paper presents a comparatively vague concept of real estate and bidders as trapezoid fuzzy number. Two different methods based on the least squares estimation are applied to fuzzy regression model in this paper. The first method is the estimating method applying substitution after obtaining the estimators of regression coefficients, and the other method is to estimate directly from the estimating procedure without substitution. These methods are provided in application for re-auction data, and appropriate performance measure is also provided to compare the accuracies.

• 한국수학교육학회지시리즈A:수학교육
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• 제50권2호
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• pp.135-148
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• 2011

We can say that the history of mathematics is the history on the development of the number system. The number starts from Natural number and is constructed to Integer number and Rational number. The Rational number is not the complete number analytically so that Real number is completed by the idea of the nested interval method. Real number is completed analytically, however, is not by algebra, so the algebraically completed type of the rational number, through the way that similar to the process of completing real number, is Complex number. The purpose of this study is to show the most appropriate way for the development of the human being thinking about the teaching and leaning of Complex number. To do this, We have to consider the proof of the existence of Complex number, the background of the introduction of Complex number and the background knowledge that the teachers to teach Complex number should have. Also, this study analyzes the knowledge to be taught of Complex number based on the anthropological theory of didactics and finally presents the teaching method of Complex number based on this theory.

• 대한수학회지
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• 제47권4호
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• pp.861-877
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• 2010

The works of Erd$\ddot{o}$s et al. about expansions of 1 with respect to a non-integer base q, referred to as q-expansions, are investigated to determine how far they continue to hold when the number 1 is replaced by a positive number x. It is found that most results about q-expansions for real numbers greater than or equal to 1 are in somewhat opposite direction to those for real numbers less than or equal to 1. The situation when a real number has a unique q-expansion, and when it has exactly two q-expansions are studied. The smallest base number q yielding a unique q-expansion is determined and a particular sequence is shown, in certain sense, to be the smallest sequence whose corresponding base number q yields exactly two q-expansions.