• Management Science and Financial Engineering
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• 제17권2호
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• pp.63-84
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• 2011

The ordinary multiple criteria decision making (MCDM) approach requires two types of input, alternative values and criterion weights, and employs two schemes of alternative prioritization, dominance and potential optimality. This paper allows for incomplete information on both types of input and gives rise to the dominance relationships and potential optimality of alternatives. Unlike the earlier studies, we emphasize that incomplete information frequently takes the form of strict inequalities, such as strict orders and strict bounds, rather than weak inequalities. Then the issues of rising importance include: (1) The standard mathematical programming approach to prioritize alternatives cannot be used directly, because the feasible region for the permissible decision parameters becomes an open set. (2) We show that the earlier methods replacing the strict inequalities with weak ones, by employing a small positive number or zeroes, which closes the feasible set, may cause a serious problem and yield unacceptable prioritization results. Therefore, we address these important issues and develop a useful and simple method, without selecting any small value for the strict preference information. Given strict information on both types of decision parameters, we first construct a nonlinear program, transform it into a linear programming equivalent, and finally solve it via a two-stage method. An application is also demonstrated herein.

• 한국수학교육학회지시리즈A:수학교육
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• 제59권3호
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• pp.217-235
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• 2020

본 연구는 TIMSS 2011와 2015 수학 성취도 평가를 바탕으로 초등학교 4학년 남녀 간의 성차가 드러나는 문항들을 내용과 인지영역에 따라 분석하였다. 연구결과, 성차가 유의미하게 차이나는 20% 문항들에서 내용 영역별 성차를 보면 남학생은 수와 측정영역에서 여학생은 도형영역에서 상대적으로 우위에 있는 것으로 나타났다. 또한 인지 영역별 성차를 보면, 남학생이 지식, 적용, 추론 영역에서 여학생보다 상대적인 우위에 있는 것으로 드러났다.

• 대한수학회보
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• 제59권3호
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• pp.529-545
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• 2022

This article concerns a ring property that arises from combining one-sided duo factor rings and centers. A ring R is called right CIFD if R/I is right duo by some proper ideal I of R such that I is contained in the center of R. We first see that this property is seated between right duo and right π-duo, and not left-right symmetric. We prove, for a right CIFD ring R, that W(R) coincides with the set of all nilpotent elements of R; that R/P is a right duo domain for every minimal prime ideal P of R; that R/W(R) is strongly right bounded; and that every prime ideal of R is maximal if and only if R/W(R) is strongly regular, where W(R) is the Wedderburn radical of R. It is also proved that a ring R is commutative if and only if D₃(R) is right CIFD, where D₃(R) is the ring of 3 by 3 upper triangular matrices over R whose diagonals are equal. Furthermore, we show that the right CIFD property does not pass to polynomial rings, and that the polynomial ring over a ring R is right CIFD if and only if R/I is commutative by a proper ideal I of R contained in the center of R.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제37권1호
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• pp.65-84
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• 2023

라그랑주 승수법(Method of Lagrange Multipliers)은 등식 제약조건하에서 미분가능한 함수의 최대, 최소를 구하는 대표적인 방법이다. 선형대수학, 최적화 이론, 제어 이론을 포함하여 최근에는 인공지능 기초수학에서도 널리 활용되고 있다. 특히 라그랑주 승수법은 미분적분학과 선형대수학을 연결하는 중요한 도구이며, 주성분 분석(Principal Component Analysis, PCA)을 포함한 인공지능 알고리즘에 많이 활용되고 있다. 따라서 교수자는 대학 미분적분학에서 처음 라그랑주 승수법을 접하는 학생들에게 구체적인 학습 동기를 제공할 필요가 생겼다. 이에 본 논문에서는 교수자가 학생들에게 라그랑주 승수법을 효과적으로 교육하는데 필요한 통합적인 시야를 제공한다. 먼저 다양한 전공의 학생들이 계산에 대한 부담을 덜고 원리를 쉽게 이해할 수 있도록 개발한 시각화 자료 및 파이썬(Python) 기반의 SageMath 코드를 제공한다. 또한 라그랑주 승수법으로 행렬의 고윳값과 고유벡터를 유도하는 과정을 상세히 소개한다. 그리고 라그랑주 승수법을 간단한 경우에 대한 증명에서 시작하여 일반화된 최적화 문제로 확장하고, 수업에서 학생들이 라그랑주 승수와 PCA를 활용하여 실제 데이터를 분석한 결과를 추가하였다. 본 연구는 대학수학을 지도하는 다양한 전공의 교수자들에게 도움이 될 기초자료가 될 것이다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권1호
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• pp.476-496
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• 2018

With the advancement and deployment of wireless communication techniques, wireless body area network (WBAN) has emerged as a promising approach for e-healthcare that collects the data of vital body parameters and movements for sensing and communicating wearable or implantable healthful related information. In order to avoid any possible rancorous attacks and resource abuse, employing lightweight ciphers is most effective to implement encryption, decryption, message authentication and digital signature for security of WBAN. As a typical lightweight cryptosystem with an extended sponge function framework, the PHOTON family is flexible to provide security for the RFID and other highly-constrained devices. In this paper, we propose a differential fault analysis to break three flavors of the PHOTON family successfully. The mathematical analysis and simulating experimental results show that 33, 69 and 86 random faults in average are required to recover each message input for PHOTON-80/20/16, PHOTON-160/36/36 and PHOTON-224/32/32, respectively. It is the first result of breaking PHOTON with the differential fault analysis. It provides a new reference for the security analysis of the same structure of the lightweight hash functions in the WBAN.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제29권3호
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• pp.465-489
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• 2015

본 연구는 중등수학 강의교재를 대상으로 네트워크 텍스트 분석을 실시하여 향후 수학영재 교재개발 및 수정에 대한 시사점을 제안하였다. 분석대상은 2002년부터 2014년까지 한 대학부설 과학영재교육원에서 사용한 110개의 강의교재에 제시되어 있는 학습목표를 활용하였다. 주제어 빈도 분석은 KrKwic, 행렬화 작업은 KrTitle, 사회 네트워크 분석은 NetMiner4.0 프로그램을 활용하였으며, 네트워크의 기본정보, 중심성, 중앙성, 컴포넌트, 그리고 k-코어 분석을 수행하였다. 구체적인 연구결과는 다음과 같다. 첫째, 전체 주제어 네트워크에는 '다양성', '이해', '개념', '방법', '적용', '연결성', '문제해결', '기본', '실생활', 그리고 '사고력' 등을 포함하는 핵심 주제어 네트워크가 형성되어 있으며, 중심성 분석 결과 지식 측면이 강의교재에 잘 반영되어 있는 것으로 나타났다. 둘째, 영재교육진흥종합계획 시기별로 주제어 네트워크를 분석한 결과, 시기에 상관없이 '이해'를 중심으로 네트워크가 구성되고, '문제', '해결', 그리고 '문제해결' 사이의 연결강도가 높게 나타났다. 반면에 중앙성 분석 결과 제1차 영재교육진흥종합계획 시기에는 '의사소통', 제2차 시기에는 '발견', 그리고 제3차 시기에는 '증명'만이 나타났다 사라지는 특성을 보였다. 이러한 연구결과를 바탕으로 강의교재에 정의적 측면과 복잡한 인지과정 차원을 수반하는 활동이 포함되어져야 하며, 학습목표의 타성화와 무역사성이 발생하지 않도록 할 것을 제안하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제59권4호
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• pp.357-371
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• 2020

2015 개정 수학과 교육과정에서 교과 역량이 '기능'과 '성취기준'으로 구체화되어 제시됨에 따라, 본 연구에서는 2015 개정 초등학교 수학과 교육과정에서 역량, 기능, 성취기준의 연계 양상을 분석하였다. 연구 결과, 여섯 가지의 수학과 역량은 '기능'으로 고르게 제시되었으나, '기능' 중 일부는 성취기준으로 제시되지 않았으며, '이해하기'와 같은 기능에 치중되는 것으로 나타났다. 연구 결과를 토대로 차기 수학과 교육과정의 역량 구현을 개선하기 위한 몇 가지의 시사점을 도출하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제55권3호
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• pp.357-382
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• 2016

The purpose of this study was to report the effects of self-directed and self-regulated learning programs on elementary, middle, and high school students through meta-analysis of previous studies. For this research, 22 of previous studies were selected which were all conducted in the country, and calculated the effect size of 'standardized change of the mean difference' for many factors included in each research. The findings were as follows: first, the overall effect sizes of self-directed and self-regulated learning programs on elementary, middle, and high school students were .665 and .702 in the affective and cognitive domain, respectively, meaning that the self-directed and self-regulated learning programs had average or greater effects on elementary, middle, and high school students and exerted somewhat greater effects in the cognitive domain. Second, when the areas of moderating effects were divided into self-directed and self-regulated learning, the former and latter had more influences on the cognitive and affective domains, respectively. Third, the elementary school level recorded a larger effect size both in the affective and cognitive domains than the secondary school level. Fourth, the findings show that the characteristics of affective domain, "reflective thinking" and "self-confidence," recorded a very large effect size both at the elementary and secondary school levels. Finally, the programs were more effective when the application period was one to four weeks in the affective domain and more than four weeks in the cognitive domain. And, Significance and implications of this research were discussed.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권2호
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• pp.191-204
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• 2006

Computer technology has a potential to change the contents of school mathematics and the way of teaching mathematics. But in our country, the problem whether computer technology should be introduced into mathematics classroom or not was not resolved yet. As a tool, computer technology can be used by teachers who are confident of the effectiveness and who can use it skillfully and can help students to understand mathematics. The purpose of this study was to investigate the effective way to introduce and utilize computer technology based on the status quo of mathematics classroom setting. One possible way to utilize computer technology in mathematics classroom in spite of the lack of computer and the inaccessibility of useful software is using domain specific simulation software like 'Polyhedron'. 'Polyhedron', as we can guess from the name, can be used to explore regular and semi regular polyhedra and the relationship between them. Its functions are limited but it can visualize regular polyhedra, transform regular polyhedra into other polyhedra. So it is easier to operate than other dynamic geometry software like GSP. To investigate the effect of using this software in mathematics class, three classes(one in 6th grade from science education institute for the gifted, two in 7th grade) were chosen. Activities focused on the relationship between regular and semi regular polyhedra. After the class, several conclusions were drawn from the observation. First, 'Polyhedron' can be used effectively to explore the relationship between regular and semi regular polyhedra. Second, 'Polyhedron' can motivate students. Third, Students can understand the duality of polyhedra. Fourth, Students can visualize various polyhedra by reasoning. To help teachers in using technology, web sites like NCTM's illuminations and NLVM of Utah university need to be developed.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제11권4호
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• pp.247-263
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• 2007

Problem solving takes place not only in mathematics classes but also in real-world. For this reason, a problem and the structure of problem solving, and the enhancing of success in problem solving is a subject which has been studied by any educators. In this direction, the aim of this study is that the strategy used by students in Turkey when solving oral problems and their achievements of choosing operations when solving oral problems has been researched. In the research, the students have been asked three types of questions made up groups of 5. In the first category, S-problems (standard problems not requiring to determine any strategy but can be easily solved with only the applications of arithmetical operations), in the second category, AS-SA problems (problems that can be solved with the key word of additive operation despite to its being a subtractive operation, and containing the key word of subtractive operation despite to its being an additive operation), and in the third category P-problems (problematic problem) take place. It is seen that students did not have so much difficulty in S-problems, mistakes were made in determining operations for problem solving because of memorizing certain essential concepts, and the succession rate of students is very low in P-problems. The reasons of these mistakes as a summary are given below: $\cdot$ Because of memorizing some certain key concepts about operations mistakes have been done in choosing operations. $\cdot$ Not giving place to problems which has no solution and with incomplete information in mathematics. $\cdot$ Thinking of students that every problem has a solution since they don't encounter every type of problems in mathematics classes and course books.