• Title, Summary, Keyword: 대수적 방법

### A Study on Solving Triangle Construction Problems Related with Radius of Escribed Circle Using Algebraic Method (대수적 방법을 이용한 방접원에 관련된 삼각형 작도문제의 해결 연구)

• Gong, Seon-Hye;Han, In-Ki
• Journal of the Korean School Mathematics Society
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• v.11 no.3
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• pp.399-420
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• 2008
• In this paper we solve various triangle construction problems related with radius of escribed circle using algebraic method. We describe essentials and meaning of algebraic method solving construction problems. And we search relation between triangle construction problems, draw out 3 base problems, and make hierarchy of solved triangle construction problems. These construction problems will be used for creative mathematical investigation in gifted education.

### A Study on Approaches to Algebra Focusing on Patterns and Generalization (패턴과 일반화를 강조한 대수 접근법 고찰)

• 김성준
• School Mathematics
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• v.5 no.3
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• pp.343-360
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• 2003
• In this paper, we deal with the teaching of algebra based on patterns and generalization. The past algebra curriculum starts with letters(variables), algebraic expressions, and equations, but these formal approaching method has many difficulties in the school algebra. Therefore we insist the new algebraic approaches should be needed. In order to develop these instructions, we firstly investigate the relationship of patterns and algebra, the relationship of generalization and algebra, the steps of generalization from patterns and levels of difficulties. Next we look into the algebra instructions based arithmetic patterns, visual patterns and functional situations. We expect that these approaches help students learn algebra when they begin school algebra.

### Algebraic Reasoning Abilities of Elementary School Students and Early Algebra Instruction(1) (초등학생의 대수 추론 능력과 조기 대수(Early Algebra) 지도(1))

• Lee, Hwa Young;Chang, Kyung Yoon
• School Mathematics
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• v.14 no.4
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• pp.445-468
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• 2012
• This study is tried in order to link informal arithmetic reasoning to formal algebraic reasoning. In this study, we investigated elementary school student's non-formal algebraic reasoning used in algebraic problem solving. The result of we investigated algebraic reasoning of 839 students from grade 1 to 6 in two schools, Korea, we could recognize that they used various arithmetic reasoning and pre-formal algebraic reasoning which is the other than that is proposed in the text book in word problem solving related to the linear systems of equation. Reasoning strategies were diverse depending on structure of meaning and operational of problems. And we analyzed the cause of failure of reasoning in algebraic problem solving. Especially, 'quantitative reasoning', 'proportional reasoning' are turned into 'non-formal method of substitution' and 'non-formal method of addition and subtraction'. We discussed possibilities that we are able to connect these pre-formal algebraic reasoning to formal algebraic reasoning.

### A study on Algebraic Approach Method for Model Reduction Via BPF (블럭펄스함수를 이용한 모델축소의 대수적 접근방법에 관한 연구)

• Cho, Young-Ho;Shim, Jae-Sun;Min, Gyeong-Seol;Lim, Yun-Sic
• Proceedings of the KIEE Conference
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• pp.2176-2178
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• 2004
• 본 논문은 고차 시스템의 응답에 가장 최적한 응답을 갖는 저차 시스템의 응답을 갖도록 최적응답 방법에 블럭펄스 함수를 적용하여 대수적인 방법으로 저차 시스템의 파라메터를 구하는 알고리즘을 제시하였다.

### Mathematical Connections Between Classical Euclidean Geometry and Vector Geometry from the Viewpoint of Teacher's Subject-Matter Knowledge (교과지식으로서의 유클리드 기하와 벡터기하의 연결성)

• Lee, Ji-Hyun;Hong, Gap-Ju
• School Mathematics
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• v.10 no.4
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• pp.573-581
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• 2008
• School geometry takes various approaches such as deductive, analytic, and vector methods. Especially, the mathematical connections between these methods are closely related to the mathematical connections between geometry and algebra. This article analysed the geometric consequences of vector algebra from the viewpoint of teacher's subject-matter knowledge and investigated the connections between the geometric proof and the algebraic proof with vector and inner product.

### Determination of Aqnifer Characteristics from Specific Capacity Data of Wells in Cheju Island (제주도 지하수의 우물 비양수량자료를 이용한 대수층상수 결정방법)

• 최병수
• Journal of the Korean Society of Groundwater Environment
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• v.6 no.4
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• pp.180-187
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• 1999
• Transmissivity is often estimated from specific capacity data because of the expense of conducting standard aquifer test to obtain transmissivity and the relative availability of specific capacity data. Most often, analytic expression relating specific capacity to transmissivity derived by Theis (1963). Brown (1963). and Logan (1964) are used in this analysis. The analytic solution typically used to predict transmissivity from specific capacity in alluvial aquifers assuming influence radius and/or storage coefficient of the aquifers. But those do not agree well with the measured transmissivity in fractured rock aquifers and in heterogeneous aquifers. Razack-Huntely (199l). Huntely-Steffey (1992). and Mace (1997) proposed emphirical rotations between specific capacity and transmissivity in heterogeneous alluvial aquifers. fractured rock aquifers, and karst aquifers. This study focuses on comparison between transmissivity and specific capacity data in volcanic rock aquifers of Jeju Island. Emphirical relation between the log of transmissivity and the log of specific capacity suggests they no linearly related (correlation coefficient 0.951) and the width of $\pm$0.25 log cycles in transmissivity includes 96.6% of data.

### On Numerical Simulation of Salt-Water Wedge in Coastal Aquifer (해안 대수층의 해수침투에 관한 수치적 고찰)

• Lee, Woo-Dong;Hur, Dong-Soo;Jeong, Yeong-Han
• Proceedings of the Korea Water Resources Association Conference
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• pp.82-82
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• 2015
• 해안 대수층은 해수와 담수가 공존하는 지역으로 상대적으로 밀도가 큰 해수가 대수층의 담수 아래에 쐐기형태로 존재하게 된다. 이러한 쐐기형태의 해수와 담수의 경계면은 압력경도의 평형에 의해 경계면이 유지되며, 해수면 또는 지하수위가 변동할 경우 해수-담수 경계면의 균형이 무너짐과 더불어 압력경도의 평행이 이루어질 때 까지 해수-담수 경계면의 이동이 계속 진행된다. 수위 변화의 주요 원인으로는 지구온난화 및 기후변화로 인한 지속적인 해수면 상승과 도서지역의 인구증가 및 산업화로 인한 무분별한 지하수의 사용 등에 의한 지하수위 저하 등을 꼽을 수 있다. 이와 같은 원인으로 해안 및 도서지역에서는 해안 대수층의 해수침투거리가 증가하여 지하수 이용에 큰 어려움을 겪고 있다. 이에 해안 대수층의 해수침투 범위 및 거리를 추정하기 위한 많은 연구들이 다양한 분야에서 지속해서 이루어지고 있지만, 서로 밀도가 다른 해수와 담수가 공존하는 해안 대수층 내의 수리특성을 명확히 파악하기에는 아직까지 미흡한 점들이 많다. 과거에는 Darcy의 법칙 및 Ghyben-Herzberg 식에 근거한 이론적인 연구들이 주로 이루어졌고, 근래에 현장관측이나 수리모형실험이 국내 외적으로 수행되고 있으나, 모든 영역의 지하수의 특성을 조사하는 것이 사실상 불가능하다. 이에 최근에는 컴퓨터 성능의 비약적인 발전과 더불어 다양한 수치해석방법에 의한 수치모델들이 개발되어 시뮬레이션에 적용되고 있다. 하지만 거의 대부분의 수치모델은 해안 대수층 수리특성을 투수계수에 의존하고 있을 뿐, 대수층 내부의 해수-담수에 의한 밀도류의 유동특성을 전혀 고려하지 못한 채 정수압에 근거한 해수-담수 경계면에 대해 모의하고 있는 정도이다. 따라서 본 연구에서는 해안 대수층 내부의 유동현상을 투수계수에 의존하는 방법에서 탈피하여 대수층 매체의 입경, 공극, 형상 등을 고려할 수 있을 뿐만 아니라, 염분 및 온도차에 의한 밀도류를 해석할 수 있는 강비선형 수치모델을 개발하여 해수침투 현상을 직접 모의한다. 나아가 대부분의 이전 연구들에서 간과하고 있는 해안지역의 대표적 물리력인 파랑과 조석의 영향이 해안 대수층의 해수침투에 미치는 영향, 해안 대수층의 지하수위 및 해수면의 수위차에 의한 해수침투 특성 그리고 이를 제어 할 수 있는 새로운 대응기술을 제안하는 것을 목적으로 한다.

### Finding New Algebraic Relations on Some Combiners with Memory And Its Applications (메모리를 가지는 Combiner 모델에 대한 새로운 대수적 방정식 구성 방법과 그 응용)

• Kim, Jaeheon;Han, Jae-Woo;Moon, Dukjae
• Journal of the Korea Institute of Information Security & Cryptology
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• v.16 no.1
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• pp.65-70
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• 2006
• It is hewn that we can apply algebraic attacks on combiners with memory such as summation generators. [1,8] To apply algebraic attacks on combiners with memory, we need to construct algebraic relations between the keystream bits and the initial bits of the LFSRs. Until now, all known methods produce algebraic relations involving several consecutive bits of keystream. [l.4.8] In this paper, we show that algebraic relations involving only one keystream bit can be constructed for summation generators. We also show that there is an algebraic relation involving only one keystream bit for ISG (9) proposed by Lee and Moon. Using this fact, we analyze the keystream generators which generate the keystreams by combining summation generators.

### Maximal Algebraic Degree of the Inverse of Linearized Polynomial (선형 다항식의 역원의 maximal 대수적 차수)

• Lee, Dong-Hoon
• Journal of the Korea Institute of Information Security & Cryptology
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• v.15 no.6
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• pp.105-110
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• 2005
• The linearized polynomial fan be regarded as a generalization of the identity function so that the inverse of the linearized polynomial is a generalization of e inverse function. Since the inverse function has so many good cryptographic properties, the inverse of the linearized polynomial is also a candidate of good Boolean functions. In particular, a construction method of vector resilient functions with high algebraic degree was proposed at Crypto 2001. But the analysis about the algebraic degree of the inverse of the linearized Polynomial. Hence we correct the inexact result and give the exact maximal algebraic degree.

### Characteristics of Algebraic Thinking and its Errors by Mathematically Gifted Students (수학영재의 대수적 사고의 특징과 오류 유형)

• Kim, Kyung Eun;Seo, Hae Ae;Kim, Dong Hwa
• Journal of Gifted/Talented Education
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• v.26 no.1
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• pp.211-230
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• 2016
• The study aimed to investigate the characteristics of algebraic thinking of the mathematically gifted students and search for how to teach algebraic thinking. Research subjects in this study included 93 students who applied for a science gifted education center affiliated with a university in 2015 and previously experienced gifted education. Students' responses on an algebraic item of a creative thinking test in mathematics, which was given as screening process for admission were collected as data. A framework of algebraic thinking factors were extracted from literature review and utilized for data analysis. It was found that students showed difficulty in quantitative reasoning between two quantities and tendency to find solutions regarding equations as problem solving tools. In this process, students tended to concentrate variables on unknown place holders and to had difficulty understanding various meanings of variables. Some of students generated errors about algebraic concepts. In conclusions, it is recommended that functional thinking including such as generalizing and reasoning the relation among changing quantities is extended, procedural as well as structural aspects of algebraic expressions are emphasized, various situations to learn variables are given, and activities constructing variables on their own are strengthened for improving gifted students' learning and teaching algebra.