• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.507-539
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• 2014

The algebra is an important tool influencing on a mathematics in general. To make good use of the algebra, it is necessary to transfer from a given situation to a proper algebraic representation. But some research in related to algebraic word problems have reported the difficulty changing to a proper algebraic representation. Our study have focused on transformation and elaboration of algebraic representation. We investigated in detail the responses and perceptions of 29 Grade 7 students while transforming to algebraic representation, only concentrating on the literature expression form the problematic situations given. Most of students showed difficulties in transforming both descriptive and geometric problems to algebraic representation. 10% of them responded wrong answers except only a problem. Four of them were interviewed individually to show their thinking and find the factor influencing on a positive elaboration. As results, we could find some characteristics of their thinking including the misconception that regard the problem finding a functional formula because there are the variables x and y in the problematic situation. In addition, we could find the their fixation which student have to set up the equation. Furthermore we could check that making student explain own algebraic representation was able to become the factor influencing on a positive elaboration. From these, we also discussed about several didactical implications.

• Communications of Mathematical Education
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• v.28 no.3
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• pp.375-394
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• 2014

The purpose of this study is to examine the transition of mathematical representation in Joseon mathematics, which is focused on numbers and operations, letters and expressions. In Joseon mathematics, there had been two numeral systems, one by chinese character and the other by counting rods. These systems were changed into the decimal notation which used Indian-Arabic numerals in the late 19th century passing the stage of positional notation by Chinese character. The transition of the representation of operation and expressions was analogous to that of representation of numbers. In particular, Joseon mathematics represented the polynomials and equations by denoting the coefficients with counting rods. But the representation of European algebra was introduced in late Joseon Dynasty passing the transitional representation which used Chinese character. In conclusion, Joseon mathematics had the indigenous representation of numbers and mathematical symbols on our own. The transitional representation was found before the acceptance of European mathematical representations.

• Journal for History of Mathematics
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• v.17 no.3
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• pp.23-32
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• 2004

In this paper, Ive investigated algebraic concepts which are contained in Euclid's Elements. In the Books II, V, and VII∼X of Elements, there are concepts of quadratic equation, ratio, irrational numbers, and so on. We also analyzed them for mathematical meaning with modem symbols and terms. From this, we can find the essence of the genesis of algebra, and the implications for students' mathematization through the experience of the situation where mathematics was made at first.

• The Transactions of the Korea Information Processing Society
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• v.3 no.3
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• pp.672-682
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• 1996

In this paper, we propose an algorithm to transform an object calculus into an object algebra. The algorithm translates the calculus expression into an equivalent algebra expression, and it maps the object algebra expression to an object algebra operator graph. This translation algorithm not only generates an efficient access plan of queries, but also proves the equivalent expressiveness of queries.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2003.04a
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• pp.221-224
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• 2003

이 연구는 국내의 균열암반에 대한 지하수 유동 연구가 대수층이 등방이라는 가정하에 진행피고 있는 방법에서 벗어나 대수층이 이방성을 띤다는 가정하에 대수층의 수리적 이방성을 해석하는데 중점을 두었다. 수리시험은 30.91 $m^3$/day로 BH-1공에서 300분간 양수였으며, 각각의 관측공 BH-2, BH-3, BH-4, 및 BH-5공에서 시간에 따른 수위강하를 관측하였다. 수리시험에 의해 얻어진 시간별 수위강하 자료를 이용하여 Jacob(1950)의 직선법에 의해서 직선의 기울기(m)와 수위강하가 영이 되는 지점에서의 시간( $t_{0}$)을 계산하였다. 대수층의 수리학적 이방성 텐서 (tensor) 즉, 최대투수량계수텐서 ( $T_{ξξ}$)와 최소투수량계수텐서 ( $T_{ηη}$)를 산출하기 위해서 Stewart(1973)에 의해서 정립된 정규최소제곱(Ordinary least-square)방법을 적용하였으며, 이 방법은 관측공이 최소한 4개를 필요로 한다. 그 결과로, $T_{ξξ}$는 12.21 $m^2$/day이고 $T_{ηη}$는 10.47 $m^2$/day로 산출되었다. 최대투수량계수텐서의 방향은 Nl9.13$^{\circ}$E 이고 이방성율은 1.17로 산출되었다. BH-1공에서 수리시험시 대수층의 이방성은 등방성에 가깝게 표현되었다. 이는 연구지역 대수층이 다수의 균열에 의해서 수리적 상호연결성이 고루 분포된 것으로 판단된다.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.83-99
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• 2012

The conic sections are defined as algebraic expressions using the focus and the directrix in the high school curriculum. However it is difficult that students understand the conic sections without environment which they can manipulate the conic sections. To make up for this weak point, we have found the evidence for generating method of a conic section through a sundial and investigated the history of terms 'focus', 'directrix' and the tool of drawing them continuously.

• Journal of the Korea Society of Computer and Information
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• v.28 no.2
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• pp.111-119
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• 2023

In this paper, we investigate the feasibility of functional programming in the Scala language. The main issue is to what extent Scala is able to handle major properties of functional programming such as lambda expression, high-order functions, generic types, algebraic data types, and monads. For this purpose, we implement an interpreter of an imperative language. In this implementation, the same functional programming techniques are applied to both Haskell and Scala languages, and then these two versions of implementations are compared and analyzed. The abstract syntax tree of an imperative language is expressed as algebraic data types with generics and enum classes in Scala, and the state transition of imperative languages is implemented by using state monad. Extension and given, new features of Scala, are used as well.

• The Journal of Natural Sciences
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• v.8 no.2
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• pp.17-20
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• 1996

We show Equivariant Serre Problem in real algebraic category is true when dimension of the fiber is one i.e., we show an equivariant line bundle over a real representation space is isomorphic to a product bundle of a real representation space and some G-module.

• Review of KIISC
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• v.2 no.4
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• pp.104-109
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• 1992

스위치 이론이나 디지탈 공학$^{2)}$, 정보보호학$^{6.8)}$등의 분야에서 자주 사용되는 많은 함수들은 유한체 GF$(q)^n$에서 GF(q)의 값을 취하는 함수들이다. 특히 q=2인 경우에 함수 f는 쉽게 진리표에 의해 표현된다. 본 글에서는 유한체 위에서 성립하는 행렬 구조를 갖는 대수적 표준형식 변환에 대하여 알아보고, 변환의 계산을 점화적으로 이행해보며, 난수함수의 복잡도에 관한 확률분포를 살펴본다. 대수적 표준형식은 함수의 비선형 위수나 복잡도에 관한 판단에 유용하게 응용할 수 있다.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.380-385
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• 2006

해안 지역의 지하수 최적 개발 또는 관리 이전 단계에 수행될 수 있는 수자원 기본계획을 위한 지하수 개발가능량 산정식이 제안되었다. 산정식은 대수층 특성, 해수침투허용 거리, 지하수 해안유출량 그리고 관정의 위치 등 주요 영향 인자들의 함수이므로 매우 포괄적이며, 잘 알려진 해석 해들을 이용하였으므로 그 근거가 타당하다. 산정식은 관련 변수들의 양 함수로 표현될 수 있으므로 그 적용이 매우 간편하다. 또한 근거없이 임의의 값들이 사용되던 관정의 영향반경을 대수층의 수리특성과 양수량 등의 함수로 표현한 합리적인 식이 제안되었다. 가상 유역에 대한 적용과 수치 해와의 비교분석을 통하여 제안된 식들이 보수적인 결과를 산출한다는 것을 보였다. 제안된 식들을 기존 관정들이 존재하는 유역에 적용하면 추가 개발가능량을 평가할 수 있다.