• East Asian mathematical journal
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• v.29 no.2
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• pp.189-205
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• 2013

Addition problems can be divided into the 'problem of quantity' which does not have the concept of object or unit, and the 'problem of number' which have the concept of object or unit. 'Additive property' is the factor which has to be considered in the former case. On the other hand, 'additive property' is not considered and meaningless in the latter case. However, this additive property is not emphasized in the elementary curriculum that mostly deals with quantitative problems, so related errors are occurred in actual life. In this study, we will investigate to the pre-service elementary teachers through the problems of deciding the additive property. The result shows that the pre-service elementary teachers' cognition of additive problems is insufficient. This study will provide focal points in the teacher education and the elementary education, and the clues for the operating programs through the information about the tendency of errors.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.271-274
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• 1994

The concept of a continuous module is a generalization of that of an injective module, and conditions ($C_1$), (C$_2$) and ($C_3$) are given for this concept in [4]. In this paper, we study modules with properties that are dual to continuity. These will be called discrete and we discuss discrete abelian groups. Throughout R is a ring with identity, M is a module over R, G is an abelian group of finite rank, E is the ring of endomorphisms of G and S is the center of E. Dual to the notion of essential submodules, we define small submodules of a module M over R.(omitted)

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.409-422
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• 2003

Let $F: \mathbb{C}^k\;{\rightarrow}\;\mathbb{C}^k$ be a dynamical system and let $\{x_n\}_{n{\geq}0}$ denote an orbit of F. We study the relation between $\{x_n\}$ and pseudoorbits $\{y_n}, y_0=x_0.\;Here\;y_{n+1}=F(y_n)+s_n.$ In general $y_n$ might diverge away from $x_n.$ Our main problem is whether there exists arbitrarily small $t_n$ so that if $\tilde{y}_{n+1}=F(\tilde{y}_n)+s_n+t_n,$ then $\tilde{y}_n$ remains close to $x_n.$ This leads naturally to the concept of sustainable orbits, and their existence seems to be closely related to the concept of hyperbolicity, although they are not in general equivalent.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.115-127
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• 2011

We study the structure of the set of nilpotent elements in various kinds of ring and introduce the concept of NR ring as a generalization of Armendariz rings and NI rings. We determine the precise relationships between NR rings and related ring-theoretic conditions. The Kothe's conjecture is true for the class of NR rings. We examined whether several kinds of extensions preserve the NR condition. The classical right quotient ring of an NR ring is also studied under some conditions on the subset of nilpotent elements.

• Lingua Humanitatis
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• v.1 no.1
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• pp.221-233
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• 2001

The purpose of this paper is twofold. On the one hand it takes issue with Engstrom's claim that conceptual metaphors are propositional; on the other, it aims to demonstrate that the mathematical term 'mapping' is inappropriate for the analysis of metaphors. To my mind, the propositional analysis of metaphors, a wrong analysis for that matter, originates in the notion 'mapping' I argue that partial 'mapping' between propositional meanings and metaphorical meanings is either mental or psychological, with no concomitant 'truth' value. When concept metaphors represent propositionality, they lose metaphoricity; when they obtain metaphoricity, they are free of propositionality. The mathematical terms 'mapping' and 'proposition,' it is stressed, should be avoided in the analysis of concept metaphors like 'A is B' because they are confusing when applied to linguistic expression. 1 suggest that the term 'mapping' be replaced by phrases such as 'interaction between two domains,' projection from source-domain to target domain,' or 'understanding the properties of two domains between A and B,' etc. This would amount to proposing a pragmatic or cognitive theory of metaphor.

• Research in Mathematical Education
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• v.10 no.2 s.26
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• pp.135-150
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• 2006

Although improper integrals constitute a concept of great utility for Mathematics students, it appears that students are unable to assimilate this concept within the wider system of concepts they learn in their first year of Mathematics studies. In this paper we describe a competence model used in a study about the kind of understanding students possess about improper integral calculus when two registers of representation come into play. Competence will be considered as the coherent articulation of different semiotic registers. After analysing the results of a questionnaire, six students were selected to be interviewed on the basis of their overall results and the significance of their answers. For the interview, five original questions from the questionnaire were used together with a new question. In this article we will analyse, from our theoretical point of view, the work carried out by one student who was interviewed to show how our competence model works and we will discuss this formal competence model used.

• The Mathematical Education
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• v.53 no.3
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• pp.313-327
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• 2014

'Tangent' is one of the most important concepts in the middle and high school mathematics, especially in dealing with calculus. The concept of tangent in the current textbook consists of the ways which make use of discriminant or differentiation. These ways, however, do not present dynamic view points, that is, the concept of variation. In this paper, after applying 'Roberval's way of finding tangent using vectors in terms of kinematics to parabola, ellipse, circle, hyperbola, cycloid, hypocycloid and epicycloid, we will identify that this is the tangent of those curves. This trial is the educational link of mathematics and physics, and it will also suggest the appropriate example of applying vector. We will also help students to understand the tangent by connecting this method to the existing ones.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.377-402
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• 2007

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Aranassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to implicative ideals in BCK-algebras. The notion of an intuitionistic fuzzy implicative ideal of a BCK-algebra is introduced, and some related properties are investigated. An extension property for intuitionistic fuzzy implicative ideals is established. Characterizations of an intuitionistic fuzzy implicative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy implicative ideal are given. Using a collection of implicative ideals, intuitionistic fuzzy implicative ideals are established.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.225-234
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• 2013

Many studies of experimental economics have produced outcomes which contradict the predictions of Nash equilibrium, which relies heavily upon the premise of selfishness of an individual. In the games involving contexts of social conflicts represented by the prisoners' dilemma game, the experiments yields outcomes quite different from what are predicted by the conventional wisdom. In order to fill this gap between the conventional Nash Equilibrium and experimental outcomes, non-selfish (or other-regarding) motives of human behavior are introduced and then a new equilibrium concept, RAE-equilibrium is developed. It is also proved that an RAE-equilibrium exists under quite general conditions. Then it is applied to the prisoners' dilemma game that some of the experimental outcomes can be explained.

• Honam Mathematical Journal
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• v.31 no.1
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• pp.125-136
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• 2009

After the introduction of fuzzy sets by Zadeh, there have been a number of generaizations of this fundamental concept. The notion of bipolar-valued fuzzy sets introduced by Lee is one among them. In this paper, we apply the concept of a bipolar-valued fuzzy set to quasi-associative ideals in BCI-algebras. The notion of a bipolar fuzzy quasi-associative ideal of a BCI-algebra is introduced, and some related properties are investigated. Characterizations of a bipolar fuzzy quasi-associative ideal are given. Extension property for a bipolar fuzzy QA-ideal is established.