• Journal of the Korean School Mathematics Society
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• v.8 no.3
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• pp.367-382
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• 2005

In this paper, we deal with various contents relating to the group concept in school mathematics and teaching of algebraic structures indirectly by combining these contents. First, we consider structure of knowledge based on Bruner, and apply these discussions to the teaching of algebraic structure in school algebra. As a result of these analysis, we can verify that the essence of algebraic structure is group concept. So we investigate the previous researches about group concept: Piaget, Freudenthal, Dubinsky. In our school, the contents relating to the group concept have been taught from elementary level indirectly. Tn elementary school, the commutative law and associative law is implicitly taught in the number contexts. And in middle school, various linear equations are taught by the properties of equality which include group concept. But these algebraic contents is not related to the high school. Though we deal with identity and inverse in the binary operations in high school mathematics, we don't relate this algebraic topics with the previous learned contents. In this paper, we discussed algebraic structure focusing to the group concept to obtain a connectivity among school algebra. In conclusion, the group concept can take role in relating these algebraic contents and teaching the algebraic structures in school algebra.

• Research in Mathematical Education
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• v.16 no.4
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• pp.217-232
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• 2012

While many studies on early algebra have been conducted, there have been only a few studies on the operation sense as the fundamental element of algebraic thinking, especially the fraction operation sense. This study explored the dimensions of fraction operation sense and then investigated students' fraction operation sense. A total of 183 of sixth graders were surveyed and 5 students who showed high operation sense were clinically interviewed in order to analyze their algebraic thinking in detail. The results showed that students had a tendency to use direct calculation or employ inappropriate operation sense rather than to use the structure of operation or the relation between operations on the basis of algebraic thinking. This study implies that explicit instruction on early algebra is necessary from the elementary school years.

• Bulletin of the Korean Mathematical Society
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• v.58 no.2
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• pp.527-535
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• 2021

The fundamental group of a high dimensional graph manifold canonically has a graph of groups structure. We analyze the group action on the associated Bass-Serre tree and study the algebraic ranks of the fundamental groups of high dimensional graph manifolds.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.623-639
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• 2021

We define a new algebraic structure called Legendrian racks or racks with Legendrian structure, motivated by the front-projection Reidemeister moves for Legendrian knots. We provide examples of Legendrian racks and use these algebraic structures to define invariants of Legendrian knots with explicit computational examples. We classify Legendrian structures on racks with 3 and 4 elements. We use Legendrian racks to distinguish certain Legendrian knots which are equivalent as smooth knots.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.12A
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• pp.1983-1989
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• 2001

A new two-step soft output Viterbi algorithm (SOVA) for turbo decoder is proposed and analyzed in 7his paper. Due to the algebraic structure of the proposed algorithm, slate and branch metrics can be obtained wish parallel processing using matrix arithmetic. As a result, the number of multiplications to calculate state metrics of each stage and total memory size can be decreased tremendously. Therefore, it can be expected that the proposed algebraic two-step SOVA is suitable for applications in which low computational complexity and memory size are essential.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.569-608
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• 1994

The subject matter of this survey has to do with holomorphic maps from a compact Riemann surface to projective space, which are also called algebrac curves; the theory we survey lies at the crossroads of function theory, projective geometry, and commutative algebra (although we should mention that the present survey de-emphasizes the algebraic aspect). Algebraic curves have been vigorously and continuously investigated since the time of Riemann. The reasons for the preoccupation with algebraic curves amongst mathematicians perhaps have to do with-other than the usual usual reason, namely, the herd mentality prompting us to follow the leads of a few great pioneering methematicians in the field-the fact that algebraic curves possess a certain simple unity together with a rich and complex structure. From a differential-topological standpoint algebraic curves are quite simple as they are neatly parameterized by a single discrete invariant, the genus. Even the possible complex structures of a fixed genus curve afford a fairly complete description. Yet there are a multitude of diverse perspectives (algebraic, function theoretic, and geometric) often coalescing to yield a spectacular result.

• 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.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.861-868
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• 2023

Nonlinear network creates complex homotopy structural communication in wireless network medium because of complex distribution approach. Due to this multicast topological connection structure, the queuing probability was non regular principles to create routing structures. To resolve this problem, we propose a Co-cluster homotopy queuing model (Co-CHQT) for Nonlinear Algebraic Topological Structure (NLTS-) for improving poison distribution network communication. Initially this collects the routing propagation based on Nonlinear Distance Theory (NLDT) to estimate the nearest neighbor network nodes undernon linear at x_(a,b)→ax²+bx² = c. Then Quillen Network Decomposition Theorem (QNDT) was applied to sustain the non-regular routing propagation to create cluster path. Each cluster be form with co variance structure based on Two unicast 2(n+1)-Z2(n+1)-Z network. Based on the poison distribution theory X_(a,b) ≠ µ(C), at number of distribution routing strategies weights are estimated based on node response rate. Deriving shorte;'l/st path from behavioral of the node response, Hilbert -Krylov subspace clustering estimates the Cluster Head (CH) to the routing head. This solves the approximation routing strategy from the nonlinear communication depending on Max- equivalence theory (Max-T). This proposed system improves communication to construction topological cluster based on optimized level to produce better performance in distance theory, throughput latency in non-variation delay tolerant.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.469-479
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• 1996

Toric variety is a normal algebraic variety containing algebraic torus $T_N$ as an open dense subset with an algebraic action of $T_N$ which is an extension of the group law of $T_N$. A toric variety can be described in terms of a certain collection, which is called a fan, of cones. From this fact, the properties of a toric variety have strong connection with the combinatorial structure of the corresponding fan and the relations among the generators. That is, we can translate the diffcult algebrogeometric properties of toric varieties into very simple properties about the combinatorics of cones in affine spaces over the reals.

• The Mathematical Education
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• v.53 no.1
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• pp.93-110
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• 2014

Algebra deals with so general properties about number system that it is called as 'generalized arithmetic'. Observing students' activities in algebra classes, however, we can discover that recognition of the generality in algebraic proofs is not so easy. One of these difficulties seems to be caused by variables which play an important role in algebraic proofs. Many studies show that students have experienced some difficulties in recognizing the meaning and the role of variables in algebraic proofs. For example, the confusion between 2m+2n=2(m+n) and 2n+2n=4n means that students misunderstand independent/dependent variation of variables. This misunderstanding naturally has effects on understanding of the meaning of proofs. Furthermore, students also have a difficulty in making a transition from algebraic proof to numerical cases which have the same structure as the proof. This study investigates whether middle school students can recognize dependent generality and make a transition from proofs to numerical cases. The result shows that the participants of this study have a difficulty in both of them. Based on the result, this study also includes didactical implications for teaching the generality of algebraic proofs.