• School Mathematics
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• v.7 no.4
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• pp.353-373
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• 2005

The purpose of this paper is to analysis the basic network problem which can be applied to the mathematically gifted students in elementary school. Mainly, we discuss didactic transpositions of the double counting principle, the game of sprouts, Eulerian graph problem, and the minimum connector problem. Here the double counting principle is related to the handshaking lemma; in any graph, the sum of all the vertex-degree is equal to the number of edges. The selection of these subjects are based on the viewpoint; to familiar to graph theory, to raise algorithmic thinking, to apply to the real-world problem. The theoretical background of didactic transpositions of these subjects are based on the Polya's mathematical heuristics and Lakatos's philosophy of mathematics; quasi-empirical, proofs and refutations as a logic of mathematical discovery.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.6
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• pp.1068-1073
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• 1987

Traditional circuit partitioning algorithm using the cluster development method, which is suitable for such applications as single chip floor planning or multiple layer PCB system placement, where the clusters are formed so that inter-cluster nets are localized within the I/O connector pins, may not be appropriate for the functiona block placement in truly 3-D electronic modules. 3-D hybrid IC is one such example where the inter-layer routing as well as the intra-layer routing can be maximally incorporated to reduce the overall circuit size, cooling requirements and to improve the speed performance. In this paper, we propose a new algorithm called MBE(Minimum Box Embedding) for the layer assignment of each functional block in 3-D hybrid IC design. The sequence of MBE is as follows` i) force-directed relaxation in 3-D space, ii) exhaustive search for the optimal orientation of the slicing plane and iii) layer assignment. The algorithm is first explaines for a 2-D reduced problem, and then extended for 3-D applications. An example result for a circuit consisting of 80 blocks has been shown.

• Communications of Mathematical Education
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• v.21 no.2 s.30
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• pp.153-176
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• 2007

The purpose of this paper is to analyze teaching-learning program which can be applied to mathematically gifted students in primary school, Our program is based on constructivist views on teaching and learning of mathematics. Mainly, we study the algorithmic thinking of mathematically gifted students in primary school in connection with the network problems; Eulerian graph problem, the minimum connector problem, and the shortest path problem, The above 3-subjects are not familiar with primary school mathematics, so that we adapt teaching-learning model based on the social constructivism. To achieve the purpose of this study, seventeen students in primary school participated in the study, and video type(observation) and student's mathematical note were used for collecting data while the students studied. The results of our study were summarized as follows: First, network problems based on teaching-learning model of constructivist views help students learn the algorithmic thinking. Second, the teaching-learning model based on constructivist views gives an opportunity of various mathematical thinking experience. Finally, the teaching-learning model based on constructivist views needs more the ability of teacher's research and the time of teaching for students than an ordinary teaching-learning model.