• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.107-116
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• 2005

We show an algorithm to draw the famous picture of Kleinian modular group PSL(2, $\mathbb{Z}$), which appears in describing the moduli space of elliptic curves.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1711-1723
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• 2013

P. V$\acute{a}$mos called a ring R 2-good if every element is the sum of two units. The ring of all $n{\times}n$ matrices over an elementary divisor ring is 2-good. A (right) self-injective von Neumann regular ring is 2-good provided it has no 2-torsion. Some of the earlier results known to us about 2-good rings (although nobody so called at those times) were due to Ehrlich, Henriksen, Fisher, Snider, Rapharl and Badawi. We continue in this paper the study of 2-good rings by several authors. We give some examples of 2-good rings and their related properties. In particular, it is shown that if R is an exchange ring with Artinian primitive factors and 2 is a unit in R, then R is 2-good. We also investigate various kinds of extensions of 2-good rings, including the polynomial extension, Nagata extension and Dorroh extension.

• School Mathematics
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• v.12 no.3
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• pp.439-454
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• 2010

This study presents how two eighth grade students generated their own algorithms in the context of fraction measurement division situations by modifications of unit-segmenting schemes. Teaching experiment was adopted as a research methodology and part of data from a year-long teaching experiment were used for this report. The present study indicates that the two participating students' construction of reciprocal relationship between the referent whole [one] and the divisor by using their unit- segmenting schemes and its strategic use finally led the students to establish an algorithm for fraction measurement division problems, which was on par with the traditional invert-and-multi- ply algorithm for fraction division. The results of the study imply that teachers' instruction based on understanding student-generated algorithms needs to be accounted as one of the crucial characteristics of good mathematics teaching.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.7
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• pp.640-650
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• 1991

In the paper, the threepoint search algorithm used direct search method for optimal design is proposed. Proposed algorithm is composed of two iteration procedure to determine the minimum value of performance index. The minumum value of three-point existing in the inner N-order searching is firstly determined and next searching space is then reduced by the result of first procedure. To compute performance index. 3N iteration for a searching is necessary. 3N searching method is also described and confirmed with exception of parameter included multiphicator and divisor. Proposed algorithm have good stability and reliability when performance index is linear or quadratic function.

• School Mathematics
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• v.6 no.3
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• pp.235-249
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• 2004

The purpose of this study was to analyze the error patterns and sentence types in word problems with respect to 1$\frac{3}{4}$$\div$$\frac{1}{2}$ which were made by the pre-service elementary teachers, and to suggest the clues to the education in pre-service. Korean elementary teachers in pre-service misunderstood 'divide with $\frac{1}{2}$' to 'divide to 2' by the Korean linguistic structure. And they showed a new error type of 1$\frac{3}{4}$$\times$2 by the result of calculation. Although they are familiar to 'inclusive algorithm' they are not good at dealing with the fractional divisor. And they are very poor at the 'decision the unit proportion' and the 'inverse of multiplication'. So, it is necessary to teach the meaning of the fractional division as 'decision the unit proportion' and 'inverse of multiplication' and to give several examples with respect to the actual situation and context.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.12C
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• pp.1288-1298
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• 2002

To implement elliptic curve cryptosystem in GF(2$\^$m/) at high speed, a fast divider is required. Although bit-parallel architecture is well suited for high speed division operations, elliptic curve cryptosystem requires large m(at least 163) to support a sufficient security. In other words, since the bit-parallel architecture has an area complexity of 0(m$\^$m/), it is not suited for this application. In this paper, we propose a new serial-in serial-out systolic array for computing division operations in GF(2$\^$m/) using the standard basis representation. Based on a modified version of tile binary extended greatest common divisor algorithm, we obtain a new data dependence graph and design an efficient bit-serial systolic divider. The proposed divider has 0(m) time complexity and 0(m) area complexity. If input data come in continuously, the proposed divider can produce division results at a rate of one per m clock cycles, after an initial delay of 5m-2 cycles. Analysis shows that the proposed divider provides a significant reduction in both chip area and computational delay time compared to previously proposed systolic dividers with the same I/O format. Since the proposed divider can perform division operations at high speed with the reduced chip area, it is well suited for division circuit of elliptic curve cryptosystem. Furthermore, since the proposed architecture does not restrict the choice of irreducible polynomial, and has a unidirectional data flow and regularity, it provides a high flexibility and scalability with respect to the field size m.