• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.265-270
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• 2007

The modern approach for wavelets imposes a Bayesian prior model on the wavelet coefficients to capture the sparseness of the wavelet expansion. The idea is to build flexible probability models for the marginal posterior densities of the wavelet coefficients. In this note, we derive exact expressions for a popular model for the marginal posterior density.

• School Mathematics
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• v.1 no.2
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• pp.605-615
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• 1999

In this paper, we explain the pedagogical phenomena appeared in the learning of 0.$\dot{9}$ = 1 in terms of its intrinsic mathematical structure, and investigate the reason why such phenomena happen. Also we analyze such phenomena through the dialogue between student and teacher, and present some instruction idea from the mathematical and educational view points.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.573-583
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• 2008

In this paper, we introduce the techniques of estimating the probability of failure in reliability analysis. The basic idea of each technique is explained and drawbacks of these techniques are examined.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.3
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• pp.307-318
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• 2020

In this paper, we extend the notion of a generalized derivation F associated with derivation d to two generalized derivations F and G associated with the same derivation d, as a new idea, to obtain the commutativity of prime rings under certain conditions.

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.233-241
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• 2005

Mathematics has developed dramatically in today's world and come to be increasingly put into practical use in various fields in society. However, many Japanese students dislike mathematics. We have to study mathematics education with this situation in our mind. When we consider a better educational material, we don't have to consider only within the framework of the current school mathematics. We can expect to find good mathematical materials in fields beyond the school mathematics. In this paper, we study how the inclusion of idea such as 'fuzzy theory' and 'graph theory' influences pupils' approaches to learning mathematics.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.9-33
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• 2004

The purpose of this paper is to contribute to the dialogue about the notion of advanced mathematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous activity. We also use the term activity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. We emphasize for these practices the changing nature of student' mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.83-103
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• 2014

The purpose of this paper is to find a method of measuring mathematical creativity reasonably. In the pursuit of this purpose, we designed four multiple solution tasks that consist of two kinds of open tasks; 'tasks with open solutions' and 'tasks with open answers'. We collected data by conducting an interview with a gifted fifth grade student using the four multiple solution tasks we designed and analyzed mathematical creativity of the student using Leikin's model(2009). Research results show that the mathematical creativity scores of two students who suggest the same solutions in a different order may vary. The more solutions a student suggests, the better score he/she gets. And fluency has a stronger influence on mathematical creativity than flexibility or originality of an idea. Leikin's model does not consider the usefulness nor the elaboration of an idea. Leikin's model is very dependent on the tasks and the mathematical creativity score also varies with each marker.

• Journal for History of Mathematics
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• v.26 no.4
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• pp.245-257
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• 2013

Hermann Grassmann classified mathematics and extended the dimension of vector spaces by using dialectics of contrasts. In this paper, we investigate his mathematical idea and its background, and the process of the classification of mathematics. He made a synthetic concept of mathematics based on his idea of 'equal' and 'inequal', 'discrete' and 'indiscrete' mathematics. Also, he showed a creation of new mathematics and a process of generalization using a dialectic of contrast of 'special' and 'general', 'real' and 'formal'. In addition, we examine his unique development in using 'real' and 'formal' in a process of generalization of basis and dimension of a vector space. This research on Grassmann will give meaningful suggestion to an effective teaching and learning of linear algebra.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.771-787
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• 2009

We use an idea of linear representations of the symmetric group to reduce the number of communication rounds in the verification protocol, proposed in Crypto 2005 by Peng et al., of a shuffling. We assume Paillier encryption scheme with which we can apply some known zero-knowledge proofs following the same line of approaches of Peng et al. Incidence matrices of 1-subsets and 2-subsets of a finite set is intensively used for the implementation, and the idea of $\lambda$-designs is employed for the improvement of the computational complexity.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1521-1536
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• 2017

This paper introduces a representation style of variable binding using dependent types when formalizing meta-theoretic properties. The style we present is a variation of the Coquand-McKinna-Pollack's locally-named representation. The main characteristic is the use of dependent families in defining expressions such as terms and formulas. In this manner, we can handle many syntactic elements, among which wellformedness, provability, soundness, and completeness are critical, in a compact manner. Another point of our paper is to investigate the roles of free variables and constants. Our idea is that fresh constants can entirely play the role of free variables in formalizing meta-theories of first-order predicate logic. In order to show the feasibility of our idea, we formalized the soundness and completeness of LJT with respect to Kripke semantics using the proof assistant Coq, where LJT is the intuitionistic first-order predicate calculus. The proof assistant Coq supports all the functionalities we need: intentional type theory, dependent types, inductive families, and simultaneous substitution.