• Journal for History of Mathematics
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• v.20 no.4
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• pp.71-84
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• 2007

J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.

• Journal for History of Mathematics
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• v.25 no.3
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• pp.29-39
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• 2012

As a product of modern proof theory, linear logic is a new form of logic developed for the purpose of enhancing programming language by Professor Jean-Yves Girard of Marseille University (France) in 1987 by supplementing intuitionist logic in a sophisticated manner. Thus, linear logic' s connectives can be explained using information processing terms such as sequentiality and parallel computation. For instance, A${\otimes}$B shows two processes, A and B, carried out one after another. A&B is linked to an internal indeterminate, allowing an observer to select either A or B. A${\oplus}$B is an external indeterminate, and as such, an observer knows that either A or B holds true, but does not know which process will be true. A ${\wp}$ B signifies parallel computation of process A and process B; linear negative exhibits synchronization, that is, in order for the process A to be carried out, both A and $A^{\bot}$ have to be accomplished simultaneously. Since the field of linear logic is not very active in Korea at present, this paper deals only with syntax aspect of linear logic in order to arouse interest in the subject, leaving semantics and proof nets for future studies.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.113-130
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• 2009

It can be said that the teaching and learning of mathematical problem solving has been greatly influenced by G. Polya. His heuristics shows down the explicit process of mathematical problem solving in detail. In contrast, Polanyi highlights the implicit dimension of the process. Polanyi's theory can play complementary role with Polya's theory. This study outlined the epistemology of Polanyi and his theory of problem solving. Regarding the knowledge and knowing as a work of the whole mind, Polanyi emphasizes devotion and absorption to the problem at work together with the intelligence and feeling. And the role of teachers are essential in a sense that students can learn implicit knowledge from them. However, our high school students do not seem to take enough time and effort to the problem solving. Nor do they request school teachers' help. According to Polanyi, this attitude can cause a serious problem in teaching and learning of mathematical problem solving.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.169-182
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• 2008

This study has been searching for reasoning process solving the problem effectively in activities related to meaningful classification of pieces and geometric properties with tangram. In activities using some pieces of tangram, we systematically came up with every solution in classifying properties of pieces and combining selected pieces. It is very difficult for regular students to do this tangram. In order to solve this problem effectively, we need to show that there are activities using the idea acquired in reasoning process. Through this process, we do not simply use tangram to understand he concept and play for interest but to use it more meaningfully. And the best solution an not be found by a process of trial and error but must be given by experience to look or it systematically and methods to reason it logically.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.355-372
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• 2020

The concept of infinite series is an important subject of major mathematics curriculum in college. For several centuries it has provided learners not only counter-intuitive obstacles but also central role of analysis study. As the understanding in concept on infinite series became foundation of development of calculus in history of mathematics, it is essential to present students to study higher mathematics. Most students having concept of infinite sum have no difficulty in mathematical contents such as convergence test of infinite series. But they have difficulty in organizing concept of infinite series of partial sum. Thus, in this study we try to analyze construct the concept of infinite series in terms of APOS theory and genetic decomposition. By checking to construct concept of infinite series, we try to get an useful educational implication on teaching of infinite series.

• Journal of Educational Research in Mathematics
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• v.26 no.2
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• pp.173-188
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• 2016

Research on didactic transposition in mathematics education has about 25-year and about 35-year long history in and out of Korea, respectively. This study attempts to investigate in trends of those research and to suggest tasks needed to be tackled. Major findings are followed. First, studies done in Korea tended to focus on the application of the didactic transposition theory for proving its effectiveness in understanding mathematics textbooks and mathematics lessons in-depth. It is suggested to conduct meta-analysis of the accumulated results or analysis of further applications of the didactic transposition theory to improve theoretical aspects of didactic transposition. Second, new categories for extreme teaching phenomenon were found and new typology in knowledge to be considered in the didactic transposition was developed in a few studies done in other subject matter education. Application of these to mathematics education may enhance research in didactic transposition of mathematical knowledge. Third, praxeology or a complex of praxeology for Korean school mathematics should be explored as did in other countries. Fourth, there have been rich attempts to link perspectives in didactic transposition to other perspectives or fields such as anthropology, human and education in technology era, praxeology theory in economics, epistemology in other countries but not in Korea. It is suggested to extend the scope of discussion on didactic transposition and to relate various concepts given in other disciplines. Fifth, clarification or negotiation of meaning for the main terms used in the discussion on didactic transposition such as personalization, contextualization, depersonalization, decontextualization, Topaze Effect, Meta-Cognitive Shift is suggested by comparing researchers' various descriptions or uses of the terms.

• Journal of architectural history
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• v.15 no.4
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• pp.23-36
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• 2006

Since he was a leading figure in nineteenth century architecture, Viollet-le-Duc's architectural theory is crucial to the foundation of modern architecture. He has been called a Gothic Revivalist, a Structural Rationalist and a Positivist. The first title was perhaps due to his vigorous restoration of Gothic works such as $N\hat{o}tre$ Dame, but he did not adore the Gothic style just for itself. Rather, he hoped to deduce some principles from the style. So how did he manage this? In his book "Entretiens sur l'Architecture (Lectures on Architecture), published between 1864 and 1872, he mentions using Descartes' four rules for reaching architectural certainty in contrast with the chaotic situation during that modernising period. Furthermore Viollet-le-Duc's theory can be seen as a serious attempt to translates Descartes' philosophical rules into systems of architectural speculation. Descartes' four rules of doubt are anchored in mathematical propositions, and without mathematical distinctions, none of these rules are valid. In other word, mathematics for Viollet is the yardstick of judgement between distinctness and indistinctness. Many architectural problems arise from this view. In this paper, the validities of applying Descartes' method of doubt to architectural discourse will be discussed in order to address the question:-Did Viollet-le-Duc clearly grasp Cartesian method by which memory was erased from the world?

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1165-1171
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• 2017

The traditional form of parallelism in Monte Carlo particle transport simulations, wherein each individual particle history is considered a unit of work, does not lend itself well to data-level parallelism. Event-based algorithms, which were originally used for simulations on vector processors, may offer a path toward better utilizing data-level parallelism in modern computer architectures. In this study, a simple model is developed for estimating the efficiency of the event-based particle transport algorithm under two sets of assumptions. Data collected from simulations of four reactor problems using OpenMC was then used in conjunction with the models to calculate the speedup due to vectorization as a function of the size of the particle bank and the vector width. When each event type is assumed to have constant execution time, the achievable speedup is directly related to the particle bank size. We observed that the bank size generally needs to be at least 20 times greater than vector size to achieve vector efficiency greater than 90%. When the execution times for events are allowed to vary, the vector speedup is also limited by differences in the execution time for events being carried out in a single event-iteration.

• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.63-82
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• 2016

Mathematical notation is the main means to realize the power of mathematics. Under this perspective, this study analyzed the difficulties of learning an irrational number concept in terms of notation. I tried to find ways to overcome the difficulties arising from the notation. There are two primary ideas in the notation of irrational number using root. The first is that an irrational number should be represented by letter because it can not be expressed by decimal or fraction. The second is that $\sqrt{2}$ is a notation added the number in order to highlight the features that it can be 2 when it is squared. However it is difficult for learner to notice the reasons for using the root because the textbook does not provide the opportunity to discover. Furthermore, the reduction of the transparency for the letter in the development of history is more difficult to access from the conceptual aspects. Thus 'epistemological obstacles resulting from the double context' and 'epistemological obstacles originated by strengthening the transparency of the number' is expected. To overcome such epistemological obstacles, it is necessary to premise 'providing opportunities for development of notation' and 'an experience using the notation enhanced the transparency of the letter that the existing'. Based on these principles, this study proposed a plan consisting of six steps.

• Journal of the Korean Data and Information Science Society
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• v.19 no.3
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• pp.819-830
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• 2008

Web recommender system was suggested in order to solve the problem which is cause by overflow of information. Collaborative filtering is the technique which predicts and recommends the suitable goods to the user with collection of preference information based on the history which user was interested in. However, there is a difficulty of recommendation by lack of information of goods which have less popularity. In this paper, it has been researched the way to select the sparsity of goods and the preference in order to solve the problem of recommender system's sparsity which is occurred by lack of information, as well as it has been described the solution which develops the quality of recommender system by selection of customers who were interested in.