• Journal for History of Mathematics
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• v.23 no.3
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• pp.121-140
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• 2010

This study presents one universal mean formula of implicate quantity for speed, temperature, consistency, density, unit cost, and the national income per person in order to avoid the inconvenience of applying different formulas for each one of them. This work is done by using the principle of lever and was led to the formula of two implicate quantity, $M=\frac{x_1f_1+x_2f_2}{f_1+f_2}$, and to help the understanding of relationships in this formula. The value of ratio of fraction cannot be added but it shows that it can be calculated depending on the size of the ratio. It is intended to solve multiple additions with one formula which is the expansion of the mean formula of implicate quantity. $M=\frac{x_1f_1+x_2f_2+{\cdots}+x_nf_n}{N}$, where $f_1+f_2+{\cdots}+f_n=N$. For this reason, this mean formula will be able to help in physics as well as many other different fields in solving complication of structures.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.129-144
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• 2009

The purpose of this study is what exactly De Morgan contributed to abstract algebra and mathematical logic. He recognised the purely symbolic nature of algebra and was aware of the existence of algebras other than ordinary algebra. He madealgebra as a science by introducing the ordered field and made the base for abstract algebra. He was one of the reformer of classical mathematical logic. Looking into De Morgan's works, we made it clear that the developments of algebra and mathematical logic in 19C.

• 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.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.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.627-641
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• 2012

We found a few students had an error in the function and equation units, because most of mathematicians omitted the multiplication signs. In the mathematical history, the multiplication and parentheses signs had various changes. Based on the Histogenetic Principle, high level students know that the letter in the functions and equations represents a number and the related principles, so they have no big problems. But since the low level students stay in the early days in the mathematical history, they have some problems in the modern function and equation. Therefore, while we study the function and equation units with the low level students, we present that we have to be cautious when we omit the multiplication and parentheses signs.

• 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.

• 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.

• International Journal of Computer Science & Network Security
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• v.22 no.2
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• pp.406-412
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• 2022

Storing large amounts of data has always been a big problem from the beginning of computing history. Big Data has made huge advancements in improving business processes by finding the customers' needs using prediction models based on web and social media search. The main purpose of big data stream processing frameworks is to allow programmers to directly query the continuous stream without dealing with the lower-level mechanisms. In other words, programmers write the code to process streams using these runtime libraries (also called Stream Processing Engines). This is achieved by taking large volumes of data and analyzing them using Big Data frameworks. Streaming platforms are an emerging technology that deals with continuous streams of data. There are several streaming platforms of Big Data freely available on the Internet. However, selecting the most appropriate one is not easy for programmers. In this paper, we present a detailed description of two of the state-of-the-art and most popular streaming frameworks: Apache Ignite and Hazelcast. In addition, the performance of these frameworks is compared using selected attributes. Different types of databases are used in common to store the data. To process the data in real-time continuously, data streaming technologies are developed. With the development of today's large-scale distributed applications handling tons of data, these databases are not viable. Consequently, Big Data is introduced to store, process, and analyze data at a fast speed and also to deal with big users and data growth day by day.

• 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?