• Communications of Mathematical Education
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• v.28 no.3
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• pp.375-394
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• 2014

The purpose of this study is to examine the transition of mathematical representation in Joseon mathematics, which is focused on numbers and operations, letters and expressions. In Joseon mathematics, there had been two numeral systems, one by chinese character and the other by counting rods. These systems were changed into the decimal notation which used Indian-Arabic numerals in the late 19th century passing the stage of positional notation by Chinese character. The transition of the representation of operation and expressions was analogous to that of representation of numbers. In particular, Joseon mathematics represented the polynomials and equations by denoting the coefficients with counting rods. But the representation of European algebra was introduced in late Joseon Dynasty passing the transitional representation which used Chinese character. In conclusion, Joseon mathematics had the indigenous representation of numbers and mathematical symbols on our own. The transitional representation was found before the acceptance of European mathematical representations.

• Proceedings of the Korea Water Resources Association Conference
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• 2011.05a
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• pp.409-413
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• 2011

유효유량이란 수년에 걸쳐 연 유사량의 대부분을 이동시키는 유량으로 정의되며 유량-빈도분포곡선과 유사량 곡선을 이용하여 산정된다. 유효유량은 하도를 설계하거나 기존 하도의 안정성을 평가하는데 있어 기준유량이 될 수 있는 필수적인 요소이지만, 현재 국내의 경우 이에 대한 분석이 충분히 수행되지 않아 특정한 패턴을 도출하기 힘든 실정이다. 특히 우리나라의 하천은 연강수량의 약 70%가 여름철에 집중되는 기후적 특성의 영향으로 하상계수가 미국과 유럽에 비해 10에서 25배 크게 나타나 외국사례를 국내에 적용하는데 어려움이 있다. 따라서 본 연구에서는 구하도복원이 계획 또는 진행되어 유효유량 산정이 필수적이며 하상계수가 매우 큰 만경강, 청미천, 함평천을 대상하천으로 선정하여 유효 유량을 산정하고 수리적, 지형학적 특성과의 연관성을 분석하고자 한다. 유효유량을 계산하는 데 있어 가장 큰 영향을 미치는 요소는 유량빈도 간격 수와 유량빈도 간격의 설정이다. 따라서 본 연구에서는 유효유량 산정을 위한 유량 간격으로 산술등간격(Arithmeic Bin)과 로그간격(Logarithmic Bin)을 모두 사용하였으며 각각 간격수가 25개, 50개, 100개인 경우에 대해 유효유량을 계산하여 비교하였다. 산술등간격과 로그간격을 사용한 유효유량 산정결과 중 최대, 최소값을 제외한 나머지의 평균값을 각 대상하천의 유효유량으로 선정하였다. 수리적, 지형학적 특성에 따른 대상하천 분석 결과 하상계수가 클수록 유효유량이 크게 산정되는 것으로 나타났으며 하상 경사, 하상토의 중앙입경 크기와 비례하는 것으로 나타났다. 반면에 수심-하폭비와 사행도의 경우 유효유량과 반비례하는 것으로 나타났다.

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.25-44
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• 2020

This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.137-159
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• 2012

In this paper, we deal with recent researches on Ying N$\ddot{u}$ and Ying Buzu(盈不足) which were addressed in the book Jiu Zhang Suan Shu(九章算術, The Nine Chapters on the Mathematical Art). Ying N$\ddot{u}$(Ying Buzu) is a concept on profit and loss problems. Ying Buzu Shu(盈不足術, the method of excess and deficit) represents an algorithm which has been used for solving many mathematical problems. It is known as a rule of double false position in the West. We show the importance of Ying Buzu Shu via an analysis of some problems in 'Ying Buzu' chapter. In 1202, Fibonacci(c.1170-c.1250) used Ying Buzu Shu in his book. This shows some of Asian mathematics were introduced to the West even before the year 1200. We present the origin of Ying Buzu Shu, and its relationship with Cramer's Rule. We have discovered how Asia's Ying Buzu Shu spread to Europe via Arab countries. In addition, we analyze some characters of Ying N$\ddot{u}$(Ying Buzu) in the book Suan Xue Bao Jian(算學寶鑑).

• Communications of Mathematical Education
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• v.36 no.1
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• pp.171-199
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• 2022

In this study, we review contents to supplement the descriptions of the history of mathematics in the 2015 mathematics textbooks and teacher guides for the elementary school level and offer our opinion on them. For this purpose, we conducted a literature review on 24 types of 2015 mathematics textbooks and teacher guides for the elementary school level. The results of this study are as follows: A total of 10 topics were found whose contents were supplemented with descriptions. They were the "Arithmetic of the Ancient Egyptians," the "A'h-mosè Papyrus in Mathematics Textbooks of the Ancient Egyptians," "The Old Akkadian Square Band in Mesopotamia," "The Relationship of the Old Babylonians in Mesopotamia with the Angle," "The Pi of the Ancient Egyptians and the Old Babylonians," "The Square Roots 2 of the Ancient Egyptians and the Old Babylonians," "The Relationship of the Islamites with the Decimal Fraction," "Two Arguments for the Roots of the Golden Ratio," "The Relationship of Archimedes with the Exhaustion Method," and "The Design of Flats." Then, their specific supplements were suggested. It is expected that this will overcome the perspective of the history of the Axial Age and acknowledge and accept the perspective evidencing the transfer of mathematical culture from Ancient Egypt and Old Babylonia to Ancient Greece and Hellenism, and then through Central Asia to Europe.

• Journal of the Korea Concrete Institute
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• v.26 no.2
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• pp.151-157
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• 2014

Since recently developed Ultra-High-Performance-Concrete (UHPC) provides very high strength, stiffness, and durability, many studies have been made on the application of the UHPC to bridge decks. Due to high strength and stiffness of UHPC bridge deck, the structural contribution of top flange of steel girder composite to UHPC deck would be much lower than that of conventional concrete deck. At this point of view, this study proposes a inverted-T shaped steel girder composite to UHPC deck. This girder requires a new type of shear connector because conventional shear connectors are welded on top flange. This study also proposes three different types of shear connectors, and evaluate their ultimate strength via push-out static test. The first one is a stud shear connector welded directly to the web of the girder in the transverse direction. The second one is a puzzle-strip type shear connector developed by the European Commission, and the last one is the combination of the stud and the puzzle-strip shear connectors. Experimental results showed that the ultimate strength of the transverse stud was 26% larger than that given in the AASHTO LRFD Bridge Design Specifications, but a splitting crack observed in the UHPC deck was so severe that another measure needs to be developed to prevent the splitting crack. The ultimate strength of the puzzle-strip specimen was 40% larger than that evaluated by the equation of European Commission. The specimens combined with stud and puzzle-strip shear connectors provided less strength than arithmetical sum of those. Based on the experimental observations, there appears to be no advantage of combining transverse stud and puzzle-strip shear connectors.

• Communications of Mathematical Education
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• v.23 no.4
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• pp.977-998
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• 2009

In this article, we give a comparative study on the last 300 years of USA and Korean tertiary mathematics. The first mathematics classes in United States were offered before July, 1638, but the real founding of tertiary mathematics courses was in 1640 when Henry Dunster assumed the duties of the presidency at Harvard. President Dunster read arithmetics and geometry on Mondays and Tuesdays to the third year students during the first three quarters, and astronomy in the last quarter. So tertiary mathematics education in United States began at Harvard which is the oldest college in USA. After 230 years since then, Benjamin Peirce in 1870 made a major and first American contribution to mathematics and got an attention from European mathematicians. Major change on the role of Harvard mathematics from teaching to research made by G.D. Birkhoff when he joined as an assistant professor in 1912. Tertiary mathematics education in Korea started long before Chosun Dynasty. But it was given to only small number of government actuarial officers. Modern mathematics education of tertiary level in Korea was given at Sungkyunkwan, Ewha, Paichai, and Soongsil. But all college level education opportunity, particularly in mathematics, was taken over by colonial government after 1920. And some technical and normal schools offered some tertiary mathematics courses. There was no college mathematics department in Korea until 1945. After the World War II, the first college mathematics department was established, and Rimhak Ree in 1949 made a major and first Korean contribution to modern mathematics, and later found Ree group. He got an attention from western mathematicians for the first time as a Korean. It can be compared with Benjamin Peirce's contribution for USA.

• Journal of Korean Society of Environmental Engineers
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• v.34 no.2
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• pp.109-118
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• 2012

This study achieves results from 22 maternity breast milk samples in total to demonstrate exposure level and risk assessment of PBDEs in Seoul area. PBDEs were detected in all the breast milk samples of the present study, indicating that general population in these Seoul area are widely exposed to these chemicals. Residue levels of total PBDEs (sum PBDEs from tri- to hepta-BDE) ranged of 0.84~13.1 ng/g lipid with an arithmetic mean and median of 3.56 ng/g lipid and 2.6 ng/g lipid, respectively. Global comparison shows that the levels of total PBDEs were relatively similar to those of China, Taiwan and European country (Sweden), and somewhat higher than those in some Asian (Vietnam, Philippines, and Indonesia). In the present study, however, the levels of total PBDEs in human milk are still one to two orders of magnitude lower than those in North America. Contribution rate of each congener appeared to be predominant with BDE-47, followed by BDE-153, BDE-100, BDE-99, BDE-154 and BDE-183. The sum of BDE-47 and BDE-153 accounted for more than 65% of total PBDEs in most samples. From the result of the human risk assessment of infants for total PBDEs and BDE-47 by breast milk feeding, we could find out that the average daily doses and hazard index (95th percentile) were 16.5 ng/kg bw/day and $1.2{\times}10^{-1}$ each other when nursing for 6 months after infants born. However, it was concluded that the infant health hardly had adverse seriously effects under this research condition.