• Communications of Mathematical Education
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• v.30 no.3
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• pp.419-434
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• 2016

Ju-Seo-Gwan-Gyeon is a mathematical book of Chosun dynasty in the early 18th century. This study is to analyze and compare the contents between Ju-Seo-Gwan-Gyeon and Gu-Jang-San-Sul. From this study, we are able to see the contents of Ju-Seo-Gwan-Gyeon that has been unknown in detail so far. In this comparative study, the following facts are found. First, many problems in Ju-Seo-Gwan-Gyeon are similar to the Gu-Jang-San-Sul on the contents and frame. Most of them are same type. But some of problems in Ju-Seo-Gwan-Gyeon have been developed. Second, there are distinct differences of description type. And Ju-Seo-Gwan-Gyeon was influenced by Gu-Jang-San-Sul but also other mathematical books. We expect that the results provide basic information for mathematics history in Korea.

• Journal for History of Mathematics
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• v.24 no.1
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• pp.1-13
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• 2011

In Tian mu bi lei cheng chu jie fa(田畝比類乘除捷法) of Yang Hui suan fa(楊輝算法)), Yang Hui annotated detailed comments on the method to find roots of quadratic equations given by Liu Yi in his Yi gu gen yuan(議古根源) which gave a great influence on Chosun Mathematics. In this paper, we show that 'Zeng cheng kai fang fa'(增乘開方法) evolved from a process of binomial expansions of $(y+{\alpha})^n$ which is independent from the synthetic divisions. We also show that extending the results given by Liu Yi-Yang Hui and those in Suan xue qi meng(算學啓蒙), Chosun mathematican Hong Jung Ha(洪正夏) elucidated perfectly the 'Zeng cheng kai fang fa' as the present synthetic divisions in his Gu il jib(九一集).

• Journal for History of Mathematics
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• v.24 no.4
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• pp.1-6
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• 2011

We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.33-48
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• 2005

The Rule of False Position is known as an arithmetical solution of algebraical equations. On the other hand, the Excess-Deficit Rule is an algorithm for calculating about excessive or deficient quantitative relations, which is found in the ancient eastern mathematical books, including the nine chapters on the mathematical arts. It is usually said that the origin of the Rule of False Position is the Excess-Deficit Rule in ancient Chinese mathematics. In relation to these facts, we pose two questions: - As many authors explain, the excess-deficit rule is a solution of simultaneous linear equations？ - Which relation is there between the two rules explicitly？ To answer these Questions, we consider the Rule of Single/Double False Position and research the Excess-Deficit Rule in some ancient mathematical books of Chosun Dynasty that was heavily affected by Chinese mathematics. And we pursue their historical traces in Egypt, Arab and Europe. As a result, we can make sure of the status of the Excess-Deficit Rule differing from the Rectangular Arrays(the solution of simultaneous linear equations) and identify the relation of the two rules: the application of the Excess-Deficit Rule including supposition in ancient Chinese mathematics corresponds to the Rule of Double False Position in western mathematics. In addition, we try to appreciate didactical value of the Rule of False Position which is apt to be considered as a historical by-product.

• Education of Primary School Mathematics
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• v.14 no.2
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• pp.103-116
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• 2011

'The nine chapters on the mathematical art' has dominated the history of Chinese mathematics. It contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs. But it has been greatly by improved by the commentary given Liu Hui and it was transformed from arithmetic text to mathematics. The improved book served as important textbook in China but also the East Asian countries for the past 2000 years. Also It is comparable in significance to Euclid's Elements in the West. In the middle of 19th century, Chosun mathematicians Nam Byung Gil(南秉吉) and Lee Sang Hyuk(李尙爀) studied mathematical structures developed in Song(宋) and Yuan(元) eras on top of their early on 'The nine chapters' and 'ShuLiJingYun(數理精蘊)'. Their studies gave rise to a momentum for a prominent development of Choson mathematics in the century. Nam Byung Gil is also commentator on 'The Nine Chapters'. His commentary is 'GuJangSulHae(九章術解)'. This book provides figures and explanations of how the algorithms work. These are very helpful for prospective elementary teachers. We try to plan programs of elementary teacher education on the basis of 'The Nine Chapters' and 'GuJangSulHae'.

• 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.