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고영미,이상욱,Koh, Youngmee,Ree, Sangwook 한국수학사학회 2016 Journal for history of mathematics Vol.29 No.3
Ancient books from East Asia, especially, Korea, China and Japan, are all written in Chinese. Ancient mathematical books like 九章算術(Gujang Sansul in Korean sound, Jiuzhang Suanshu in Chinese) is not exceptional and also was written in Chinese. The book 九章算術音義(Gujang Sansul Eumeui in Korean, Jiuzhang Suanshu Yinyi in Chinese), a dictionary-like book on 九章算術was published by official 李籍(Lǐ Jí) of 唐(Tang) dynasty (AD 618-907). We discuss how to pronounce Chinese characters based on 九章算術音義. To do so, we compare the pronunciation of the characters used in the words which are explained in 九章算術音義, to those of the current Korean and Chinese. Surprisingly, the pronunciations of the Chinese characters are almost all accordant with those of both Korean and Chinese.
고영미,이상욱,Koh, Youngmee,Ree, Sangwook 한국수학사학회 2014 Journal for history of mathematics Vol.27 No.2
In this paper we investigate how Newton discovered the generalized binomial theorem. Newton's binomial theorem, or binomial series can be found in Calculus text books as a special case of Taylor series. It can also be understood as a formal power series which was first conceived by Euler if convergence does not matter much. Discovered before Taylor or Euler, Newton's binomial theorem must have a good explanation of its birth and validity. Newton learned the interpolation method from Wallis' famous book ${\ll}$Arithmetica Infinitorum${\gg}$ and employed it to get the theorem. The interpolation method, which Wallis devised to find the areas under a family of curves, was by nature arithmetrical but not geometrical. Newton himself used the method as a way of finding areas under curves. He noticed certain patterns hidden in the integer binomial sequence appeared in relation with curves and then applied them to rationals, finally obtained the generalized binomial sequence and the generalized binomial theorem.
고영미,이상욱,Koh, Youngmee,Ree, Sangwook 한국수학사학회 2016 Journal for history of mathematics Vol.29 No.5
Mathematics is a kind of language, and even a tool of cognition for human beings. Mathematics has been used to communicate and to develop the civilizations through the history. So mathematics is one of the most important subjects for human to teach and learn. Especially, developed countries believe that mathematics will play very important roles in the developments of future industries and so future society. In this article, we clarify that combinatorics which is mainly represented by counting is an important ingredient of future mathematics education. To do so, we investigate the characteristics of combinatorics from the educational and cognitive perspectives.
고영미,이상욱,Koh, Youngmee,Ree, Sangwook 한국수학사학회 2015 Journal for history of mathematics Vol.28 No.2
Elliptic curves are a common theme among various fields of mathematics, such as number theory, algebraic geometry, complex analysis, cryptography, and mathematical physics. In the history of elliptic curves, we can find number theoretic problems on the one hand, and complex function theoretic ones on the other. The elliptic curve theory is a synthesis of those two indeed. As an overview of the history of elliptic curves, we survey the Diophantine equations of 3rd degree and the congruent number problem as some of number theoretic trails of elliptic curves. We discuss elliptic integrals and elliptic functions, from which we get a glimpse of idea where the name 'elliptic curve' came from. We explain how the solution of Diophantine equations of 3rd degree and elliptic functions are related. Finally we outline the BSD conjecture, one of the 7 millennium problems proposed by the Clay Math Institute, as an important problem concerning elliptic curves.
고영미,이상욱,Koh, Youngmee,Ree, Sangwook 한국수학사학회 2021 Journal for history of mathematics Vol.34 No.6
Mathematical induction is one of the deductive methods used for proving mathematical theorems, and also used as an inductive method for investigating and discovering patterns and mathematical formula. Proper understanding of the mathematical induction provides an understanding of deductive logic and inductive logic and helps the developments of algorithm and data science including artificial intelligence. We look at the origin of mathematical induction and its usage and educational aspects.
고영미,이상욱,Koh, Youngmee,Ree, Sangwook 한국수학사학회 2014 Journal for history of mathematics Vol.27 No.3
After algebraic expressions for the roots of 3rd and 4th degree polynomial equations were given in the mid 16th century, seeking such a formula for the 5th and greater degree equations had been one main problem for algebraists for almost 200 years. Lagrange made careful and thorough investigation of various solving methods for equations with the purpose of finding a principle which could be applicable to general equations. In the process of doing this, he found a relation between the roots of the original equation and its auxiliary equation using permutations of the roots. Lagrange's ingenious idea of using permutations of roots of the original equation is regarded as the key factor of the Abel's proof of unsolvability by radicals of general 5th degree equations and of Galois' theory as well. This paper intends to examine Lagrange's contribution in the theory of polynomial equations, providing a detailed analysis of various solving methods of Lagrange and others before him.
이상욱,고영미,Ree, Sangwook,Koh, Youngmee 한국수학사학회 2021 Journal for history of mathematics Vol.34 No.5
A functional equation is an equation which is satisfied by a function. Some elementary functional equations can be manipulated with elementary algebraic operations and functional composition only. However to solve such functional equations, somewhat critical and creative thinking ability is required, so that it is educationally worth while teaching functional equations. In this paper, we look at the origin of functional equations, and their characteristics and educational meaning and effects. We carefully suggest the use of the functional equations as a material for school mathematics education.
홍정하의 구일집의 저술에 관하여 - 홍정하 탄생 330주년을 기념하며 -
이상욱,고영미,REE, Sangwook,KOH, Youngmee 한국수학사학회 2015 Journal for history of mathematics Vol.2 No.1
Year 2014 was very special to Korean mathematical society. Year 2014 was the Mathematical Year of Korea, and the International Congress of Mathematicians "ICM 2014" was held in Seoul, Korea. The year 2014 was also the 330th anniversary year of the birth of Joseon mathematician Hong JeongHa. He is one of the best, in fact the best, of Joseon mathematicians. So it is worth celebrating his birth. Joseon dynasty adopted a caste system, according to which Hong JeongHa was not in the higher class, but in the lower class of the Joseon society. In fact, he was a mathematician, a middle class member, called Jungin, of the society. We think over how Hong JeongHa was able to write his mathematical book GuIlJib in Joseon dynasty.
사상의학적으로 치료하여 호전된 주요 신경인지장애 치험 2례
박정환,곽진영,고영미,윤지원,안택원,Park, Junghwan,Kwak, Jinyoung,Koh, Youngmee,Yun, Geewon,Ahn, Taekwon 대전대학교 한의학연구소 2017 혜화의학회지 Vol.26 No.1
Objectives:This study was designed to report treatment by Sasang Constitutional Medicine to the patients with Major Neurocognitive Disorder(Dementia) from various causes. Methods:These two patients were diagnosed as Taeeumin and Soyangin according to the result of Sasang constitutional diagnosis, and treated by Sasang constitutional medications. The progress was evaluated with the Korean version of Mini-Mentel State Exam(KMMSE) and Global Disorientation Scale(GDS). Result:The symptoms like wandering, insomnia, cognitive disorder was improved in these patients. Also, KMMSE and GDS score were highly improved. the one patient was cured with Cheongsimyeonja-tang and and the other was cured with Jihwangbaekho-tang and Yanggyuksanhwa-tang. Conclusion:This cases show that Sasang constitutional herbal medications are an effective treatment for the patients with Major Neurocognitive Disorder.