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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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Journal for History of Mathematics
Journal Basic Information
Journal DOI :
The Korean Society for History of Mathematics
Editor in Chief :
Volume & Issues
Volume 27, Issue 6 - Dec 2014
Volume 27, Issue 5 - Oct 2014
Volume 27, Issue 4 - Aug 2014
Volume 27, Issue 3 - Jun 2014
Volume 27, Issue 2 - Apr 2014
Volume 27, Issue 1 - Feb 2014
Selecting the target year
Hong JeongHa's Tianyuanshu and Zhengcheng Kaifangfa
Hong, Sung Sa ; Hong, Young Hee ; Kim, Young Wook ;
Journal for History of Mathematics, volume 27, issue 3, 2014, Pages 155~164
DOI : 10.14477/jhm.2014.27.3.155
Tianyuanshu and Zengcheng Kaifangfa introduced in the Song-Yuan dynasties and their contribution to the theory of equations are one of the most important achievements in the history of Chinese mathematics. Furthermore, they became the most fundamental subject in the history of East Asian mathematics as well. The operations, or the mathematical structure of polynomials have been overlooked by traditional mathematics books. Investigation of GuIlJib (九一集) of Joseon mathematician Hong JeongHa reveals that Hong's approach to polynomials is highly structural. For the expansion of
, Hong invented a new method which we name Hong JeongHa's synthetic expansion. Using this, he reveals that the processes in Zhengcheng Kaifangfa is not synthetic division but synthetic expansion.
Lagrange and Polynomial Equations
Koh, Youngmee ; Ree, Sangwook ;
Journal for History of Mathematics, volume 27, issue 3, 2014, Pages 165~182
DOI : 10.14477/jhm.2014.27.3.165
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.
'Cultural' Prime Numbers: 2, 3, and 5
Bae, Sun Bok ; Park, Chang Kyun ;
Journal for History of Mathematics, volume 27, issue 3, 2014, Pages 183~195
DOI : 10.14477/jhm.2014.27.3.183
In mathematics a prime number is the natural number that has no positive factors other than 1 and itself. As natural numbers greater than 1 can be factored characterized by prime numbers, identities of a culture could be understood if its cultural phenomena are analyzed through cultural prime numbers(CPN). It is not easy to resolve cultural phenomena into CPN and analyze them through CPN due to complexities of culture. Though it is difficult, however, it is not impossible. For CPN keeps relative independence in the context of history and thought. We call 2, 3 and 5 as CPN: 2 is representative of Yin and Yang theory, 3 of Three Principles theory, and 5 of Five Elements theory. We argue that the Ten Celestial Stems and the Twelve Earthly Branches, the core principles in the oriental tradition, could be factored by the CPN. Analyzing Sil-Hah Woo's arguments, we discuss that the CNP 3 achieved more qualitative valuation than the others in Korean culture.
A Historical Review on Discrete Models of Population Changes and Illustrative Analysis Methods Using Computer Softwares
Shim, Seong-A ;
Journal for History of Mathematics, volume 27, issue 3, 2014, Pages 197~210
DOI : 10.14477/jhm.2014.27.3.197
Species like insects and fishes have, in many cases, non-overlapping time intervals of one generation and their descendant one. So the population dynamics of such species can be formulated as discrete models. In this paper various discrete population models are introduced in chronological order. The author's investigation starts with the Malthusian model suggested in 1798, and continues through Verhulst model(the discrete logistic model), Ricker model, the Beverton-Holt stock-recruitment model, Shep-herd model, Hassell model and Sigmoid type Beverton-Holt model. We discuss the mathematical and practical significance of each model and analyze its properties. Also the stability properties of stationary solutions of the models are studied analytically and illustratively using GSP, a computer software. The visual outputs generated by GSP are compared with the analytical stability results.
Students' Understanding and Application of Monty Hall Dilemma in Classroom
Park, Jung Sook ;
Journal for History of Mathematics, volume 27, issue 3, 2014, Pages 211~231
DOI : 10.14477/jhm.2014.27.3.211
Although Monty Hall dilemma is used in many areas including philosophy, economics, and psychology, it is used in the current mathematics textbooks only as a material for reading or one of probability questions. The present study tries to explore students' understanding of Monty Hall dilemma through a class case. In this study, a group of high-school students participated in group activities, in which they read an argument about Monty Hall dilemma, and tried to resolve it through small-group and whole-class discussions, and then studied the conditional probability. The analysis supports the studies in psychology that intuitive understandings on probability do not change easily, and that counter-intuitivity in Monty Hall dilemma induces confusion and offers a basis for discussions among students. Similar results are anticipated when other dilemmas on probability are used.
Kindergarten and Primary School Teachers' Perceptions about the Level Relevance of the 2009 Revised Mathematics Curriculum
Kwon, Jeom Rae ;
Journal for History of Mathematics, volume 27, issue 3, 2014, Pages 233~253
DOI : 10.14477/jhm.2014.27.3.233
In this study, the kindergarten teachers and elementary school teachers were surveyed to see the level relevance of the kindergarten and primary school curriculums. As a result, first, the kindergarten curriculum was generally appeared appropriate to the level of kindergarten students. However, in practice, a significant amount of the first grade curriculum were taught in the kindergarten. Second, the variation of mathematical abilities among the begining students was very large, and this variation also affected the students' achievements. Third, both kindergarten teachers and elementary school teachers wished for adjustments of the level of mathematics curriculum.