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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 25, Issue 4 - Nov 2012
Volume 25, Issue 3 - Aug 2012
Volume 25, Issue 2 - May 2012
Volume 25, Issue 1 - Feb 2012
Selecting the target year
TianYuanShu and Numeral Systems in Eastern Asia
Hong, Sung Sa ; Hong, Young Hee ; Lee, Seung On ;
Journal for History of Mathematics, volume 25, issue 4, 2012, Pages 1~10
In Chinese mathematics, there have been two numeral systems, namely one in spoken language for recording and the other by counting rods for computations. They concerned with problems dealing with practical applications, numbers in them are concrete numbers except in the process of basic operations. Thus they could hardly develop a pure theory of numbers. In Song dynasty, 0 and TianYuanShu were introduced, where the coefficients were denoted by counting rods. We show that in this process, counting rods took over the role of the numeral system in spoken language and hence counting rod numeral system plays the role of that for abstract numbers together with the tool for calculations. Decimal fractions were also understood as denominate numbers but using the notions by counting rods, decimals were also admitted as abstract numbers. Noting that abacus replaced counting rods and TianYuanShu were lost in Ming dynasty, abstract numbers disappeared in Chinese mathematics. Investigating JianJie YiMing SuanFa(簡捷易明算法) written by Shen ShiGui(沈士桂) around 1704, we conclude that Shen noticed repeating decimals and their operations, and also used various rounding methods.
Mathematics Educational Constructions and Structures in Suan Xue Qi Meng(算學啓蒙) and Muk Sa Jib San Bub(黙思集算法)
Yun, Hye Soon ;
Journal for History of Mathematics, volume 25, issue 4, 2012, Pages 11~19
Zhu Shi Jie's Suan Xue Qi Meng (算學啓蒙) is one of the most important books which had a great influence to the development of Chosun Mathematics and Gyung SunJing's Muk Sa Jib San Bub is the oldest Chosun mathematics book. In this paper, comparing Suan Xue Qi Meng (算學啓蒙) with Muk Sa Jib San Bub, we study the mathematics educational constructions and structures in books and then conclude that their structure can be used in present school mathematics.
Model-theoretic Consequence and Modality
Choi, Wonbae ;
Journal for History of Mathematics, volume 25, issue 4, 2012, Pages 21~36
It is commonly believed that the model-theoretic account of logical consequence is originated from Tarski' s 1936 paper. But Etchemendy has denied this. This paper discusses and evaluates the recent controversies over whether the definition of logical consequence presented in Tarski' s paper is based on the fixed-domain conception or the variable-domain conception.
A study on the rectangular coordinate system via comparing the interrelated influence between mathematical knowledge evolution and historical development of Cartography in Europe
Lee, Dong Won ;
Journal for History of Mathematics, volume 25, issue 4, 2012, Pages 37~51
By comparing the development history of rectangular coordinate system in Cartography and Mathematics, we assert in this manuscript that the rectangular coordinate system is not so much related to analytic geometry but comes from the space perceiving ability inherent in human beings. We arrived at this conclusion by the followings: First, although the Cartography have much influenced to various area of Mathematics such as trigonometry, logarithm, Geometry, Calculus, Statistics, and so on, which were developed or progressed around the advent of analytic geometry, the mathematical coordinate system itself had not been completely developed in using the origin or negative axis until 100 years and more had passed since Descartes' publication. Second, almost mathematicians who contributed to the invention of rectangular coordinate system had not focused their studying on rectangular coordinate system instead they used it freely on solving mathematical problem.
Three body problem in early 20th century
Lee, Ho Joong ;
Journal for History of Mathematics, volume 25, issue 4, 2012, Pages 53~67
Today, it is necessary to calculate orbits with high accuracy in space flight. The key words of Poincar
in celestial mechanics are periodic solutions, invariant integrals, asymptotic solutions, characteristic exponents and the non existence of new single-valued integrals. Poincar
define an invariant integral of the system as the form which maintains a constant value at all time
, where the integration is taken over the arc of a curve and
are some functions of
, and extend 2 dimension and 3 dimension. Eigenvalues are classified as the form of trajectories, as corresponding to nodes, foci, saddle points and center. In periodic solutions, the stability of periodic solutions is dependent on the properties of their characteristic exponents. Poincar
called bifurcation that is the possibility of existence of chaotic orbit in planetary motion. Existence of near exceptional trajectories as Hadamard's accounts, says that there are probabilistic orbits. In this context we study the eigenvalue problem in early 20th century in three body problem by analyzing the works of Darwin, Bruns, Gyld
n, Sundman, Hill, Lyapunov, Birkhoff, Painlev
The De Morgan's Perspective on the Teaching and Learning Complex Number
Lee, Dong Hwan ;
Journal for History of Mathematics, volume 25, issue 4, 2012, Pages 69~82
The objective of this paper is to study De Morgan's perspective on teaching and learning complex numbers. De Morgan's didactical approaches reflect the process of development of his thoughts about algebra from universal arithmetic, symbolic algebra to meaning algebra. De Morgan develop his perspective on algebra by justifying and explaining complex numbers. This implies that teaching and learning complex numbers is a catalyst for mathematical development of De Morgan.
The history of conic sections and mathematics education
Jin, Man Young ; Kim, Dong Won ; Song, Min Ho ; Cho, Han Hyuk ;
Journal for History of Mathematics, volume 25, issue 4, 2012, Pages 83~99
The conic sections are defined as algebraic expressions using the focus and the directrix in the high school curriculum. However it is difficult that students understand the conic sections without environment which they can manipulate the conic sections. To make up for this weak point, we have found the evidence for generating method of a conic section through a sundial and investigated the history of terms 'focus', 'directrix' and the tool of drawing them continuously.
Mathematical Study on the Removal of the Go Stones
Lee, Gwang Yeon ; Cho, Seong Hoon ; Yang, Seung Bum ;
Journal for History of Mathematics, volume 25, issue 4, 2012, Pages 101~119
The removal of the Go Stones is a game that anyone can play through simple rules. It is not only an interesting game but also a mathematical game that requires comprehensive knowledge of several mathematical theories. Through analyzing the rules and theories of this game, students can get a new mathematical perspective and recognize something that they didn't realize as important before. Furthermore, this game is given to students as a mathematical problem unconsciously. This helps them get a mathematical approach to understanding the actual concept of the problem as well as the basic principle of the problem.
Study of the educational meaning of Statistical Literacy
Kang, Hyun Young ;
Journal for History of Mathematics, volume 25, issue 4, 2012, Pages 121~137
Recently Statistical literacy, reasoning, and thinking become a educational issue. Especially the important of Statistical literacy in purpose of statistics education has be discussed and come to the fore. So we research about Statistical literacy mainly with advanced researches. We consider about the definition and components of Statistical literacy which is discussed in the meantime. And we look into the purpose of statistics education in the school mathematics curriculum and discuss about the implications for the statistics education from the Statistical literacy.
Analysis of Trends of Mathematics Education in Korean Classes Based on TIMSS
Kim, Sun Hee ; Kim, Soojin ;
Journal for History of Mathematics, volume 25, issue 4, 2012, Pages 139~155
This study researched the trends of mathematics education in Korean mathematics class in the aspects of teaching and learning method, assessment and teachers' competency based on TIMSS 1995, 1999, 2003 and 2007. For the mathematics teaching and learning method, the differentiated instruction rate is higher. The activities focused on students not teacher are more, and frequencies of homework are higher but time spent for homework is less than the past. Especially, mathematics teachers link homeworks to instructions. And mathematics teachers uses more multiple choice items and more various assessment methods than the past. The average age of mathematics teachers tends to become older since 1995. The major of mathematics teacher are primarily mathematics and mathematics education. Korean mathematics teachers have less self-esteem for teaching mathematics contents and have more various interactions with peers. The rate of participating in-service training is more or less according to training contents.