Go to the main menu
Skip to content
Go to bottom
REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
> Journal Vol & Issue
Journal for History of Mathematics
Journal Basic Information
Journal DOI :
The Korean Society for History of Mathematics
Editor in Chief :
Volume & Issues
Volume 24, Issue 4 - Nov 2011
Volume 24, Issue 3 - Aug 2011
Volume 24, Issue 2 - May 2011
Volume 24, Issue 1 - Feb 2011
Selecting the target year
Yang Hui's NaYinFa
Hong, Sung-Sa ; Hong, Young-Hee ; Lee, Seung-On ;
Journal for History of Mathematics, volume 24, issue 3, 2011, Pages 1~12
It is well known that the sexagesimal cycle(干支) has been playing very important role in ordinary human affairs including astrology and almanacs and the arts of divination(術數). Yin-Yang school related the cycle with the sixty four hexagrams and the system of five notes(五音) and twelve pitch-pipes(十二律), and the processes to relate them are called respectively NaJia(納甲) and NaYin(納音) and quoted in Shen Kuo's Meng qi bi tan(夢溪筆談, 1095). Yang Hui obtained the process NaYin in the context of mathematics. In this paper we show that Yang Hui introduced the concept and notion of functions and then using congruences and the composite of functions, he could succeed to describe perfectly the process in his Xu gu zhai qi suan fa(續古摘奇算法, 1275). We also note that his concept and notion of functions are the earliest ones in the history of mathematics.
Cantor's Theology and Mathematics of the Infinite
Hyun, Woo-Sik ;
Journal for History of Mathematics, volume 24, issue 3, 2011, Pages 13~21
This mathematico-theological study addresses the Cantor's mathematics and theology of the infinite. From the scientific perspective, Cantor's landmark works opened the definition and logic of infinity in concreto, in abstracto, and in Deo. According to Cantor, the absolute infinite
could imply God's property beyond the actual infinite in physical and mathematical worlds.
History and Development of Sphere Theorems in Riemannian Geometry
Cho, Min-Shik ;
Journal for History of Mathematics, volume 24, issue 3, 2011, Pages 23~35
The sphere theorem is one of the main streams in modern Riemannian geometry. In this article, we survey developments of pinching theorems from the classical one to the recent differentiable pinching theorem. Also we include sphere theorems of metric invariants such as diameter and radius with historical view point.
Hilbert's Program as Research Program
Cheong, Kye-Seop ;
Journal for History of Mathematics, volume 24, issue 3, 2011, Pages 37~58
The development of recent Mathematical Logic is mostly originated in Hilbert's Proof Theory. The purpose of the plan so called Hilbert's Program lies in the formalization of mathematics by formal axiomatic method, rescuing classical mathematics by means of verifying completeness and consistency of the formal system and solidifying the foundations of mathematics. In 1931, the completeness encounters crisis by the existence of undecidable proposition through the 1st Theorem of G?del, and the establishment of consistency faces a risk of invalidation by the 2nd Theorem. However, relative of partial realization of Hilbert's Program still exists as a fruitful research program. We have tried to bring into relief through Curry-Howard Correspondence the fact that Hilbert's program serves as source of power for the growth of mathematical constructivism today. That proof in natural deduction is in truth equivalent to computer program has allowed the formalization of mathematics to be seen in new light. In other words, Hilbert's program conforms best to the concept of algorithm, the central idea in computer science.
A reconstruction of the G
del's proof of the consistency of GCH and AC with the axioms of Zermelo-Fraenkel set theory
Choi, Chang-Soon ;
Journal for History of Mathematics, volume 24, issue 3, 2011, Pages 59~76
Starting from a collection V as a model which satisfies the axioms of NBG, we call the elements of V as sets and the subcollections of V as classes. We reconstruct the G
del's proof of the consistency of GCH and AC with the axioms of Zermelo-Fraenkel set theory by using Mostowski-Shepherdson mapping theorem, reflection principles in Tarski-Vaught theorem and Montague-Levy theorem and the fact that NBG is a conservative extension of ZF.
Comprehending the Symbols of Definite Integral and Teaching Strategy
Choi, Jeong-Hyun ;
Journal for History of Mathematics, volume 24, issue 3, 2011, Pages 77~94
This study aims to provide a teaching strategy accommodating the symbols of the definite integral and guiding students through the meaning of notations in area and volume calculations, based on characterization as to how students comprehend the symbols used in the Riemann sum formula and the definite integral, and their interrelationship. A survey was conducted on 70 high school students regarding the historical background of integral symbols and the textbook contents designated for the definite integral. In the following analysis, the comprehension was qualified by 5 levels; students in higher levels of comprehension demonstrated closer relation to the history of integral notations. A teaching strategy was developed accordingly, which suggested more desirable student understanding on the concept of definite integral symbols in area and volume calculations.
Analysis on Korean Middle School Mathematics Textbooks Published in the Syllabus Period Centered on the Concept 'Straight Line'
Do, Jong-Hoon ;
Journal for History of Mathematics, volume 24, issue 3, 2011, Pages 95~108
In this paper we analyse the contents of middle school mathematics textbooks published in the Syllabus Period centered on the concept 'straight line'and discuss how they are different from contemporary mathematics textbooks.
From a Young Mathematics Professor to a Great Mathematics Teacher: Considering Characteristic Features of the Education of Pure Mathematics in the Social, Institutional and Interdisciplinary Contexts of UCL
Cho, Su-Nam ;
Journal for History of Mathematics, volume 24, issue 3, 2011, Pages 109~143
Augustus De Morgan became to be deeply interested in the education of pure mathematics since he came to teach in UCL because of the specific nature of natural philosophy lectures, the academical knowledge and reasoning powers of the students, and the negative attitudes of London society on mathematics. During his long tenure, he really tried his best to make his students understand the important concepts and the principles of pure mathematics, and logically explain the processes of inducing and proving the laws of pure mathematics. When he could not stay as a mere researcher, he had to concern himself with and pay attention to the problems of educating students. And then his teaching style was constructed in a specific way by the various attitudes about mathematics, the boundary relationship between the adjacent academical branches, and the social and systematic nature of UCL.
Establishment of Affective Achievement Criteria and Investigation of 8th Grade Students' Affective Characteristics in Mathematics
Kim, Sun-Hee ;
Journal for History of Mathematics, volume 24, issue 3, 2011, Pages 145~163
This study sets the cut points of affective achievement scores based on the criteria referenced assessment. The modified Angoff method is applied to the standardized mathematics affect inventory which had validity and reliability. The cut points are set for 6 factors i.e. learning directivity, self control, anxiety, interest, cognizing value and confidence. As the results, among percentages of factor that middle school 2nd grade students in Korea achieved, the proportion of cognizing value is the highest. And there are no difference of the proportions as for gender, differentiated instruction, and region.