中等學校 數學의 位相幾何에 관한 考察

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Issued Date
중등수학 위상기하 거리 위상공간 오일러 정리
Topology is rapidly developing field which applies not only to subsidiary field of mathematics, but also applies to astrophysics, computer science, information technology and molecular biology. It helps students to improve geometric sense and space perception so that they analyze the given subject quickly and perceive characteristic. I have a think about it's necessary to prepare paper since this ability is one of the prerequisites that human resources of modern society should acquire.
As for theoretical background of topology, I would like to take a look at historical overview of topology in the second chapter of this paper and summarized basic concept of topology which is represented by metric, topology, continuous and homeomorphic. In the third chapter, I researched into current status of topology in secondary school and Euler's theorem treated as high class education material in the first grade of middle school. And I also presented brief summary of one writing along with 'Koonigsberg's bridge problem' in relation with discrete mathematics of high school education.
The trend of secondary school is reducing importance of topology, however research for better education involving easy understanding of students and practical use is constantly required since topology teaches students how to analyze mathematical circumstances in their life and helps to improve geometrical intuition.
Alternative Title
A study on topological geometry in mathematics of secondary school
Alternative Author(s)
Youn, Young-Eun
조선대학교 교육대학원
교육대학원 수학교육
Awarded Date
2007. 8
Table Of Contents
Ⅰ. 서론 = 1
A. 중등수학에 있어서 위상기하의 필요성 = 1
B. 위상기하학의 역사적 개관 = 3
Ⅱ. 위상기하의 기본 개념 고찰 = 9
A. 거리 = 9
B. 위상공간 = 12
C. 연속성 = 16
D. 위상동형 = 19
Ⅲ. 중등학교 수학에서의 위상기하 = 26
A. 현행 중등 교육과정의 분석 = 26
B. 오일러 정리 = 27
C. 한 붓 그리기 = 35
Ⅳ. 결론 및 제언 = 39
참고문헌 = 41
조선대학교 교육대학원
윤영은. (2007). 中等學校 數學의 位相幾何에 관한 考察
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Education > Theses(Master)(교육대학원)
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