中等學校 數學의 位相幾何에 관한 考察

Abstract

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.