初等数学中的一些拓扑思想

Some topological ideas in elementary mathematics

拓扑学是高师院校数学专业的一门重要课程.拓扑学的思想和方法已经渗透到现代数学的很多领域,并且广泛地应用在许多学科中.通过我国部分地区中考、高考及竞赛数学试题实例,阐述了初等数学中出现的一些拓扑学思想,论证了在高师院校数学专业开设拓扑学的必要性.这样才能使拓扑学的研究方法和思想更好地渗透到初等数学的教学中,使中学生更好地认识数学的本质,掌握一些数学方法,提高分析问题和解决问题的能力,增加数学学习兴趣.

Topology is an important course of mathematics in normal universities.The ideas and methods of topology have permeated many fields of modern mathematics,and they have been widely used in many disciplines.Some topological ideas in elementary mathematics are stated by the examples of mathematics questions in senior high school entrance examination and college entrance examination and competition in some regions of China.The necessity of setting up topology in the subject of mathematics in normal universities are discussed.In this way,the ideas and methods of topology can preferably permeated in the teaching of elementary mathematics.For middle school students,the nature of mathematics can be better understood,and some mathematical methods can be mastered, and the ability to analyze and solve problems can be improved,and the interest in mathematics study can be increased.