关于数学分析教学改革的几点思考和尝试

Some Thoughts and Attempts on Teaching Reform of Mathematical Analysis

一提到高等数学,通常人们首先想到的就是微积分.微分与积分是数学分析的主体结构,因此,数学分析的教学改革在21世纪的大学数学教育中显得尤为重要,文章从以下几个方面谈关于数学分析教学改革的研究:1)数学分析教材的处理;2)注意问题之间的密切相关性与系统性,挖掘问题的内在联系,培养学生掌握看问题的角度;3)注意各门学科之间的交叉关系,将高等代数、实变函数、泛函分析、点集拓扑等相关内容与数学分析进行整合;4)注意渗透现代数学思想,培养学生掌握看问题的高度.

Usually,people think of the differential calculus and integral calculus as soon as you mention higher mathematics. The differential calculus and integral calculus were the main structure of mathematical analysis. Therefore, it is very important that we make the reform of mathematical analysis in new century. There we study this problem as follows：deal with the teaching material of mathematics; we should pay attention to the system and close relativity among the question,excavate the intrinsic relation of the question from the source considering, train the student to handle the question method;we should pay attention to the cross relation of all kinds subject, arrange and merge relative content of mathematical analysis in the advance algebra,the real analysis, function analysis and the point topology ;we should pay attention to the educated value of the idea of morden mathematical.