数学分析的教改札记

On Reading Notes of Teaching Reform in the Mathematical Analysis

以信息社会为特征的新世纪开始便提出扫“数学盲”的历史任务,脱盲的标志则是要懂得微积分基础,微分与积分是数学分析的主体结构.21世纪的大学数学教育应该搞好数学分析课程改革与建设,开展教学研究:(1)数学分析教改与教材建设必须融于大学与中小学数学教育改革的整体之中.(2)注意问题之间的密切相关性与系统性,从唯有源头活水来出发,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.

In the new century, the informal society required us to wipe out the mathematical illiteracy historical task, its symbol was understanding the basic of differential and integral calculus, the differential calculus and integral calculus were the main structure of mathematical analysis. We must make the reform of mathematics analysis and development of the teaching material in the whole construct of the reform of college, middle school and elementary school mathematics education and make its system. 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.