基于PBL和CBT的Lusin定理的证明及其应用教学  

Demonstration and Application Teaching of Lusin Theorem Based on PBL and CBT

作　　者：赵江林 严勇 ZHAO Jianglin;YAN Yong(School of Science and Technology,Sichuan Minzu College,Kangding,Sichuan 626001,China)

机构地区：[1]四川民族学院理工学院,四川康定626001

出　　处：《西昌学院学报（自然科学版）》2020年第1期38-40,共3页Journal of Xichang University(Natural Science Edition)

基　　金：国家自然科学基金(114661058);四川民族学院数学分析示范课程(sfkc201701);四川民族学院“应用型转型背景下近世代数课程实践教学体系的构建与实践”教学改革项目(川民院发〔2019〕9号)。

摘　　要：研究了基于PBL和CBT的Lusin定理的证明及其应用教学。在实际教学过程中,通过构造问题,提出猜想,证明猜想形成Lusin定理,给出应用Lusin定理证明的例子,构建了Problem-driven-Conjecture-Theorem-Cases of applying theorem教学范畴。学生能更好地知道Lusin定理的来源,理解Lusin定理的结论及其推广结论,掌握Lusin定理证明的思想方法和技巧。In this paper we focus on the demonstration and application teaching of Lusin Theorem based on PBL and CBT.In teaching of the course,by inventing problems,offering conjectures and proving them,we develop the Lusin theorem and present examples for applying Lusin theorem.We develop a new teaching mode of problem-driven-conjecture-theorem-cases of applying theorem,so that students can better understand the origin,conclusion and extension of Lusin theorem and grasp the idea,method and skill of applying Lusin theorem.

关 键 词：Lusin定理 可测函数 连续函数 教学 

分 类 号：D174.1[政治法律—政治学] G642.0[政治法律—国际共产主义运动]