中国剩余定理在研究性教学中的探讨

Exploration on Chinese Remainder Theorem in Research Teaching

结合教学实践和科研工作的体会,首先讨论了中国剩余定理证明,并将其推广到多项式形式,其次给出了其在多项式环和IMO竞赛中等方面的应用,最后在对研究性教学进行了深刻分析,为数学本科教学改革提供了若干有意义的参考.

Combining teaching practice with research work experience,this paper firstly discusses two different kinds of proof of Chinese Remainder Theorem of elementary number theory. Secondly,it gives its polynomial form and some applications in polynomial ring and IMO. Finally,it analyzes the research - based teaching based on Chi-nese Remainder Theorem and provides some beneficial references for undergraduate mathematical teaching reform.