联想类比在近世代数定理证明中的运用

The Application of Association and Analogy in Proving Modern Algebra Theorems

联想与类比既是一种普遍的科学思维方式,也是一种有效的教学手段,它是运用已经掌握的知识、方法及解决问题思路等来探索与之类似的问题。该文通过类比Lagrange定理和Sylow第三定理(计数定理)的证明思路,归纳总结其相同的思想方法并加以推广,从而打开学生的解题思路、激发学生的创新思维,提高学生学习近世代数的兴趣.

Association and analogy is a common way of scientific thinking.It is also a kind of effective teaching method.It uses acquired knowledge,methods and problem solving thinking to explore a similar problem.Through the analogy of the proofing ideas of the Lagrange theorem and the Third Sylow theorem(counting theorem),this paper summarizes the same thinking methods and promote them.This opens students'problem solving ideas,stimulates students'innovative thinking and improves the students'interest in learning modern algebra.