高等代数中两道习题的问题变式

The Variation of Problems in Two Exercises of Advanced Algebra

通过对高等代数考研题中两组变式题组的变式分析以及问题解决的过程,可以看到:在进行考研复习的解题训练时,学生首先应立足于课本,熟练掌握课本习题提供的解题思想、方法和结论.其次应多关注题题之间的关系,从中抽取出问题表面特征以外的结构特征,建立起题目的数学结构.再次应学会对问题进行多层次变式分析(或构造),对问题解决过程及问题本身的结构有清晰的认识,从而积累问题解决的经验,提高解决问题的能力.

By analyzing two groups of variant exercises of advanced algebra in the review for postgraduate entrance examination and their solving process,it can be seen that in preparation for the examination,students can improve their ability to solve problems by accumulating the problem-solving experience in three ways.First,students should base their training on the textbook and master the idea,method and conclusion that textbooks provide in solving the given exercises.Second,students should pay more attention to the relations between exercises and extract the structural characteristics besides their superficial ones in order to establish the mathematical model of the problem.Third,students should learn to analyze problems and their variants at different levels.Only with a clear understanding of the mathematical structure of problems and their solving process can students improve their ability to solve problems.