CAJ | 학술논문

恰当的反例能很好地帮助学生正确地理解和掌握相关数学概念及定理.本文研究了高等代数中有关矩阵、多项式和线性变换中的典型问题,并通过修改命题的条件或结论构造了反例,深入探讨了特殊矩阵及其联系、多项式的整除性等方面的命题.高等代数的反例研究对于高等代数教学具有较好的指导意义.
흡당적반례능흔호지방조학생정학지리해화장악상관수학개념급정리.본문연구료고등대수중유관구진、다항식화선성변환중적전형문제,병통과수개명제적조건혹결론구조료반례,심입탐토료특수구진급기련계、다항식적정제성등방면적명제.고등대수적반례연구대우고등대수교학구유교호적지도의의.
The proper counterexamples can help the students to understand and grasp the mathematic concepts and the theories. In this paper, the typical questions about matrices, polynomial and linear transformation in the advanced algebra were researched. Some counterexamples were constructed by changing the conditions and conclusions,and special matrices and their connections, polynomial divisi- bility were further studied. The research about the counterexamples has a better aignificance for higher algebra teaching.