| 高等代数中的反例研究 |
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| 引用本文： | 梁武,杜玉霞,段鹏举.高等代数中的反例研究[J].甘肃联合大学学报(自然科学版),2012(4):93-95. |
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| 作者姓名： | 梁武 杜玉霞 段鹏举 |
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| 作者单位： | 宿州学院智能信息处理实验室;宿州学院数学与统计学院 |
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| 基金项目： | 安徽省教育厅教学研究项目(20101071);宿州学院智能信息处理实验室开放课题(2010YKF12);宿州学院教学研究项目(szxyjyxm201143) |
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| 摘 要： | 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.
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| 关 键 词： | 反例 矩阵 多项式 线性变换 |
The Counterexamples of the Advanced Algebra |
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| LIANG Wu,DU Yu-xia,DUAN Peng-ju.The Counterexamples of the Advanced Algebra[J].Journal of Gansu Lianhe University :Natural Sciences,2012(4):93-95. |
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| Authors: | LIANG Wu DU Yu-xia DUAN Peng-ju |
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| Institution: | 1.Lab of Intelligent Information Processing,Suzhou University,Suzhou 234000,China;2 School of Mathematics and Statistics,Suzhou University,Suzhou 234000,China) |
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| Abstract: | 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 divisibility were further studied.The research about the counterexamples has a better significance for higher algebra teaching. |
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| Keywords: | counterexample matrix polynomial linear transformation |
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