代数教学中的组合方法  

Combinatorial Approach in Algebra Teaching

作　　者：张军阳 

机构地区：[1]重庆师范大学数学科学学院,重庆

出　　处：《教育进展》2023年第7期4628-4633,共6页Advances in Education

摘　　要：代数学是最重要和基础的数学分支之一。有数学专业的高校都开设了《高等代数》和《抽象代数》课程。组合数学是一门技巧性很强的数学学科。在代数课的教学过程中,引入组合的方法不但能开阔学生的眼界,还能让学生体会到数学专业不同课程之间交叉应用的重要性。本文给出了两种运用组合技巧解决代数问题的方法,其一是通过构造图来求排列的逆序数;其二是将霍尔定理运用到子群陪集的理论中。这两种方法不仅可以帮助学生理解和掌握相关知识点,还能够激发学生探索未知的兴趣。Algebra is one of the most important and basic branches of mathematics. Universities with mathematics majors have offered courses of “Advanced Algebra” and “Abstract Algebra”. Combinatorics is a highly skilled mathematics subject. In the teaching of algebra, the introduction of combinatorial method can not only broaden the horizons of students, but also let students realize the importance of cross-application between different courses in mathematics. The paper presents two methods of solving algebraic problems using combinatorial techniques. One is to find the reverse sequence number of the arrangement by constructing a graph. The other is the application of Hall’s Theorem to the study of the theory of subgroup cosets. These two methods can not only help students understand and master relevant knowledges, but also stimulate students’ interest in exploring the un-known.

关 键 词：逆序数 群论 图论 霍尔定理 

分 类 号：G63[文化科学—教育学]