由划分、等价关系到陪集与Lagrange定理——离散数学中几个相关概念教学方法刍议

From Partition and Equivalence Relation to Coset and Lagrange Theorem——Discussion about the Teaching Method of Several Concepts Included in Discrete Mathematics Course

以逻辑思维训练为主要目的之一的离散数学课程中包含大量概念和结果,为了便于理解且使学生容易接受,选择了若干具有较强相关性但章节上又不集中的重要概念,首先通过分析相互间的关联说明它们之间应有的相互次序,其次说明了如何利用更通俗的示例解释相关的概念,并重点说明了由已知概念合理过渡到一个新概念(陪集)和结果 (Lagrange定理)的教学方法。教学实践说明,这样的教学安排有利于使学生摆脱理论课程的枯燥感,更容易建立起连续、完整的知识构架。

With one of the goals of the training of logic thinking, a lot of concepts and results are in- cluded in Discrete Mathematics Course. For theses content can be understood and accepted easily by students, several important concepts which are relative to each other but separated in different sections are discussed in this paper. Firstly, through analyzing their relation, we explain the correct order, and then illustrate how to explain related concepts with the help of common examples. Among theses we focus on the method how to rea- sonably elicit a new concept （ coset ） and a result （ Lagrange Theorem） from known concepts. The teaching practices shows that the arrangements are helpful to make students get rid of the dull sense of theory course, and a continuous and complete knowledge structure may be easily built.