《抽象代数》教学探讨：群的表示与置换表示

Teaching Research of Abstract Algebra: The Representations and Permutation Representation of Groups

摘要: 本文对《抽象代数》中群的置换表示的教学进行了探讨，并将之与群的典范表示、群在集合上的作用进行了比较。由于《抽象代数》课程的高度抽象化和逻辑化，且许多教师在《抽象代数》教学过程中对算例本身的重视程度不足，因此本科生学习抽象代数时，其理解能力受到了很大的限制。为此，本文还提供了一些教学用的简单算例，并在课堂利用这些算例进行教学。相比较不使用算例的教学而言，拥有算例的抽象代数教学产生的教学成果有着明显的提升。

Abstract: This paper we consider the teaching research of Abstract Algebra, and the relations of permutation representations of groups, canonical representations of groups, and the actions on sets. Due to the highly abstract and logicality of Abstract Algebra, and the insufficient emphasis placed by many teachers on the examples themselves during the teaching process, undergraduate students’ understanding ability is greatly limited when studying abstract algebra. Thus, this article provides some simple examples for teaching purposes, and uses these examples for teaching in the classroom. Compared to teaching without using examples, teaching abstract algebra with examples has a significant improvement in teaching outcomes.