以爱国主义深情开启高等数学第一课——以“数列的极限”为例开展思政教学

Start the First Lesson of Advanced Mathematics with Patriotic Affection—Taking “the Limit of the Sequence” as an Example to Carry Out Ideological and Political Education

极限是高等数学中的基本概念,是微积分整个知识框架的基础。高等数学中的若干概念,例如,连续、间断、可导、可积、级数收敛等,均通过极限来定义。深刻透彻地理解极限,尤其是数列的极限,是学好高等数学的关键。本文通过解析数列极限中蕴含的量变与质变的辩证关系,详细透彻地分析了数列极限的概念。在增强学生辩证思维的同时,通过介绍中国古代数学家的研究思想和研究方法,增强了学生的民族自豪感,激发了学生的爱国主义热情。从而,在高等数学第一课中,“润物细无声”地实施了思政教学。

The limit is a fundamental concept in Advanced Mathematics and it is the basis of the entire intel-lectual framework of Calculus. The concepts of continuity, discontinuity, derivability, integrability, and convergence of series are all defined by limits. A deep and thorough understanding of limits, especially the limits of sequences, is the key to learning Advanced Mathematics. This paper analyzes the dialectical relationship between quantitative change and qualitative change contained in the limit of equence, and analyzes the concept of the limit of a sequence in detail. While enhancing students’ dialectical thinking, through the introduction of the research ideas and research methods of ancient Chinese mathematicians, the students’ national pride is enhanced and the students’ patriotism is stimulated. Thus, in the first lesson of Advanced Mathematics, ideological and political education is implemented “imperceptibly”.