“高等代数”教材教改探索

Exploration on Teaching Reform of Advanced Algebra

从高等代数现有教材出发,分析了国内外高等代数教材的现状,探讨了高等代数教材改革的背景、方向和目标,在研究现有各类教材的基础上取长补短,编写了适合学生学习的高等数学讲义。其编写内容体系依次为:多项式理论,行列式、矩阵、线性方程组、线性空间、线性映射、特征值、若当标准型、二次型理论、内积空间、实际应用案例。其特点为:对每个概念的引入采用了更加通俗易懂的方法,内容作了适当整合,加强理论联系实际,增加教学实用案例。该教材更适合理工科学生对本课程的要求。

This paper analyzes the current situation of domestic and foreign teaching materials of advanced algebra based on the existing textbooks of advanced algebra,and discusses the background,direction and target of teaching reform of advanced algebra,and discusses the attempts and efforts we made in this respect. We wrote an advanced algebra textbook adapted to students of our university on the basis of various existing teaching materials. The content system of this textbook is as follows： polynomial theory,determinant,matrix,linear equations,linear space,linear mapping,characteristic value,Jordan standard,theory of quadratic form,inner product space and the practical application cases. Some characteristics of this textbook are obvious. Firstly,we introduce each concept in an easier way; secondly,we integrate some contents;thirdly,we put more attention on combining the theory with practice; fourthly,we increase practical cases. The textbook is more suitable for the students of science and engineering.