数学思想方法在高等代数教学中的应用

The Applicationof Mathematical Thinking Methods in Higher Algebra Teaching

高等代数是一门抽象的数学课程,此学科着重于探究代数结构和代数对象的性质,而不是仅着眼于数值的计算。然而目前高等代数教学中存在学生对抽象概念的理解不够深入,缺乏数学思想方法的训练等问题。文章阐述了高等代数中的抽象化、归纳与演绎、构造性和对偶性数学思想方法,便于学生更好理解并拨开高等代数的神秘面纱,从而培养学生优良的数学思维品质,进一步提升高等代数教学水平。

The Advanced algebra is an abstract mathematical course,which focuses on algebraic structures and the properties of algebraic objects rather than specific numerical calculations.However,there are problems in teaching of advanced algebra,such as insufficient understanding of abstract concepts and lack of training in mathematical methods.The article describes the abstraction,induction and deduction,constructive and dyadic mathematical ideas and methods in advanced algebra,so that students can better understand and open the mystery of advanced algebra,so as to cultivate students'excellent quality of mathematical thinking and further improve the teaching level of advanced algebra.