高等代数与解析几何的穿插与渗透教学

Interpenetrating and penetrating teaching of higher algebra and analytic geometry

高等代数与解析几何是理工科类与师范类高校必学科目,在数学知识的发展进程上二者相互完善共同推进.研究了当二者合并为一门课程时的内容编排问题,从几何向量的坐标表示法是沟通代数与几何的关键,线性方程组解的结构体现了几何中的平面关系,解析几何中旋转坐标变换是矩阵代数中线性变换在几何中的应用,数量积等向量乘法的运算是行列式在几何中的应用,几何空间中平面与直线的关系是代数中线性空间与子空间结构的几何体现等方面阐述了高等代数与解析几何知识间的相互穿插与渗透,探讨了如何在保持代数与几何相对完整的情况下使得2部分内容融会贯通.

Higher algebra and analytic geometry are required subjects of science and engineering and normal universities,and in the process of the development of mathematical knowledge,they improve each other and promote together.The problem of content arrangement was studied when the two are combined into one course.The interpenetration and penetration between higher algebra and analytic geometry are expounded from some aspects that the coordinate representation of geometric vectors is the key to the communication between algebra and geometry,the structure of the solution of the system of linear equations represents the plane relationship in geometry,rotation coordinate transformation in analytic geometry is the application of linear transformation in matrix algebra in geometry,the operation of scalar product equal vector multiplication is the application of determinant in geometry,the relationship between plane and line in geometric space is the geometric representation of the structure of linear space and subspace in algebra,and so on.It was discussed that how to make the two parts connected while keeping the relative integrity of algebra and geometry.