中文摘要：

针对学生难以理解高等代数中的基本概念,在高等代数的教学过程中,结合具体教学内容加入一些应用实例帮助学生更好的理解相关概念和体会数学的广泛应用.以讲述矩阵特征值和特征向量为例,除讲解基本概念和计算方法外,结合自己的研究工作介绍了人口模型和传染病模型,给学生展示了特征值和特征向量应用的例子,使得学生对特征值和特征向量有了更深入的理解.

英文摘要：

Most concepts and theorems in advanced algebra are quite abstract and less applicable, which are difficult for freshmen to understand. Application examples in teaching advanced algebra can help students to understand the abstract concept and theorems and their applications. In order to make our teaching more interesting, understandable, and applicable, we have chosen population model and epidemic model as our application examples when we teach matrix, eigenvalues, and eigenvectors. Those models, closely related with our research projects, have given students typical application examples of matrix, eigenvalue and eigenvector. Those examples are very good application which help students to experience the role of mathematics in solving real world problems, and to give students more motivation to learn matrix, eigenvalues, and eigenvectors better.