新工科背景下应用统计学专业高等代数课程的案例式教学——以机器学习中的核方法为例

Case-Based Teaching of Advanced Algebra in the Applied Statistics under the New Engineering Discipline—A Case Study of Kernel Methods in Machine Learning

摘要: 在新工科背景下，传统高等代数课程亟需与现代工程技术相结合，以提升学生的实际应用能力。本文以机器学习中的核方法为例，探讨如何通过案例式教学法创新高等代数课程的教学模式，以促进应用统计学专业学生对高等代数知识的深入理解与应用。通过引入支持向量机，系统性地讲解核函数、特征空间映射及相关代数运算在高维数据分析中的重要作用，从而帮助学生更好地理解高等代数在数据分析中的实际应用。教学反馈表明，案例式教学提高了学生对高等代数核心概念的掌握，促进了理论与实践的有效结合，从而推动了高等代数与现代工程技术的深度融合。

Abstract: In the era of the New Engineering Discipline, traditional advanced algebra courses must urgently integrate with modern engineering technologies to enhance students’ practical application skills. This paper uses kernel methods in machine learning as a case study to explore how case-based teaching can innovate the teaching model of advanced algebra, fostering a deeper understanding and application of advanced algebra concepts among students in the Applied Statistics program. By introducing support vector machines, the paper systematically explains the role of kernel functions, feature space mapping, and associated algebraic operations in high-dimensional data analysis, thereby helping students better grasp the practical applications of advanced algebra in data analysis. Teaching feedback indicates that case-based teaching has improved students’ mastery of key advanced algebra concepts, facilitated a more effective integration of theory and practice, and thus fostered a deeper connection between advanced algebra and modern engineering technologies.