面向数学专业本科生的《多元统计分析》课程教学改革研究——融合AI工具的教学优化策略

Research on Teaching Reform of Multivariate Statistical Analysis for Undergraduate Students in Mathematics—Optimization Strategies for Teaching Integration of AI Tools

摘要: 人工智能技术的迅猛发展正在重塑高等教育的人才培养模式。传统《多元统计分析》课程以经典统计理论推导为核心，却在知识传授与能力培养、工具滞后与需求脱节等方面存在深层困境。研究以多元正态总体推断、判别分析、聚类分析与主成分分析四大专题为改革抓手，构建AI工具融合与课程定位更新的双轨策略。基于理论诊断教学难点，设计AI辅助配合独立验证的学习机制，提出将课程定位为AI数学基础衔接课。研究表明，协方差矩阵结构、特征值分解、高斯混合分布、线性或非线性降维等核心概念，构成了理解现代AI模型数学基础的必要前提。

Abstract: The rapid development of artificial intelligence technology is reshaping the talent cultivation model in higher education. The traditional Multivariate Statistical Analysis course focuses on the derivation of classical statistical theories, but faces deep dilemmas in knowledge transmission and ability cultivation, as well as the lagging of tools and the mismatch of demands. This study takes four major topics: inference of multivariate normal populations, discriminant analysis, cluster analysis, and principal component analysis as the reform focus, and constructs a dual-track strategy of integrating AI tools and updating the course positioning. Based on theoretical diagnosis of teaching difficulties, a learning mechanism of AI assistance combined with independent verification is designed, and the course is proposed to be positioned as a bridge connecting AI mathematics and basic courses. The research shows that core concepts such as covariance matrix structure, eigenvalue decomposition, Gaussian mixture distribution, linear or nonlinear dimensionality reduction, etc., constitute the necessary prerequisites for understanding the mathematical foundation of modern AI models.