AI赋能研究生数学基础课的教学改革与探索——以《矩阵分析》课程为例

Reform and Exploration of Postgraduate Basic Mathematics Course Teaching Empowered by AI—A Case Study of the Course “Matrix Analysis”

摘要: 随着人工智能技术的飞速发展，教育领域正经历着深刻变革。《矩阵分析》作为研究生阶段最重要的数学基础课程之一，其抽象性强、知识点多而且复杂的特点导致传统的教学模式面临诸多问题。本文基于AI技术与矩阵分析教学相融合的视角，讨论AI赋能矩阵分析课程教学改革的途径与方法。通过分析传统教学方法的痛点，构建“AI + 矩阵分析”的混合式教学模式，从教学内容重构、教学方法创新、评价体系优化三个维度设计改革方案，为研究生数学基础课程的教学改革提供参考。

Abstract: With the rapid development of artificial intelligence technology, the field of education is undergoing profound changes. “Matrix Analysis”, as an important basic mathematics course at the postgraduate level, is characterized by strong abstraction, multiple knowledge points and a complex theoretical system, which brings many challenges to traditional teaching modes. This article, based on the perspective of integrating AI technology with matrix analysis instruction, discusses approaches and methods for AI-enabled matrix analysis course teaching reform. By analyzing the pain points of traditional teaching methods, a blended teaching model based on “AI + Matrix Analysis” is constructed. A reform plan is designed from three perspectives: reconstructing teaching content, innovating teaching methods, and optimizing the evaluation system. This provides a reference for teaching reform in foundational mathematics courses for graduate students.