人工智能背景下研究生“矩阵分析”智慧课堂建设实践探索

Practical Exploration of Building a Smart Classroom of “Matrix Analysis” for Postgraduates in the Context of Artificial Intelligence

摘要: 研究生“矩阵分析”课程是一门涉及深刻数学理论及高效数值方法的数学基础课程，课程内容在众多科学研究和工程实践领域有着广泛的应用。随着人工智能在各个领域的广泛推广和应用，“矩阵分析”课程的传统教学模式局限性日益凸显，在有限的课堂时间内难以有效完成预期的教学内容和达成人才培养目标。基于人工智能背景下的“矩阵分析”智慧课堂模式应运而生。该模式基于学情分析和课程主要内容，以分类培养、提升教学质量和激发创新潜力为核心目标，以“教”与“学”为主线，在课前、课中、课后三个阶段分别展开智慧课堂的构建和持续优化，达到提升教育教学效果等多维度教育价值。

Abstract: The “Matrix Analysis” course for postgraduate students is a foundational mathematics program that delves into profound mathematical theories and efficient numerical methods, with applications spanning a wide range of scientific research and engineering practices. With the widespread adoption and application of artificial intelligence (AI) across various fields, the limitations of traditional teaching methods in this course have become increasingly apparent—struggling to effectively deliver the intended curriculum and achieve talent development goals within limited class hours. In this context, the AI-driven smart classroom model for “Matrix Analysis” has emerged. This model is designed around learner profiling and core course content, with the primary objectives of categorized talent cultivation, enhanced teaching quality, and stimulated innovation potential. Centered on the dual pillars of “teaching” and “learning”, the model implements smart classroom construction and continuous optimization across three phases: pre-class, in-class, and post-class. By doing so, it achieves multidimensional educational value, including improved teaching effectiveness and learning outcomes.