以应用为导向的矩阵论课程教学改革的探索与实践

Exploration and Practice of Teaching Reform in Matrix Theory Courses Oriented by Applications

摘要: 矩阵作为数学和工程领域的核心工具，能够高效表示与操作多维数据，广泛应用于线性代数、最优化理论、机器学习及深度学习等学科，是解决复杂系统模型、算法优化及跨学科问题的重要桥梁。本文围绕以应用为导向的矩阵论课程教学改革展开研讨，针对传统教学中存在的问题，提出了切实可行的改革方案，重点聚焦课程思政与“人工智能+”课程建设的融合、教材改革与后续课程的衔接、案例与实践教学的强化以及多元化评价体系的构建。通过广度与深度相结合的方式，突出矩阵论知识在数学建模中的应用，旨在提升学生的实践能力与创新思维，进而提高课程教学质量。

Abstract: Matrices, as a core tool in mathematics and engineering, are widely used in disciplines such as linear algebra, optimization theory, machine learning, and deep learning. It serves as the foundational bridge for solving complex system models, algorithm optimization, and interdisciplinary problems by efficiently representing and manipulating multidimensional data. This paper focuses on the teaching reform of matrix theory oriented towards applications. It addresses the existing issues in traditional teaching and proposes reform ideas. The emphasis is on the integration of course ideology and politics with the construction of artificial intelligence-plus courses, the reform of teaching materials and their connection with follow-up courses, the enhancement of case and practical teaching, and the establishment of a diversified evaluation system. By combining breadth and depth, the paper highlights the application of matrix theory knowledge in mathematical modeling, aiming to improve students’ practical abilities and innovative abilities, and thereby enhance the quality of teaching in the course.