AI赋能数值分析教学改革探索与实践——以理工科研究生数值分析为例

AI-Enhanced Curriculum Reform in Numerical Analysis: Exploration and Practice—A Case Study of Graduate Numerical Analysis in Engineering and Science

摘要: 在新工科建设与人工智能(AI)技术深度融合的时代背景下，研究生数值分析课程面临着传统数学理论与智能算法融合、工程实践与教学内容衔接等关键性挑战。本文构建以AI技术赋能为核心的课程改革框架，通过“经典基础–现代前沿”两层递进的内容体系重构和智能化个性化教学平台建设，形成了“理论基础–算法实现–工程应用”三位一体的创新教学模式。该模式采用问题驱动式教学方法，融合混合式教学手段，实现了知识传授与能力培养的有机统一。教学实践验证表明，改革方案在提升学生数学建模能力、算法设计能力和工程实践能力方面效果显著，学生在解决复杂工程问题的综合能力上获得了显著提升。研究成果为新工科背景下理工科高阶课程的智能化改革提供了可借鉴的理论框架和实践路径。

Abstract: Under the dual driving forces of emerging engineering education and the rapid development of artificial intelligence (AI) technology, graduate numerical analysis courses face critical challenges in bridging classical mathematical theories with intelligent algorithms and connecting engineering problems with pedagogical content. This paper establishes an AI-empowered curriculum reform framework through the reconstruction of a two-tier progressive content system combining “classical foundations with modern frontiers”, the development of intelligent personalized teaching platforms, and the implementation of deep industry-academia integration mechanisms, forming an innovative three-dimensional teaching model that integrates “theoretical foundations-algorithmic implementation-engineering applications”. The model employs problem-driven teaching methods and blended learning approaches, achieving organic unity between knowledge transmission and competency development. Pedagogical practice validation demonstrates that the reform initiative significantly enhances students’ mathematical modeling capabilities, algorithm design skills, and engineering practice abilities, with notable improvements in their comprehensive capacity to solve complex engineering problems. The research outcomes provide a referenceable theoretical framework and practical pathway for the intelligent transformation of advanced STEM courses under the emerging engineering education paradigm.