人工智能时代研究生数理基础贯通课程体系建设研究

Research on the Construction of an Integrated Curriculum System for Mathematical Foundations in Graduate Education in the Era of Artificial Intelligence

摘要: 人工智能的迅猛发展对研究生阶段的数据科学与数学基础教育提出了前所未有的挑战。传统的高等数学、线性代数与概率论课程多以理论体系为导向，缺乏对人工智能算法与数据分析实践的呼应，导致学生数学知识割裂、应用理解不足。本文以“人工智能时代数据科学基础课程体系建设”为研究主题，聚焦研究生阶段的高等数学与微积分课程，探索如何通过贯通式教学实现数学原理、算法逻辑与数据实践的深度融合。研究提出“数学–算法–数据”三层贯通模型，并基于课程内容共现分析与教学案例词云，揭示AI核心算法与数学基础的映射关系。通过案例驱动、混合式教学和可视化实验的有机结合，显著提升了学生的数学应用意识与跨学科理解能力。本文的研究为高校数学类课程在人工智能时代的结构重构与教学创新提供了可推广的范式。

Abstract: The rapid development of artificial intelligence (AI) has posed unprecedented challenges to graduate education in data science and mathematical foundations. Traditional courses such as Advanced Mathematics, Linear Algebra, and Probability Theory are primarily theory-oriented and often lack alignment with AI algorithms and data analysis practices, leading to fragmented mathematical knowledge and insufficient application-oriented understanding among students. This study, entitled “Construction of a Data Science Foundation Curriculum System in the Era of Artificial Intelligence”, focuses on graduate-level courses in Advanced Mathematics and Calculus. It explores how integrated teaching can achieve a deep fusion of mathematical principles, algorithmic logic, and data-driven practice. The research proposes a three-layered “Mathematics-Algorithm-Data” integration model and, through co-occurrence analysis of curriculum content and keyword-based visualization of teaching cases, reveals the mapping relationships between core AI algorithms and fundamental mathematical concepts. By organically combining case-driven learning, blended teaching, and visualization-based experimentation, this reform significantly enhances students’ awareness of mathematical application and their interdisciplinary comprehension ability. The findings of this paper provide a replicable paradigm for structural reconstruction and pedagogical innovation of mathematics-related curricula in the era of artificial intelligence.