Research on enhancing research and innovation capabilities of mathematics graduate students in the context of artificial intelligence
人工智能背景下数学专业研究生科研创新能力提升研究

摘要

人工智能在当前社会有着极为广泛的应用，随着人工智能的快速发展，在国家发展中占据了重要地位。众所周知，数学与人工智能密切相关，数学不仅是人工智能的理论基础，还在其算法、模型和应用中发挥着关键作用，人工智能又能将数学理论应用在实际生活中。数学与人工智能相辅相成，互相促进。因此，数学和人工智能的交叉融合成为当前和未来高校教育的一个重要方向。鉴于此，本文聚焦于数学与人工智能交叉融合教育及学生创新能力培养，面对当前学科融合的复杂性、课程设计与教学方法的整合以及缺乏跨学科项目实践与创新机会三方面挑战，提出数学基础与人工智能的交叉点分析、跨学科课程融合与设计以及跨学科科研能力提升的应对策略。

Abstract

Artificial intelligence has found widespread applications in contemporary society and has gained prominence in national development with its rapid advancement. Mathematics and artificial intelligence are closely interconnected: mathematics serves not only as the theoretical foundation of artificial intelligence but also plays a pivotal role in its algorithms, models, and applications. Conversely, artificial intelligence facilitates the practical application of mathematical theories. These two disciplines are mutually reinforcing and synergistically integrated. Consequently, the interdisciplinary convergence of mathematics and artificial intelligence has emerged as a significant direction in current and future university education. Focusing on interdisciplinary integration education and the cultivation of students' innovative capabilities, this paper addresses three critical challenges: the complexity of current disciplinary integration, the integration of curriculum design and teaching methodologies, and the scarcity of interdisciplinary project practice and innovation opportunities. Corresponding strategies are proposed, including analysis of the intersection between mathematical foundations and artificial intelligence, interdisciplinary curriculum integration and design, and enhancement of interdisciplinary scientific research capabilities.