AI赋能的高等数学可视化研究——以二次曲面为例

AI Empowered Visualization in Advanced Mathematics—A Case Study of Quadratic Surfaces

摘要: 数学可视化并非新兴研究领域，但随着生成式人工智能大模型的兴起，该领域正经历全方位的深刻变革。本文简要梳理了数学可视化的发展脉络，系统归纳总结了AI技术驱动下数学可视化演示项目的核心特征，详细阐述了依托此类工具开发数学可视化演示内容的一般方法与流程。本文以高等数学课程核心知识点二次曲面作为应用案例，完整呈现了从需求构思、方案设计到交互式可视化演示网页开发实现的全流程，并对AI赋能科研与教学工作的未来发展进行了展望。

Abstract: Mathematical visualization is not a new research field, but with the rise of large generative artificial intelligence models, this field is undergoing profound, all-round changes. This paper briefly sorts out the development context of mathematical visualization, systematically summarizes the core characteristics of AI technology-driven mathematical visualization demonstration projects, and elaborates in detail the general methods and processes for developing mathematical visualization demonstration content relying on such tools. Taking quadratic surfaces, the core knowledge point of advanced mathematics courses, as an application case, this paper fully presents the entire process from demand conception and scheme design to the development and implementation of interactive visualization demonstration web pages, and prospects the future development of AI-enabled scientific research and teaching work.