项目式学习在工科研究生优化理论与方法课程中的应用研究

Research on the Application of Project-Based Learning in the Course of Optimization Theory and Methods for Engineering Graduate Students

摘要: 优化理论与方法是工科研究生重要的数学基础课程，在信号处理、人工智能、工业生产等领域具有广泛应用。针对传统优化理论与方法教学中存在的理论抽象、应用薄弱、教学方法单一、考核方式固化等问题，本文将项目式学习(Project-Based Learning, PBL)引入优化理论与方法的课程教学，构建了“问题驱动–理论支撑–项目实践–成果评价”的教学框架。结合课程核心知识点，设计了基于经验模态分解与稀疏表示的信号降噪、基于主成分分析的图像降维以及基于支持向量机的手写字体识别三个教学项目，详细阐述了项目的知识点映射、任务设计与实施过程。教学实践表明，项目式学习有效提升了学生的学习主动性、理论应用能力和项目总结能力，为研究生数学基础课程的教学改革提供了可参考的实践路径。

Abstract: Optimization Theory and Methods is an important basic mathematics course for engineering graduate students, and it has wide applications in fields such as signal processing, artificial intelligence and industrial production. To address the problems existing in the traditional teaching of Optimization Theory and Methods, including abstract theories, insufficient practical application training, monotonous teaching methods and rigid assessment modes, this paper introduces Project-Based Learning (PBL) into the teaching of this course, and constructs a teaching framework of “problem driving - theoretical support - project practice - achievement evaluation”. Combined with the core knowledge points of the course, three teaching projects are designed: signal denoising based on empirical mode decomposition and sparse representation, image dimensionality reduction based on principal component analysis, and handwritten character recognition based on support vector machines. The knowledge mapping, task design and implementation process of these projects are elaborated in detail. Teaching practice shows that Project-Based Learning can effectively improve students’ learning initiative, theoretical application ability and project summarization capability. It provides a referable practical path for the teaching reform of basic mathematics courses for graduate students.