基于预测案例的马尔科夫链教学方法研究

Study on the Teaching Method of Markov Chains Based on Prediction Cases

马尔科夫链由于其对过去、现在、未来状态关系的物理内涵,是实际工程经常运用的数学概念,多用于对未来状态的预测,广泛应用于态势估计、模型构建、趋势预测等方面中。在高校随机过程课程安排中,针对马尔科夫链的教学内容公式化,学生理解较浅,不利于工程实践能力培养。该文重点采用案例教学法,以飞机目标跟踪预测实际工程案例为主线,马尔科夫链物理内涵实现的课程内容为辅线,结合生活中诸多案例讲授本节课程的教学重点及其应用,激发学生对随机过程课程的探索兴趣,锻炼学生自主思考能力。课程强调理论与实践相结合体系,提升学生运用课程内容解决实际问题的能力,并根据马尔科夫链的物理内涵,启发学生保持对未来积极向上、努力拼搏的精神。

Markov chains,due to their physical implications regarding the relationships between past,present,and future states,are concepts frequently applied in practical engineering,primarily for future predition.They are widely used in situation estimation,model construction,trend forecasting,and other areas.In the course design for stochastic processes at universities,the teaching content on Markov chains is too formulaic for students to develop a deep understanding and hindering the cultivation of engineering practice skills.This paper focuses on the case-based teaching method,using an engineering example of aircraft target tracking and prediction as the main thread,supplemented by cases from daily life,to explain the concept and physical significance of Markov chains.This approach emphasizes the mathematical content and their applications,encouraging students to think and explore engineering problems independently.The course integrates theory with practice to enhance students'ability to solve real-world problems using theoretical content.Additionally,based on the physical implications of Markov chains,students are guided to maintain a positive and proactive outlook on life,striving for success in the future.