马氏链平稳分布应用案例的教学设计  

Teaching Design of Application Cases of Markov Chain Stationary Distribution

作　　者：刘秀芹[1] 李娜[1] 张志刚[1] LIU Xiuqin;Li Na;ZHANG Zhigang(School of Mathematics and Physics,University of Science and Technology Beijing,Beijing 100083,China)

机构地区：[1]北京科技大学数理学院,北京100083

出　　处：《大学数学》2022年第2期98-103,共6页College Mathematics

基　　金：北京科技大学教学改革项目(JG2019ZD05,JG2017M40,KC2021SZ17)。

摘　　要：马氏链的平稳分布在实际中应用非常广泛,本文介绍了它的一个经典应用案例——市场占有率预测问题的教学设计.本设计从实际生活中的问题引入,以问题为导向,引发同学们的好奇心,从提出问题、分析问题、介绍解决问题的基本原理和方法、再拓展问题,从形象的描述引出抽象的概念,讲解过程中适当融入思政元素,让随机过程教学起到“润物无声”教书育人的效果.The stable distribution of Markov chain is widely used in practice.This paper introduces a classic application case,market share prediction,combined with the current practical background,the design is introduced from the problems in real life,guided by problems,arousing students'curiosity from asking questions,analyzing problems,basic principles of solving problem,and then expanding problems,presenting abstract concept vividly.In the process of explanation,the ideological and political elements are properly integrated,so that random process teaching can play the effect of"moistening things silent"teaching and educating people.

关 键 词：马氏链 思政元素 平稳分布 市场占有率 马氏链基本方程 

分 类 号：O177.5[理学—数学]