组合数学中链与反链的教学探索及实践

Exploration and Practice of Teaching Chain and Antichain in Combinatorics

组合数学作为计算机科学的基础课程,在计算机领域有着重要地位。为了改进数学学科传统的定义、定理、证明的教学模式,以组合数学中链与反链的知识点为例,探索如何将数学类课程讲解得更加通俗易懂,并发掘数学与计算机学科的结合点,提升数学类课程的应用性。首先,用矩阵形象地解释链与反链长度与个数的关系,帮助学生更好地理解。然后,给出反链在计算机领域的一个应用实例及其应用前景。通过一“讲”二“应用”的教学方式,极大地调动了学生兴趣,加深了对知识的理解,从而成为数学教学过程中的一个经典案例,非常值得借鉴与推广。

Combinatorics is a foundamental course which is important in the area of computer science.To change the teaching pattern,definition-theorem-proof,of traditional mathematical courses,the teaching module of chain and antichain is taken as an example to explore how to make mathematical courses more popular and easier to understand,and how to use mathematical knowledge in comput⁃er science.Firstly,the relation between length and number of chain and antichain is introduced by using matrix to make it easier to un⁃derstand.Secondly,an example of application of antichain in computer science and its further application prospect are presented.The teaching module of chain and antichain explains profound mathematics theories in simple language,and its relation with computer sci⁃ence is discussed,which arouse students’interest.This teaching pattern is valuable for learning and promotion.