组合数学课程的教学实践

The teaching practice of combinatorics

组合数学从广义上讲是一门研究离散对象的科学,从狭义上讲主要研究满足一定条件的组态(也称组合模型)的存在、计数以及构造等方面的问题,它的主要内容包括组合计数、组合设计、组合结构和组合优化等,是数学专业高年级本科生和研究生的必修课程,也是计算机专业本科生离散数学课程的重要组成部分.从一些教学的设计出发,探讨如何在教学中引入和展开以及如何在该课程的教学过程中激发学生的学习兴趣,最大限度地调动学生学习的主动性和培养学生发现和解决问题的能力,为学生今后做毕业论文或者进一步从事科学研究工作打下坚实的基础.

Combinatorics is a science researching discrete objects. In narrow sense, it mainly researches the existence, counting as well as structure questions on configuration （also called combinatorial model） which satisfies the fixed conditions. The primary con- tent of combinatorics includes combinatorial counting, combinatorial design, combinatorial structure, and combinatorial optimization and so on. It is a required course for mathematics higher grade undergraduate students and graduate students, also an important compo- nent of discrete mathematics for undergraduate students in computer science. This study main explores how to introduce and expanse in the beginning, and how to stimulate students＇ study interest, transfer students＇study initiative in maximum limit and foster students＇a- bility of finding and solving the problem in eombinatorics teaching design. Thus this can make a solid foundation for the students to ac- complish the research for the future.