1
课程详述
COURSE SPECIFICATION
以下课程信息可能根据实际授课需要或在课程检讨之后产生变动。如对课程有任何疑问，请联
系授课教师。
The course information as follows may be subject to change, either during the session because of unforeseen
circumstances, or following review of the course at the end of the session. Queries about the course should be
directed to the course instructor.
1.
课程名称 Course Title
组合数学 Combinatorics
2.
授课院系
Originating Department
数学系 Department of Mathematics
3.
课程编号
Course Code
MAT8010
4.
课程学分 Credit Value
3
5.
课程类别
Course Type
专业选修课 Major Elective Courses
6.
授课学期
Semester
春季 Spring
7.
授课语言
Teaching Language
英文 English
8.
授课教师、所属学系、联系方
式（如属团队授课，请列明其
他授课教师）
Instructor(s), Affiliation&
Contact
（For team teaching, please list
all instructors）
李才恒 LI Caiheng
数学系 Department of Mathematics
lich@sustech.edu.cn
朱一飞 ZHU Yifei
数学系 Department of Mathematics
zhuyf@sustech.edu.cn
9.
实验员/助教、所属学系、联系
方式
Tutor/TA(s), Contact
待公布 To be announced
10.
选课人数限额(可不填)
Maximum Enrolment
（Optional）
授课方式
Delivery Method
习题/辅导/讨论
Tutorials
实验/实习
Lab/Practical
其它(请具体注明)
Other（Please specify）
总学时
Total
11.
学时数
Credit Hours
45
2
12.
先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
抽象代数（MA214）
Abstract Algebra (MA214)
13.
后续课程、其它学习规划
Courses for which this course
is a pre-requisite
代数图论 Algebraic Graph Theory (MAT7012)
14.
其它要求修读本课程的学系
Cross-listing Dept.
教学大纲及教学日历 SYLLABUS
15.
教学目标 Course Objectives
组合数学是一门研究离散结构及其构造的学科，它由众多分支组成。本课程针对基础及应用数学方向本科生设置，教学内
容将覆盖组合计数、组合极值理论、图论、设计理论、有限几何、编码和密码学。教学目标旨在让学生了解和掌握组合数
学的基础理论、基本方法、重要例子以及主要结果，培养学生在组合数学领域初步的科研能力。
Combinatorics is the study of discrete structures and configurations. It consists of several sub-areas. This course is for
students majoring in mathematics and applied mathematics. The course will cover enumerative combinatorics, extremal
combinatorics, graph theory, design theory, coding theory, finite geometry, and some parts of cryptography. The goal is
to make sure that the students understand fundamental theories, important examples and main results, and can use
combinatorial methods in future study and research.
16.
预达学习成果 Learning Outcomes
完成本课程后，学生应掌握组合数学的基本概念和方法，熟悉各种组合方法和技巧，并能解决现实生活提出的问题。特别
地，在学习本课程后，学生应该能够达到以下几点。
掌握基本知识，深入理解和掌握定义、定理、原则和公式本质。学习后，学生应该能够不仅记住概念和基本组合
方法，同时也能深刻理解组合数学的基本原理和理念。
培养思维能力，提高对事物的观察、研究组合结构的能力。
提高解决实际问题的能力。学习本课程后，学生应该能够使用学到的知识解决相关的数学问题。
After completing this course, students should master the basic concepts and methods in combinatorics. After learning
the course, students should be familiar with a range of methods and techniques for solving real-life problems. In
particular, the students should achieve the following.
Master the basic knowledge and acquire an in-depth understanding of the definitions, theorems, combinatorial
principles and formulas. After the study, students should be able not only to remember the concepts and the
basic combinatorial laws, but also understand the basic principles and ideas of combinatorial theory.
Enhance the ability of thinking and doing research in combinatorics.
Improve the ability of solving practical problems. After learning this course, students should be able to use the
learned knowledge to solve real-life problems.
17.
课程内容及教学日历 （如授课语言以英文为主，则课程内容介绍可以用英文；如团队教学或模块教学，教学日历须注明
主讲人）
Course Contents (in Parts/Chapters/Sections/Weeks. Please notify name of instructor for course section(s), if
this is a team teaching or module course.)
3
Recurrence relations and generating functions (2 lectures)
The principle of inclusion and exclusion (2 lectures)
Latin squares, systems of distinct representatives, Hall’s marriage theorem (4 lectures)
Extremal set theory, including Sperner’s theorem and the Erdős–Ko–Rado theorem (4 lectures)
Finite geometry, including Gaussian coefficients, projective planes, and the Bruck–Ryser–Chowla theorem (4
lectures)
Ramsey’s theorem, including the pigeonhole principle, Ramsey numbers (3 lectures)
Basic graph theory, including trees, Eulerian graphs, Hamiltonian graphs (3 lectures)
18.
教材及其它参考资料 Textbook and Supplementary Readings
J.H. van Lint and R.M. Wilson, A course in combinatorics, Cambridge University Press
R.P. Stanley, Enumerative combinatorics, Vol. I, Second Edition, Cambridge University Press
课程评估 ASSESSMENT
19.
评估形式
Type of
Assessment
评估时间
Time
占考试总成绩百分比
% of final
score
违纪处罚
Penalty
备注
Notes
出勤 Attendance
课堂表现
Class
Performance
小测验
Quiz
课程项目 Projects
平时作业
Assignments
50
三次章节作业，设置助教批改
Three chapter assignments, with a
grader
期中考试
Mid-Term Test
期末考试
Final Exam
50
闭卷 Closed-book
期末报告
Final
Presentation
4
其它（可根据需要
改写以上评估方
式）
Others (The
above may be
modified as
necessary)
20.
记分方式 GRADING SYSTEM
A. 十三级等级制 Letter Grading
B. 二级记分制（通过/不通过） Pass/Fail Grading
课程审批 REVIEW AND APPROVAL
21.
本课程设置已经过以下责任人/委员会审议通过
This Course has been approved by the following person or committee of authority