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
群论及其应用 Group Theory and Its Applications
2.
授课院系
Originating Department
数学系 Department of Mathematics
3.
课程编号
Course Code
MA440
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
秋季 Fall
7.
授课语言
Teaching Language
中英双语 English & Chinese
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，教授，数学系
慧园 3 栋 528
邮箱: lich@sustc.edu.cn
电话: 0755-88018755
Caiheng Li, Professor, Department of Mathematics
Room 528, Block 3, Wisdom Garden.
email: lich@sustc.edu.cn
phone: 0755-88018755
9.
实验员/助教、所属学系、联系
方式
Tutor/TA(s), Contact
无 NA / 待 公 布 To be announced / 已 确 定 的 实 验 员 /助 教 联 系 方 式 Please list all
Tutor/TA(s)
（请保留相应选项 Please only keep the relevant information）
10.
选课人数限额(可不填)
Maximum Enrolment
（Optional）
2
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
48
12.
先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
MAT7044 代数专题-群论、MAT7012 代数图论
MAT7044 Topics in Algebra- Group theory、MAT7012 Algebraic Graph Theory
13.
后续课程、其它学习规划
Courses for which this course
is a pre-requisite
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
让学生熟练掌握群论及对称图论的基本知识、方法，及其主流问题和重要问题；通过学习有限单群分类定理，了解该领域
的发展趋势。学生学习内容包括 Structures and actions of finite groups，group representations over finite fields,
subgroups of finite classical groups, group actions on graphs and graph symmetries, and isomorphism problems for
Cayley graphs.
Students are supposed to understand basic knowledge and methods of group theory and symmetric graph theory, as
well as their mainstream and important problems. Students can also understand the development tendency of group
theory by learning the classification of finite simple groups. The main content includes Structures and actions of finite
groups，group representations over finite fields, subgroups of finite classical groups, group actions on graphs and graph
symmetries, and isomorphism problems for Cayley graphs.
16.
预达学习成果 Learning Outcomes
为学生进入群论及其相关领域的研究工作打下基础，掌握必要的知识和技能。通过对有限单群分类定理的学习，以及有限
单群在对称图、表示论等方向中的应用，对前沿的发展动态有所了解，找到适当的研究问题并解决。
Lay the foundation of the research of group theory and related areas. Understand frontier development trend of group
theory by learning the classification of finite simple groups and its applications on symmetric graphs and representation
theory. Find and try to solve some research 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.)
1. 有限群的结构和群作用 Structures and actions of finite groups (10 credit hours)
2. 群在有限域上的表示 Group representations over finite fields (10 credit hours)
3. 有限典型群的子群 Subgroups of finite classical groups (10 credit hours)
4. 群在图上的作用和图的对称性 Group actions on graphs and graph symmetries (10 credit hours)
5. Cayley 图的同构问题 Isomorphism problems for Cayley graphs (8 credit hours)
18.
教材及其它参考资料 Textbook and Supplementary Readings
3
1. Lecture Notes on Symmetric graphs, by LI Cai Heng
2. The Finite Simple Groups, GTM 251, by Robert Wilson
3. Permutation Groups, by Peter Cameron.
4. Algebraic Graph Theory, by Norman Biggs
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
50
平时作业
Assignments
期中考试
Mid-Term Test
期末考试
Final Exam
2 小时
50
期末报告
Final
Presentation
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