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
几何与拓扑讨论班 Seminar in Geometry and Topology
2.
授课院系
Originating Department
理学院数学系 Department of Mathematics, School of Sciences
3.
课程编号
Course Code
MA423
4. 课程学分 Credit Value
1
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）
朱一飞，数学系，zhuyf@sustech.edu.cn
Ingrid Irmer，数学系，ingridmary@sustech.edu.cn
Stavros Garoufalidis，数学系，stavros@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
（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
11.
授课方式
Delivery Method
讲授
Lectures
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
学时数
Credit Hours
32 0 0 0 32
12.
先修课程、其它学习要求
Pre-requisites or Other
Academic Requirements
MA323 拓扑学 Topology, MA327 微分几何 Differential Geometry
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
几何与拓扑和代数、分析一道是基础数学的三大领域，强调几何直观，包括微分几何（几何分析）、代数几何、代数拓
扑、几何拓扑（低维拓扑）等活跃的研究方向。本讨论班旨在发挥数学系几何与拓扑方向的师资优势，由相关教员组织感
兴趣的同学围绕前沿、交叉专题滚动开设。形式为学生分工轮流主讲，负责教师指导并与该方向其他教师及外校专家参与
选讲。近期可能讨论的专题包括应用与计算拓扑、流形与模形式、四维流形的拓扑与几何、纽结论与代数数论等。
Geometry and topology, algebra, and analysis are the three major fields of pure mathematics. It emphasizes geometric
intuition and visualization, and includes active research areas such as differential geometry (geometric analysis),
algebraic geometry, algebraic topology, and geometric topology (low-dimensional topology). The seminar grows out of a
strong representation of the field by faculty in the Department. Relevant faculty members will take turns over semesters
to organize interested students for directed reading on hot topics. Registered students will present assigned topics
under supervision of the instructor, with supplementary lectures by the instructor, other relevant faculty members, as well
as experts in the field from other universities. Recent proposed topics include applied and computational topology,
manifolds and modular forms, the topology and geometry of four-manifolds, knot theory and algebraic number theory.
16.
预达学习成果 Learning Outcomes
掌握几何与拓扑专题的基本理论和实例。
初步具备研究的意识和能力。
Learn the basic theory and examples of topics in geometry and topology.
Acquire a scientific mentality and basic abilities for research.
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
Introduction and organization (1 lecture)
Student presentations (3 lectures)
Supplementary examples and applications (1 lecture)
Student presentations (3 lectures)
Supplementary examples and applications (1 lecture)
Student presentations (3 lectures)
Supplementary examples and applications (1 lecture)
Additional topics and applications, further readings (2 lectures)
18.
教材及其它参考资料 Textbook and Supplementary Readings
教材 Textbook
Herbert Edelsbrunner and John L. Harer, Computational Topology: An Introduction, American Mathematical
Society
Friedrich Hirzebruch, Thomas Berger, and Rainer Jung, Manifolds and Modular Forms, Viewweg
Alexandru Scorpan, The Wild World of 4-Manifolds, American Mathematical Society
Masanori Morishita, Knots and Primes: An Introduction to Arithmetic Topology, Springer
参考书 References
Raúl Rabadán and Andrew J. Blumberg, Topological Data Analysis for Genomics and Evolution: Topology in
Biology, Cambrige 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
%offinal
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
60
参与，包括讨论班做报告
Participation, including presentations
期中考试
Mid-Term Test
期末考试
Final Exam
40
读书报告 reading report
期末报告
Final
4
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
