MATH4030 - Differential Geometry - 2025/26
Announcement
- Assignment 5 is posted and due on Nov 17 (Monday).
- The statistics for midterm are as follow: mean=62.2, median=63, SD=10.8, highest=79.
- Assignment 4 is posted and due on Nov 3 (Monday).
- Assignment 3 is posted and due on Oct 20 (Monday).
- There is one more typo found in Q3 of Assignment 2. The latest version is updated below. The deadline for submission is extended to Oct 6, 2025.
- The midterm will be held in-class on Oct 22, 2025 (Wed) at CYT 214 from 2:30PM to 4:00PM.
- Assignment 2 is posted and due on Sep 29 (Monday). There was a typo in Question 3 and a revised version has been uploaded on Sep 17.
- Assignment 1 is posted and due on Sep 15 (Monday). Please submit your assignments via Gradescope.
- Please note that there is no tutorial during the first week. The first lecture will meet on Tuesday, Sep 2.
General Information
Lecturer
-
LI Martin Man-chun
- Office: LSB 236
- Tel: 3943-1851
- Email:
- Office Hours: By appointment
Teaching Assistant
-
LU Haowen
- Office: LSB G05
- Email:
- Office Hours: Wed 4:30pm - 6:15pm
-
ZHANG Xinfang
- Office: SC 333B
- Email:
- Office Hours: Mon 1:00pm - 3:00pm
Time and Venue
- Lecture: Tue 10:30am-12:15pm, MMW 707; Wed 2:30pm-3:15pm, NAH 213
- Tutorial: Wed 3:30pm-4:15pm, NAH 213
Course Description
This is a first course on differential geometry at the advanced undergraduate level. It focuses on the basic theory of curves and surfaces in three dimensional Euclidean space. Topics to be covered include local and global theory of plane and space curves, regular surfaces in R3, the intrinsic and extrinsic geometry of surfaces, various notions of curvatures, concepts of parallel transport, covariant derivative and geodesics, local and global aspects of differential geometry including Gauss-Bonnet theorem. We assume as prerequisite a solid understanding of linear algebra (at the level of MATH2040), multivariable calculus (at the level of MATH2010 and 2020) and point-set topology (at the level of MATH3070). Knowledge on differential equations (at the level of MATH3270) and complex analysis (at the level of MATH2230) will be helpful on some specific topics.
Textbooks
- Manfredo do Carmo, Differential Geometry of Curves and Surfaces, Prentice Hall, 1976
References
- M. do Carmo, Differential Forms and Applications, Universitext, Springer-Verlag
- S. Montiel and A. Ros, Curves and Surfaces, 2nd ed., Graduate Studies in Mathematics, Vol. 69, American Mathematical Society, 2009
- W. Kuhnel, Differential Geometry: Curves - Surfaces - Manifolds, 2nd ed., Student Mathematical Library, Vol 16. American Mathematical Society, 2005
Pre-class Notes
Lecture Notes
- Lecture Notes 1
- Lecture Notes 2
- Lecture Notes 3
- Lecture Notes 4
- Lecture Notes 5
- Lecture Notes 6
- Lecture Notes 7
- Lecture Notes 8
Assignments
- Assignment 1 (due on Sep 15)
- Assignment 2 (due on Sep 29) - revised on Sep 29
- Assignment 3 (due on Oct 20)
- Assignment 4 (due on Nov 3)
- Assignment 5 (due on Nov 17)
Assessment Scheme
| Homework assignments | 10% | |
| Midterm ( | 30% | |
| Final Exam (centralized by university) | 60% |
Honesty in Academic Work
The Chinese University of Hong Kong places very high importance on honesty in academic work submitted by students, and adopts a policy of zero tolerance on cheating and plagiarism. Any related offence will lead to disciplinary action including termination of studies at the University. Although cases of cheating or plagiarism are rare at the University, everyone should make himself / herself familiar with the content of the following website:
http://www.cuhk.edu.hk/policy/academichonesty/and thereby help avoid any practice that would not be acceptable.
Assessment Policy Last updated: November 03, 2025 21:18:37