MATH4030 - Differential Geometry - 2017/18

Course Name: 
Differential Geometry
Teacher: 
Prof. Martin Man Chun LI
Course Year: 
2017/18
Term: 
1

Announcement

  • Problem set 6 has been posted and is due on Dec 1 (Fri) at 5PM.
  • The statistics for midterm is as follows: mean = 64.57, median = 67, standard deviation = 12.
  • Problem set 5 has been posted and is due on Nov 17 (Fri) at 5PM.
  • Problem set 4 has been posted and is due on Nov 3 (Fri) at 5PM.
  • The midterm will take place on Oct 25 (Wed) 2:30-4:00PM at the usual classroom LSB C2 . It will cover all the materials up to the including the lectures/tutorials on Oct 18. Please be there at least 5 minutes before the start time and take alternate seating. Remember to bring your student ID and no calculator is allowed for the test.
  • A hint is added to Q.7 in Problem Set 2.
  • Problem set 3 has been posted and is due on Oct 20 (Fri) at 5PM.
  • Problem set 2 has been posted and is due on Oct 6 (Fri) Oct 11 (Wed) at 5PM.
  • Special class arrangements : Sep 25 (Mon) Tutorial 2:30-3:15PM, Sep 27 (Wed) Lectures 2:30-4:15PM.
  • Problem set 1 has been posted and is due on Sep 22 (Fri) at 5PM.
  • The lectures on Sep 4 (Monday) will be cancelled. There is no tutorial in the first week but we will have a lecture at the tutorial time instead. In summary, we will only have lectures on Sep 6 (Wed) 2:30-4:15PM and no tutorial during the first week.

General Information

Lecturer

  • LI Man-chun Martin
    • Office: LSB 236
    • Tel: 3943 1851
    • Email:

Teaching Assistant

  • CHOW Chi Hong
    • Office: AB1 505
    • Tel: 3943 4298
    • Email:
    • Office Hours: Mon 11:30AM - 12:15PM, 4:30PM - 6:15PM; Tue 11:30AM - 12:15PM, 2:30PM - 4:15PM; Wed 4:30PM - 6:15PM

Time and Venue

  • Lecture: Mon 2:30PM - 4:15PM at LSB C1 and Wed 3:30PM - 4:15PM at LSB C2
  • Tutorial: Wed 2:30PM - 3:15PM at LSB C2

Course Description

This course covers basic theory on curves, and surfaces in the Euclidean three space. Topics include: regular curves, Frenet formulas, local theory of curves, global properties of curves such as isoperimetric inequality, regular surfaces, 1st and 2nd fundamental form, Gaussian curvature and mean curvature, Gauss map, special surfaces such as ruled surfaces, surfaces of revolution, minimal surfaces, intrinsic geometry: geodesic, and Gauss-Bonnet Theorem. Students taking this course are expected to have knowledge in advanced calculus, linear algebra, and elementary differential equations.


Textbooks

  • "Differential Geometry of Curves and Surfaces" by M. do Carmo, Prentice Hall 1976

References

  • "Curves and Surfaces (2nd ed)" by S. Montiel and A. Ros, Graduate Studies in Mathematics, Vol.69, American Mathematical Society, 2009
  • "Differential Geometry: Curves - Surfaces - Manifolds (2nd ed)" by W. Kuhnel, Student Mathematical Library, Vol.16, American Mathematical Society 2005
  • "Differential Forms and Applications" by M. do Carmo, Universitext, Springer-Verlag 1998

Pre-class Notes


Lecture Notes


Tutorial Notes


Assignments


Solutions


Assessment Scheme

Homework 10%
Midterm (Oct 25, in class 2:30PM - 4:15PM) 40%
Final Exam 50%

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 21, 2017 16:05:31