MATH 4033 - Calculus on Manifolds

Syllabus PDF: [here]

Contact of Instructor and TA:

Instructor: Frederick Tsz-Ho Fong (frederick.fong@ust.hk)
TA: Nicholas Chin (nchchin@connect.ust.hk)

Reference Materials:

Major Reference:

  • Instructor's Lecture Notes: [here]
    (MATH 4033 covers Chapters 1 ~ 5)

Recommended References:

  • Introduction to Smooth Manifolds (John M. Lee): [here]
  • Differential Forms and Applications (Manfredo Do Carmo): [here]
  • Prof. Hitchin's Lecture Notes on Differentiable Manifolds: [here]
  • A Comprehensive Introduction to Differential Geometry, Vol. 1 (Michael Spivak): Buy [here (Amazon)]
  • Lectures on Differential Geometry (S.S. Chern, Weihuan Chen, K.S. Lam): Buy [here at Amazon for the English version] or《微分幾何講義》陳省身、陳維桓: Buy [here at Taobao for the Simplified Chinese version]

Homework and Solutions

Problem Set 1 [Download] - Due 24/02/2019, 11:59pm
Problem Set 2 [Download] - Due 10/03/2019, 11:59pm
Problem Set 3 [Download] - Due 31/03/2019, 11:59pm
Problem Set 4 [Download] - Due 12/05/2019, 11:59pm

Problem Set 5 [Download] - No need to turn it in, but strongly recommended to do it.

Some selected HW solutions:
[here] -- HW1Q2
[here] -- current progress: HW2Q1, HW3Q3, HW3Q6 -- more will be updated
[here] -- selected solutions for HW4 (thanks the current TA for that)
[here] -- selected solutions for HW5 (thanks the former TA for that)

Selected Solutions to Lecture Notes exercises (Chapters 1, 2, 3): [here]
(written by former 4033 students, not guaranteed to be perfect)

Lecture Slides and Videos

Week 1 (30/1 - 8/2): [Slide (30/1, 1/2, 8/2)][Video (30/1)][Video (1/2)][Video (8/2)]
Week 2 (11/2 - 15/2): [Slide (13/2, 15/2)][Video (13/2)][Video (15/2)]
Week 3 (18/2 - 22/2): [Slide (20/2, 22/2)][Video (20/2)][Video (22/2)]
Week 4 (25/2 - 1/3): [Slide (25/2, 1/3)][Video (27/2)][Video (1/3)]
Week 5 (4/3 - 8/3): [Slide (6/3, 8/3)][Video (6/3)][Video (8/3)]
Week 6 (11/3 - 15/3): [Slide (13/3, 15/3)][Video (13/3)][Video (15/3)]
Week 7 (18/3 - 22/3): [Slide (20/3, 20/3)][Video (20/3)][Video (22/3)]
Week 8 (25/3 - 29/3): [Slide (27/3, 29/3)][Video (27/3)][Video (29/3)]
Week 9 (1/4 - 5/4): [Slide (3/4)][Video (3/4)]
Week 10 (8/4 - 12/4): [Slide (10/4, 12/4)][Video (10/4)][Video (12/4)]
Week 11 (15/4 - 26/4): [Slide (17/4, 24/4, 26/4)][Video (17/4)][Video (24/4)][Video (26/4)]
Weeks 12 and 13 (29/4 - 9/5): [Slide (3/5, 8/5)][Video (3/5)][Video (8/5)]

Student Presentations

Click here.

Examinations

Spring 2019:
[Midterm Solutions][Anonymous Score Table]
[Final Solutions][Addition Solution to Q2b(i)][Anonymous Score Table]

Spring 2017: [Exam][Solutions]
Spring 2018: [Exam][Solutions]

Grades

[Anonymous Grade Book] -- HW and Presentation scores hide for privacy reason.
Letter grades will be reported to department head on Wednesday (28/5) for endorsement.

Course Summary:

Date Details Due