MA 556 Differential Geometry 2018-19

Instructor: Prof. Akhil Ranjan

Course Name: Differential Geometry (MA 556 )

Course Type: Theory (Elective)

Credits: 6

Pre-requisites: Multivariable Calculus

Course Content: 

Theory of curves:
Re-parameterization, arc length parameterization, Serre Frenet Apparatus, curves in a plane, Hopf's Theorem
Theory of surfaces:
Gauss map, First and Second Fundamental forms, Weingarten map, Principal and Gaussian Curvature, Gauss Bonnet theorem

Books:

Millman and Parker (Differential Geometry)

Lectures:

The prof teaches on the board and encourages discussion. The pace is also good (not too fast). 

Assignments:

Tutorials were mostly questions from the back of Millman and Parker. They were not graded. No assignments as such.

Exams and Grading:

There were three written exams: Midsem, quiz after it, and endsem. Weightage of each was not revealed. 

Online Useful Material:
None

Advanced Follow up Courses:
I am not aware of any.

Pro-Tips:

Attend the lectures. The prof does a lot of examples in the class. Similar questions appear in exams.

Personal Comments:
Note that the course was not as I expected. I had taken the course, thinking it would aid the study of General Relativity. But the course doesn't venture to higher than 3 dimensions at all. It is much more of a pure math type course about curves and surfaces (far away from applications in physics). 

Respondent: Manu