MATH 136: Differential Geometry

In the area below, provide basic, standard course information ahead of registration period to help students make informed course choices. Click the EDIT button and input your responses by over-writing the field description below each bolded heading. Consult the IT Help knowledge base or reach out to FAS Academic Technology at for assistance.

Course goals:

This is an introduction to Riemannian geometry and in particular to Riemannian geometry of curves and surfaces for which the fundamental notions can be visualized. We also will also develop some discrete differential geometry which is much less technical. Low dimensional Riemannian geometry is an extremely active area of mathematics with many applications, especially in computer science, physics or computer graphics. It is not only the language of gravity, it is an inspiration for art and architecture for example. The subject is also full of unsolved problems. 

Course format:

This is a lecture course. 

Typical enrollees:

Students interested in math (theorems and structures), applied math (applications to other sciences) physics (like relativity) or computer science (like computer graphics). Prerequisites are multi-variable calculus and linear algebra. 

When is course typically offered?

In the past, the fall course was MWF at 12. 

What can students expect from you as an instructor?

I hope to get a fresh approach to the topic, develop the material together with the class. There will be notes, developed together with the class. Just to see previous examples of course notes: (course notes for a multivariable calculus course taught in 2022  [PDF])  and (a course in geometry taught 30 years ago at Caltech (forbidding for today's standards) [PDF]). 

Assignments and grading:

There is a weekly problem set. There is a midterm paper on a topic covered in the course. There is a cumulative take home exam.    HW 50 percent, midterm 20 % final 30 %.

Sample reading list:

A handout [PDF] from a course Math 22b from Spring 2022 about surfaces in space gives an idea  how lecture notes will look like. 

Enrollment cap, selection process, notification:

This is usually a small course. There is no enrollment cap. 

Past syllabus:

Here are some topics which have been covered in this course and we will certainly get into all of them. 

 -Parametrized and implicit surfaces
- Curves and Frenet formulas
- Notions of Curvature
- Parallel transport and Geodesics
- Gauss Bonnet theorem
- Differentiable manifolds
- Riemannian metrics
- Curvature
- Riemannian geometry applications

Absence and late work policies:

Attendance is required. There are no PSet extensions but the least 2 PSet scores will be discarded. 



Course Summary:

Date Details Due