MATH 136: Differential Geometry

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Course goals:

This is a rigorous 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.
What can students expect from you as an instructor?

When is course typically offered?

Fall.

What can students expect from you as an instructor?

We develop the material together with the class. The course has already been taught in this way two times already.

Assignments and grading:

There is a weekly problem set. There is a midterm, mixed take home and in class. For the final, there is an in-class component as well as a final paper.   HW 30 percent, midterm 30 % final 40 %.

Sample reading list:

See the last two semesters for lecture notes. 

Past syllabus:

last year's syllabus

We cover the following topics.

 -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
- General relativity application

 

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Course policies:

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