MATH 136: Differential Geometry
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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. The website for the course is here.
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?
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 |
---|---|---|
Fri Sep 13, 2024 | Assignment Homework 01 | due by 11:59pm |
Fri Sep 20, 2024 | Assignment Homework #2 | due by 11:59pm |
Fri Sep 27, 2024 | Assignment Homework #3 | due by 11:59pm |
Fri Oct 4, 2024 | Assignment Homework #4 | due by 11:59pm |
Wed Oct 9, 2024 | Assignment Quiz | due by 4pm |
Fri Oct 11, 2024 | Assignment Homework #5 | due by 11:59pm |
Fri Oct 18, 2024 | Assignment Midterm | due by 11:59pm |
Fri Nov 1, 2024 | Assignment Homework #7 | due by 11:59pm |
Fri Nov 8, 2024 | Assignment Assignment #8 | due by 11:59pm |
Fri Nov 15, 2024 | Assignment Assignment #9 | due by 11:59pm |
Fri Nov 22, 2024 | Assignment Homework #10 | due by 11:59pm |
Tue Dec 3, 2024 | Quiz Homework 11 | due by 11:59pm |
Wed Dec 4, 2024 | Assignment Final quiz | due by 11:59pm |
Sun Dec 15, 2024 | Assignment Final Paper | due by 11:59pm |
Assignment Homework #6 |