MATH-UA 377: Differential Geometry (Revised March 22, 2020)

Instructor: Deane Yang
Email: deane.yang@nyu.edu
Lectures (Zoom): Mondays and Wednesdays 2-3:15pm
Recitation (Zoom): Mondays 8-9:15apm (Taught by Kai Shao)
Office Hours (Zoom): Mondays and Wednesdays, 4-5:30pm
Mondays and Wednesdays, 10-11pm

Calendar (subject to change)
The rest of the semester will follow O'Neill, Chapters 4, 6, 7, 8
Experimental Notes on Elementary Differential Geometry
(Updated regularly during semester)
NYU Classes

All announcements and information about the course will be emailed to you and posted here. You are responsible for keeping track of everything, including newly added assignments, exam dates, homework due dates, etc. NO EXCUSES.

Homework: Overleaf, Gradescope
Questions?
Course Grade Factors (subject to change)
Textbooks

Barrett O'Neill, Elementary Differential Geometry, Revised 2nd Edition. Used and new copies are available from several sellers and in the NYU bookstore.

Other textbooks that might be used, including for homework problems:
Homework (Overleaf, Gradescope)
Special Accommodations

If you are student with a disability who needs special accommodations, please contact New York University’s Moses Center for Students with Disabilities (CSD) at 212-998-4980 or mosescsd@nyu.edu. You must be registered with CSD to receive accommodations. Information about the Moses Center can be found at www.nyu.edu/csd. The Moses Center is located at 726 Broadway on the 2nd floor. (See Diagnosing A Learning Disability In College for more information. If you believe you might have a learning disability, please get tested.)

About the course

This course is an introduction to differential geometry, which can be described as studying the geometric properties of a curved space using calculus. The focus will be on the geometry of curves and surfaces in 3-space but with an eye on how to extend the concepts to abstract geometric spaces. After building the foundations of the subject, specific topics to be covered include the Gauss-Bonnet theorem, which links the differential geometric properties of a surface to its topological properties, and the geometry of hyperbolic space, which is the negatively curved analogue of the sphere.

Prerequisites