Instructor: 
Deane Yang 
Email: 
deane.yang@nyu.edu 
Lectures (Zoom): 
Mondays and Wednesdays 23:15pm 
Recitation (Zoom): 
Mondays 89:15apm 
Office Hours (Zoom): 
Mondays and Wednesdays, 45:30pm
Mondays and Wednesdays, 1011pm

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 3space but with an eye on how to extend the concepts to abstract geometric spaces. The approach taken will be more abstract than found in existing textbooks, and therefore we will rely mostly on
notes I have written.
The homework and exams will focus on applying the concepts to both concrete and abstract examples using both calculations and logical reasoning. The latter is often called "doing proofs".
Prerequisites

Precalculus, single and multivariable calculus

Linear algebra, preferably at the honors level. Key concepts include abstract vector spaces and subspaces, linearly independence, bases, linear transformations.

Fundamentals of deductive logic

Strong skills in doing rigorous calculations and proofs.

Strong problem solving skills, including identifying and testing useful examples and counterexamples, when trying to prove or disprove a statement.

Willingness to struggle with abstract mathematical concepts, statements, calculations, and proofs.
Mandatory tools you will use in this course

Gradescope:

Your homework and exam solutions will be submitted and graded using Gradescope. Detailed instructions are below.

Set up your Gradescope account by going to Gradescope and sign up for this course using the entry code 2RRNKD.

LaTeX

Homework solutions must be prepared using LaTeX either Overleaf or LaTeX software installed on your computer.

Using Overleaf:

Go to Overleaf and set up an account.

Each week you will get a link to a project containing the new assignment. Click on it to open the project. Under Menu in the upper left corner, click on Copy Project.

You enter your solutions using LaTeX in the left window, and the formatted document will appear on the right.

If you have never used LaTeX before, please look at the Overleaf Documentation.

There will often be error messages that you'll need to fix. If you cannot figure out how to fix the errors, share the project with me and I'll help you.

If you prefer to install and use LaTeX on your own computer, check out Getting LaTeX or Getting Started with LaTeX.

Campuswire

All math questions should be posted here. You can also post answers to questions asked by other students.
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.
Questions?

Work together with classmates. But be careful! If you simply copy someone else's answers without struggling through the problem yourself, you will not be ready for the exams. Get help from other students but, when preparing final version of your solutions, do it alone.

Ask me during office hours. If you cannot make it during the scheduled times, please email me to make an appointment.

Email me
Course Grade Factors (subject to change)

Homework (50%)

Midterm (20%)

Final Exam (30%)

Homework assignments will be posted every week and due by 11:59pm a week later. You are encouraged to start working on the homework immediately, so you'll be prepared with specific questions to ask me during class or office hours, the TA during recitation, or either of us by email.

Homework solutions must be prepared using LaTeX either Overleaf or LaTeX software installed on your computer and submitted via Gradescope.

Using Overleaf:

Go to Overleaf and set up an account.

Each week you will get a link to a project containing the new assignment. Click on it to open the project. Under Menu in the upper left corner, click on Copy Project.

You enter your solutions using LaTeX in the left window, and the formatted document will appear on the right.

If you have never used LaTeX before, please look at the Overleaf Documentation.

There will often be error messages that you'll need to fix. If you cannot figure out how to fix the errors, share the project with me and I'll help you.

If you prefer to edit the LaTeX using your own editor, you can keep the local version synced with the Overleaf version using git or Dropbox.

Using Gradescope:

Set up your Gradescope account by going to Gradescope and sign up for this course using the entry code MG7N48.

To submit an assignment, save it from Overleaf on your computer as a PDF and follow the instructions on Gradescope to upload the PDF.
 Optional: Install LaTeX on your computer.