Instructor: 
Deane Yang 
Email: 
deane.yang@nyu.edu 
Lectures: 
Tuesdays and Thursdays, 11am12:15pm 

Warren Weaver Hall, 517 
Recitation: 
Mondays, 8am9:15apm 

Warren Weaver Hall, 512 
Office Hours: 
TBA 
PLEASE DO THE FOLLOWING IMMEDIATELY:
Prerequisites
 Crucial skills

Doing rigorous calculations and proofs

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

Struggling with abstract mathematical concepts, statements, calculations, and proofs.
 Crucial knowledge

Precalculus, single and multivariable calculus

Fundamentals of deductive logic

Linear algebra, preferably at the honors level. Key concepts include abstract vector spaces and subspaces, linear independence, bases, linear transformations. See, for example, the first 3 chapters of Axler, Linear Algebra Done Right (PDF available free to NYU students)
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".
Mandatory tools you will use in this course

Gradescope:

Please email me if you need a Gradescope account.
 Homework:
There will be a weekly homework assignment. Your solutions must be written using LaTeX and saved as a PDF. You then follow the instructions on Gradescope to upload the PDF.

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.

Piazza:

All questions about course material and logistics should be asked here.

You are also encouraged to try to answer questions posted.

You may post anonymously.

Use LaTeX for mathematical formulas and equations. You must always enclose the LaTeX with $$...$$. Using $...$ does not work.

Brightspace:
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.

All math questions should be posted to Campuswire, so all students can see the question and answers. If, however, you have any personal questions or issues that you need to discuss with me, please email me.
Course Grade Factors (subject to change)

Weekly Homework (50%)

Midterm (25%)

Final Exam (25%)

Tweaks