Below are some of my lecture notes, typed in LaTeX.
Disclaimer: These notes are inspired by lectures given by the professors; however, I also try to use other sources and inject my own intuitions in them as I see fit. As such, any errors found are my own.
Measure Theory (PDF)
Complex Analysis (PDF)
Analytical Mechanics (PDF)
Abstract Algebra (PDF)
From the course MATH-UA 348 with Professor Fengbo Hang.
Real Analysis (PDF)
From the course MATH-UA 328 with Professor Jalal Shatah.
Linear Algebra (PDF)
From the course MATH-UA 140 with Professor Sylvia Serfaty.
Electricity and Magnetism (PDF)
From the course PHYS-UA 93 with Professor David W. Hogg.