I like to write up notes for things I am studying. The process of writing these helps me learn; the note is really just a byproduct of me putting something in my own words. Nevertheless, maybe someone finds these useful, so I will post some of my longer ones.

Oral Exam Notes

These are notes I made from textbooks while studying for my oral exams. Here is a list of topics I looked at.

Partial Differential Equations

Functional Analysis

Real Analysis

Complex Analysis

Probability Theory

Here are some final exam study sheets for courses I took:

Final Exam Study Sheets

Stochastic Calculus
PDE for Finance
Here are some other miscellaneous notes on things.

Misc. Probability Notes

Convergence of Probability Measures by Patrick Billingsley
Markov chains and mixing times by David A. Levin, Yuval Peres and Elizabeth L. Wilmer
Extreme Values, Regular Variation, and Point Processes by Sidney I. Resnick
Random Graphs and Complex Networks by Remco van der Hofstad
Random Graphs by Joel Spencer
Concentration by Michel Ledoux
(These are from the Minerva Lecture Series given at Columbia University, March 26-April 2 2013)