This page is a collection of notes that I wrote in my undergraduate and graduate studies. Due to a Google Drive privacy update, some of the links may be broken; in this case, request permission to access the file and I will update the link. If you would like the source code for my notes, click here.

Here is a collection of notes that I have written as an undergraduate at UC Berkeley. I also contributed to the course notes for EECS 126 in Spring 2018 and prepared slides and notes for COMPSCI 70 in Summer 2018, which can be found on the respective course websites: here and here. Finally, here is a collection of other miscellaneous notes and pieces.

- Midterm 1 Review Slides (Fall 2016)
- Continuous Probability Review Slides (Fall 2016)
- Tips & Tricks in Probability Slides (Fall 2016)
- Final Review Slides (Fall 2016)
- Markov Chains & Continuous Probability Slides (Spring 2017)
- Extra Note 1: Cauchy Induction
- Extra Note 2: Top Trading Cycles (TTC) Algorithm
- Extra Note 3: Chinese Remainder Theorem
- Extra Note 4: Hard Problems & Public Key Cryptosystems
- Extra Note 5: Eisenstein's Criterion
- Extra Note 6: Algebraic Coding Theory
- Extra Note 7: Cantor-SchrÃ¶der-Bernstein Theorem
- Extra Note 8: Generating Functions
- Extra Note 9: Generating Functions II
- Extra Note 10: Pairwise Independent Hash Functions
- Extra Note 11: Moment-Generating Functions
- Extra Note 12: Jensen's Inequality
- Extra Note 13: Martingales
- Extra Note 14: PageRank
- Extra Note 15: Beta Distribution
- Propositional Logic: Quantifier Distribution Problem
- Induction: Celebrity Algorithm Problem
- Continuous Probability: Continuous Conditional Expectation Problem

- COMPSCI 271 (Randomness & Computation)
- EL ENG 223 (Stochastic Systems: Estimation & Control)
- EL ENG 226A (Random Processes in Systems)
- MATH 115 (Introduction to Number Theory)
- MATH 135 (Introduction to the Theory of Sets)
- MATH 141 (Elementary Differential Topology)
- MATH 185 (Introduction to Complex Analysis)
- MATH C218A/STAT C205A (Probability Theory)
- MATH C218B/STAT C205B (Probability Theory)
- STAT 210A (Theoretical Statistics)
- STAT 210B (Theoretical Statistics)

Here is a collection of notes that I have written as a PhD student at MIT.

- 18.137 (Topics in Geometric PDEs)
- 18.1521 (Introduction to Partial Differential Equations)
- 18.158 (Topics in Differential Equations)
- 18.176 (Stochastic Calculus)
- 18.338 (Eigenvalues of Random Matrices)
- 18.966 (Geometry of Manifolds II)
- COMPSCI 229R (Topics in Theoretical Computer Science: Interactions between Physics and Computation)