Coursework
MAS651: Theory of Stochastic Processes
This is a graduate-level course on rigorous theory of probability and stochastic processes. This course covered Chapter 5~8 of the main textbook “Probability: Theory and Examples (The fifth edition)”, written by Rick Durrett, and the list of topics covered in this course includes
- Theory of discrete-time Markov chains.
- Ergodic theorems.
- Theory of Brownian motions and its applications to random walk.
The grading of this course was based on weekly assignments (60%) and the final exam (40%). The solutions to all homework problems of this course can be found below:
If you have any questions about homework problems and solutions, please contact me via e-mail.
MAS575: Combinatorics
This is a graduate-level course on various topics in combinatorics. The lecture videos for this course were periodically uploaded here. The list of topics covered in this course includes
- many results in extermal set theory with emphasis on linear-algebraic methods in combinatorics.
- the chromatic number on $\mathbb{R}^n$ and disproof of Borsuk’s conjecture.
- communication complexity.
- slice rank: applications in the cap set problem and Erdos-Szemeredi sunflower conjecture.
- a broad range of applications of the combinatorial nullstellensatz.
- existence of a certain object (e.g., Ramsey’s theorem, Hales-Jewett theorem, Van der Waerden’s theorem, and so on).
- some recent results in combinatorics.
The grading of this course was based on biweekly assignments (50%) and the final report (50%). Each student was required to submit a final report on an open problem related to this course and explain why it is interesting, what is known so far, and what could be a potential approach or write a report on interesting recent results related to this course. My final report for this course can be found here.