Here are some miscellaneous other fun things that I've created over the past few years :)
This past summer (2021), I participated in the Caltech SURF program under the mentorship of Professor Leonard Schulman. Here's the final report that I produced.
In the summer of 2020, I participated in the Texas A&M Probability and Algebra REU; here are the presentation slides and final report that I produced. You can also read the paper from our group here!
I've written a few problems for the HMMT competition; here are a few that I'm particularly proud of. (All of the past problems and solutions can be found on the HMMT site as well!)
HMMT February 2019 G8: In triangle ABC with AB < AC, let H be the orthocenter and O be the circumcenter. Given that the midpoint of OH lies on BC, BC=1, and the perimeter of ABC is 6, find the area of ABC.
HMMT February 2020 C3: Each unit square of a square grid is colored either red, green, or blue. Over all possible colorings of the grid, what is the maximum possible number of L-trominos that contain exactly one square of each color? (L-trominos are made up of three unit squares sharing a corner.)
HMMO 2020 T5: The classrooms at MIT are each identified with a positive integer (with no leading zeroes). One day, as President Reif walks down the Infinite Corridor, he notices that a digit zero on a room sign has fallen off. Let N be the original number of the room, and let M be the room number as shown on the sign. The smallest interval containing all possible values of M/N can be expressed as [a/b, c/d) where a,b,c,d are positive integers with gcd(a,b) = gcd(c,d) = 1. Compute 1000a + 100b + 10c + d.
- The MIT Video Game Orchestra has a YouTube channel with some of our past performances. My favorite arrangement that I've done so far is this medley of tracks from Paper Mario: The Thousand-Year Door.
- Our final project of 21M.303, Writing in Tonal Forms I, was to compose a minuet and trio for string quartet. You can find the score for my composition here, as well as a recording of it performed by the Worcester Chamber Music Society.
At MIT, I was an Undergraduate Assistant for 18.100B (Real Analysis), as well as a Teaching Assistant for 18.600 (Probability and Random Variables). Those were some of my academic highlights during my time as an undergrad, and I'm happy to talk to anyone who's also interested in exploring in these directions! I've also done some other assorted teaching (because it's fun and rewarding to get better at explaining things!):
- I was one of the lecturers for 18.S097, an undergrad-led proof-writing workshop, during IAP 2021. Here are the lecture notes that I produced for the last two lectures of the class.
- I was a JC at Canada/USA Mathcamp in Summer 2019 and taught two short classes based on material I had learned a few months ago in 18.212: an evening talk on the matrix-tree theorem, as well as a Week 5 class cotaught with Shiyue Li on a proof of the hook-length formula.