chess board
earlygrad, Columbia, 2024
I made the more…minimalist pieces.
Teaching
I have worked as a TA for the following courses at Columbia.- COMS4774 Unsupervised Machine Learning (Fa24, Nakul Verma)
- MATH4041 Modern Algebra I (Fa24, Robert Friedman)
- CSOR4231 Probability Theory (Su24B, Ioannis Karatzas)
- MATH2500 Analysis and Optimization (Su24B, Jingbo Wan)
- COMS4771 Machine Learning (Sp23, Sp24, Su24A Nakul Verma; Fa23, Daniel Hsu)
- COMS4705 Natural Language Processing (Fa22, Daniel Bauer)
- DIMACS Tutorial on Fine-grained Complexity (Rutgers, July 2024)
- Fall Fourier Talks (UMD, October 2023)
- MihalisFest (Columbia, August 2023)
- Geometric Group Theory (Tufts, August 2023)
- FODSI Computational Complexity of Statistical Problems (MIT, June 2023)
How to graduate early from Columbia
earlygrad, Columbia, 2024
I graduated in three years from Columbia College (the one in New York, not Chicago). To my knowledge, graduating a full year early and foregoing senior year is not a very popular course of action (*1) at elite private colleges, even though many students are perfectly capable of doing so. Some colleges (like Brown) don’t even allow it. Most colleges offer accelerated master’s degree programs to incentivize students to stay the fourth year or even stick around for a fifth or sixth.
Lectures for the Undergraduate Math Society
Club, Columbia Undergraduate Math Society, 2023
I have given a number of lectures to the Undergraduate Math Society, on topics ranging from topological data analysis to combinatorics to spectral graph theory. Here are some lecture notes and slides.
Regression on Ice: Function approximation for the mathematically-inclined glaciologist.
Outreach, Glaciology Hub at University of Buffalo, 2023
I am writing a mini-textbook on the mathematics of regression in the context of glaciology research. The motivation is to bring awareness of mathematical methods and mindsets to practicing scientists and scientists-in-training.
Notes on Unsupervised Learning
Independent Studies, Verma Lab, Columbia University, 2023
Unsupervised machine learning (UML) is about finding structure in unlabeled data: for instance, partitioning datapoints into groups or finding informative low-dimensional representations of high-dimensional datasets. Theory research in UML is largely concerned with developing algorithms with provable guarantees and establishing the complexity of UML objectives (e.g. density estimation, k-means clustering, manifold hypothesis testing).
Lectures on Enumerative Combinatorics
Undergraduate course, MATH 3952, Columbia University, 2023
I gave a couple of lectures on q-analogs in enumerative combinatorics. The first two are from a course I took in spring 2023. The last one was from a directed reading in fall 2022.
Notes on Probability Theory
Notes from Coursework, MATH4155, 4156, 2023
Here are some typeset notes from probability classes I took at Columbia.