Theorems are like libraries
Theorems are like libraries
Sarah's Blog
About me
Thanks for visiting my blog! I am in my third year at Columbia University, studying CS and math. I’m involved in a lot of seemingly unrelated research, tied together by a faint interest in math and a passion for creating. Outside of research, I play violin and help lead the Columbia Robotics Club.
My blogs are similarly sporadic in frequency and topic, but I write mainly on cool algorithms, math, and personal epiphanies.
My research
I’m currently involved in three research projects.
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MOSES (Columbia Gang Lab) - A foundational algorithm applying the group theoretic concept of ‘symmetry’ to chemical engineering. An information-minimizing method for to designing self-assembling DNA origami nanoparticle lattices. Our paper was accepted to ACS Nano! This blog post also talks about it more in depth.
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Synchrony (NYU Dennis Shasha Group) - An opinionated practice tool for musicians, which compares a user’s recording to a MIDI score and computes the user’s mistakes in real-time. Uses a probabilistic pitch detection method that utilizes the MIDI to detect note events. Under supervision of the kind NYU professor Dennis Shasha.
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RichCluster (UND Hur Lab) - An Rcpp library for performing hierarchical clustering on multiple enriched genomics datasets. Clusters different biological ‘terms’ based on overlapping gene content. Coded in C++ for fast clustering, with customizable linkage / distance metrics and supporting visualizations. (Paper-in-progress)
For fun, I also play violin in the Barrio Tango Orchestra with some really amazing people. My friend and I have both started learning tango as well. 👯♀️
Recent posts
Why are vectors vertical?
My math professors in college would often intimidate us into writing vectors as vertical, transposing them when convenient, without explaining why. This alwa...
A comprehensive look into the YIN algorithm
For my Numerical Methods course last semester, we had to create a final project on a computational project of some interest to us. We were given the entire l...
A rough introduction to groups
I’m currently taking an abstract algebra course, taught by the amazing but quirky Michael Thaddeus. On the first day of class, he told us that this would be ...
Visualizing the string edit algorithm
For my research with Professor Dennis Shasha from NYU, we’re using the string edit algorithm to compare two ‘strings’, user-notes and midi-notes, to return a...
A life lesson I learned from a violent video game
I watched a documentary this morning on Silent Hill 2, a Crime and Punishment-esque video game about a man who killed his own terminally ill wife out of love...
Visualizing combinatorics with trees
In all counting problems, we have some $n$ number of items and we want to choose some $k$ of them. There are two fundamental tools for computing this - permu...
WTF is compactness
A compact set is one where every open cover has a finite subcover. WTF?
Balls and sets: Topological logic gates
In my Modern Analysis class, we went over a significant amount of basic topology. I was confused at first, but I found it ultimately gave us a toolkit of con...
The art of naming variables
The helix problem Just as I thought I had finally debugged all of the edge cases of the algorithm, last week I went into the lab and was asked to try out the...
A foray into metric and vector spaces
The metric space bridges real analysis with topology by introducing the notion of a distance onto a set of elements. They are a general setting for studying ...
The real numbers are an ordered field
Real numbers The set of real numbers $\mathbb{R}$ is an ordered field, meaning it’s defined as being a “tuple” of four elements, which includes An ordered...
My monitor problem; an algorithm
The monitor problem I ordered a new monitor for my dorm last week, and it arrived yesterday! But it’s 16 inches large, and I’m quite lazy to retrieve it from...
A gentle introduction to the MOSES algorithm
Ganglab - Fall 2024 This past summer, I started working with the Gang Lab at Columbia University as a chemical engineering research assistant. I received a g...