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<!DOCTYPE html>
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<title>chirprush - Articles</title>
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<h2 class="grid-title">Rushil Surti</h1>
<p class="grid-email">rush040507@gmail.com</p>
<div class="grid-icons"><a href="https://www.github.com/chirprush/" target="_blank"><i class="fa-brands fa-github"></i></a> <a href="https://www.youtube.com/channel/UCSc-MTo8KGPDMLszD6jYjxA" target="_blank"><i class="fa-brands fa-youtube"></i></a> <a href="https://www.instagram.com/chirprush/" target="_blank"><i class="fa-brands fa-instagram"></i></a> <a href="https://math.stackexchange.com/users/1128617/chirpyboat73" target="_blank"><i class="fa-brands fa-stack-exchange"></i></a></div>
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<h2>Description</h2>
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<p>My list of articles so far and this website's homepage. I primarily write about math and comp sci.</p>
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<a href="/index.html">Articles</a>
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<h1>Articles</h1>
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<div class="thumbnail" onclick="location.href='/articles/lean-foray/index.html';">
<h3>A Foray Into Lean, Markov Chains, and Automated Theorem Proving</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> March 16, 2026</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#markov-chains"><span class="info-tag">markov-chains</span></a> <a href="/tags.html#automated-theorem-proving"><span class="info-tag">automated-theorem-proving</span></a> <a href="/tags.html#linear-algebra"><span class="info-tag">linear-algebra</span></a> <a href="/tags.html#lean"><span class="info-tag">lean</span></a> <a href="/tags.html#functional-programming"><span class="info-tag">functional-programming</span></a> <a href="/tags.html#formalization"><span class="info-tag">formalization</span></a> <a href="/tags.html#pedagogy"><span class="info-tag">pedagogy</span></a> <a href="/tags.html#machine-learning"><span class="info-tag">machine-learning</span></a></span>
</div>
<p>It's been a while! (see the intro for a quick CMU brain-dump)
I've been working on formalizing (finite-state) Markov chains in Lean
<a href="https://github.com/chirprush/lean-markov-chains">here</a>. In this article,
I'll talk about the experience of working in Lean, advice for people
similarly starting, and some discussion on automatic theorem proving :D</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/project-euler-956/index.html';">
<h3>Project Euler: Problem 956</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> October 15, 2025</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#project-euler"><span class="info-tag">project-euler</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a> <a href="/tags.html#fft"><span class="info-tag">fft</span></a> <a href="/tags.html#finite-fields"><span class="info-tag">finite-fields</span></a> <a href="/tags.html#roots-of-unity"><span class="info-tag">roots-of-unity</span></a></span>
</div>
<p>Solving Project Euler Problem 956 in a little bit of an overkill way. Stick
around for some fast Fourier transforms over finite fields!</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/electromagnetism-cycloid/index.html';">
<h3>An Electromagnetism Cycloid</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> April 1, 2025</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#mini"><span class="info-tag">mini</span></a> <a href="/tags.html#physics"><span class="info-tag">physics</span></a> <a href="/tags.html#linear-algebra"><span class="info-tag">linear-algebra</span></a> <a href="/tags.html#differential-equations"><span class="info-tag">differential-equations</span></a> <a href="/tags.html#complex-numbers"><span class="info-tag">complex-numbers</span></a></span>
</div>
<p>Not an April Fool's joke! This is a mini article on an electromagnetism problem mentioned in one of our class's textbooks. The exact solution was said to be beyond the scope of the textbook, so, don't mind if I do!</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/music-inspired-mathematics/index.html';">
<h3>Music-Inspired Mathematics</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> March 21, 2025</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#fourier-transform"><span class="info-tag">fourier-transform</span></a> <a href="/tags.html#signal-processing"><span class="info-tag">signal-processing</span></a> <a href="/tags.html#analysis"><span class="info-tag">analysis</span></a> <a href="/tags.html#linear-algebra"><span class="info-tag">linear-algebra</span></a></span>
</div>
<p>An orchestra assignment special! In this article, I explore the connection
between music and math concretely. In particular, we'll take a look at some
signal processing and some even more out there connections to springboard
into some fun pure math.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/convolution-canonicity-dirichlet/index.html';">
<h3>Convolution Canonicity: Dirichlet Convolutions!</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> January 13, 2025</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#group-theory"><span class="info-tag">group-theory</span></a> <a href="/tags.html#abstract-algebra"><span class="info-tag">abstract-algebra</span></a> <a href="/tags.html#lie-theory"><span class="info-tag">lie-theory</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a> <a href="/tags.html#linear-algebra"><span class="info-tag">linear-algebra</span></a> <a href="/tags.html#matrices"><span class="info-tag">matrices</span></a> <a href="/tags.html#finite-fields"><span class="info-tag">finite-fields</span></a></span>
</div>
<p>The primer article in a series exploring convolution in group theory. The
topic? Dirichlet convolutions! We'll generalize them over arbitrary fields
and classify some certain cases.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/combinatorial-totient-sum-identity/index.html';">
<h3>A Combinatorial Totient Sum Identity</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> December 21, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#mini"><span class="info-tag">mini</span></a> <a href="/tags.html#combinatorics"><span class="info-tag">combinatorics</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a></span>
</div>
<p>A very small article before winter break, featuring a clean double counting argument for a sum involving the Euler totient function.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/project-euler-752/index.html';">
<h3>Project Euler: Problem 752</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> December 5, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#project-euler"><span class="info-tag">project-euler</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a> <a href="/tags.html#matrices"><span class="info-tag">matrices</span></a> <a href="/tags.html#abstract-algebra"><span class="info-tag">abstract-algebra</span></a> <a href="/tags.html#group-theory"><span class="info-tag">group-theory</span></a></span>
</div>
<p>Solving Project Euler Problem 752, a nice problem on orders in fields with square roots.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/pumac-power-round-2024/index.html';">
<h3>PUMAC Power Round 2024: The Hausdorff Measure</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> November 28, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#notes"><span class="info-tag">notes</span></a> <a href="/tags.html#contest"><span class="info-tag">contest</span></a> <a href="/tags.html#topology"><span class="info-tag">topology</span></a> <a href="/tags.html#measure-theory"><span class="info-tag">measure-theory</span></a></span>
</div>
<p>Notes on and a review of what our team managed to solve in PUMAC Power Round 2024! Featuring measure theory, topology, and fractals.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/commuting-matrix-remarks/index.html';">
<h3>A Remark on Commuting Matrices</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> November 9, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#linear-algebra"><span class="info-tag">linear-algebra</span></a> <a href="/tags.html#matrices"><span class="info-tag">matrices</span></a></span>
</div>
<p>Suppose matrices \( A \) and \( B \) commute. We explore the question of when one matrix can be expressed in terms of the other.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/project-euler-421/index.html';">
<h3>Project Euler: Problem 421</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> August 2, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#project-euler"><span class="info-tag">project-euler</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a> <a href="/tags.html#group-theory"><span class="info-tag">group-theory</span></a> <a href="/tags.html#probability"><span class="info-tag">probability</span></a> <a href="/tags.html#combinatorics"><span class="info-tag">combinatorics</span></a> <a href="/tags.html#cryptography"><span class="info-tag">cryptography</span></a></span>
</div>
<p>Solving Project Euler Problem 421, a beautiful number theory puzzle on counting roots modulo primes with a cryptographic and probabilistic flavor.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/euler-totient-even/index.html';">
<h3>Proving that the Euler Totient is Even</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> July 23, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a> <a href="/tags.html#group-theory"><span class="info-tag">group-theory</span></a></span>
</div>
<p>We prove that the Euler totient function is even using group theory.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/codeforces-problem-1916H1/index.html';">
<h3>Codeforces: Problem 1916H1</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> July 21, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#codeforces"><span class="info-tag">codeforces</span></a> <a href="/tags.html#linear-algebra"><span class="info-tag">linear-algebra</span></a> <a href="/tags.html#matrices"><span class="info-tag">matrices</span></a> <a href="/tags.html#combinatorics"><span class="info-tag">combinatorics</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a></span>
</div>
<p>A very mathy and beautiful 2700 rated Codeforces problem. This one had me really excited to solve.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/matrix-modular-arithmetic/index.html';">
<h3>Matrices Over Modular Arithmetic</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> July 11, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#matrices"><span class="info-tag">matrices</span></a> <a href="/tags.html#linear-algebra"><span class="info-tag">linear-algebra</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a> <a href="/tags.html#combinatorics"><span class="info-tag">combinatorics</span></a> <a href="/tags.html#group-theory"><span class="info-tag">group-theory</span></a></span>
</div>
<p>Exploring properties of powers of matrices who have entries in the ring of integers modulo some integer.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/codeforces-problem-1763D/index.html';">
<h3>Codeforces: Problem 1763D</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> July 5, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#codeforces"><span class="info-tag">codeforces</span></a> <a href="/tags.html#combinatorics"><span class="info-tag">combinatorics</span></a> <a href="/tags.html#permutations"><span class="info-tag">permutations</span></a></span>
</div>
<p>A 2200 rated Codeforces combinatorics problem with a whole lot of casework.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/binomial-coefficient-matrices/index.html';">
<h3>Binomial Coefficient Matrices</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> June 30, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#linear-algebra"><span class="info-tag">linear-algebra</span></a> <a href="/tags.html#matrices"><span class="info-tag">matrices</span></a> <a href="/tags.html#combinatorics"><span class="info-tag">combinatorics</span></a> <a href="/tags.html#binomial-coefficient"><span class="info-tag">binomial-coefficient</span></a></span>
</div>
<p>Let's explore the properties of lower triangular matrices filled with binomial coefficients.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/project-euler-743/index.html';">
<h3>Project Euler: Problem 743</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> June 25, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#project-euler"><span class="info-tag">project-euler</span></a> <a href="/tags.html#combinatorics"><span class="info-tag">combinatorics</span></a> <a href="/tags.html#matrices"><span class="info-tag">matrices</span></a></span>
</div>
<p>Solving Project Euler Problem 743, a really nice combo problem using a sliding window approach.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/project-euler-779/index.html';">
<h3>Project Euler: Problem 779</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> June 23, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#project-euler"><span class="info-tag">project-euler</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a> <a href="/tags.html#analysis"><span class="info-tag">analysis</span></a> <a href="/tags.html#primes"><span class="info-tag">primes</span></a></span>
</div>
<p>Solving Project Euler Problem 779, a really beautiful number theory problem.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/perspective-projection/index.html';">
<h3>Perspective Projection</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> June 17, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#linear-algebra"><span class="info-tag">linear-algebra</span></a> <a href="/tags.html#graphics"><span class="info-tag">graphics</span></a></span>
</div>
<p>Developing a perspective projection for use in rendering 3D graphics. This particular derivation was used in my AP CSA final project :D</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/drawing-equipotential-lines/index.html';">
<h3>Drawing Equipotential Lines</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> June 9, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#physics"><span class="info-tag">physics</span></a> <a href="/tags.html#linear-algebra"><span class="info-tag">linear-algebra</span></a> <a href="/tags.html#multivariable-calculus"><span class="info-tag">multivariable-calculus</span></a></span>
</div>
<p>Deriving an algorithm to draw equipotential lines for a vector field starting from a point with lots of fun math along the way.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/project-euler-549/index.html';">
<h3>Project Euler: Problem 549</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> June 7, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#project-euler"><span class="info-tag">project-euler</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a></span>
</div>
<p>Solving Project Euler Problem 549, a nice number theory problem revolving around the factorization of factorials.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/gradient-ascent-eigenvectors/index.html';">
<h3>Gradient Ascent Eigenvectors</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> May 13, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#linear-algebra"><span class="info-tag">linear-algebra</span></a> <a href="/tags.html#matrices"><span class="info-tag">matrices</span></a> <a href="/tags.html#gradient-descent"><span class="info-tag">gradient-descent</span></a></span>
</div>
<p>Finding real eigenvectors of an arbitrary matrix using geometric intuition and gradient ascent.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/codeforces-problem-1909D/index.html';">
<h3>Codeforces: Problem 1909D</h3>
<div class="info-holder">
<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> April 7, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#codeforces"><span class="info-tag">codeforces</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a> <a href="/tags.html#optimization"><span class="info-tag">optimization</span></a></span>
</div>
<p>A nice little 1900 rated Codeforces problem on making all elements equal with operations.</p>
</div>
<div class="thumbnail" onclick="location.href='/articles/yukicoder-problem-2664/index.html';">
<h3>Yukicoder: Problem 2664</h3>
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<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> April 1, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#yukicoder"><span class="info-tag">yukicoder</span></a> <a href="/tags.html#graph-theory"><span class="info-tag">graph-theory</span></a> <a href="/tags.html#dfs"><span class="info-tag">dfs</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a></span>
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<p>Solving Yukicoder Problem 2664, a quick little graph and number theory problem, with the extra challenge of having to read the problem description in Japanese.</p>
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<h3>Codeforces: Problem 1902C</h3>
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<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> March 24, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#codeforces"><span class="info-tag">codeforces</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a> <a href="/tags.html#optimization"><span class="info-tag">optimization</span></a></span>
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<p>A quick little number theory Codeforces problem on minimizing costs.</p>
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<h3>Codeforces: Problem 1948E</h3>
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<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> March 15, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#codeforces"><span class="info-tag">codeforces</span></a> <a href="/tags.html#graph-theory"><span class="info-tag">graph-theory</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a> <a href="/tags.html#permutations"><span class="info-tag">permutations</span></a></span>
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<p>A fun (slightly brute-force) constructive graph theory Codeforces problem, rated 2100.</p>
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<h3>Codeforces: Problem 1758D</h3>
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<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> March 9, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#codeforces"><span class="info-tag">codeforces</span></a> <a href="/tags.html#number-theory"><span class="info-tag">number-theory</span></a></span>
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<p>A nice 1800 rated Codeforces problem on constructing an integer sequence. Multiple attempts, because an initial strategy doesn't always work but is nice to document.</p>
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<h3>Project Euler: Problem 323</h3>
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<span class="info-value"><b>Author:</b> Rushil</span>
<span class="info-value"><b>Date:</b> January 12, 2024</span>
<span class="info-value"><b>Tags:</b> <a href="/tags.html#project-euler"><span class="info-tag">project-euler</span></a> <a href="/tags.html#bitmasks"><span class="info-tag">bitmasks</span></a> <a href="/tags.html#probability"><span class="info-tag">probability</span></a></span>
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<p>Solving Project Euler Problem 323, a fun problem involving bitwise OR and expected values.</p>
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