The Algebraic Arcanum

Thoughts, discoveries, and mathematical curiosities.

March 4, 2024 · 3 min read

Inside the Wolfram Student Ambassador Program

Whether it's helping with my USAMTS problems or with that pesky Calc homework problem, Wolfram Alpha is pretty great. I mean, I remember plugging in this really complex two-variable system of equations, and it just solved it! Ok, as a mathematician, that could be counted as shortcutting, but I do this since it's inproductive to just keep bashing at an unrealistic system of equations that you cannot solve. And as my appreciation for Wolfram Alpha increased, I applied to become a Wolfram Student Ambassador.

WOLFRAM ALPHA MATHEMATICA WOLFRAM STUDENT AMBASSADORS
October 8, 2023 · 10 min read

The Weight of Error — How Mistakes Shape History More Than Plans

I recently entered the John Locke Institute Global Essay Competition which is held by the John Locke Institute sponsored by Oxford and Princeton. It's an essay competition that encourages you to explore college level academic writing through thought provoking questions that go beyond the bounds of school essays. You can receive many prizes through the competiton, and I myself got a Commendation for the essay I submitted into the History section...

ACADEMIC WRITING JIL COMPETITION WORLD WARS
August 16, 2023 · 5 min read

The Zeta Function: A Gentle Introduction

I recently attended the PROMYS program as a second year, and I wanted to encapsulate a bit of the cool math that I learned there! The primary class that I took was Prime and Zeta Functions, where we learned about zeta functions, Dirichlet Functions, Gauss sums, etc. It was all so cool! In my attempt to not forget any of it, I'll give a beginner's introduction to Reimann Zeta Functions (the beginning of the course).

ZETA FUNCTIONS EULER PRODUCT TRIGONOMETRY
June 9, 2023 · 4 min read

Christiaan Huygens and the Birth of the Pendulum Clock

Christaan Huygens, a highly gifted physicist and astronomist who is most known for his work on the centrifugal force (yes, that one concept you may have hated in AP Physics), the wave theory of light, and lastly ... dun dun dun, the pendulum clock! Whenever you spend the hours away procrasinating, be thankful to Huygens for that clock you always glance over. No really! Clocks before Huygen's clock were highly inaccurate and times would be as much as an hour off...

CHRISTIAAN HUYGENS PENDULUM SCIENTIST
May 25, 2023 · 4 min read

How I Built This Website

I think that having a website is great for anyone whether it's advertising your personal portfolio or creating a blog (like me!) My website is just a culmination of all the things that I enjoy in life from art to math and it's a little passion project of mine. On top of that, it's really easy to begin whether you can code or not! Of course, there are templates on Squarespace but there is something personal about coding your own website from scratch...

WEBSITE CREATION HTML CSS
May 10, 2023 · 8 min read

Blaise Pascal and the Triangle That Bears His Name

While I was doing some AMC and AIME problems, I encountered Pascal's triangle endless times. In came up a lot in combinatorial problems, and it's quite cool how theorems like the Hockey Stick Identity come from it. Although, I do think Sierpinski's triangle is the best triangle of all --- no one can beat that one. I also always thought mathematicians like Gauss had a interesting childhood, I mean he solved the n(n+1)/2 problem in Elementary. So, was Pascal the same? Let's find out...

MATH HISTORY PTOLEMY
April 9, 2023 · 4 min read

Getting Started with LaTeX: A Beginner's Guide

I've used LaTeX since probably 7th grade, and it's helped me tremoundously. Being a math buff, there was no way I couldn't learn this incredible language that makes mathematical formulas in a document appear seamless. Even to just to change the format of the document, you can edit the preamble of the document which is superior to any Google Doc or Word feature I've encountered...

LATEX PACKAGES TUTORIAL
April 1, 2023 · 5 min read

My First Research Experience: Dynamical Physics

Independent research is actually quite common and it's how most prolific ISEF qualifers start their journey! In general, it's nice to have a resume of research to learn various skills from computing to engineering. Honestly, I was very overwhelmed with trying to find a topic. Lots of the websites that I checked out either had that staple exploding Volcano or a topic that exceeded the 500 word limit. There was never an in between!

INDEPENDENT RESEARCH SCIENCE FAIR DATA
February 20, 2023 · 4 min read

A USAMTS Year 34 Round 3 & Overall Review

USAMTS is a free, high school oriented, proof based contest that is funded by NSA. The contest consists of three rounds, each with 5 problems and worth 5 points. The contest is fully remote and is a month long since the problems are hard enough to not get immediately. The contest is a great way to think about problems constantly and sharpen your math skills...

CONTEST MATH PROOF USAMTS SOLUTIONS
December 6, 2022 · 7 min read

A USAMTS Year 34 Round 2 Review

USAMTS is a free, high school oriented, proof based contest that is funded by NSA. The contest consists of three rounds, each with 5 problems and worth 5 points. The contest is fully remote and is a month long since the problems are hard enough to not get immediately. The contest is a great way to think about problems constantly and sharpen your math skills...

CONTEST MATH PROOF USAMTS SOLUTIONS
October 30, 2022 · 6 min read

The President Who Proved the Pythagorean Theorem

Well, that title is quite strange! Who would have thought that our 20th president and Pythagoras could be in the same sentence? Getting to that later, who even is James Garfield? No, he is not the orange talking cat. Some may know him as our 20th president or a mathematician. The former is more probable. James Garfield was born in...

GARFIELD PYTHAGORAS HISTORY
October 16, 2022 · 6 min read

A USAMTS Year 34 Round 1 Review

USAMTS is a free, high school oriented, proof based contest that is funded by NSA. The contest consists of three rounds, each with 5 problems and worth 5 points. The contest is fully remote and is a month long since the problems are hard enough to not get immediately. The contest is a great way to think about problems constantly and sharpen your math skills...

CONTEST MATH PROOF USAMTS SOLUTIONS
October 6, 2022 · 8 min read

My Experiences at PROMYS (Program in Mathematics for Young Scientists)

So PROMYS (Program in Mathematics for Young Scientists) is a 6 week residential math summer camp that is held at Boston University in Massachussets.The point of the program is to essentially live, breathe, and eat math. Specifically, the number theory parts of math. This is because a lot of research has shown up in the recent years regarding number theory. Although, the main point of the program is not to just teach high schoolers a bunch of number theory...

PROMYS MATH SUMMER CAMP LECTURE
August 22, 2022 · 9 min read

A Chain of Reasoning in Number Theory (part 2)

In the previous article, we discussed the proofs of the chain up to Bezout's. Although the next two steps look quite cryptic. FTA? UPF? Those are acryonyms since the names are quite long. FTA stands for the Fundamental Theorem of Arthimetic. UPF stands for Unique Prime Factorization. We will proceed similarly as we did in the beginning steps of the chain. We will try and use the previous steps of the chain in our proof of the step we want to prove...

FTA PROOF NUMBER THEORY
August 22, 2022 · 7 min read

A Chain of Reasoning in Number Theory

Ever wonder how mathematicians build big results from tiny axioms? This article traces a chain of proofs in Number Theory, starting from a deceptively simple principle and working up to one of the field's most useful identities. It's the first part of a two-part series that ultimately leads to Unique Prime Factorization.

WOP PROOF NUMBER THEORY