Wolfram Student Ambassadors: My Experience with Wolfram

March 04, 2024 - Wolfram Alpha, Mathematica, Wolfram Student Ambassadors

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.

Which has a bigger effect on history: the plans of the powerful or their mistakes?

October 08, 2023 - Academic Writing, Jil Competition, World Wars

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...

Introduction to the Zeta Function

August 16, 2023 - Zeta Functions, Euler Product, Trignometry

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).

Christaan Huygens: The Father of the Old Clock

June 09, 2023 - Christiaan Huygens, Pendulum, Scientist

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...

The Long Awaited: How did I create this website?

May 25, 2023 - Website Creation, Html, Css

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...

Blaise Pascal: Well, there's the triangle.

May 10, 2023 - Math, History, Ptolemy

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...

Latex for beginners: How I got Started

April 09, 2023 - Latex, Packages, Tutorial

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...

My Independent Research Journey: Dynamical Physics

April 01, 2023 - Independent, Science Fair, Data

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!

A USAMTS Year 34 Round 3 & Overall Review

February 20, 2023 - Contest Math, Proof, Usamts, Solutions

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...

A USAMTS Year 34 Round 2 Review

December 06, 2022 - Contest Math, Proof, Usamts, Solutions

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...

James Garfield and Pythagoras?

October 30, 2022 - Garfield, Pythagoras, History

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...

A USAMTS Year 34 Round 1 Review

October 16, 2022 - Contest Math, Proof, Usamts, Solutions

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...

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

October 06, 2022 - Promys, Math Summer Camp, Lecture

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...

A Chain of Reasoning in Number Theory (part 2)

August 22, 2022 - Fta, Proof, Number Theory

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...

A Chain of Reasoning in Number Theory

August 22, 2022 - Wop, Proof, Number Theory

This article assumes basic proof knowlegdge. The Chain of Reasoning sounds quite general, and it is! There are multiple definitions to this term, and the basis would be that it’s a multi layer argument. Although, I’m not here to lecture about all the types of chains there could be. Rather, I’ll be discussing a rather important chain in Number Theory. This Chain of Reasoning flows as below ...