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Why Integrals? – Cat's Out of Box
We've looked at how limits explain derivatives in an unambiguous and somewhat elegant manner. Unsurprisingly, limits seems to be the foundation for integrals as well. It might, however, be a longer pathway, not just because of the proof but also because of the definition of the integral. Defining the Integral I find that the definition…
Explaining Derivatives – Cat's Out of Box
Purpose Some people told me that I should explain derivatives in my Mean Value Theorem post if I wanted it to be accessible to younger readers. Because that post was already long, I decided to make a separate post for it. This took a while because I wanted to find an intuitive explanation for derivatives,…
Modular Arithmetic and Large Exponents – Cat's Out of Box
What are the last two digits of 20192019? These types of questions are popular in tests like the AMC or MMPC, and often seem daunting, but modular arithmetic simplifies the problem down easily. Modular arithmetic can be described as using the remainder of a number when it's divided by another number. Before we solve the…
The Other Cat-unboxer – Cat's Out of Box
Hi! It's been two years since Dixie, the Schrodinger behind this website, gave me admin access and after countless half-written posts and edits, I thought it was time to finally introduce myself on here. I'm Swathy, an undergraduate at UC, Berkeley pursuing chemistry, with a concentration in computational chemistry and a minor in materials science.…
This blog changed my personal mission – Cat's Out of Box
Hi! This isn't the kind of article you would normally find on here, but I was reflecting on the past year to write my cover letter, and I realized that a large change to it stems from an article that I've been working on for this blog, and I thought that it might be worth…
Journal Club: Posterior Parietal Cortex Guides Visual Decisions in Rats – Cat's Out of Box
What is this? Hi! Some of you may know that I'm an undergraduate studying neuroscience. Well, as someone hoping to work in the field, I have to read journal articles. However, as an undergraduate, there's a lot that they cover that I have to break down for myself and look up explanations. Academia is infamous…
Cat’s Out of Box – Cat's Out of Box
Hi there! If you're here, thank you! In this blog, I really just want to look at science/math phenomena and try to break them down. Basically, I want to take the mystery out of things that are hard to wrap our heads around. If you're wondering, the blog's name alludes to Erwin Schrödinger's thought experiment…
LR 1: Mean Value Theorem – Cat's Out of Box
As you're driving through a highway with a speed limit of 75 mph, you notice that cops are logging cars' speeds (because they have nothing better to do, I guess). Let's call this checkpoint A. 20 miles and 15 minutes later, you notice another cop car, but this time, the cops are pulling you over…