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An Introduction to Metric Spaces
This article is meant to be an intuitive introduction to metric spaces. We aim to motivate the concept of a metric space and some fundamental theorems about them, and have as much fun as we can along the way. To begin, let me…
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The Ultimate Guide to Compactness
Note that this article assumes that the reader is familiar with metric spaces. At least at the level where open sets, closed sets, and subspaces are used. I am in the process of writing an article to describe the basics of metric spaces…
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Limsup’s and Liminf’s (Again)
A while back, we discussed what the limit superior and limit inferior are. (See here) In that article, we defined these two concepts as follows, In that article, we built some intuition for what these strange-looking limits are. In particular, we saw that…
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The Euler-Mascheroni constant γ
Today, we look at one of my favorite mathematical constants, the Euler-Mascheroni γ\gamma constant. I’m sure that you are aware of Euler’s number e≈2.718…e \approx 2.718… which is a staple of calculus classes everywhere. However, not many people are aware of the Euler-Mascheroni…
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May the F=ma be With You
Happy Star Wars Day, everyone, and May the Fourth be with you! Today, we will discuss a little physics. In particular, we will look at some of the fundamentals of classical physics: Newton’s three laws of motion. We will not go through the…
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Maximal and Prime Ideals
*Note this article assumes that the reader is somewhat familiar with rings and ideals. If you aren’t, feel free to continue reading. I hope that it will be mostly understandable! Today, we will learn about two types of ideals. These will help us…
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Irrationally Happy it’s π Day!
Achievements Unlocked Today is a big day for akickinthediscovery.com! Not only is today π\pi day, basically the holiday that celebrates math(s), but this π\pi day article will be the 50th50^{th} article written on akickinthediscovery.com. Also, just as significant, it’s Einstein‘s birthday! Last π\pi…
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Cauchy’s Theorem for Finite Abelian Groups
Note that this article assumes that the reader is comfortable with normal subgroups and quotient or factor groups. Today’s article will be relatively short. However, I hope that it is both enjoyable and useful to you! Today, we will prove Cauchy’s theorem for…
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AM-GM and Circles
Last time, we gave a few proofs of the AM-GM inequality. They were proofs that were based on induction and some analysis. Today, we give a quick geometric proof of the original AM-GM. I hope you enjoy! I did! The AM-GM (Original) We…
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AM-GM and George Pólya
A while back, we had mentioned the AM-GM inequality: I had said something like, there are many great resources out there where you can find a proof of the inequality. And so, I skipped the proof! But this will stand no longer! I…
What Comes Next: 1, 2, 4, 8, 16, … hint it’s not 32
Hello,
Welcome to A Kick in the Discovery! If you’re curious where this phrase came from, that’s good! It came from the great physicist Richard Feynman. He was curious about anything and everything and he loved to explain science to others. I want to communicate the same enthusiasm about things that I find amazing! More than that, I want to practice teaching and explaining more and more complex ideas. Communication is very important and very challenging, and I hope this blog helps me learn this skill. With all this said, please bear with me while I practice my writing skills! It will be a process.
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