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Newbie at Number Theory (Part Two): The Euclidean Algorithm
Today’s part two of our dive into number theory. For those who haven’t read part one about the division algorithm click here, because we plan to use it! We talk everything Euclidiean, except for Euclidean geometry! We will learn about another algorithm which…
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Newbie at Number Theory (Part 1): The Division Algorithm
Today’s a very special day! We’re about to discuss some number theory! It’s important for anyone interested in mathematics to know the basics of number theory. Maybe not to the level of Fermat’s Last Theorem, but definitely enough to know Fermat’s Little Theorem…
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Cosets are Cool Sets (Even I Know This is a Lame Title!)
*Note that it’s assumed the reader is familiar with groups and subgroups. And note to subscribers, the way that the math (or maths for my British friends) is formatted on phones in emails is downright awful! I recommend you read this online. *…
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Normal Subgroups
*It is assumed that the reader is familiar with mathematical Groups.* Imagine this: You’re in the middle of a lecture in your abstract algebra course discussing group theory and all of a sudden you hear that a subgroup is normal. What’s so normal…
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Induction and Well-Ordering
Ok, forewarning this will be covering deeeeeep mathematics. For those who already know of induction and/or well-ordering this’ll be a treat! We are going to describe the connections between these two concepts. For those who have not heard of either induction and/or well-ordering…
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A Strenuous Sequence
Thank you for coming to see a more challenging example! I commend your enthusiasm! For those not sure what I mean by this, check out this post before you read this one! One last thing, remember that: Let’s get into it! Practice makes…
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Incredibly Serious, Inductive Sequences
In my last blog, we discussed how to use the awesome tool of induction to prove a countably infinite number of statements P(n). So, if you are unfamiliar with induction, I recommend you check it out (or another resource)! This blog post is…
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Incredible Induction
Aggravating Addition Let’s get straight into it and try to add every counting number from 1 to 100. Basically, what is 1+2+3+…+99+100 = ??? There’s a long way and a short way to do this. Let’s be lazy and do it the short…
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Funky Functions and Cool Continuity!
Thomae’s Function aka The Stars over Babylon aka The Popcorn Function * Note it’s assumed the reader has heard of limits for both sequences and functions, the connection between limits for sequences and functions (Called Heine’s Continuity Criterion), and continuity for functions. I…
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Math That Counts
Have you ever found it interesting that one of the first things we learn in school (and sometimes even before we start school) is how to count, and yet there are many interesting and challenging problems/concepts that can come from simply counting?1 For…
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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A Kick in the Discovery 