Jeremy Côté

Bits, ink, particles, and words.

A Nice Way to See the Identity for Binomial Coefficients

As someone who likes to learn new concepts, I’m guilty of “knowing” a bunch of mathematical concepts without knowing the “why” behind them. In other words, I’ve come across many neat bits of mathematics, yet I only understand them at a surface level. However, as I continue through my mathematical education, every now and then I’ll formally learn something that I came across before, and the explanation makes the concept that much more interesting in my mind.

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Guided Learning Through Problems

I love new information. I read all the time (both fiction and non-fiction), and I like to learn new things about the world. I have interests in mathematics, science, and plenty of other niche topics like typography and running. As such, I’m frequently consuming information. I begin my day by reading, and I must spend at least an hour each day reading (particularly when I have time off between semesters, as is the case now). Put simply: I love learning new things.

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Teasing Out One's Reasoning

I pride myself on being honest with the students I tutor. I don’t like the idea of telling a student that they’ve made a “good” attempt when really there answer is incorrect. My goal with them is to help them learn whatever material they are struggling with, not to give them what some people call “compliment sandwiches”. These are the result of giving someone a piece of criticism in between two compliments in order to make the criticism easier to digest. Perhaps that works for some people, but for myself, I find it more efficient to simply tell the student what’s right and what isn’t.

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Calculating $\pi$ Factorial

One of the things I like most about mathematics is its ability to generalize results to realms that one might not have previously thought of before. Historically, this is what happened with rational numbers, negative numbers, irrational numbers, complex numbers, and so on.

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