Jeremy Côté

Bits, ink, particles, and words.

Levelling Up

We enjoy doing comfortable things.

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The Rational Roots Theorem

One of the skills students learn in secondary school is to factor quadratic expressions. In particular, they learn how to solve equations like x2+2x+1=0. There are a slew of techniques one can use to deal with quadratics, and they mostly rely on the fact that questions asked in assignments and tests have “nice” factorizations. Most expressions have integer solutions, or at worst rational ones. This makes it straightforward to factor. Of course, this might take a while to get used to, but it’s a skill that many students pick up.

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Mathematics Isn't Just Numbers

We often equate mathematics with numbers, as if mathematics doesn’t extend further than doing arithmetic. Each time this happens, I have to restrain myself from going on a rant. I want to grab the person by the collar and exclaim, “There’s so much more to mathematics than just numbers! It’s like saying that running is just a bunch of one-legged hops. While that might be technically true, it’s not the way most people would describe their experience. In the same way, mathematics is way larger than just numbers.”

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Degeneracy of the Quantum Harmonic Oscillator

Note: This post uses MathJax for rendering, so I would recommend going to the site for the best experience.

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