Jeremy Côté

Bits, ink, particles, and words.

Control of the Future

It’s tempting as a student to think that nothing is in your control. We often feel like our whole lives revolve around the whims of professors and their decisions for assignments and tests. It can be easy to retreat into “reactive” mode, making sure that everything which is thrown at you gets done. When we operate like this, we tend to be exhausted, since we can never look further than a week.

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Slick Versus Pedagogical Proofs

In mathematics, there’s almost always an opportunity to make proofs more concise. For example, when you first learn a concept, it might take a while to prove a result using the definitions that were developed. The reason it’s longer to do is because the definitions require you to spell out ideas explicitly. As a result, you might get to the end of the proof, but it takes a bunch of little intermediate steps to do so.

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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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