Jeremy Côté

Bits, ink, particles, and words.

The Limits of Life

Note: I received a copy of this book as an ARC from NetGalley. It comes out next week. I tried to stick to the concepts he describes, but I’m sorry if you see any bias.

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Hidden Assumptions

I remember when I first took a class in linear algebra, and we were talking about vector spaces. In addition to the definition of a vector space, we were also given multiple axioms that define what the structure of a vector space looks like. This included a bunch of boring things, like the fact that if you have a vector v, you should have a corresponding vector -v such that v+(-v)=0, where 0 is the zero vector. There are eight of these axioms, and together they describe exactly what can be called a vector space.

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Misaligned Incentives

There’s a saying among students regarding preparing for an exam. In short, it goes like this: Study a lot before the test, and then you can forget most of what you know.

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Stating One's Goal Clearly When Solving a Problem

Everyone solves problems differently. Some like to work directly with the mathematics head on, while others prefer to have a more intuitive approach. This includes studying simpler cases of a problem, or looking at examples in order to really understand what’s happening. These are all valid approaches, but the point I want to highlight is that these are all strategies. There’s a certain method to tackling a problem. It’s not that you can’t solve a problem through trial and error, but if you want to solve more problems more quickly, your best bet is to figure out a strategy.

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