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\chapter{How to learn math}

Now that that's all out of the way, let's talk a little about math. When this
chapter is over, we're going to dive right in to proving a bunch of things you
already know to be true. We feel that without a little explanation, these
proofs may leave you a little lost or confused. We'll save the explanation of
the proofs for later, but right now, we're going to talk about how to actually
learn math, and the proofs are a great example.

Most people's experience with math is through their primary and possibly
secondary education, which is or was a dreary affair in general, and math
probably even moreso, unless you're one of the lucky few. By lucky few, we
don't mean those wizards with a sort of inherent ability to do math--the first
thing you need to know about learning math is that math is for everyone with a
brain--that's you, right? You see, your brain is a pattern recognition engine,
and that's all math is: the study of patterns. Unlike reading or history, your
body comes with a biological imperative to know math. There's some really great
brain studies on the topic, but that's boring, and I said we're already done
with the boring part, so let's move on.

In that last paragraph, we presented what we hold to be the proper answer to
'what is math': the study of patterns. This is completely different from most
people's interaction with math: in primary school, we are taught how to apply
four operations to solve math problems. You're given something about two trains
leaving a station and going different speeds and different directions and yadda
yadda yadda and before you know it your teacher turned everything into a math
problem and it all seemed so forced--a layer on top of what was intuitive, and
made everything complicated. We agree--this is a counterintuitive approach to
math, and it makes math very confusing and disconnected. Math is just the study
of patterns. That is, math is not so much a way to solve a set of problems that 
exist in a sphere apart from what is natural, but a way to understand what's 
going on in the world around us. When you learn math, you should think of it as 
a science--another level of detail in the amazing world we live in.

That's how this book is written. It's written to reflect that math is a single 
unified study. While you're reading it, try to think of how what you're learning
clarifies or refines early material. This is a big deal to us, because one thing
we dislike most about the standard way of learning math is that at some point in 
everyone's math career, they learn they were taught something that wasn't actually
true. We want to avoid that.