This.
Is.
Fascinating.
Via GeekPress, we discover a wonderful post on learning mathematics. Before you click on to another blog, this is different from anything else I can remember reading on the subject. And it's great.
From Stevey's Blog Rants ("random whining and stuff") comes a post called Math for Programmers. But don't let that put you off. It's far more useful for non-programmers than the title implies. Oh, yes.
They teach math all wrong in school. Way, WAY wrong. If you teach yourself math the right way, you'll learn faster, remember it longer, and it'll be much more valuable to you.
...Math is... ummm, please don't tell anyone I said this; I'll never get invited to another party as long as I live. But math, well... I'd better whisper this, so listen up: (it's actually kinda fun.)
Well, heck, we knew that already.
I've found it's much easier to learn and appreciate geometry and trig after you understand what exactly math is — where it came from, where it's going, what it's for. No need to dive right into memorizing geometric proofs and trigonometric identities. But that's exactly what high schools have you do...Schools are teaching us the wrong math, and they're teaching it the wrong way.
...[Probability theory is] the first thing they should teach you after arithmetic, in grade school. What's probability theory, you ask? Why, it's counting. How many ways are there to make a Full House in poker? Or a Royal Flush? Whenever you think of a question that starts with "how many ways..." or "what are the odds...", it's a probability question...It starts with flipping a coin and goes from there. It's definitely the first thing they should teach you in grade school after you learn Basic Calculator Usage.
...The right way to learn math is breadth-first, not depth-first. You need to survey the space, learn the names of things, figure out what's what [emphasis mine].
...The right way to learn math is to ignore the actual algorithms and proofs, for the most part, and to start by learning a little bit about all the techniques: their names, what they're useful for, approximately how they're computed, how long they've been around, (sometimes) who invented them, what their limitations are, and what they're related to.
...don't let exercises put you off the math. If an exercise (or even a particular article or chapter) is starting to bore you, move on. Jump around as much as you need to. Let your intuition guide you. You'll learn much, much faster doing it that way, and your confidence will grow almost every day.
If you're anything at all like me, you'll find yourself hooked after only a minute or so.
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