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[Solifuge]

So, I had to skip a few years of foundational Algebra to get into College Prep courses, and that's kind of left me on uneasy footing for the rest of my academic career. Additionally, I don't feel like I've ever been taught the reasons why the equations I've been memorizing work, which is clashing with the whole way my brain thinks and learns... it's like I'm being told to go through motions, without ever getting the reasons why. I tested my way into Calculus at my University, but I don't personally feel like I have a strong enough foundation.

To fix this before I get back to school in Winter, I'm considering picking up a decent math text to self-teach from. Can anyone suggest a good one? Ideally, something that doesn't skimp on teaching underlying rules, so it's not about taking their word for it, or memorizing without understanding. And which I could find older versions of, because I am pretty poor right now.

[Vector]

This is a Mathematician textbook, but if you're asking why equations work then you have to go to the source--you won't get this viewpoint from any high school text.  Algebra by Birkhoff and Mac Lane.  The first chapter will tell you way more than you ever wanted to know.

Otherwise, if you can get an old copy of A Survey of Modern Algebra, I think that would be even better.  It's basically the same book but it feels easier.

[Solifuge]

Thanks! I tracked down a copy of A Survey of Modern Algebra. Looks a bit dense, but I'll give it a proper read this weekend, and see how overwhelmed I feel.

This would be the first math text I've read that actually defines things, though. I definitely like that.

[Vector]

It is dense.  Don't worry if it takes you an hour per page to read and really, deeply understand at first.  It's one of those things where, if you keep plugging at it, you'll actually feel yourself getting smarter.

If you're really trying to learn how to manipulate equations, then the first section of the first chapter could be enough.

[MaximumZero]

Wait, there are books that tell you why math is the way it is, and not just throw problems at you? Why don't we learn about this stuff in like...5th grade?

[Vector]

Wait, there are books that tell you why math is the way it is, and not just throw problems at you? Why don't we learn about this stuff in like...5th grade?

Because it requires substantially more mental firepower and abstraction skill than most 5th graders have, and because the more abstract, the more pure, the more explaining why it is how it is, the more effort it takes to apply to the real world.

And then. . . "when will we use this?"

[MaximumZero]

The thing about that, though, is that through 13 years of standard education and 3 years of college, I still don't know why any of math is the way it is. Sure, I know a little about trig, and the barest bones of calculus (mostly thanks to you guys, actually,) but I don't know the first thing about why.

The question "when will we use this," is largely attributed to the prevailing attitude toward math. It's difficult, arcane, and the meanings of mathematical objects and subjects are purposely obfuscated because math is only for the elite of the smartypants. Math is only to be used as a last ditch effort or as a tool to do something specific. It's not artistic, it's not beautiful, it's not elegant. Math is that specific set of wrenches that you hate but have to have in the garage, just in case. There is no why, there only is. These are the rules, and if you don't memorize this book full of them, we'll move on without you and you're an idiot.

Maybe if we started teaching students why math is instead of just what it is, that perception would begin to change a little.

[Virex]

Would it even be realistic to introduce group theory and abstract algebra during high school? Those aren't exactly fields that are easy to grasp even for people that graduated high school with flying colours.

[MonkeyHead]

If you ask me, maths is at its most beautiful when used to model a physical process - I find this often helps me understand the "why" behind the numbers and thier manipulations, in some kind of reverse engineering process.

[Vector]

Bleh.  That's why you're a physicist.  I think it just makes the pure math-oriented people confused.

[MonkeyHead]

I suppose its probably as i have a very utilitarian way of thinking.

[Furtuka]

Spoiler:  I'm pretty sure I'm suppose to solve this by solving for t in the Dot product between the vectors representing the line and the segment between the point, but I've gotten stuck how to write said vectors down. Halp please (click to show/hide)

[MagmaMcFry]

The dot coordinates are P = (2.4, 0.7, -0.2), the parametric line point coordinates are L(t) = (-1.3 + 1.2*t, 5.6 + 7.3*t, -0.2 - 3.6*t), and the line direction is d = (1.2, 7.3, -3.6). You want to find the point L(t) with d·(P-L(t)) = 0.

[Furtuka]

Thanks.

[Pnx]

Quick question, doing limits stuff and there's a number of questions where for example, you have a graph depicting a function like y = x, except when x = 0, y = 3.
Would the limit of x as x approaches 0 be undefined, or just 0?