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Comments
I wasn't very good at it in Middle School, but I did well enough. I don't think I really thought about it then. I don't think it was until the latter part of 9th grade Geometry that I realized I hated the subject. The teacher that year certainly didn't help. It came down to my final exam that allowed me to move on. This trend continued for the text three years. In fact, I flunked Algebra the first time. Had to retake it. And then the second time I only barely passed by the skin of my teeth.
I dunno, I like math fine and still suck at it.
Of course, I'm probably going to be stuck working in a grocery store for the remainder of my life. So maybe I'm not the best person to ask about higher-level mathematics.
I think that's less a case of not knowing and more one of not caring. There's some stuff about grammar I genuinely can never remember, but I know my basics enough to be intelligeble to more or less anyone. I don't say things like "cuz" "b/c" and so on because I think they're real words, I say them because I'm being lazy and rarely care what people on the internet think of my grammar skills. I think that's true for most people who do the same.
And the reason I am so good at English is because I care about how I speak, read and write, a lot. I have my mother to thank for those ideals.
Okay then, solve the problem I gave.
The "stupid unnecessary parts" are necessary because they give you the logical grounding to actually understand this stuff. I mean, if you can't understand a quadratic equation, which is pretty much the simplest nontrivial equation there is, how the fuck do you expect to understand the exponentials required to solve the equation I gave? Compound interest is a strictly more complicated problem than fucking parabolas.
That said, your education was probably far from ideal. You were probably taught how to solve problems with vapid "If Train A leaves from LA Union Station at 8am and Train B leaves from Riverside at 9am, blah blah blah"-style word problems*. When you are taught at this level of concreteness, you associate the methods to solve these problems only with that specific circumstance. But if you're instead taught to solve more abstract problems like "3t=75-2t" and then to convert problems like the former into problems like the latter, you can work with a much wider range of problems.
But advocating "cutting the stupid unnecessary parts" is advocating a more rote-memorization-based course, which is the exact opposite of one that actually teaches.
*This includes the one I gave, frankly, although that one has the advantage of being something directly useful to the millions of Americans who are in debt.
Is the formula for that
A = P(1 + r/n)^(n)(t)?
Or is it freaking ln/log crap?
The point is, if someone told me how to do that problem, I could then do it right then. If I aboslutely couldn't remember it (like I'm drawing a blank now), I could write it down on my bulletin board.
There. Didn't have to waste 16 weeks and like 300 bucks.
Both, really.
That's not quite the right equation when you're also paying off interest; being able to derive that one is nice, and I'd go through the derivation if I didn't need to go to sleep soon in preparation for an exam tomorrow; you'll get a remarkably similar equation, though, with some weird numbers for A and P.
The "freaking ln/log crap" is how you solve such an equation as
for t, which is the unknown variable in the problem I posed, because you can get it into the form
rather easily, and the logarithm is defined by the previous equation being equivalent to 
. A logarithm is a function that you should never, ever, ever have to calculate by hand or even really estimate; even in ye olden days, they had tables full entirely of logarithms. The main thing you should know about logarithms is how to change the base; tomorrow, after I've slept, I will explain this formula, since I would feel guilty about just throwing it out by rote without actually explaining how it comes about.
Yes, that formula with the exponential is the compound interest formula. (Though logarithms are basically reverse exponents.)
Edit: ninja'd. Yeah. As ponicalica points out, the "how long" is that little "t" in the formula...and to take it out of the exponent you have to use logarithms.
i hate logs.
Also radicals and exponents. All the ones where you have to switch the stuff around. Even though it should be easy for me, it just isn't.
I'm not going to make up an excuse like having a disability. I just don't care enough.
Exponents I actually tend to find easy-ish just because it's usually doable on a calculator.
Honestly I think in my case I have way more problems with basic arithmetic than the conceptual parts of other math. Of course, I only ever got as high as "Senior Mathematics" in high school. So idk.
Exponents are numbers that stick to something even more closely than multiplication/division does.
Let's just say that there are things people don't like and they only do the bare minimum of what is necessary and leave it at that. I will take this test, get the credit, and only do loan/debt stuff when I need to in life.
I was going to say "no, exponents are [explanation of exponents]", but it occurs to me I don't really know how to explain them. Other than "exponential multiplication" which helps so little I might as well be saying "hullabaloo and howdy-do".
Exponentiation is to multiplication as multiplication is to addition. Or, exponentiation is just... start at one, and then multiply by the number [exponent] times.
$8000 = an increase of $80 a month.
Paying $100 = $7980.
It would be easier to mark it down on paper, as I'd be able to use shorthand to get this done in about a minute. Via text, let's see:
- $20.20 = $7959.80.
- $20.41 = $7939.39.
- $20.61 = $7918.78
Etcetera, etcetera. It's slower than using an algebraic expression, yes, but you can figure it out all the same, and there's no confusing symbols and crap.
However, that's not really a situation I'd find myself in, as I wouldn't pay a base $100 off a week; I'd pay off the interest every week, plus $20 and however much else I had spare. And I can't account for variables such as spare money in advance, so I'd look up to my notes above and calculate a vague time period, and then run with that give or minus a few months.
That's assuming that I'd ever be silly enough to get a loan, however. The only instances where I would would be if I was buying a large-sum thing, such as a house or car, in which case the price required to pay it off would be substantially larger than $100 a month, and I would want to, again, pay as much as I could off every month while still keeping enough in savings to accomodate for financial problems later in the debt's period, because otherwise the debt would stretch for too long and the accumulated interest would be more of a kick in the teeth.
The high school stuff, we didn't get a formula sheet either, but there's really not that much to memorize as faceless formulas because they're all interrelated.
Like, most of the trig identities came down to fucking around with sin^2 + cos^2 = 1 (which is itself the Pythagorean Theorem transcribed on a unit circle, so all you really need to remember is trig definitions and a triangle). Double angle identities were important, but it was basically just the next floor down on a Pascal's Triangle expansion from sin^2 + cos^2, split between sine and cosine terms, the sum and difference identities are just minor tweaks of that, and you could always plug in easy ones if you weren't sure about minus signs and whatnot. Half angle identities were just inverting that. Law of sines was an extension of similar triangles. Law of cosines was Pythagorean Theorem plus an adjustment term that was basically a polynomial middle term and vanished if you stuck in a right angle.
I mean, the grand revelation of trig is that it all looks the same because it is all the same. Most of the formulas reduce to each other when you plug in border cases.
Most of the discrete math bits came down to a fancy way of writing counting. So you didn't even have to remember any formulas at all as long as you knew what factorials concretely translated to.
I mean shit, the last thing I remember arbitrarily memorizing without knowing where it came from and why was a few derivatives/integrals, and they were all stand-out "special cases" that you use too often to forget.
I think the only thing we were expected to memorize in college math were careful definitions of Green/Stokes/Gauss, and that's mostly because you use them for everything ever in physics.
What if you don't plan on taking Physics? You were forced to memorize something you didn't need?
Well, that was Math 283, Multivariable Calculus II. So if you weren't taking it as part of a major that would regularly use it, it was kind of your own fault by then.
Other than that...I mean, I can't really think of anything in the entire 200-300-level math stuff we were expected to memorize. Either it was on the formula sheet, or the road getting to the formula was more important than the end result.
Throughout high school, the good teachers didn't focus on memorizing formulae. Ever. They focused on techniques and methods to zero in on a game plan to tackle something, how to swing the algebraic hammer of justice for yourself. The formulae fall out as a natural result of that -- not the other way around.
Like, here's an example. This is the formula for a Taylor expansion of a function.
That's an ugly bag of ass. I'm not going to remember that. But I understand completely what a Taylor series is on a conceptual level, how it was constructed, and what every term in it represents. If you asked me to write it down, I wouldn't regurgitate the formula -- I'd think of what characteristics it needs to do that stuff, construct a silhouette of sorts, and fill it in from there.
There's also a formula that lets you determine how many terms of a Taylor series you'd need to approximate a function to any desired precision. It's even uglier. But I know it's a Squeeze Theorem between two integrals of the function by representing the Taylor as a series of rectangles that outline the curve, and from that conceptual image I could pull the formula out after a couple minutes. Which sounds complicated, but what I basically described was "how did I get there again?" followed by a picture that condenses Big Ugly down to "how big are the rectangles?"
Whether or not you understood what I was specifically describing, that's not the point. The point was that the trick with math is to think in patterns, not numbers. We're not computers, we're creatures of art and action and muscle memory. We have a little troglodyte in the back of our heads that sees big animals, instantly recognizes the neck, and tells us "throw spear here, eat good food". We relate to pictures, strategies, analogues. We build houses by building a framework and filling it in. We remember the direction we went, the logs we climbed over, and the rocks we tripped over more than where we ended up. So abuse the piss out of that.
Solving an algebraic equation is like chipping a fossil out of a rock. Trig is a Swiss Army knife that's just trying to troll you by looking like a huge knife rack. Stats and discrete are just shorthand for counting. Matrices are just shelves of completely boring linear equations you've been doing since middle school. And so on.
@Saturn: I don't intend to offend, but it's very annoying of you to keep saying an academic field is stupid just because you happen to dislike it and generally being obtuse ("neh neh I don't fucking care maths sucks") when folks are trying to help.
"I'm ignoring my problem because it's dumb, I hate it also what's the point" is not a healthy attitude to have.
P.S. I may be biased 'cause I freaking adore maths, but it saddens me to see mathematics so hated.
If you don't intend to offend, you shouldn't tell people they need to grow up. Just a tip.
You know, that's not actually what he's saying.
The thing is, algebra is not something that a lot of people will use. There are certainly uses for it- it makes a lot of long, complicated problems a lot simpler, and it is a good way to teach people reasoning skills- but it's not by any means necessary for people to learn.
And, despite what some people here will say, it is possible to simply not have a head for numbers. And being constantly forced to deal with maths and numbers when you suck at them gets incredibly frustrating, and can lead the people in to resent the subject.
If you're going into a job that requires algebra- such as, I'unno, being a builder or something- then yeah, you should suck it up and deal with it. If you're not, though, then you're going to be putting yourself through a lot of trouble and stress to learn something that's going to only vaguely benefit you in life.
^Agreed wholeheartedly. I'm sorry to blow my fuse like that.
Happens to the best of us.
I'm sure nobody here minds.
Anyway, to amend my previous post, advanced algebra is not something most people will use. Something as simple as "I have a hundred dollars and I need to save sixty-two, how much can I spend", most people will use (although personally I reduce that to a simple equation in my head- 100 - 62 = how much I can spend).
Most of algebra is not that, however, and it's that stuff that most people won't use. There are a lot of professions where people will, and in those cases, it's entirely valid that even people with no head for numbers need to suck it up and power through it. If your profession doesn't require it, however- well, even high school dropouts who never took maths beyond eighth grade survive, so I'm pretty sure it's not at all necessary for regular life.
Algebra is not technically required for most things, but it is a more rigorous and reliable way to do calculations and solve problems that turns out to be more convenient for more complex problems, including problems of resource management, making predictions, understanding trends, etc..
By reliable I mean this: As we were discussing on IRC earlier, we could do everything using long-form arithmetic by hand, as you say you do. But if we wanted to go back and check the numbers, we'd have to do it all from scratch again. With algebra, (1) we can do pre-calculation manipulations of variables, to minimize the number of numerical calculations necessary, and minimize the number of times digit transfers and addition errors and such can crop up, and (2) we can do error-checking becomes much easier because we can separate conceptual errors (such as using the right number in the wrong place) from calculation errors (such as carrying a bad digit), making it much easier to zoom in on problems and fix them.
Which makes it almost essential to career advancement ambitions. True, someone working at the bottom rung might not need it, but managerial positions frequently find it useful.
My career is in, dundundun, libraries. Okay, let's check my duties as both a library assistant and a library officer:
As a library assistant, my primary duties are the charging and discharging of materials to customers. Secondary duties include maintenance of the library area (keeping the library tidy basically), returning books to shelves, and assisting customers to find materials. Tertiary duties involve answering phone calls, handling funds (repayment of library fines and people buying odds and ends, for the most part), and tracking statistics (drawing a tally mark when you field an inquiry).
As a library officer, my primary duties are promoting library services (newspaper advertisements, radio interviews, etc), compiling statistics (entering the statistics marked down by library assistants onto spreadsheets), and ensuring each member of the library has a job to be doing. This is on top of a library assistant's duties.
The closest you come to algebra in my career is entering statistics, unless you are a financial librarian.
Note that this is a simplistic view of duties, but it covers the main points.
The most common application of algebra is probably cooking. A tablespoon of milk to two eggs per a serve, serving four? That's a + 2b = x, and if the required outcome is 4x, then it's 4a + 8b = 4x.
Mind you, serving two eggs and a tablespoon of milk is a peculiar dish. But still.
Alternately, it's 4*1 (the milk) and 4*2 (the eggs).
That's more efficiently expressed via the single equation 4a + 8b = 4x, though, since you can use a single equation rather than two expressions. The single equation also contains more information, since in the expressions 4*1 and 4*2 the 1 and the 2 stand for nothing but their actual values. In the equation, however, "a" is a representative value that stands in for "tablespoon of milk", so it's a container for information in a way the value of 1 isn't.
It's also silly, because it's easier to just go "Okay, I needed one tablespoon of milk before, now I need four, so I need four tablespoons of milk."
Abstracted, it's more efficient, but practically, it's more complicated than it needs to be.
You're not going to write down the equation or anything, but it's the same thought process. You use a known relationship and known values to find an unknown value.