That wasn’t out of kindness 
Just me covering all my bases, because there’s a fair chance that engineers don’t use much algebra when they’re, like, eating, sleeping or having sex (to the extent they do have sex) 
ahem Substitutional algebra has been around since well before 1600 AD.
Fuckin’ algebra, how does it work?
That probably depends on whether you’re top or bottom
As noted, not explicitly.
Implicitly:
M(0) = 80
Pay $10 at the door: M(1) = M(0)-10 = 80 - 10 = 70.
Buy two drinks at 6 each: D = n * p = 2 * 6 = 12. M(2) = M(1) - D, bringing variables forward, = 70 - 12 = 58.
How many lap dances can you afford?
N = floor(M(2) / P), bring vars forward, = floor( 58 / 25 ) = floor (2.32) = 2.
Leftover: M(3) = .32 * 25 = 8.
Hopefully that’s enough for cab fare.
ETA due to post spacing timer:
… or irrational.
Oh,
You’d be surprised…
And we won’t even get into graphs and spreadsheets…
But literal notation (using x,y,z to represent variables, writing equations) hasn’t. Diophantus made some early steps towards literal notation in the 3rd century, which was promptly abandoned for over a millennium. A few mathematicians started toying around with notation in the 1500s, until Rene Descartes invented the modern notation (more-or-less) in the 1600s.
Before the 1600s, there were basically no equations as we think of them today. Mathematics problems were posed in common language, and they were solved in common language, with perhaps some geometric diagrams to aid in understanding. The idea that algebra and literal notation are the same thing is a modern one.
If I understand that correctly, all math issues were treated in the bane of 6th grade math classes – WORD PROBLEMS! :eek:
Correct. Well, word problems with diagrams alongside, and they didn’t attempt to spin a cutesy story to dress the problem up; it was more along the lines of “When you have a quantity that is to twelve as six is to fourteen, …” and so on.
The worst of it was that, for the longest time, Europeans were stuck using Roman numerals to do arithmetic. I could just about survive without literal notation; I’d take up poetry or animal husbandry without place-value notation.
I forgot all about this thread. I was really tired last night.
Yea I’m not hating on math. Quite the opposite. I think it’s a wonderous thing the way logic works. Like finding intercepts of lines. Basically you start with the proposition that two lines intersect. Then using logical deduction cancels out the variables. If they do the system is coherent and you get numbers that make sense. If your assumption is correct it produces answers that makes sense. If they don’t intersect then your premise is nonsense and produces nonsense logic like 0 = 5. In otherwords it works because valid logic produces valid logic. Pretty simple, but pretty cool.
Further there’s a ray of hope today! Turns out there’s this thing the Fundamental theorem of Algebra, the proof of which explains a good chunk of the polynomial voodoo.
In other words, I’m going to get answers. The day of reckoning is at hand.
Do you know how to make an elephant fly?
First, get a GREAT BIG zipper…
The thing to keep in mind when you’re learning algebra is that it doesn’t have a lot of utility by itself. But it’s a fundamental building block for the really useful stuff that comes later.
It’s like learning the alphabet. There are not many times in life when you need to recite the whole alphabet from start to finish. But knowing the alphabet lets you read, which is where the real action is.
Algebra is just a set of rules for manipulating equations. You want to get those rules drilled so thoroughly into your head that you use them unconsciously. That way when you’re learning calculus, or linear algebra, or differential equations (which ARE very useful) you can concentrate on the hard stuff and the algebraic bookkeeping will take care of itself.
You’re in a nightclub. You meet Danica McKellar there. You want to chat her up.
Bet you wished you knew some algebra now.
So now I know what made Algebra hard.
I think math and music are linked, and if you are able to do things like intuitively predict which note comes next in a scale, you will also be able to understand math intuitively. It might be that she understood math in a way the other teachers didn’t, because of music.
Bollocks. I’m a decent musician ( on several instruments), and I can’t do anything beyond simple math. In fact, I had to teach myself a simpler, “add up” system to get around my inability to understand higher math of any sort. Simple algebra, like estimating feet of pipe or wire, isn’t really the sort of math most people have trouble with. That’s just adding up fast. It’s the pointless equations, graphs, and such that the vast majority of people will never use in their lives. On the other hand, I was able to answer most word problems fine by using my system of adding up and refining the nearest guess. I learned in math that they don’t care if you get the right answer, they care that you got it the correct way.:rolleyes: That has pretty much zero real life application where it’s results, not method that counts.
I have never experienced this. Both Algebra teachers I’ve had in my two classes seem to have a whatever works philosophy. If you can show your work and your answer is correct it’s all good.
Some of it’s pretty interesting like i. i is the square root of negative one. It doesn’t exist. It’s made up, fiction, lies, call it what you want. You can’t square a negative number. However you can pretend to square a negative number. You end up with i times the square root if that number was positive.
For example √(-4) = 2i. The exact details of how that works I won’t bug ya want since this post unsolicited.
Anyway you can check this with 2²i)². Which is -4. 2 * 2 = 4, and since i by definition is the squareroot of -1 then it’s a matter of 4 + -1 which is -4.
What’s interesting is the powers of i:
i¹ = i
i² = -1
i³ = -i because i is a negative number.
i⁴ = 1 because i⁴ = i² * i² and i² = -1 so it really says -1*-1 which is 1.
i⁵ = i because i⁴ = 1 and 1 times a number is that number.
so starting at the 5th power it loops back on it’s self. If you a make graph where i replaces y. you can have equations that make circles, more importantly you can model AC current using i. Replacing the wave with a circle that maps the cicles of the AC power wave.
Here’s the part i rocks out. By tweaking your numbers to make the loop more ovalish, leaning, or otherwise change it’s shape you change the sound that comes out AC devices.
So if you play electric guitar you’re using algebra. as soon as you turn your amp on.
Not always. Sometimes, method counts, not just results. For example, if you’re a soccer player, it’s not enough to get the ball into the goal; you have to do it the correct way. It’s not good enough to pick it up, run down the field, and toss it into the net. If you’re a cop or detective, it’s not enough to catch a criminal; you have to obey the law and tell how you know the person you caught is really whodunnit.
I can think of several possible answers to this; you can decide if any fit your experience.
(1) If the point of the class is to teach you how to use a particular method, then of course they only care that you got the answer the correct way. If they’re trying to teach you how to play Beethoven’s Moonlight Sonata, they don’t want you to give them a recording on CD. If they’re trying to teach you how to cook friend chicken, they don’t want you to give them a bucket you picked up at KFC. Even though you got results.
(2) They may not care that you got your answer the correct way, just that you got it a correct way. What matters isn’t getting an answer that happens to be correct; it’s getting an answer that you know is correct. In real life, there is no Answer Key in the back of the book. They want to make sure you got your answer using a method that always works, not one that just happened to give you the right answer this time. If you can’t explain what you did to get your answer (and why), how can you or anyone else feel confident that you did get the right answer?
(3) Some teachers are dumb—or at least, their knowledge is limited. They can recognize when someone’s solving a problem the way they were taught, but if you take an alternative approach or do something they’re not expecting, rather than take the trouble to try to understand what you’re doing, they’ll just tell you you’re wrong.
For that matter, does negative one exist? What does it mean for a number to “exist,” anyway?
I heard a really good metaphor for learning math.
It’s like blowing up a balloon, everything you know is inside and is trivial, everything outside is beyond your comprehension and the tiny scrap of balloon between them is what is difficult but you can figure out.
I think that frustrates people and makes math seem far harder than it is.