b0rsuk
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I HATE, HATE, HATE, HATE badly explained math. By this I mean math with just formulas and no examples to show how to use them in practice. I've just spent last several days trying to figure out how to calculate this:

http://pl.wikipedia.org/wiki/Iloraz_r%C3%B3%C5%BCnicowy#Rz.C4.85d_ilorazu_r.C3.B3.C5.BCnicowego

Several days and two logical errors* later I've found this:

http://wazniak.mimuw.edu.pl/index.php?title=MN09
(the first flash animation from the top)
And suddenly I understood.

I don't think math is that hard, actually. But the hardest part certainly is finding documentation you can actually learn from.

Every formula should be backed up by an example with numbers. RAAAHAWhRAHHH RARqararAR h Rararar !
Har !

Formulas without examples are like linux man pages. Ok, that's a bit unfair because about 1 in 20 mans contains an example, but still.

I'm going to find someone and make him hurt.

*logical errors which caused my python program to produce bad output... I've spent most of this day working on it.

And I HATE anyone who considers raising an objection to any of the points I made above.

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[Last edited by b0rsuk at 01-18-2007 11:15 PM]

TripleM
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Theres always a DROD forum I'd bet you'd get better explanations from people here than in most places on the web. DROD is very mathematical, after all. Maybe.

b0rsuk
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No need, that stupid little flash animation made me understand.
It's shocking that flash can actually be used to make sumething useful. This is the first time I see it happen.

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coppro
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If only I could read... uh... Polish, right?

Fafnir
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It looks vaguely like the Runge-Kutta method?

And right now I'm going through a phase of blind rage at formulae without proofs. Examples I can almost live without, since in most cases I can learn by playing around with the formula, but proofs...

Right now I'm going through vectors and matrices on the A level syllabus (pre-university), and there are almost no proofs. The textbook generally shows a single example where the formula holds in a twisted mockery of the idea that maths students shouldn't accept results on trust, but that's it. And of all the formulae that are proved, most of them are identities that hold for for all nxn matrices but are only proved for 3x3 or 2x2 matrices, thus crippling them. Those basically include every single determinant and eigen[value|vector] identity and a few others besides - identities that form the underpinning of the whole of matrix theory. Oh yes, and when they do bother to prove a formula, they do it in the most unimaginative and unenglightening way possible.

As an example, this is a highly useful formula for the inverse of a 3x3 matrix, which can in fact be generalised to an nxn matrix:

            [ |ef| -|bc|  |bc|]
            [ |hi|  |hi|  |ef|]
[a b c]     [                 ]   |a b c|
[d e f] :-> [-|df|  |ac| -|ac|] / |d e f|
[g h i]     [ |gi|  |gi|  |df|]   |g h i|
            [                 ]
            [ |de| -|ab|  |ab|]
            [ |gh|  |gh|  |de|]

The book "proof" of this basically takes that monster matrix, expands it all out over several pages and multiplies it with the original matrix to get the identity matrix. It proves the result for 3x3 matrices, but it does it by plucking the identity from thin air - rendering the result horribly arbitrary and difficult to remember - and it doesn't show that it's a general law. ARGH!

So far, I'd guess I've spent about six or seven hours just finding/working out the proofs the exam board thinks I'm too stupid to learn and my teachers don't know. And there are a lot of statements still unproven...

In short, if I ever find the person who wrote the official textbook, I will maim him.

Care to join forces, b0rsuk?

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b0rsuk
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The k-what method ?

I were trying to understand divided differences of higher orders. How to calculate them, preferably in recursive way. I should've searched the english wikipedia first. Only I didn't know how they're called in english.

Now I only have to implement a numerical quadrature based on three Chebyshev nodes. Chebyshev nodes - Chebyshew roots of Chebyshew Polynomial. Fun.

Did I mention I'm not supposed to use the usual |-1, 1| interval ? There are several other snags as well.

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[Last edited by b0rsuk at 01-19-2007 07:34 PM]

stigant
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So this guy is in a hot air balloon and he's lost. He comes down over a field in the midle of nowhere and sees another guy on the ground. The guy in the balloon shouts down to the guy on the ground: "Can you tell me where I am?" The guy on the ground says "You're about 50 feet up in the air in the middle of nowhere." The guy in the balloon says, "Are you an engineer?" to which the the guy on the ground says "Why yes, I am, how did you know?" Balloon guy says "Well, I asked you a simple question, and your response, while technically correct is totally useless." Ground guy says "Are you a manager?" to which balloon guy says "why yes, how did you know?" "Because you don't know where you are, you don't know where you're going, I've answered your questions truthfully, and now somehow its my fault."

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Syntax
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Oooh that reminds me of a similar joke I read earlier in the week:

A shepherd was herding his flock in a remote pasture when suddenly a brand-new BMW advanced out of the dust cloud towards him. The driver, a young man in a Broni suit, Gucci shoes, Ray Ban sunglasses and YSL tie, leaned out the window and asked the shepherd... "If I tell you exactly how many sheep you have in your flock, will you give me one?" The shepherd looked at the man, obviously a yuppie, then looked at his peacefully grazing flock and calmly answered "sure".

The yuppie parked his car, whipped out his IBM ThinkPad and connected it to a cell phone, then he surfed to a NASA page on the internet where he called up a GPS satellite navigation system, scanned the area, and then opened up a database and an Excel spreadsheet with complex formulas. He sent an email on his Blackberry and, after a few minutes, received a response. Finally, he prints out a 130-page report on his miniaturized printer then turns to the shepherd and says, "You have exactly 1586 sheep. "That is correct; take one of the sheep." said the shepherd. He watches the young man select one of the animals and bundle it into his car.

Then the shepherd says: "If I can tell you exactly what your business is, will you give me back my animal?", "OK, why not." answered the young man. "Clearly, you are a consultant." said the shepherd. "That's correct." says the yuppie, "but how did you guess that?" "No guessing required." answers the shepherd. "You turned up here although nobody called you. You want to get paid for an answer I already knew, to a question I never asked, and you don't know crap about my business...... Now give me back my dog."

BeefontheBone
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In all fairness, wikipedia isn't the place to look for proofs in many cases; it's an encyclopedia, not a textbook.

The main reason most of the general proofs are left out of things like the A-level syllabus is that they're much more time-consuming than memorising a few rules of thumb as well as being more difficult for the bulk of students, and there's not enough time in (especially a single A-level) course to fit as much of the syllabus in as everyone'd like to. There's more of it in the Further Maths syllabus; a teacher worth their sort should be able to lend you some more advanced textbooks, or they'll be in your library, and a healthy interest in it will be a huge boon if you want to do any maths at university - the people who struggled when I was there were the ones who were used to getting by memorising things without understanding the underlying reasoning. You're absolutely right, it's far more satisfying that way, and much easier to build on, but it's of only limited use in completing an A-level course which is necessarily tailored to cover a lot of ground quite thinly in a short amount of time.

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coppro
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Meh. I found something today that basically decided that the following equation was true:
if x + y = a + b then x=a and y = b. They do this without any mention of the fact that since y and b are imaginary. Kind of irritating since they assume that it's automatically true, and don't even explain it. I had to go over the proof they used it in several times before I realized that it was correct.

Mattcrampy
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BeefontheBone wrote:
it's an encyclopedia, not a textbook.

I would have said that it's an argument, not an encyclopedia. You can't rely on Wikipedia for something where there is no consensus, and that is unlikely to change.

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eytanz
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Mattcrampy wrote:

BeefontheBone wrote:
it's an encyclopedia, not a textbook.

I would have said that it's an argument, not an encyclopedia. You can't rely on Wikipedia for something where there is no consensus, and that is unlikely to change.

True, but I don't think that's an issue here, I doubt that there's less of consensus about this particular entry (though I can't be sure since I don't read Polish).


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Pilchard VIII
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No I like this kind of math.



It's probably really old by now, but...

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Chaco
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I've heard that one before, and you're wrong - that's x there on that paper, not x

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BeefontheBone
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It's a giraffe riding a unicycle. That, or 5cm. It's hard to say.

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b0rsuk
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And finally, my favourite:


more here: http://haha.nu/funny/funny-math/

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[Last edited by b0rsuk at 01-21-2007 03:03 PM]

trick
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[from xkcd #184]

Syntax
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coppro wrote:
Meh. I found something today that basically decided that the following equation was true:
if x + y = a + b then x=a and y = b. They do this without any mention of the fact that since y and b are imaginary. Kind of irritating since they assume that it's automatically true, and don't even explain it. I had to go over the proof they used it in several times before I realized that it was correct.

Sorry about the late post but... well... The above assumption can't be true.

5 + 3 = 2 + 6

Maybe I missed something.

Syntax
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trick wrote:

[from xkcd #184]

That's actually my Fedora backdrop at work

zex20913
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You did indeed miss something.

5+3i/=2+6i.

(y and b are supposed to be imaginary.)

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Syntax
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zex20913 wrote:
You did indeed miss something.

5+3i/=2+6i.

(y and b are supposed to be imaginary.)

In that case, I'm still missing something.

What's an "imaginary" number? I'm guessing you mean complex. Also, does /= mean "not equal to"? Otherwise you're just agreeing with me.

zex20913
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Yeah, "imaginary" is the term often used in American high school to describe i, and I haven't gotten it out of my system (mainly because I never took a complex analysis course in college.)

And I didn't have a "not equal" key, so I used /= to represent an equal sign with a slash through it...I should have been more clear.

But my point was that the intention of the author was to say that x+y=a+b only if x=a and y=b for complex numbers[, as was discovered belatedly by...whoever posted this thing first, because I forgot.]

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[Last edited by zex20913 at 01-26-2007 02:59 PM : Edit in []s.]

Mattcrampy
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I understood that 'imaginary' numbers were numbers of the form 0+yi, expressed in complex form. That is, they're complex numbers without any real component. Is that not accurate?

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Syntax
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zex20913 wrote:
Yeah, "imaginary" is the term often used in American high school to describe i, and I haven't gotten it out of my system (mainly because I never took a complex analysis course in college.)

And I didn't have a "not equal" key, so I used /= to represent an equal sign with a slash through it...I should have been more clear.

But my point was that the intention of the author was to say that x+y=a+b only if x=a and y=b for complex numbers[, as was discovered belatedly by...whoever posted this thing first, because I forgot.]

Thanks for clearing that up I didn't realise they were called imaginary across the pond (bearing in mind they're actually quite real seen as so many proofs rely on them ).

Back on the proof however... It seems like it's equivalent to x = y iff x = y.

Weird.

zex20913
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Mattcrampy wrote:
I understood that 'imaginary' numbers were numbers of the form 0+yi, expressed in complex form. That is, they're complex numbers without any real component. Is that not accurate?

I'm pretty sure that, technically, sqrt(-1)=i is the only imaginary number, and complex numbers are linear combinations of real and imaginary numbers. The imaginary part of a complex number is the coefficient of i, certainly. However, I also think that "imaginary" has been used in HS to describe any imaginary part...basically, it's overused, and uncertain because of it.

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coppro
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Officially, sqrt(-1) is equal to i. Complex numbers are composed of real and imaginary components. Some complex numbers are said to behave like real or imaginary numbers, that is, they can be used in equations as if they were. So, while 0+yi is technically not imaginary, it can be used as if it was. At any rate, that's what my textbook says.

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[Last edited by coppro at 01-26-2007 10:54 PM]