At 11/29/09 12:22 PM, trig1 wrote: At what point in education do you learn about real maths? I've just spent ages looking into the Riemann Zeta function and I'm frustrated that I've never been taught anything like it before. What goes on in university maths? For now I'm stuck with logs and vectors and other boringly simple things.

I'm guessing you are also doing Further Maths A level, it starts to get interesting once you get onto Further M1, with imaginary numbers, but it doesn't get hardcore until uni. As gust said, if it is a field you are interested in then the best way to learn is independantly, you can't expect others to speed up for you or you'll get nowhere.

At 11/29/09 12:22 PM, trig1 wrote: What goes on in university maths? For now I'm stuck with logs and vectors and other boringly simple things.

Depends on your major and your required maths. Even in some of the more math intensive majors, you may only go up to trig, calculus, linear algebra and some discrete math.

Like Gust said, it's generally best if you hunt down and learn the math you want on your own terms/time.

At 11/29/09 12:22 PM, trig1 wrote: And if anyone can explain why 1+1+1+1+... = -1/2 and not infinity I would appreciate it.

I have no idea where you could learn more about subjects like this.

Here's the thing: your series does not converge, it's divergeant. The approach you're taking results in saying that the partial sums in all divergeant series tend towards +inf or -inf, but that's not incredibly useful, is it? Instead, what you read about is the Cesàro summation. Note that not all divergeant series tend towards infinity. Take for example 1 - 1 + 1 - 1 ... It's obviously bound to [0, 1], yet it doesn't converge towards anything.

as n tends towards +inf, so does 1+1+1... n times. But so does 1+2+3 n times, k^1 + k^2 + k^3 n times, etc, yet they are all different series and therefore, evaluating the convergence of a divergeant series is pointless as it doesn't say anything about the series itself.

Anyway have a look at it for yourself. Here's a useful link. You can use wikipedia if you're curious about something, but I'd recommend reading official documents like university papers etc. Also, you'll see that much of the information on wikipedia is basically copy-pasted from this paper.

Gust, using seemingly complicated words doesn't make your answers right. Your post didn't make much sense. Divergeant series don't have a definite value as n->inf by definition (which is pretty much the answer to trig's question) it DOES tend towards infinity but that's not what Cesaro sums are about.

On the subject of maths, what are the chances of getting into Cambridge to do pure maths?

At 11/29/09 02:30 PM, Depredation wrote: I'm guessing you are also doing Further Maths A level, it starts to get interesting once you get onto Further M1, with imaginary numbers

That said, you hardly touch them. In Further Maths, imaginary numbers are pretty standard to deal with once you've gotten the basics down.

At 11/29/09 03:31 PM, Deadclever23 wrote: On the subject of maths, what are the chances of getting into Cambridge to do pure maths?

Chance has nothing to do with it =P
But I see what you're saying. I think one or two of my friends are applying for that at Cambridge this year, and they're amazing mathematicians.
When are you heading to Uni (I presume that's the intention of your asking)?

At 11/29/09 03:31 PM, Deadclever23 wrote: On the subject of maths, what are the chances of getting into Cambridge to do pure maths?

You better diversify, mang...

At 11/29/09 03:31 PM, Deadclever23 wrote: On the subject of maths, what are the chances of getting into Cambridge to do pure maths?

I love math and my school luckily has a ton of advanced math in it.

But seriously be practical. Pure math will only allow you to do 1 thing in the future and that is teach math (since after a certain point math has very limited practical purpose, other than as a gateway to discovering possibly practical new branches of math).

At 11/29/09 04:05 PM, Glaiel-Gamer wrote:

At 11/29/09 03:31 PM, Deadclever23 wrote: On the subject of maths, what are the chances of getting into Cambridge to do pure maths?

I love math and my school luckily has a ton of advanced math in it.

But seriously be practical. Pure math will only allow you to do 1 thing in the future and that is teach math (since after a certain point math has very limited practical purpose, other than as a gateway to discovering possibly practical new branches of math).

Yea there's a surprising amount of mathematicians needed for engineering departments to manually derive equations and do research for the labs. If you really learn that much math, and apply that to VERY basic physics equations, you could probably do a ton with it. Sciences in general are mainly for research purposes and publishing papers as well as teaching.

Can somebody please explain the ads in some people's signatures?

At 11/29/09 08:46 PM, zrb wrote:

At 11/29/09 08:33 PM, Josh-B wrote: Can somebody please explain the ads in some people's signatures?

Tom israndomly replacing ads by sigs everyday for the next few weeks.

I got word of it early, and that's why I have no signature.
See, I'm smarter than you all think.

"But seriously be practical. Pure math will only allow you to do 1 thing in the future and that is teach math "

Smartest thing I've seen posted on NG in a long ass time. If theoretical mathematics is your bag of crisps, you can easily master things that do not yet have any practical application whatsoever. The sad truth, but don't let it depress you. On the journey there, you may find that you are in possession of a universe of interesting solutions, to problems vexing others. I'll give you a crude example:

Not so long ago, no one knew what backface culling was.

:]

Well in that case imma just test this out to see if i have an ad or my sig O.o

Imagine my responses depending on if its a sig/ad

IF ITS A SIG:

Huh, well right on ^_^

IF ITS AN AD

Well, hopefully it'll gain me some ad money, i'll go post elsewhere now.

YOU WANT SOME KNOWLEDGE. The universe is flat VIDEO, what I got from this is that the universe is neither accelerating nor decelerating and so it could have come from nothing. BUT IM NOT SURE SO JUST FUCKING WATCH IT FUCK.

it's also not by richard dawkins he just intros...

it's seriously good watch it...

I was thinking that if I wanted to keep my options open i could always go into programming after maths, or if that never works out I could do engineering and so forth.

Also I'm just coming up to do sixth form which is obviously a way away from uni but for somewhere like Cambridge the right kind of A levels will matter greatly.

Also, surely there is more practical uses for pure maths that you lot make it out to be.

Ads in people signatures? That sounds strange, can someone post a screenshot of what it looks like?

I've almost recovered from Thanksgiving. What a busy holiday.

Awww...

At 11/29/09 09:23 PM, doctormario wrote: "But seriously be practical. Pure math will only allow you to do 1 thing in the future and that is teach math "

Smartest thing I've seen posted on NG in a long ass time. If theoretical mathematics is your bag of crisps, you can easily master things that do not yet have any practical application whatsoever. The sad truth, but don't let it depress you. On the journey there, you may find that you are in possession of a universe of interesting solutions, to problems vexing others. I'll give you a crude example:

Not so long ago, no one knew what backface culling was.

]

Sorta what I meant was math is only useful in conjunction with other subjects.

Physics, biology, accounting, economics, politics, computer science, engineering, etc.
It mixes well with almost everything, but PURE MATH is relatively pointless.

Thanksgiving came and past and I didn't even realise.

Bring on christmas.

At 11/30/09 01:29 AM, Coaly wrote: YOU WANT SOME KNOWLEDGE. The universe is flat VIDEO, what I got from this is that the universe is neither accelerating nor decelerating and so it could have come from nothing. BUT IM NOT SURE SO JUST FUCKING WATCH IT FUCK.

it's also not by richard dawkins he just intros...

it's seriously good watch it...

That's one of the most interesting videos that I've seen in a while. What he said about observing the universe 100 billion years from now was very interesting.

At 11/30/09 08:14 PM, matrix5565 wrote: That's one of the most interesting videos that I've seen in a while. What he said about observing the universe 100 billion years from now was very interesting.

What's interesting about it is that if that IS the case, then how would we know our current observations aren't ALSO based on a universe which is hiding information from us?

you guys aren't dead yet
(my annual post)

If it is possible to create artificial universes, who's to say we're not living in an artificial universe right now? He said we needed energy to begin with since it's flat.

Or we could even be in the matrix....

Or we could just be a part of a The Simpsons episode. Or Sims. You know guys, I really feel like setting myself on fire right now

ooOoOOooo im a ghost

At 11/30/09 11:01 PM, Glaiel-Gamer wrote: What's interesting about it is that if that IS the case, then how would we know our current observations aren't ALSO based on a universe which is hiding information from us?

At 12/1/09 01:25 AM, Starogre wrote: If it is possible to create artificial universes, who's to say we're not living in an artificial universe right now? He said we needed energy to begin with since it's flat.

Or we could even be in the matrix....

At 12/1/09 09:14 AM, Zyphonee wrote: Or we could just be a part of a The Simpsons episode. Or Sims.

Come now, guys. Let's not get involved in a nonstandard religious debate here.
Although, if we do continue down this path, let's not forget about the Truman theory.
One of us is the main character in a television-like show. The rest of us are all actors and actresses in this made-up world. Of course, I know that I'm the main character, since I haven't been given anything to act out. Yet you would know that you're the main character and that I'm one of those actors (probably one who wanted you to know the truth, but phrasing it in a manner so as to not get 'ejected' from the show), if it wasn't for the fact that you're all actors and fully aware that I'm the main character.
Phew, I'm tired.

is it cool to get Turd of the week?

At 12/1/09 05:16 PM, Deadclever23 wrote: is it cool to get Turd of the week?

Only if you already have a bunch of awards

At 12/1/09 01:46 PM, Doomsday-One wrote: Truman theory.
Phew, I'm tired.

you should have watched the video

At 12/1/09 01:25 AM, Starogre wrote: If it is possible to create artificial universes, who's to say we're not living in an artificial universe right now? He said we needed energy to begin with since it's flat.

Or we could even be in the matrix....

Personally, I'm not entirely convinced on the existence of Germany.