The Geniuses' Thread

Pygmalion

Lawliet wrote: »

...Although on second thoughts I'd probably be awful no matter how well it was taught.

Realistically though, it's not really possible to say whether you would be, which I gather is the point.
Being awful at memorising facts and formulae doesn't really say **** about whether you would actually understand the maths behind them if it was taught.

I used to never be able to remember the distance formula (among others, I had an awful tendency of doing things backwards) for a few years, just glancing over it before every exam to make sure I remembered it, until one day I started doodling on a question when I finished early and was like "Holy ****, if I draw a horizontal line here and a vertical one here it's just using Pythagoras' theorem".
Not my proudest moment, considering I was pretty consistently top of the class :P.

Maybe it was my fault for not really thinking about it properly, or maybe it's expected to be obvious, but why skip a 2 minute explanation of a formula that's needed all throughout school, and why present it as though it's a completely different formula?

Davidius

I haven't read very far yet but something about it as irked me a little so far. The author seems to have a worrying adherence to some traditionalist idea that mathematics is pure art through and through. Maybe I've been misreading or simply misinterpreting his view but he seems to be downplaying applicability/generality as one of the finer points of mathematics as a study.

Pygmalion

Davidius wrote: »

Maybe I've been misreading or simply misinterpreting his view but he seems to be downplaying applicability/generality as one of the finer points of mathematics as a study.

He definitely downplays applicability, but I'm not entirely sure I'd fault him on that.
If you want to do something that involves a specific formula/rule on a regular basis you'll do so without much hassle, and remembering it/understanding it will probably come naturally.
I doubt much people actually get themselves into situations that require these things regularly unless they actually are interested in it, or need to know it.
If it's something you might have to do once or twice a year then why waste time memorising off the formulae, when you can just google for them when needed?

If you try and teach kids a ****load of formulae/rules because they might actually be used by some small percentage of them it's a lot of wasted time for little gain.
Realistically people don't use much beyond basic arithmetic in their day-to-day lives, I certainly don't and I'm much more interested in mathematics than most people.

As for generality though, I gathered that's part of the "beauty" he's talking about though, and when he talks about learning the history and philosophy of mathematics I find it hard to imagine this wouldn't come into it a lot.
I'd argue that one can't gain an appreciation for the beauty of maths without paying a lot of attention to the generality.
Maybe I'm just projecting my own opinion onto it though.

My main problem with his arguments is just that it's really just impractical, as long as we have a system in which we're assigned a number between 0 and 100 and use this to get into college/university people who actually go and try work things out by themselves will fail hard compared to people who memorise off facts and figures.

Davidius

Pygmalion wrote: »

He definitely downplays applicability, but I'm not entirely sure I'd fault him on that.
If you want to do something that involves a specific formula/rule on a regular basis you'll do so without much hassle, and remembering it/understanding it will probably come naturally.
I doubt much people actually get themselves into situations that require these things regularly unless they actually are interested in it, or need to know it.
If it's something you might have to do once or twice a year then why waste time memorising off the formulae, when you can just google for them when needed?

If you try and teach kids a ****load of formulae/rules because they might actually be used by some small percentage of them it's a lot of wasted time for little gain.
Realistically people don't use much beyond basic arithmetic in their day-to-day lives, I certainly don't and I'm much more interested in mathematics than most people.

When I mentioned applicability I was more talking about how he doesn't seem to put any weight on mathematical results that come with a notable application. It might just be me but a lot of results in mathematics seem to lose their lustre if they're mostly inconsequential. I'm not just talking about results that have any physical meaning but also those which give other mathematical insight that is not necessarily a generalisation.

Also worthy of note is that mathematical structures or abstractions based on more intuitive/"real" notions tend to be more interesting, at least in my opinion. Not that I have any issue with the idea that mathematics can be about the art of problem solving because it is. I just get the impression he sees other philosophies toward mathematics as bastardisations of some pure art form rather than the creative freedom being only one of the elements that makes it easy to appreciate. He might have addressed that in the article and I'll be honest that I only read about half of it if that.

I think teaching kids about the merits of problem solving as an art form is a nice idea but I don't really see it ever being an effective teaching practice. Of course giving them formulae to learn off and teaching them specific algorithms doesn't get much done either. I do think algorithmic procedures have their place though they really shouldn't be a major component of a post-primary maths course.

I should actually go read the full article instead of rambling on about **** I don't know anything about. If he really does suggest that mathematics should be seen as a creative subject in schools then I disagree more or less. All I can see it bringing is an unnecessary surplus of pure mathematicians. Aside from that I'm doubtful that kids would have enough of an inclination toward abstract thought for it to ever really mean anything.

My views on the matter are:

• Less material on the course
• Much less emphasis on formulae
• Much more emphasis on showing things for themselves, including teaching them how to do so

The first is to facilitate the last.

Grindylow

I was going over Maths for my pre tomorrow in complex numbers, and there's just one bit I don't get! If anyone could help it'd be unreal!

Right so the question is:

Let u = 3 + 2i
(i) Find the value of u^2 + ū^2, where ū is the complex conjugate of u.

cocoa

Noel2k9 wrote: »

I was going over Maths for my pre tomorrow in complex numbers, and there's just one bit I don't get! If anyone could help it'd be unreal!

Right so the question is:

Let u = 3 + 2i
(i) Find the value of u^2 + ū^2, where ū is the complex conjugate of u.

Do you understand what a complex conjugate is?

(3+2i)^2 + (3-2i)^2 = 9 + 12i + 4i^2 + 9 - 12i + 4i^2

= 18 + (12i - 12i) - 4 - 4

= 10

Grindylow

cocoa wrote: »

Do you understand what a complex conjugate is?

(3+2i)^2 + (3-2i)^2 = 9 + 12i + 4i^2 + 9 - 12i + 4i^2

= 18 + (12i - 12i) - 4 - 4

= 10

Yeah I figured it out a while ago, just changing the i sign! Thanks

Jay P

I'm current;y undertaking a small project which requires making pentagons. Does anyone know if it's possible to construct a regular pentagon using just a pencil and ruler? Or even with a compass. I've done a lot of messing about but can only manage to draw them using a protractor, which is painfully time-consuming...

Edit:
I did find this video, but it looks just as time-consuming, if not more so, as using a protractor...

https://www.youtube.com/watch?v=nXqDg7FD9nM

jumpguy

Just wondering this from LC physics in radiation...

If alpha particles are the most ionizing, but they can't penetrate anything, and gamma rays have very little ionizing ability, but penetrate everything, then how is radiation harmful? If gamma rays get through you but can't ionise anything, then what harm are they doing?

sock puppet

jumpguy wrote: »

Just wondering this from LC physics in radiation...

If alpha particles are the most ionizing, but they can't penetrate anything, and gamma rays have very little ionizing ability, but penetrate everything, then how is radiation harmful? If gamma rays get through you but can't ionise anything, then what harm are they doing?

In fairness I wouldn't consider gaining superpowers to be harmful.

Davidius

jumpguy wrote: »

Just wondering this from LC physics in radiation...

If alpha particles are the most ionizing, but they can't penetrate anything, and gamma rays have very little ionizing ability, but penetrate everything, then how is radiation harmful? If gamma rays get through you but can't ionise anything, then what harm are they doing?

I can barely remember LC physics and don't know much about particle physics in general but if gamma rays have little relatively little ionising ability it still stands that it has the ability. A high dose coupled with its penetrative properties will probably lead to ionisation/cell damage on a larger number of cells than what you'd get with just surface contact.

Richard Cranium

Question for the techies here.

Is there any way I can get my really old walkman that only works on Sonicstage to start working on Windows Media Player (or itunes or anything else for that matter)? I'd rather not buy a new mp3 player, as there's nothing wrong with the one I have right now, but it's a terrible pain trying to get music onto it, especially since I only have Sonicstage on an ancient dinosaur of a PC that takes half an hour to boot up.

Insect Overlord

Insect Overlord

Davidius

Insect Overlord wrote: »

sqrt(-16)!

Gamma(4i+1)? That's the worst insult I've ever heard.

Insect Overlord

http://imgur.com/EvZ3p.png

suitcasepink

My laptop bluescreens every time I plug in my ipod.

What does a non nerd do?

jumpguy

deise_girl wrote: »

My laptop bluescreens every time I plug in my ipod.

What does a non nerd do?

A non-nerd? Get frustrated and say "I'm never buying a fúcking laptop from [whatever manufacturer] again!"

suitcasepink

jumpguy wrote: »

A non-nerd? Get frustrated and say "I'm never buying a fúcking laptop from [whatever manufacturer] again!"

But you see I cant do that, Id rather blame my ipod than laptop, coz I love my laptop as a mother would love her kid.


And... its pink.

jumpguy

deise_girl wrote: »

But you see I cant do that, Id rather blame my ipod than laptop, coz I love my laptop as a mother would love her kid.


And... its pink.

Then you're clearly a nerd! :P

suitcasepink

jumpguy wrote: »

Then you're clearly a nerd! :P

Imma nerd but not a technically minded, smart, maths loving logical nerd! :L

amacachi

Delete iTunes and your Library (make sure the Music itself is backed up somewhere else) and reset your iPod seperately. Think you have to hold down play and the centre button for a good while. After that turn on the iPod, download iTunes and plus in the iPod. If it blue screens again you've a registry problem.

suitcasepink

amacachi wrote: »

Delete iTunes and your Library (make sure the Music itself is backed up somewhere else) and reset your iPod seperately. Think you have to hold down play and the centre button for a good while. After that turn on the iPod, download iTunes and plus in the iPod. If it blue screens again you've a registry problem.

I think thats an easter holiday job if it involves backing up everything...

But cheers dude!

sock puppet

amacachi wrote: »

Delete iTunes and your Library (make sure the Music itself is backed up somewhere else) and reset your iPod seperately. Think you have to hold down play and the centre button for a good while. After that turn on the iPod, download iTunes and plus in the iPod. If it blue screens again you've a registry problem. and then throw your ipod out the window

Sorted:)

amacachi

deise_girl wrote: »

I think thats an easter holiday job if it involves backing up everything...

But cheers dude!

Is your music not all in one folder? Should take an hour at most to put it all onto an external harddrive. Even just moving it to another folder on your computer would be fine, keep it away from iTunes during the cleansing.

Richard Cranium

Q: What's the value of a contour integral around Western Europe?

A: Zero, because all the Poles are in Eastern Europe.

:pac:

As for my non-joking contribution to the nerd thread, my life would be so much more fulfilling if I knew how to use pointers (dynamically allocated arrays in C++, to be more precise) properly. I'd love to find a halfway decent online tutorial, but so far I've found nothing that's been of much use.

Any suggestions?

**Timbuk2**

Richard Cranium wrote: »

As for my non-joking contribution to the nerd thread, my life would be so much more fulfilling if I knew how to use pointers (dynamically allocated arrays in C++, to be more precise) properly. I'd love to find a halfway decent online tutorial, but so far I've found nothing that's been of much use.

Any suggestions?

Chapter 4 of these notes aren't bad. Try getting a book from the library as well, usually pointers are well explained. They confuse me as well. I try and avoid using them as much as possible by using arrays (Without pointers), but once I read through some C++ books they're not as bad as I thought!

Richard Cranium

Yeah I tried a couple of library books but there wasn't much in them that I found helpful at the time. I suppose I could always try again.

Unfortunately there's no way to avoid them for me, as the summer exam will look for explicit (and efficient) use of pointers all over the place.

/moan.

**Timbuk2**

Clearly I'm an idiot, I forgot to put the link in my last post. I forget what link I was trying to put there, so ignore the Chapter 4 reference.

I found a better one (treats the reader like an idiot, which I prefer as that way I can understand these things :P )
http://alumni.cs.ucr.edu/~pdiloren/C++_Pointers/index.htm