I actually also think P != NP, but I've no good reason to think that, and I wouldn't say I "believe" in it.
I do not see how knowing that the cardinality of the integers is smaller than the cardinality of the continuum is a discontinuity in mathematics at all.
The continuum hypothesis is a bit different though, and it is equally valid for it to be true or false. Maybe it is equally valid for P = NP to be true or false, mathematically, but that would leave us in a difficult position for the applied side of it, since we'd have to start thinking about which applied to "our world". I've just decided that I 'believe' that cannot be the case, on the grounds it is far too messy!
An interesting and related problem is the Church-Turing thesis since it is too vague (as the Wikipedia article says) for it to be proved true using mathematics, but it could be proved false using a good enough counter example. I'm sure most computer scientists here strongly believe it to be true, though.
Seriously though, some Calculus results aren't that difficult (although others are, but we can ignore them, ey?). For example, the rule that says "If you have two functions of x added together, then you can differentiate them separately and add them together" (That is if f(x) = g(x) + h(x) then f`(x) = g`(x) + h`(x) ):
Let u and v be functions of x, and y be their sum: y = u + v
If you increase x by an amount, call it Dx (normally written "Delta-X", but I don't want to cause display problems, so I'm just using a capital D), then u and v and y will also increase by some amount (since they are all functions of x): u = u + Du v = v + Dv y = y + Dy
So:
y + Dy = u + Du + v + Dv
and subtracting the original y=u+v from this, leaves:
Dy = Du + Dv
Dividing by Dx, leaves you:
Dy / Dx = Du / Dx + Dv / Dx
This is pretty much it (You can take it through to the end, too, using limits, but it all gets a bit difficult to type here on Slashdot. And it's not like anyone is going to read this post, anyway)
I apologise if you actually do have a background in mathematics and this is patronising you. I apologise if you actually do not have a background in mathematics, since in that case you probably don't care!
As for Fermat's Last Theorem, read this book. I can't tell you how good it is though, since it is outside of my price range, and my local library doesn't have it (and refuses to believe it exists, on the grounds that I must mean that stupid Simon Singh book.)
"No, he proved that they can't be both consistent and complete"
No, that was his first theorem. I am speaking of his second. I even gave you a link to find that out for yourself:-\ His second theorem says you cannot use axioms to prove that the axioms do not cause contradictions (obviously you can use them to prove they do, though!)
Whether it is a stunt or not, I'm never going to buy a Samsung again.
After owning first a Nokia, and then a Sony Erikson, I now own a Samsung phone, and although the phone looks nice, it is horrible to use compared to my old phone. The care wasn't taken to make it useable.
Things like text messages being start in Upper Case (without settings to change it) and if you were to press the Big-Red-Button by accident whilst typing a text message, the message will be lost without any confirmation, nor does it save it to "Drafts", for example. The better hardware was made less useful due to bad userinterface. The Sony, on the other hand, was made far more useable and a better phone, even lacking the extra features of the Samsung Hardware (big colour screen, video recording, lots of memory, etc).
Although the phones this article is about are very different to the phone I have, I still don't think I could trust buying another Samsung phone, after getting this one and being constantly irritated by it.
Saying that, how deep does Windows Mobile go? As much as people reading this message will hate Microsoft, they'll probably admit they constantly do a good job of user interfaces, so maybe these ones won't be too bad? Although a phone which can play music... Hmm. Not sure I want one of those.
Nobody actually says 'snog'. Well, I certinally wouldn't and nobody around me would! (I am a teenage Brit).
"Nappy" is pretty much always used, but I like 'diaper' is starting to replace it, with all this Americanization. I don't like either words very much, to be honest.
And I think more people drink Coffee than Tea, really. I, for one, hate Tea.
Yes, I agree. This has the side effect we don't get to learn it, though.
In the UK, the A-Level Maths coursework by MEI does actually have a module, called Further Pure 3, which does have some more "modern" things in. However, it is too hard and my school, for one, doesn't really want to make people do it (since it will bring down our overall grades). You can see it, in DOC format, here.
For a student to take this module, they must use two of their 3 or 4 A-Level choices on Mathematics.
Another popular board, AQA, have nothing like this in A-Level Further Maths, though.
Anyway, thought that might be of some interest to you!
(I haven't spellchecked, since I think you'll be the only one to read this!)
Just want to say Good Luck:) That was an inspiring post.
Personally, I quite like abstract maths myself. I'm perfectly happy (happier, in-fact) with Maths which doesn't do anything useful - but of all the people I know, only one other person doesn't mind maths without a purpose.
Complex Numbers were developed at the time of the renaissance.
Differntial and Integral Calculus was 1600's, so post-renaissance, but some existed before that at any rate.
Logarithms were invented near the end of the renaissance, but the work was not published until the 1600's, also.
The Binomial Theorem is very, very old!
The Cartesian coordinate system is from the 1600's.
So although there are bits from Post-Renaissance (taking that as anything from the 17th centry onwards), there isn't really anything from after the 1600's, is there?
Or, to put more bluntly, if I hear one more person tell my kids that math is hard and no one really understands it, I will likely go on a mad rage.
I'm interested - have people said this to them, then? Who? Why?
Re:Examples of Math books for lay people
on
Prime Obsession
·
· Score: 1
I recently took Infinity and the Mind from the school library, and I'd like to warn you to take what it says with a pinch of salt. It is wrong and over-simplified (Whilst claiming it is the truth) in many places!
Heh, I was just reading the KDE news bar on the left, and this came up: KDE 3.4 Will Talk to You
The KDE Accessibility team is in the process of integrating speech synthesis into KDE. Not only does this mean better support for visually-impaired and speech-impaired users, but the new features should also prove for a fun desktop experience overall.
Okay, I notice the offical docs doesn't mention it, however the Wiki does here.
For those not bothered to click the link, an interesting cut from it:
How extensive is Rockbox's support for blind users?
The Archos Jukebox is an embedded device and as such there are space limitations to what can be done to support blind accessibility within Rockbox. All of the configuration options have voice prompts, and Rockbox can speak directory and file names, but in general informational messages displayed on the screen and detailed debugging information are not available to blind users. For the Recorder, specifically, the quick settings menus are not spoken - although they can still be used by memorising what each key does while in these modes. Sorry.
Rockbox is however fully usable and configurable by the blind, and many sighted users are using the voice user interface by preference so they can operate their Jukebox without looking at the screen - while driving, for instance (isn't that reassuring?).
Regarding the MP3 player, make sure he checks out Rockbox.
Rockbox is an open source (GPL) firmware project for the Archos Recorder MP3 player (among others). They've done great work, which included Talkbox - extra code which can allow the MP3 player to 'talk' to the users.
Now the problem is that the actual hardware itself is terrible - that is not the Rockbox teams fault, of course, though.
I've seen on the mailing list some blind users who've written in just to comment about how helpful and useful the Talkbox features of Rockbox are. So it seriously does help people. It is an amazing project, and I really wish I had worked on it myself.
Anyway, check out the manual or something to check that it is suitable.
I see what you are saying, but surely this is only a problem in cases when the calculator is working out the Standard Deviation, or the Integral of your expression, or something?
Surely a simple calculator which can work out square roots, powers, and simple operations is still helpful and not harmful?
Slashdot Mirror
I actually also think P != NP, but I've no good reason to think that, and I wouldn't say I "believe" in it.
I do not see how knowing that the cardinality of the integers is smaller than the cardinality of the continuum is a discontinuity in mathematics at all.
The continuum hypothesis is a bit different though, and it is equally valid for it to be true or false. Maybe it is equally valid for P = NP to be true or false, mathematically, but that would leave us in a difficult position for the applied side of it, since we'd have to start thinking about which applied to "our world". I've just decided that I 'believe' that cannot be the case, on the grounds it is far too messy!
An interesting and related problem is the Church-Turing thesis since it is too vague (as the Wikipedia article says) for it to be proved true using mathematics, but it could be proved false using a good enough counter example. I'm sure most computer scientists here strongly believe it to be true, though.
All the proofs you ever need are here.
Seriously though, some Calculus results aren't that difficult (although others are, but we can ignore them, ey?). For example, the rule that says "If you have two functions of x added together, then you can differentiate them separately and add them together"
(That is if f(x) = g(x) + h(x) then f`(x) = g`(x) + h`(x) ):
Let u and v be functions of x, and y be their sum:
y = u + v
If you increase x by an amount, call it Dx (normally written "Delta-X", but I don't want to cause display problems, so I'm just using a capital D), then u and v and y will also increase by some amount (since they are all functions of x):
u = u + Du
v = v + Dv
y = y + Dy
So:
y + Dy = u + Du + v + Dv
and subtracting the original y=u+v from this, leaves:
Dy = Du + Dv
Dividing by Dx, leaves you:
Dy / Dx = Du / Dx + Dv / Dx
This is pretty much it (You can take it through to the end, too, using limits, but it all gets a bit difficult to type here on Slashdot. And it's not like anyone is going to read this post, anyway)
I apologise if you actually do have a background in mathematics and this is patronising you. I apologise if you actually do not have a background in mathematics, since in that case you probably don't care!
As for Fermat's Last Theorem, read this book. I can't tell you how good it is though, since it is outside of my price range, and my local library doesn't have it (and refuses to believe it exists, on the grounds that I must mean that stupid Simon Singh book.)
"No, he proved that they can't be both consistent and complete"
:-\ His second theorem says you cannot use axioms to prove that the axioms do not cause contradictions (obviously you can use them to prove they do, though!)
No, that was his first theorem. I am speaking of his second. I even gave you a link to find that out for yourself
You can prove one exists since it is the size of the set { {} } which must exist.
I believe the axioms of Set Theory are consistant, however Godel proved it impossible to prove.
The most important problem in Mathematics is unproveable. This is worrying. You just gotta believe it is true.
Whether it is a stunt or not, I'm never going to buy a Samsung again.
After owning first a Nokia, and then a Sony Erikson, I now own a Samsung phone, and although the phone looks nice, it is horrible to use compared to my old phone. The care wasn't taken to make it useable.
Things like text messages being start in Upper Case (without settings to change it) and if you were to press the Big-Red-Button by accident whilst typing a text message, the message will be lost without any confirmation, nor does it save it to "Drafts", for example. The better hardware was made less useful due to bad userinterface. The Sony, on the other hand, was made far more useable and a better phone, even lacking the extra features of the Samsung Hardware (big colour screen, video recording, lots of memory, etc).
Although the phones this article is about are very different to the phone I have, I still don't think I could trust buying another Samsung phone, after getting this one and being constantly irritated by it.
Saying that, how deep does Windows Mobile go? As much as people reading this message will hate Microsoft, they'll probably admit they constantly do a good job of user interfaces, so maybe these ones won't be too bad? Although a phone which can play music... Hmm. Not sure I want one of those.
Nobody actually says 'snog'. Well, I certinally wouldn't and nobody around me would! (I am a teenage Brit).
"Nappy" is pretty much always used, but I like 'diaper' is starting to replace it, with all this Americanization. I don't like either words very much, to be honest.
And I think more people drink Coffee than Tea, really. I, for one, hate Tea.
Maybe insightful, probably not.
Actually, This says that the iRiver supports OGG out of the box.
So iRiver does.
iRiver seem to make great players in any case. When I get a new MP3 player, I'll get an iRiver. Especially if Rockbox is ported to it!
Seeing as you're lazy, I'll click those little hyperlinks for you. Maybe I'll get like modded up or something for my efforts:
The FIC Vassili is limited to MPEG4, MP3, WMA, WAV, ASF, AVI, and JPEG.
The iRiver PMP-120 does not currently support it, but they promise it will soon, I think.
The VeriTouch iVue doesn't mention which formats it supports.
Zupera Technology's one is limited to MP3, WMA, WAV, CD and AC-3.
So none of them support it.
As interesting as the SETI project is, I just wonder how they manage to find the funding to build massive Laser detection devices.
Really, what are the chances of this finding anything?
BBC Radio 4 did a radio program about the publish problems in Science, especially Physics, recently. I thought it was very good.
You can listen to it online from the BBC website. It requires Real Player, however.
Points taken and accepted :)
.
"is a bit advanced for high school students"
Yes, I agree. This has the side effect we don't get to learn it, though.
In the UK, the A-Level Maths coursework by MEI does actually have a module, called Further Pure 3, which does have some more "modern" things in. However, it is too hard and my school, for one, doesn't really want to make people do it (since it will bring down our overall grades). You can see it, in DOC format, here.
For a student to take this module, they must use two of their 3 or 4 A-Level choices on Mathematics
Another popular board, AQA, have nothing like this in A-Level Further Maths, though.
Anyway, thought that might be of some interest to you!
(I haven't spellchecked, since I think you'll be the only one to read this!)
...you're American? ;)
(Merry Christmas!)
Just want to say Good Luck :) That was an inspiring post.
Personally, I quite like abstract maths myself. I'm perfectly happy (happier, in-fact) with Maths which doesn't do anything useful - but of all the people I know, only one other person doesn't mind maths without a purpose.
Read this -- it is truely amazing.
Complex Numbers were developed at the time of the renaissance.
Differntial and Integral Calculus was 1600's, so post-renaissance, but some existed before that at any rate.
Logarithms were invented near the end of the renaissance, but the work was not published until the 1600's, also.
The Binomial Theorem is very, very old!
The Cartesian coordinate system is from the 1600's.
So although there are bits from Post-Renaissance (taking that as anything from the 17th centry onwards), there isn't really anything from after the 1600's, is there?
Or, to put more bluntly, if I hear one more person tell my kids that math is hard and no one really understands it, I will likely go on a mad rage.
I'm interested - have people said this to them, then? Who? Why?
I recently took Infinity and the Mind from the school library, and I'd like to warn you to take what it says with a pinch of salt. It is wrong and over-simplified (Whilst claiming it is the truth) in many places!
Semi-Seriously, a standard for 10 hour days does exist.
Unfortinuely the Wikipedia articles have been edited such that they point back and forth to each other. This version from the history is better.
Heh, I was just reading the KDE news bar on the left, and this came up: KDE 3.4 Will Talk to You
The KDE Accessibility team is in the process of integrating speech synthesis into KDE. Not only does this mean better support for visually-impaired and speech-impaired users, but the new features should also prove for a fun desktop experience overall.
Seems very relevent!
For those not bothered to click the link, an interesting cut from it:
The Archos Jukebox is an embedded device and as such there are space limitations to what can be done to support blind accessibility within Rockbox. All of the configuration options have voice prompts, and Rockbox can speak directory and file names, but in general informational messages displayed on the screen and detailed debugging information are not available to blind users. For the Recorder, specifically, the quick settings menus are not spoken - although they can still be used by memorising what each key does while in these modes. Sorry.
Rockbox is however fully usable and configurable by the blind, and many sighted users are using the voice user interface by preference so they can operate their Jukebox without looking at the screen - while driving, for instance (isn't that reassuring?).
Regarding the MP3 player, make sure he checks out Rockbox.
Rockbox is an open source (GPL) firmware project for the Archos Recorder MP3 player (among others). They've done great work, which included Talkbox - extra code which can allow the MP3 player to 'talk' to the users.
Now the problem is that the actual hardware itself is terrible - that is not the Rockbox teams fault, of course, though.
I've seen on the mailing list some blind users who've written in just to comment about how helpful and useful the Talkbox features of Rockbox are. So it seriously does help people. It is an amazing project, and I really wish I had worked on it myself.
Anyway, check out the manual or something to check that it is suitable.
I didn't think the article was too good. The following two are better:
Swiss Info
Reuters
Okay, that is strange. I clicked "Parent" when viewing this post, and a porn website came up :| I'd never seen it before, either.
Seriously weird! (Using Firefox)
Silly question from Non-American: What age is High School?
I see what you are saying, but surely this is only a problem in cases when the calculator is working out the Standard Deviation, or the Integral of your expression, or something?
Surely a simple calculator which can work out square roots, powers, and simple operations is still helpful and not harmful?