Pure Maths: I have decided to better myself!

[Zak33]

Hiya Forum dudes.

Althought my mathematics skills are somewhat....lacklustre, and because I found O level maths SO EASY and A level maths QUITE IMPOSSIBLE, I finally gave up and thought I'd found my place in the maths hierarchy of the world.

That was waaaay back in the late 80's and so I used my maths knowledge throught the 90's and 2000's in the work place, in a various hobbies, and that's that.

But a few weeks ago I picked up a book about Fermat's Last Theorem.It's a clever book because it simply didn't tell me WHAT Fermat's ;ast theorem was...it presumed, quite wrongly, that I was interested in maths and knew all about "it", whatever "it" was.

In my life, this leads to walking a knifes edge, for a very short time. I either
A: Give up, thinking "sod you, you self opinionated thwaite, if you cant be arsed to break the news early on, go jump"
or
B: This book's written in such a clever way that it's given me more already, in a few short pages, than I expected to gain.

In the case of Simon Singh's book, Fermat's Last Theorem, it was a resounding B.

Hooked, I read on, and frankly whilst the old boy, Fermat, is dead interesting, and so is his eternal tease on how to prove his "last theorem" I learned soooo much more as to want to expound some of it.

I shall, in the vein of my own brilliant ignorance, keep it simple.

This thread is about the sheer, shiny brilliance on numbers.

If it bores you, don't post. I dont want this turning into a flamer, or a mass attack on the rank stupidity of mathematics deliberately finding problems that aren't there. I've been there, and swum in the thick gloop of that arguement. I argued it myself.

This is simply about the beauty of numbers.

Let us begin with our perceptions of our own brains and our ability to "judge" stuff.

[finlay666]

If your going to learn about maths, avoid bad maths!

Question.... what is 0 to the power of 0?

Is it 0 (0 divided by anything is 0), 1 (any number to the power of 0 is 1), infinity (anything divided by zero) or somethiing else?

Zak edit: lets do this later, I would like to discuss WHO invented the number zero later

[Zak33]

I credit Mr Singh with a lot of this, though I'm sure he may not jhave been the first to use such analogies.

Human's have evolved because we can make "judgements", and we can weigh up "probability".

When I step into a road, at 6pm ona busy weekday evening, I'm in some danger. But a little country lane, in the middle of no where, in the dark at 2am... I coud prolly walk up the middle of the road for some time, eyes, shut, MP3 player blaring in my ears, and not get run down.

But my brain can mislead me:

Take a football pitch. It has 23 people upon it. 11 from each team, and one referee.

What is the probability that any two of the 23 people share a birth day? (not the YEAR, just the day and month)

With 23 people and 365 days to choose from, what do you think?

[pollaxe]

I can just about work out how much change I should have when I hand over a note or two at the supermarket.

Anything else is, frankly, beyond me. I never found maths beautiful just bewildering, nasty and full of concepts I could not get my head around.

[finlay666]

IIRC the probability is 0.5

I'll try and remember the working out but it involves either permutations or combinations...

[Whiternoise]

I think maths is a bit of a marmite subject, you can do it or you can't - and not in an insulting way. I don't mean basic arithmetic, like the sort of stuff you're expected to do on tax returns and adding up totals, but proper algebra. There are people who genuinely don't see what you're going on about if you try and explain Pythagoras' theorem or basic calculus to them and others who will see in an instant. I've found that, being reasonably maths minded, i don't have a problem with some of the whacky concepts that you come across in A level and now degree standard stuff. If you can do it, it's easy peasy once you get the tricks, if you can't then it's difficult as hell.

Maths is an incredibly interesting subject, but it's something of an educational taboo. Too many people are put off by this absurd stigma that learning = bad, and the stereotypical "mathmo". It's a real shame that stuff like this effectively gets swept under the consumer rug because people are more interested in pop science and doomsday prophecies.

And Zak, the birthday problem is a good example of a poorly worded question, it's misleading and therefore you make false assumptions. Think about it logically and it's actually not such a crazy answer.

You want to know, in a group of people, what is the probability that one person shares the same birthday with any other. It's not as small as you'd think, remember you're not just talking about one person, it can be any person with any other. That increases the odds a LOT. I'm going to paraphrase wiki here as it's got a good explanation:

Imagine you meet someone, you and the other person have a 1/365 chance of sharing the same birthday.

Now, lets say that you and the person are a pair. So, now we can say that the odds of a pair of people sharing the same birthday is equal to 1/365.

Next, we've got a room of people (23 to be exact). They can make quite a lot of pairs between themselves, i believe it's 253. So you've got 253 chances of finding two people with the same birthday.

That isn't the end of the story and it's not how you get the answer, but it's a nice way of seeing why it isn't such a weird answer.

To do it properly, as follows:

Work out the probability that no one shares a birthday - this is easier to calculate. If you take the first person, the probability that his birthday is different from the second person is (1-1/365), the probability that his is different from the third AND the second is (1-1/356)(1-2/365) and so forth. Note the laws of probability say that if you want to know the combined probability for multiple events, you multiply the probabilities together and simplify a bit - we end up with this: (365!/(365-23)!(365*23) - where ! is the factorial symbol. And if you work that out, take it away from 1 and the answer is about 50%.

[0iD]

Have a go at some of these http://forums.hexus.net/general-disc...ead-knobs.html

[Zak33]

Well, you guys are correct with your approx 50% likelyhood.
The thing is, I didn't see that coming. I was suprised. Hence my further interest.

And to Pollaxe: my intention is to try very very hard to show you some of the beauty that I've seen in the last few days.

Things which, frankly, make you stop and take note of the sheer brilliance of them.

[Funkstar]

Mathematics is a really interesting subject, it's just a shame I don't "get it" as easily as I would like.

Fermat's Last Theorem is a good book

[Zak33]

I think one of the fundamentals of this is to understand WHY maths is different to other subjects.

It is, I think, because in Maths, a PROOF should be undeniable, for all time. Litereally, no matter what occurs in the universe, the calculation should still work. And it should be a PROVEABLE theorem, which you dot NEED to do over and over on millions of examples, because you can PROVE it with a theorem.

This is where the brain rebels. But it mustn't. Mine did. I re read several pages until it sank in.

This the Mutilated Chessboard

#With those two corners removed, we have left 62 squares.

Take 31 domino pieces, and each domino piece will perfectly fill two squares on the chessboard.

Question: Is it POSSIBLE to arrange the 31 dominoes so that they cover all 62 squares?

The Scientific Approach:
vs
The Mathematical Aproach:

hit me with it WITHOUT looking on any other websites

[TheAnimus]

Zak33, you come accross The Tiger That Isn't?

its a much lighter read than Fermat's Last Theorem, as its statistics, but its intresting none the less.

[Zak33]

has anyone decided if it's possible yet? and why?

[Tumble]

I haven't...



BUT.. I bet you could do it if you chopped the dominos in two

[Zak33]

I haven't...



BUT.. I bet you could do it if you chopped the dominos in two

lol....the engineers joins.

No Tumble, this is maths, no cutting. it's not a trick question...it's real.

[0iD]

I'm guestimating 'no'
it's a 50/50 bet

[Zak33]

well dear OiD, that's not match OR science is it?