Brain-melting mathematics

[MeridiaNx]

I've picked up a copy of Fermat's Last Theorem (http://www.amazon.co.uk/Fermats-Last-Theorem-Simon-Singh/dp/1841157910/ref=pd_bbs_sr_1/026-2338302-4866858?ie=UTF8&s=gateway&qid=1202162603&sr=8-1), supposedly just for kicks, but it's hurting my head...a lot. I can't put it down even though it takes me 15 minutes to work through every concept. Some of it seems pointless twaddle, other bits really intriguing and I'm sure it boils down to personal preference or understanding as to where you draw the line.

Is anyone out there on the .org really into their stuff and knows what they're talking about? Any ideas of similar concepts that a layman could read for interest?

Just thought I'd throw that out there for consideration (or shunning!) to see if I'm the only one that finds it interesting/can't understand it.

Apart from something stupidly basic (which I know I learned at school) as to why multiplying 2 negatives gives a positive - anyone? - it's now throwing this concept of modular equations at me and I am finding their 4d-ness a little tough to comprehend! Had to put the book down when it said that mathematicians know that some infinities can be bigger than other infinities :smt099

[sarah]

Is that what this (http://forums.sv650.org/showthread.php?t=99080&highlight=infinity)thread is about?

[dizzyblonde]

try....C.F.D and F.E.A. computational, fluid, dynamics and finite element analysis.
I don't know what it is but Im Indoors studies it amongst other things. Last year i had many a book of this subject thrown at me during his third year at uni. Made my eyes go square followed by a long period of zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

[Richie]

Apart from something stupidly basic (which I know I learned at school) as to why multiplying 2 negatives gives a positive - anyone? -


does that mean if I multiply my overdraft with my creditcards I get a possitive outcome...:razz:

[dizzyblonde]

does that mean if I multiply my overdraft with my creditcards I get a possitive outcome...:razz:
:smt043:smt043:smt043:smt043

[Ace-T]

Superstring Theory is always good for a brain burn:smt045. I read FLT and was struggling a bit with the more advanced maths but was genuinely surprised about the stuff that had stuck from school. The Joy of Pi and Curious and Interesting Mathematics are also interesting as is of course the ubiquitous Brief History of Time.

Oh apparently Black Holes and Timewarps by Kip S Thorne is a bit difficult according to the hubby, so no hope for me then :help:;)

Trace :)

[the_lone_wolf]

Is anyone out there on the .org really into their stuff and knows what they're talking about? Any ideas of similar concepts that a layman could read for interest?
a slight tangent, as personally i find maths is essentially physics with no point;) - it's been years since i read it, but if you are at all interested in physics i can recommend "In Search Of Schroedinger's Cat" by John Gribbin - it's not exactly mind blowing but considering the book was published the same year i was born, it's not doing too bad for something almost a quarter of a century old.

or without wanting to appear too 'Oprah's book club' - dare i suggest reading "The God Delusion" ???

[MeridiaNx]

Made my eyes go square followed by a long period of zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Tried that last night, was reading the damn thing til 4.30am but when I put it down and rolled over my brain was in meltdown and I had disturbing dreams involving groups of numbers doing horrible things to me :(

was genuinely surprised about the stuff that had stuck from school.

I'm the other way around, had to ask my girlfriend, who's younger than me and has therefore had less time to forget, why the simplification of (x + y)² resulted in the following:

x² + y² + 2xy

Couldn't for the life of me figure out where the 2xy came from, even though I knew it to be true based on plugging numbers into the equation. Then she reminded me to put (x + y)(x + y) and multiply everything by everything. Doh! It was part of Pythagoras proof that his equation held true for all right-angles triangles without having to test them.

The Joy of Pi

I shall look this up, but the film Pi (http://www.imdb.com/title/tt0138704/) is good for a semi-serious mathematical workout, especially the cool stuff on code-work/substitution/patterns in the Torah.

Gonna look up all these references to books and Superstring theory etc.

[the_lone_wolf]

I'm the other way around, had to ask my girlfriend, who's younger than me and has therefore had less time to forget, why the simplification of (x + y)² resulted in the following:

x² + y² + 2xy
eyebrows and double chin...

;)

[MeridiaNx]

Is that what this (http://forums.sv650.org/showthread.php?t=99080&highlight=infinity)thread is about?

Oh, and regarding that example, and to keep it in this thread rather than an older one, is that definitely right, as agreed by mathematicians rather than an amateur's error?

If it is, then I can't argue with them, but I would've thought the logical inconsistency must be to do with....hmm, oh balls that doesn't work. Or at least it does to me but someone will say that's the problem with infinity. Was gonna ask if it's because 10 x 0.999 recurring should, due to adding two 9s together, give an 8 as the final decimal. If ever you could get there :confused:

Problem with that sort of trick is that I can't see the application other than as a neat trick?

[dizzyblonde]

[quote=MeridiaNx;1406313]Tried that last night, was reading the damn thing til 4.30am but when I put it down and rolled over my brain was in meltdown and I had disturbing dreams involving groups of numbers doing horrible things to me :(



I'm the other way around, had to ask my girlfriend, who's younger than me and has therefore had less time to forget, why the simplification of (x + y)² resulted in the following:

x² + y² + 2xy

Couldn't for the life of me figure out where the 2xy came from, even though I knew it to be true based on plugging numbers into the equation. Then she reminded me to put (x + y)(x + y) and multiply everything by everything. Doh! It was part of Pythagoras proof that his equation held true for all right-angles triangles without having to test them.



Iquote]

lol...his head hurts all day long, because he has to deal with it all day long, but just a few months left now and he'll have finished his final year..and yes he probably dreams of nasty number chasing too......
as for the rest its them damn bracket equation jobbies,I used to love them at school but thats as far as my maths goes, although I tried reading his calculus books once but that ended with the same zzzzzzzzzzzzzzzzzzzzzzzz

[MeridiaNx]

eyebrows and double chin...

;)

Oh crap that didn't work, dodgy pasting of a squared symbol that I didn't know how else to make. Will try to remedy that with an edit.

[MeridiaNx]

"In Search Of Schroedinger's Cat"..."The God Delusion" ???

I had to struggle to get my head round Schroedinger's bl**dy 'maybe it's dead, maybe it's not' cat for AS Physics. That hurt my head too!

Read the God Delusion though, good book if you can take some of the more ranty portions with a pinch of salt.

[the_lone_wolf]

Oh crap that didn't work, dodgy pasting of a squared symbol that I didn't know how else to make. Will try to remedy that with an edit.

i was refering to the method of remembering how to simplify (x+y)^2

write down (x+y)(x+y)

now draw two arcs over the top of the brackets, one from x to x, the other from y to y

these are your eyebrows

now draw two arcs under the brackets, one from the x on the far left to the y on the far right, the other from the y in the left bracket to the x in the right bracket

that's your double chin

now multiply the letters on each end of each line and you have:

(x*x) + (y*y) + (x*y) + (y*x)

or x^2 + y^2 + 2xy

it honestly is very simple, i must've learned it yeeeeears ago as i'd completely forgotten about it until i saw your post...

[the_lone_wolf]

I had to struggle to get my head round Schroedinger's bl**dy 'maybe it's dead, maybe it's not' cat for AS Physics. That hurt my head too!

there is no maybe, it's alive and dead until you look;)

[dizzyblonde]

thats right mr wolf, exactly as we were taught. Did loads of them for my G.C.S.Es years ago,

[MeridiaNx]

Sorry for this string of posts, just keep thinking of new things.

I liked the bit in Fermat where he gives an example of mathematical fact that can defy intuition. He explains that the probability of 2 people involved in a game of football, that is 23 people in total, sharing a birthday, is actually slightly over 50% !

Still makes no sense to me from the point of view of intuition as he is quite clearly right, but it's like an Escher or something where what you know to be the truth is so incompatible with what you naturally think.

[MeridiaNx]

these are your eyebrows...that's your double chin

Now I see what you mean, never learned it with that reminder, just the boring lines but it had totally slipped my mind. I did feel suitably dunce-like!

there is no maybe, it's alive and dead until you look;)

Forgotten that one too. Maths was obviously a traumatic experience for me :rolleyes:

[the_lone_wolf]

Maths was obviously a traumatic experience for me :rolleyes:

or was it?

;)

[MeridiaNx]

Oh you mathematical jester you. Bet that one's a hit with the ladies!

[Rog]

Anything by Paul Davies is pretty cool although he is more physics than maths, but maths is in there. The ones I would recommend are his books "the last three minutes", "how to build a time machine" and "about time" if you think maths is freaky check out the last book as time is something else !. I guarantee when you read this you will never look at time in the same way again.

If you like reading about mathmatical formulae then check out bernuolli. His formulae relate to pressure and velocity and are used in all industries dealing with fluids.

I am a great beleiver in teaching maths as a practical subject. If you are going to teach kids abstract algebra then you should also tell them about the myriad of applications it has in the real world.

[gettin2dizzy]

Read the God Delusion though, good book if you can take some of the more ranty portions with a pinch of salt.
He's a very interesting man but I know what you mean, it does get wearing at times; especially as he's preaching to the converted. I can't imagine anyone religous reading it at all. I suggest 'why god is not great' as a better read.
try....C.F.D and F.E.A. computational, fluid, dynamics and finite element analysis.
I don't know what it is but Im Indoors studies it amongst other things. Last year i had many a book of this subject thrown at me during his third year at uni. Made my eyes go square followed by a long period of zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
CFD and FEA has a nice mathmatical flow to it if you're mathmatically minded. You want to try flight dynamics, you've suddenly got an extra 3 axes to deal with on top of it all ;)

[Kinvig]

i can recommend "In Search Of Schroedinger's Cat" by John Gribbin

Did he look on the window sill in the spare bedroom? I find mine's always there.


HTH

[Pedro68]

I am a great beleiver in teaching maths as a practical subject. If you are going to teach kids abstract algebra then you should also tell them about the myriad of applications it has in the real world.
+1 to that ... that's what makes Maths sooooooo interesting.

I'm quite interested in maths and that book in the OP looks quite intriguing (in a geeky sorta way :-P).

I used to do a bit of tutoring in GCSE maths ... I was amazed at how much I remembered 10 years on! Matrices, pythagoras' theorem, differentiation (calculus). I had a brilliant maths teacher (immortalised in the speccy game - Manic Miner - Dr Jones' Math Room!). I could pretty much do the maths, but I didn't put a lot of effort into it ... so after my mock exams, I'm sure he intentionally marked me down a grade and said, "you'll be lucky to get that in your O-level exam - if you really TRY - but in all honesty I can only see you getting a C!".
I thought, "I'll show you!" ... so I revised damned hard, and got an A :D
On the day I collected my results he was in the school admin office and I said, "Hey, Doc Jones, I got an A in maths!" ... he said, "Yeah, well done, I knew you would" :scratch: damned reverse psychology!
I went on to do A-level maths, but lost interest in it after he left the school to go back to work in industry, and eventually failed the exams. The other teachers just didn't have the motivational skills or the ability to make the topic interesting :(

[MiniMatt]

Oh god, I love brain achy stuff. Not very good at it mind :D

Personally I still struggle with Einstein's two relativity theories. I can accept them, and even understand them, but actually internalising them, getting them "in my head" if that makes sense - I only get that eureka moment every now and again, then I always later lose it and struggle again.

Another good one to ponder over is predicting prime numbers. On the face of it prime numbers appear to be a creation of maths, therefore there must be a mathematical way to predict them. But there's not. It's kind like the "what's the next number in this sequence" puzzles, except no-one's cracked this one - 2, 3, 5, 7, 11, 13, 17 - what comes next (it's 19 - but where's the pattern, why can't that be predicted?)

[MeridiaNx]

It's kind like the "what's the next number in this sequence" puzzles, except no-one's cracked this one - 2, 3, 5, 7, 11, 13, 17 - what comes next (it's 19 - but where's the pattern, why can't that be predicted?)

Yeah that one cropped up in the book too. And another one I liked posed the problem of whether any map could be drawn which required more than 4 colours to shade it, such that no two areas sharing a common border were shaded the same colour. :D

[timwilky]

For some crazy reason I did an additional maths options at uni. Which was helpful as I was there through an ONC route instead of traditional A levels.

So those with a phyics/maths A levels used to struggle with some stuff, especially Thermodynamics, fluids and even general mechanics, such as Coriollis, Castigliano etc. I found it "Interesting".

However, I never could get my head round Fourier transforms etc.


Crazy friend did his maths degree part time and took it through to a full PHD still part time all based of Steiner triple series mathematical quirks. Now that is brain ache stuff

[stewie]

I got a C.S.E. grade 4 in maths in '76' ( which is why Im driving a truck on the night shift and not head of theoretical astrophysics at cornell like I was planning) so feel eminitely qualified to add to this debate ;) try 'parallel worlds' by michio kaku for a bit of light reading or 'Chaos : making a new sceince' by James Gleick.

[MeridiaNx]

I had a problem at school where, when I chose to do Physics AS, I got put in the top set. Not meaning to blow my own trumpet or anything, but I was always in the top set for everything so they did it automatically. Problem was, I ended up as the only AS student in the class, doing English, History & Economics as my main subjects. The rest of the class were all full A-level students, half of them Chinese, and all of them doing Physics, Maths, Further Maths & Electronics.

I was a little out of my depth! :rolleyes:

[Fizzy Fish]

yeah i used to think i was good at maths until i took a mathsy option too far at uni and ended up WAAAY out of my depth with all the egg heads!!

I still have nightmares about those text books now... :lol:

[Ceri JC]

I've not read this book, but I'd just like to comment that Simon Singh is an excellent writer and I've been very impressed with his ability to explain complex concepts in (comparatively) simple, easy to understand terms, without resorting to significantly dumbing it down. I will check it out (once I get through my current year long reading list ;)).

[skidmarx]

Some good books here!
If your interested in this kinda stuff then http://en.wikipedia.org/wiki/The_Fabric_of_Reality
by David Deutch is well worth looking at. He blends physics and epistemology into a compelling argument that supports the idea of parrallel worlds. Some really interesting philosophical discussions for those that like that kind of stuff.

[MCN_LiamM]

I find The Hungry Caterpillar quit a god mathematical read :smt040:smt040

[Ceri JC]

I find The Hungry Caterpillar quit a god mathematical read :smt040:smt040

Ha ha, read that to my niece a few weeks back. It's very challenging. :D

[Ed]

Hands up everyone who remembers SMP maths - School Mathematics Project - just what was all that about. Piggy Deeprose (maths teacher at school) suddenly woke up to how useless it was and we did traditional maths in 1 year for O level - this is 1977. I got a B:cheers: And look where I am now!!! - Chancellor of the Exchequer!!!!! See, it was all false, fibs and lies, I still can't add up, not even using a computer!!!!