binomial theorem (1 Viewer)

[batigol]

does anyone have materials (apart from textbooks that is) for binomial theorem, or know where to find it? this topic is so fweakin hard!

 

[Slidey]

I hate to be unhelpful, but I suggest you take the time to grab the texbook and sit down and nut it out. You don't really have another option.

Which are you using? If it's, say, Fitzpatrick, perhaps use Maths in Focus. Not every textbook is the same. Some explain things better.

Try the questions, if you get stuck, refer to the examples.

 

[who_loves_maths]

google it.

 

[currysauce]

not hard, this is my favourite topic...!!

it will all click - eventually

 

[FinalFantasy]

Click Click Click!

 

[who_loves_maths]

PHYS= 99% 1st

wow? either you're REALLY good currysauce, or your exams are REALLY easy.
btw, do you like the new hcs style of physics? ie. watch out for the verbs....
or, do you prefer the old quantitive nature of hsc physics?
just out of curiosity. cause i don't know anyone, incl. those that like the new physics, who does that well in physics.

 

[currysauce]

i like the old physics, but the new on eis easy!

 

[KFunk]

wow? either you're REALLY good currysauce, or your exams are REALLY easy.
btw, do you like the new hcs style of physics? ie. watch out for the verbs....
or, do you prefer the old quantitive nature of hsc physics?
just out of curiosity. cause i don't know anyone, incl. those that like the new physics, who does that well in physics.

I suspect that I would have prefered the old syllubus to the new one, but if it's just the difference between a several more basic equations then it's much of a muchness really. If anything gets to me it's the questions in the vein of 'assess the affect of the transistor on society'. By the way, I noticed the QED references in your signature and you're obviously very competent mathematically so I was wondering whether you'd ever looked into the mathematics behind QED (Feynman Calculus etc)? I've just been curious about how it all fits together from a mathematical standpoint, that is, quantum physics and modern physics in general.

 

[who_loves_maths]

Originally Posted by KFunk
so I was wondering whether you'd ever looked into the mathematics behind QED (Feynman Calculus etc)? I've just been curious about how it all fits together from a mathematical standpoint, that is, quantum physics and modern physics in general.

hahaha... i'm very interested in the QED theory and the mathematics behind it (physics is my fav. subject in fact)... however, through independent learning, i've learnt a long time ago (since yr 9) that pupils of the HSC level and of the high school level in general are not equipped with the appropriate tools to even begin to delve into the mathematical world of post-classical physics.
consequently, i read about disciplines like QED, etc, only from a qualitative and descriptive perspective rather than from a technical one. so in the attempt at sustaining my passion for physics and simultaneously preventing any large degree of disillusionment and convolution that comes with frustrated efforts in understanding the mathematics behind it, i generally try to abstain from the technical side of high-level physics.
i find that, at this level, intepreting the mathematical models of physics potentially provides a more grand, stimulating, and beautiful picture of the universe than does deconstructing these models mathematically. and that's what drew me to physics in the first place.
i recognise that revolutions in physics have had in the past catalysed positive progress in mathematics, both fields of study go hand in hand; but at this stage, my appreciation of physics blooms purely from the aesthetics that it tallies to our existing picture of the universe, and not its intrinsic mathematical potentials.

lol, i'm sure my current attitude towards the study of physic will inexorably change in future years. but right now, i like it the way it is.
so, in short, no i haven't looked into the mathematics behind high-level subjects such as QED Theory; not because i don't want to or plan to, but because i know that by looking i'll only be adding to the confusion... i don't need another thing to blemish the splendid picture of Physics yet, i have the HSC Physics syllabus doing that already

 

[richz]

LoL QED - Quite easily done

 

[who_loves_maths]

^ haha... was that adopted from §eraphim?

 

[richz]

nah, it was from signpost maths 10 , that book had so many jokes in it..

another one.. in the logarithms section it had some cartoon character and he said "i better log it done in my note book"

 

[acmilan]

Here are some sites i gave to my student. Dont see them helping any more than a textbook would though:

http://www.acts.tinet.ie/binomialtheorem_674.html
http://library.thinkquest.org/C0110248/algebra/biexpintro.htm
http://hsc.csu.edu.au/maths/ext1/binomial_theorem/140/binomial.html
http://www.mansw.nsw.edu.au/members/reflections/vol21no1_larkin.htm (permutations & combinations)
http://www.hsccoaching.com/Downloads.html (chapter 26)

 

[who_loves_maths]

nah, it was from signpost maths 10 , that book had so many jokes in it..

^ haha, nice. i think my maths teacher was one of the co-writers of the Signpost maths book series.

 

[KFunk]

however, through independent learning, i've learnt a long time ago (since yr 9) that pupils of the HSC level and of the high school level in general are not equipped with the appropriate tools to even begin to delve into the mathematical world of post-classical physics.

This is a fact that I have spent quite some time trying to deny . Physics was the reason I got interested in maths in the first place because I had that drive to understand those abstract symbols and what they imply for the world around us.

I find that, at this level, intepreting the mathematical models of physics potentially provides a more grand, stimulating, and beautiful picture of the universe than does deconstructing these models mathematically. and that's what drew me to physics in the first place.
i recognise that revolutions in physics have had in the past catalysed positive progress in mathematics, both fields of study go hand in hand; but at this stage, my appreciation of physics blooms purely from the aesthetics that it tallies to our existing picture of the universe, and not its intrinsic mathematical potentials.

It's actually the interpretation of the mathematical models which I have in mind but I geuss what I'm interested in attaining is the ability to interpret them myself rather than relying on reading someone elses'. One of the more interesting lay-person's examples that I have come across is in the huge generalization of T-duality in string theory. If you consider a closed string the idea is that you have 'momentum' modes where the energy of the mode comes in integer multiples of 1/R (where R refers to a kind of 'dimensional radius') and then you have 'winding' modes where the energy is proportional to R (since the string wraps around an integer number of times). This then gives an equivalence between a circular dimension with a radius of R and one with a radius of 1/R. It's such a simple idea (and very generalized of course) but the implications are fascinating to think about.

I figured an example would be the easiest way for me to explain what I was getting at. If you have found, or if anyone else reading this has found, anything of a similar nature, I'd be very interested to know what it is.

 

[richz]

for Binomial theorem just remeber pascal's triangle.

 

[who_loves_maths]

Originally Posted by KFunk
It's actually the interpretation of the mathematical models which I have in mind but I geuss what I'm interested in attaining is the ability to interpret them myself rather than relying on reading someone elses'. One of the more interesting lay-person's examples that I have come across is in the huge generalization of T-duality in string theory. If you consider a closed string the idea is that you have 'momentum' modes where the energy of the mode comes in integer multiples of 1/R (where R refers to a kind of 'dimensional radius') and then you have 'winding' modes where the energy is proportional to R (since the string wraps around an integer number of times). This then gives an equivalence between a circular dimension with a radius of R and one with a radius of 1/R. It's such a simple idea (and very generalized of course) but the implications are fascinating to think about.

I figured an example would be the easiest way for me to explain what I was getting at. If you have found, or if anyone else reading this has found, anything of a similar nature, I'd be very interested to know what it is.

eventually i think that everyone or anyone who's interested in the abstracts of physics will need to start intepreting the mathematical models for themselves in order to gain a personal understanding and appreciation of physics, and to perhaps contribute and expand to the stash of knowledge of physics at hand.

however, i think that independent learning and discovery in a scientific field such as physics must begin in the right direction - under some sort of guidance. and at our level this guidance comes from "reading someone elses" perpective - those that know what they are talking about. after that, if we find ourselves even more intrigued by the workings of the universe, can our imagination and creativity bloom via our own accord.
an example isn't far away - our wish is one day to fully comprehend the mathematics behind, say, M-Theory, but we start right now at school with 4u mathematics. we need the guidance of teachers to grasp the basics of mathematics, before we can move on to more 'outlandish' endeavours - perhaps on our own with the skills we've gained from others that are apart of our early learning experience (ie. teachers, tutors, etc...).
even genii or prodigies start out like this too.

but KFunk, what you've said about mathematics being the key incentive and drive behind your affinity toward physics is very enlightening to me. the contrast between our (and many more others i'm sure) individual reasons for the pursuit of physics really serves to remind me of the 'unifying' (excuse the pun) power of physics over the human mind and its curiosities - the fact that so many different ppl can 'gravitate' toward a single goal for whatever their disparate reasons attests to the extraordinary subjugating power of physics. for me, that's another reason why physics steals my awe ... the ppl involved in it are every bits as interesting as the discipline itself, and that includes you :uhhuh:

so i'm happy just to be part of physics right now. worrying about the complex maths behind it remains an endeavour for my uni years

P.S. i'm sure i know some examples such as the one you gave about T-duality before, except i can't recall them atm... i'll get back to you on it if i remember later. but btw, tell me something, String Theory has not yet been 'proven'... so do you really believe in extra dimensions to this universe? (other than the four we already know) because they might just turn out to be fancy mathematical/abstract constructs, and that's also one of the problems of using abstract mathematics in building physical theories and models for our universe - you don't know if it's real or imaginary.

 

[KFunk]

but btw, tell me something, String Theory has not yet been 'proven'... so do you really believe in extra dimensions to this universe? (other than the four we already know) because they might just turn out to be fancy mathematical/abstract constructs, and that's also one of the problems of using abstract mathematics in building physical theories and models for our universe - you don't know if it's real or imaginary.

As far as physical 'extra dimensions' go, I'm skeptical, but as far as fancy mathematical constructs go I think that they can work even though the conceptual premise behind them might be incorrect. While there might not actually be (10/11/26 etc.) dimensions, it's still possible that particles/strings could behave as though there were when you take into account various degrees of freedom and force interactions. The conceptual basis for much of the standard model could potentially be upturned but that wouldn't change the fact that it has afforded us a lot of very accurate predictions. My personal interest in string theory actually comes from the fact that I have something of a musical background. I've always played stringed instruments (bass, guitar, double bass, mandolin etc.) and so the idea that our world could be summed up in the harmonic oscillations of little strings kinda strikes a chord with me (excuse my pun also).