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Maths and Further Maths

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www.ocr.org.uk
Partial Differentiation uses the curly, roundback dz/dy and dz/dx instead of the classic dy/dx. Thats the only name I can think of for partial differentiation and I'm the biggest fan of calculus bar none. Hence my username, the greatest man that ever lived and gave the world calculus along with leibniz.

Reply 21

bloodhound

i used to think same but i realised. there were alos many ohter greats like cauchy , gauss , euler. who extended everything. newtons notation was very cumbersom . and it was leibniz who wrote dy/dx and came up the the integral notaion

Reply 22

Sir I. Newton

I agree but Newton's my top scientist because he thought different about things, he went into unknown terroritory like Galileo, Eratosthenes and Copernicus. Yeah leibniz did use dy/dx, Newton used "X" with a dot on top of it. There are lots of all time greats but I think Newton is the greatest, he's in the top 3 Greatest Mathematicians and top 3 Greatest Physicists of all time. Has any read his mathematical paper, The Principia? The maths inside it is mind blowing, and to think he didn't even have a calculator. Thats a true great, not like stephen hawkings and his telescopes and computers, Newton made his own telescope, and he did all this while most of England had the plague.

Reply 23

Unregistered

Originally posted by Sir I. Newton
I agree but Newton's my top scientist because he thought different about things, he went into unknown terroritory like Galileo, Eratosthenes and Copernicus. Yeah leibniz did use dy/dx, Newton used "X" with a dot on top of it. There are lots of all time greats but I think Newton is the greatest, he's in the top 3 Greatest Mathematicians and top 3 Greatest Physicists of all time. Has any read his mathematical paper, The Principia? The maths inside it is mind blowing, and to think he didn't even have a calculator. Thats a true great, not like stephen hawkings and his telescopes and computers, Newton made his own telescope, and he did all this while most of England had the plague.

Ahem, Stephen Hawking was equally as great, being able to contribute significantly to the field of Astronomy despite having to endure a rare disorder.

Reply 24

Unregistered

Originally posted by Sir I. Newton
Thats a true great, not like stephen hawkings and his telescopes and computers, Newton made his own telescope, and he did all this while most of England had the plague.

Ahem, Stephen Hawking was equally as great, being able to contribute significantly to the field of Astronomy despite having to endure a rare disorder.

Reply 25

Sir I. Newton

Equally as great, lol. Did he discover the basis of maths and physics? Does he have a SI Unit named after him? Did he invent his own mathematical way of rates of variation? Did he invent his own telescopes and construct them single handedly? Did he use his own knowledge of maths instead of a Calculator? Does he have a law of cooling named after him? Did he derive the equation of motion? Did he model the motion of planets like Newton, Kepler and Hooke? Rare disorder or no rare disorder, he has done any of these, thats why hes a second rate scientist, not in the premier league of science like the above and Einstein, Eratosthenes, Pythagoras, Coloumb, Faraday, Maxwell, Galileo, Ptolemy, Copernicus. He cannot match any of these names for breakthroughs in science.

Reply 26

It'sPhil...

Originally posted by Sir I. Newton
... Did he discover the basis of maths and physics?

...Did he use his own knowledge of maths instead of a Calculator?

Are you saying Newton discovered the basis of mathematics, a subject that had existed for 3,500 years before he was even born!??

And I really dont see how the calculator comment is in any way relevant - most mathematics is done without calculators as they are only useful really to speed up arithmetic and to give approximations for things such as pi, logarithms etc

Reply 27

bloodhound

phil is rite. Imagine explaing the world of today without using calculus. the basis of most mathematical techniques. i would be useless. stephen hawking would get nowhere. einestien would have got nowhere with his relativity. newton was definitely one of the greatest. einsteing and gauss both conceded that they thought he was the greatest mathematiciena ever. netwon approach to calculus is genrerally regarded as more rigorous that liebnizes. and his notation for fluxions altouhg cumbersome in some instances, was of great use in mechanics. i think he is great, but i resepect all the the other greats equally as well. gauss for instansce did great work on electromagnetism and he is immortalised in the unit Gauss. althought many pple just use Tesla.

Reply 28

Sir I. Newton

Originally posted by It'sPhil...
most mathematics is done without calculators as they are only useful really to speed up arithmetic and to give approximations for things such as pi, logarithms etc

So your telling me that you could do any sum in the world without a calculator? LOL. Newton did all his sums without calculators and got them extremely accurately, don't think you'd see Hawkings doing the same. What actually has Hawking done? I think he discovered quasars, but i can't think of anything else, but for any other scientist i can think of most of there work.

Reply 29

Unregistered

the ability of being able to do calculations in your head does not imply that u r a great mathematician. It only "suggests" that you are.It wouldnt make any diff if I found Calculus today with a calculator. Its a matter of "finding" the path to a problem rather than "walking" the path that matters.

Reply 30

Sir I. Newton

I'd like to know how you can find the fundamental theorem of calculus with a calculator. Simply answer: You Can't. Say Newton had an sum which was similair to this: 345754835892509/(345231*(sqrt(58674) - cuberoot(3223) + 232523535)). He didn't have a calculator to do it on, he'd of had to do it using his mathematical skills, not like the rest of us who would instinctively reach for the calculator.

Reply 31

It'sPhil...

most people could do that sum given enough time - its just long, complicated and almost entirely pointless arithmetic. the point is that being good at arithmetic or 'sums' doesnt make you a great mathematician and is almost entirely irelevant to this discussion. Newton was undoubtedly a great mathematician - not bacause he was very good at arithmetic as you claim he was - but because he had new ideas and devised concepts which where unthought of.

the fact that he didnt have a calculator does not make his acheivement any more or less great - most of his theorems and indeed most mathematics has very little to do with numbers.

"I'd like to know how you can find the fundamental theorem of calculus with a calculator. Simply answer: You Can't."

Youre almost arguing against yourself there - the point is Stephen Hawkings should not be considered a worse mathematician because he is sensible enough to do long trivial calculations on a calculator rather than spend a long time working them out in his head or on paper - but he should be considered a great mathematician/physicist because he has explored new ideas and aided our understanding of the universe

Lastly - do you think Newton did calculations in his head out of choice, to demonstrate his great mathematical ability? no, he did because he had to and if he were alive today and had the option of using a calculator he obviously would

Reply 32

Sir I. Newton

I can't agree more with you on the point that Newton, if alive today, would use a calculator, but he didn't have the luxury of this. I'm not desputing Hawkings achievements, I just think Newton gave the world far more useful techniques to use. I remember once my Physics told me to learn the basics of physics and understand them to the fullest extent before moving on to the more advanced stuff because I had asked a difficult question about special relativity. He was right, but the point i'm trying to make is, without Newtons discovery of Calculus and modelling motion with maths, Hawkings would not be able to do his calculations, with or without a calculator, because there wouldn't be this diverse way of thinking or the mathematical techniques to do them with. Newton and Galileo layed the foundations of modern physics upon which Einstein and Maxwell have built to its present state. I think I've been a bit harsh on Stephen, but I feel Newton is the greatest of the greatest given the things he discovered and the tools he had to do it with.

Reply 33

bloodhound

dont forget the others as well. like cauchy euler gauss liebniz green everyone is great i am great as well

ps and by the way i think ur username must break some law. u cant just BE isaac newton

Reply 34

It'sPhil...

i agree with bloodhound - newton may be accredited with the fundamental theorem of calculus but many people developed ideas long before his time that are very similar. for example euclid worked on the idea of a limit in attempting to find the are under a graph which he did succesfully without using modern integration techniques.

Also euler and fermat developed these ideas as well as many others. iwould say newton should be more highly regarded as a physicist than a mathematician because although his contribution to mathematics is significant, it cannot match that of the true mathematical greats such as euler, diophantus, lame, galois etc

Reply 35

cayley-hamilton

physists are cool coz they actually get things done and WORK towards solving problems. mathematicians solve the problems but worry about trying to proove things too much and in the process they are dull creatures and are the lowest in the social hierarchy.

Reply 36

cayley-hamilton

Originally posted by bloodhound
i disagree totally with you. first of all physists wouldnt get things done without the fundamentals of mathematics. what would they do without the elliptic integrals or other special functions. what would they do if the exponential function wasn not defined. physists didnt break the cyphers during the war. mathematicians did. I had this argument with one of the students doing physics at imeprial. she said mathematicians are fialed physiest. but i said physissts are failed mathematicians. Although with all the respect to physics as a branch of science. i regard physics as a SUBSET of Mathematics.

Biologists think they are bio-chemists,
Bio-chemists think they are chemists,
Chemists think they are physical chemists,
physical chemists think they are physists,
physisists think they are god
and God thinks hes a mathematician.

SORTED

Unfortunately it isn’t SORTED. I think biologists are biologists; and chemists are chemists (I don’t believe in god so can’t really comment of your physists and mathematicians bit but am sure its not true).

Maths is merely a communicating tool in physics (so physics is no subset of maths.) It’s a bit like comparing grand ideas and the bigger picture (physics) and writing it down neatly with a pen (maths).

I don’t think maths people are failed physist or the other way round. I think mathematicians with their pedantic nature are confined to a little space making sure all the details are correct; physists look at the bigger picture (the cosmos!) are don’t get hung up over finer details! Would a mathematician ever have the courage to propose what theoretical physists do???

Reply 37

Unregistered

i still disagree with you. eisnstien would have gone nowhere with his relativity if there was not the work in various spaces by gauss, reimaan and others. i still think physic is a subset of mathematcis. mathematicians can do whatever physicists can . physiscst cannot do what mathematicians can. All the great pple were mathematicians. or mathematical physiscit. Maxwell was a mathematician. Newton i take to be a mathematician. Poisson, Stokes. You name one physists who changed the face of science. except plank and einstien.

Reply 38

Unregistered

The more I dio math the more I love it. The more I love the more I understand it. The more I understand it the more I see that its all boiling down to nothing!

Reply 39

cayley-hamilton

Originally posted by bloodhound
you comment about rigour of mathematicians. thats the best part. what would science be if we didnt know what 2+2 was. what would science be if we didnt know the intergfral of squarert(x^2 - 1) . we cant assume eveything to be correct just because a small part of it is correct. if we did then all the misfortunes and the accidents of space shuttles would be blamed on us.

i think the rigour of mathematics is the thing that makes it beautiful. without rigour there is nothing. mathematics is an absolute perfection. Physics will never achieve that. How many models of universe and space and time and light and all the other things has be overthrouwn and proven to be wrong. i dont think physisixt will ever explain universe perfectecly. while mathematicians explain the mathematical universe abosuly to perfection even to infinity. Hilbert defined varous types of infinity. there are infinity which are greater than others. You get results so astounding and beutiful . you never dream of getting tha in physics. i think theoritical physics is a mess like my teacher said. 1/3 chaege?? what the hell. they are making stuff up to explain. not expalining the stuff.

its not true that mathematics can be of none practical vaule. Take the example of the famous 4 colour problem. How many colours does it take to colour a map without having adjcent areas being of the same colour. This saves map makers time and money.

You are right about maths being rigourous. I don’t know what you consider mathematicians to be but they are certainly not physists because, they hate speculating, being unrefined and experimental. Newton, with his view of the universe was most certainly a physist at heart, he USED calculus for modelling purposes and didn’t bother writing “lim dx tends to 0” in each calculation or whatever.

I am not that passionate about maths to call it beautiful! But I think einstein did once say that all laws should be beautiful and symmetrical (I don’t really know what that means) so I think I’ll be better of switching my argument slightly: it pays to be ‘experimental’ rather than slog thru maths:

For your information there has been evidence for the existence of quarks (with fractional charges) by deep inelastic scattering. EVIDENCE. Infact the standard model is near complete, if the Higgs boson (Higgs- an example of your physist) is found and this will have profound consequences because it will change our view of the universe. Surely this is more profound then worrying about rigour.

Your first sentence perfectly explains why mathematics are sooo pedantic. Its obvious that 2+2=4. In fact it reminds me of the Matrix: “you only believe what you want to believe”.