Search results

Can be pretty pure too; c.f. http://en.wikipedia.org/wiki/Hall's_marriage_theorem

I really haven't done enough applied maths to know, but I really like discrete mathematics (graph theory!) and number theory (and what I've seen of its university extension in abstract algebra). I did a kinda no rigorous course in topology a while ago that was fun but occasionally kinda...

Anyway so results of enrolment day: MATH1901, MATH1902, MATH2961, MATH2962. And wrarrr Im going to through my hands into the pure camp. But as much as I understand it, some aspects of cosmology/theoretical physics are actually much closer to pure maths (topology etc) than they are to anything...

Re: 2012 HSC MX2 Marathon Consider R(x) = P(x) - Q(x): note that it is of degree at most n. Now suppose R(x) is not the zero polynomial; in this case it has at most n roots (from unique factorisation, which is provable from the division algorithm). However it clearly has n+1 roots x1, x2...

Oh I really like discrete maths, but thats sorta why Im not going to take it straight away :P And Im doing physics anyway as one of the compulsory non-maths science subjects. Yeah looking at my level of overload doing both is probably too much... so Ill probably do metric spaces and not galois...

I was told that 2961 isnt that bad if you teach yourself some of the 1901 stuff before the start of the course, which Id plan to do anyway so I can get away with skipping some of the lectures :P And some close friends of mine who did logic and foundations say it became really boring after a...

You can do it by just counting it. So if you think about it, the nPk = n(n-1)(n-2)...(n-k+1) right? Thats pretty easy to justify; n possibilities for the first, n-1 for the second, ... n-k+1 for the kth. So thats nPk. Now the question is, whats the relationship between nPk and nCk? Now if you...

Have you seen the counting argument version?

Yup thats exactly right. You construct a number that has at least one digit different from every number on the list (precisely, it differs from the kth number on the list in the kth digit), giving a contradiction coz then it couldn't be on the list.

Alright its pretty late but still, time for largarithmic does cardinality! Basically we want to come up with an idea for what it means for a set to have "the same size" as another set. Now this is pretty obvious for finite sets: {1,2,3} has the same number of elements as {2,3,4}, for instance...

Nah I meant like, an actual mathematical proof that uses sorta really abstract "symmetry". Can't really think of an example right now though :P I really like number theory too, in particular arguments from polynomials and stuff when they get involved. Something I really enjoyed proving at one...

I don't think there's any one particular thing that I love above all others - but I guess I really like really beautiful symmetric arguments, can't think of an amazing example right now. But something that IS amazing: diagonalisation arguments. I mean the very idea that "some infinities are...

Re: 2012 HSC MX1 Marathon You've answered a slightly different question - I said *sum* of distinct integer powers of phi - you can't have differences. But if you could, yeah that still works ^^ And I believe that theorem is actually pretty easy to prove (you can induct with a pretty simple...

Re: 2012 HSC MX1 Marathon Uses the first property only - don't need anything to do with fibonacci numbers. Try it, its a fun question :)

Re: 2012 HSC MX1 Marathon really cool fact (kinda unrelated but alright...) you know every positive integer can be written as sum of distinct integer powers of phi? e.g. 1 = \phi^0 2 = \phi^0 + \phi^{-1} + \phi^{-2} 3 = \phi^1 + \phi^0 + \phi^{-2} 4 = \phi^2 + \phi^0 + \phi^{-2} (where \phi...

I don't know whether you're a troll or not, but could you please shut up about IQ? Natural intelligence counts a tiny amount in life for most of us; the most of it is hard work and learning how to learn. And to the extent of it does, your intelligence is proven by what you actually do - and no I...

No, that isnt a situation that corresponds with the actual question. The reason is in giving the sides vectors you havent given them directions. For the angles between Z1 and Z2 to actually be alpha, you need Z3 = Z1-Z2 or Z3 = Z2-Z1. If you want Z3=Z1+Z2 (so that it actually corresponds to the...

MORE GEOMETRY! edit: should probably be a bit more specific. The syllabus has scope for some really interesting and actually quite hard pieces of Euclidean geometry near the end, which unfortunately are quite rarely touched upon. In particular I'd love to see a question where you prove a simple...

gogogogogo!

Re: 2012 HSC MX2 Marathon Hey your thing says HSC 2011, are you doing science / advanced maths this year and if so at which uni? Also may as well post a question. Dunno how suitable thing one is but its neat: Part (A). Trapezium ABCD is given with AB parallel to CD. Let diagonals AC and BD...