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Because it is the mathematical equivalent of using a sledgehammer to kill an ant, the DCT is a tool that takes some time to develop, it is regarded as a much deeper fact than the fact that the harmonic series diverges. Mathematicians find it funny when a powerful tool can be used to prove...

Re: HSC 2013 4U Marathon Its pretty good, certainly everything you have said is true and this method extends nicely to more complicated situations. The main question is why a given algebraic number must be the root of a unique minimal (with respect to degree) monic irreducible polynomial...

Re: HSC 2013 4U Marathon Am disappointed that no-one has answered Sy's conjugate root question!

Re: HSC 2013 4U Marathon I don't think so but post your working for zeta(4) if you believe so.

Re: HSC 2013 4U Marathon Its a bit more complicated than that but I remember that it can be done.

Re: HSC 2013 4U Marathon Haha a bit. Euler had a knack for doing some whacky things on intuition that turned out to be things you could make rigorous. Its a pretty bad habit to get into unless you have the intuition of Euler :P. (He never claimed that the random manipulations comprised a proof...

Re: HSC 2013 4U Marathon Armed with the knowledge that it does happen to work though it does make for a pretty efficient way of computing zeta(2n) inductively.

Re: HSC 2013 4U Marathon Haha except the ideas needed to make that proof rigorous are deeper than the ideas in most of the other proofs.

Very impressed with your recent work in the MX2 threads mate. I can't remember if I asked you before but what are you planning on doing at uni?

Re: HSC 2013 4U Marathon Keeping the ideas behind the complex conjugate root theorem at the back of your mind leads to a pretty slick proof.

Re: HSC 2013 4U Marathon Good question, I hope some students can make progress on it as it certainly can be done using syllabus methods. (Just a quick note, the desired equality will only hold in the interval (0,2*pi). Using the 2pi-periodicity of the LHS and the fact that it is trivially...

Re: MX2 Integration Marathon Ah well, am interested to know.

Re: MX2 Integration Marathon How does that lead to something faster than the previous solutions?

Re: MX2 Integration Marathon Good solution Sy, pretty much the same speed as mine really:

Re: MX2 Integration Marathon Not the way I did it.

Re: MX2 Integration Marathon To me that final integral seems harder than the first...may be wrong though.

Re: HSC 2013 4U Marathon He eventually found a rigorous proof. You actually need quite a lot of machinery to make that particular proof work (much more than you have stated I am pretty sure). Edit: To be a little more concrete in my criticism, my main objection is that it is not at all clear...

Re: HSC 2013 4U Marathon Lol rather large assumptions there Realise.

Sometimes music helps me out, its more that it can hype me up to throw myself into my work than any actual cognitive benefits. Eventually I take off my headphones when I really need quiet, but it can help me get started / is decent background for doing routine stuff. Its definitely not helpful...

Re: MX2 Integration Marathon It is quite tricky, probably one of the hardest in this thread that doesn't require out of syllabus techniques.