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Re: HSC 2013 4U Marathon Sy your summation of products of triangular numbers & sines question is raping me. Hint plz? :) so far I've been working with Re( (z+z^2+...+z^n) + 2(z^2 + ... + z^n) + ... + n(z^n) ), then simplified that with geometric series, but it's not getting anywhere.

Why do you want full marks, 99.95, etc if you aren't willing to put the work in? Most people who aim for 99.95 do it because it motivates them to work their hardest. You realise that in the real world, outside of this insular little HSC community, no one cares about your HSC results right? A...

Computer science IS a mathematical discipline. The problem is that people are career-oriented, so they want to learn practical skills in uni, so CS courses end up being mostly about software engineering. What a pity.

almonds are a good source of fats (the healthy kind)

An upgrade from last time :D - black coffee, no sugar - 4 slices wholemeal toast - 3 eggs - glass of OJ - banana - mango - nectarine - 170g yoghurt - 30g almonds/pistachios - 200g brown rice - tablespoon of natural peanut butter - 150g black beans - half cucumber - 100g snow peas + green beans...

The best known general strategy over multiple iterations of Prisoner's dilemma (and I assume for this game as well) is called tit-for-tat. In the first round you play 'nice' i.e. cooperatively, and in every subsequent round, you do whatever the opponent did to you the last round. How they came...

I've never actually finished a course on it before, only gotten partway through three. They were fun and informative and all, but none felt like proper study. I think many of the top universities dumb down their courses significantly for coursera (at least, this is true for the 3 courses I've done).

Re: Which univeristy is best for engineering, specifically computer engineering/Comp Is there any particular need to do both degrees? You can do the relevant courses from a comp eng. degree in compsci and vice versa I'm pretty sure.

Sounds good, I'll sign up. The coursera course I'm doing right now (Stanford's Algorithms II) finishes next week and I'm in the mood for another.

brown rice + spoonful of natural peanut butter mixed in is the shit. no extra seasoning needed. edit: crunchy natural peanut butter for optimal texture

yes. start by multiplying all terms by x.

What's the rush? It's the holidays, it's not due tomorrow (I assume). Sit down with a textbook and learn the damn content.

Re: Which univeristy is best for engineering, specifically computer engineering/Comp UNSW is the best university for compsci, but USyd is good too. Dunno about UTS.

Re: HSC 2013 4U Marathon mission accomplished :D:D:D

Re: HSC 2013 4U Marathon Hehe nice one. n^2 - 3n + 2 = n(n-3) + 2. An even number * an odd number = an even number. n, n-3 are even, odd in some order. +2 leaves it even, and the only even prime is 2. So it's only true when the result is 2, that is for n=0 and n=2.

what kind of school gives out a hand-in assignment for maths? especially over the holidays?

Re: HSC 2013 4U Marathon Syyy i'm bored post another question. P.S. my reasoning for the x \rightarrow f^{-1}(x) roots thing was the same as yours i think. if (x-a_1)(x-a_2)...(x-a_n) = 0 is our original polynomial, then we can create one with the new roots as...

Re: HSC 2013 4U Marathon $degree of $P(Q(x)) = mn$ \\ \\ If $P(x)$ is of degree $n$ then $P(P(P(x))) - 3P(x)$ is of degree $n^3$, but $P(P(P(x))) - 3P(x) = -2x$ so $n = 1$. \\ \\ Let $P(x) = ax + b$. $P(P(P(x))) - 3P(x) = a(a(ax+b)+b)+b - 3(ax + b) = a(a^2x + ab + b) + b - 3ax - 3b = a^3x +...

Re: HSC 2013 4U Marathon I was playing around with these sorts of problems on the bus the other day, but I ended up confusing myself and didn't get very far. Say you had a polynomial with roots a_1, a_2, ..., a_n and you want to find a polynomial with roots f(a_1), f(a_2), ..., f(a_n) (Sy's...

Re: HSC 2013 4U Marathon Sy posted that easy polynomial roots question at the bottom of pg 27, that's definitely approachable by any 4u student, and no one else's tried it yet... weird