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Being open-minded and at least moderately intelligent.

Re: HSC 2013 4U Marathon A man walks into a casino with $10 and the only bet he knows how to make is on a colour in roulette (the probability of winning this bet is 18/37, and you win as much as you bet). Rather than spending all his money at once with one bet, he decides to "play it safe" and...

A few 100% exams in high school. At uni: 86% in a stats course in which I did not do two 10% assessments (thank you scaling). 95% in a 3rd year applications of complex analysis course (stuff on Painleve analysis) where I knew very little beyond the prereq stuff and probably deserved...

Re: HSC 2013 4U Marathon To be on the safe side I would say continuously differentiable on (a,b) and continuous on [a,b]. Continuity of the derivative implies that the integral exists, which we would not get from differentiability alone.

Re: HSC 2013 4U Marathon You will need to assume more than continuity if you are going to differentiate your y.

It doesn't have to be, the earlier solutions posted work fine. Drogonski's method is an illustration of a more powerful tool.

To add to this more sophisticated method: 1. The "similarly" follows from the fact that the multivariate polynomial on the LHS of this equation is symmetric: that is, interchanging any two of a,b,c does not change it as a polynomial. 2. The LHS must be of the form k(a+b)(a+c)(b+c) after...

Re: HSC 2013 4U Marathon bump. Difficulty: 3.14159/5 That should be enough to keep 2013'ers busy for a while.

Re: HSC 2013 4U Marathon bump. Difficulty: 1.5/5.

Re: HSC 2013 4U Marathon bumpage.

Re: HSC 2013 4U Marathon In the following question you may assume without proof that if a continuous function f is positive at some c, then there is a small interval centred at c in which f > f(c)/2. 0. Prove that a non-negative continuous function with integral 0 over some interval of...

Re: HSC 2013 4U Marathon 1. Because sin(x) is asymptotically equivalent to x as x - > 0, as is assumed without proof in the mx2 syllabus. Similarly sin(x)/(pi-x) tends to 1 as x - > pi. 2. 0. Simply apply the rule: \int_0^a f(x)\,dx =\int_0^a f(a-x)\, dx and the result is...

Re: HSC 2013 4U Marathon A lattice point is a point in the cartesian plane with integer coordinates. Prove by induction or otherwise that the area of a polygon in the cartesian plane with vertices on lattice points is given by: {Number of lattice points strictly inside P} - {Number of lattice...

Well I am doing it to get into research/academia. And I suppose there would also be the same opportunities I had after undergrad: some graduates from my undergrad degree went into jobs in things like trading / risk analysis / applied mathematics jobs for companies like CSIRO. Academia is much...

Love what I am doing. (Otherwise I wouldn't be doing it!)

oh awesome, I keep forgetting no-one else lives here. that makes it much easier.

Ah of course! A lot of friends are going to that so I was strongly considering getting a ticket off scalpers. Amity Affliction <3.

one kati roll one t-bone steak, rare with mushroom sauce c&c ice cream with maple syrup

haha what for?