Yep that's right. I know most people on that list of 8 medallists, and I know for a fact that only 2 of them did honours in maths. The others did either computer science, chemistry, or physics honours.
I think it is quite possible that UNSW maths has slightly inflated grades, the dux of UNSW...
Like you can have UNSW pride or whatever, but when giving out advice don't put your own bias into it and claim facts, e.g. that USYD gives out more maths medals when in fact UNSW has a higher percentage of medals.
UNSW has like 2 or 3 pure maths honours students and gave out 1 medal.
USYD has like 10 pure maths honours students and gave out 2 medals.
Seems like you guys give out a higher percentage?
From memory, pure maths grads have a lower unemployment rate than law grads.
Well those jobs pay pretty well themselves, but there are plenty of others. Oceanology and meteorology come to mind straight away.
The highest paying grad job I know of is for trading firms, and they hire...
Nah I would say any maths or stats is good to do. Maths/stats majors (regardless of pure/applied/financial) I know seem to get the best internships/grad jobs srs.
Here's a nice approach to question 2 which highlights a neat way of thinking about questions like this:
Consider an arbitrary 6 digit number:
A B C D E F
We must have 456 in here somewhere. So we already know 3 of the digits, meaning we really only have this:
_A_B_C_
Now we need...
A much easier method is to notice that any 2x2x2 cube has a vertex (at the centre) which is common for all 8 cubes. So clearly you need at least 8 colours.
You could go ahead and find an 8-colouring, but for an a more satisfying proof that 8 colours is sufficient:
Start with a 2x2x2 cube where...