Search results

Re: 2012 HSC MX2 Marathon Here is a decent question: The three roots of the complex polynomial: p(z)=z^3+az^2+bz+c all lie on the unit circle in the complex plane. Prove that the three roots of: q(z):=z^3+|a|z^2+|b|z+|c| also lie on the unit circle.

Re: MX2 Integration Marathon Cool, yep complex is very nice!

Re: MX2 Integration Marathon In what sort of thing? Using contour integration to evaluate real integrals isn't exactly an honours project...

A short list of mathematical things I find cool, either because the result is nice or there is a really nice proof. -Euclid's proof of the infinitude of primes. A VERY old theorem but the proof is strikingly elegant. -Prime Number Theorem & Dirichlet's Theorem on Arithmetic Progressions This...

http://en.wikipedia.org/wiki/Converse_%28logic%29#Converse_of_a_theorem

Typical graduates from my undergrad degree go into things like finance/risk analysis/applied mathematics consulting for companies like CSIRO. A PhD offers the same opportunities with the additional option of academia. (Which is the main point of a PhD and is what I have my heart set on). The...

Cool! I hope that works out for you.

+1 By the way, what are you planning on doing?

Prefer uni. People are more mature and you have the freedom to make what you want out of yourself academically and socially.

In fact, I think a maths hd average is MUCH easier to attain than a humanities hd average.

I respectfully beg to differ. The further you go in life the more you realise that hard work trumps nearly any amount of natural talent. MX2 is certainly not so difficult that natural talent should pose a real barrier to those who are determined enough.

Perhaps the mathematics faculty is separately moderated. Out of the people I knew well in mathematics at usyd, (mostly those who did honours with me), somewhere between a third and a half of them would have had a HD average through their undergrad. Mind you, 3% of the candidature for the...

Estimate of what?

For mathematics/sciences an 85+ HD average is more common than you would think. In the context of your question, 75+ for commerce is decent enough that it won't hurt you at all.

The 1 and -1 are no problem here as they are removable singularities. It is understood that you just give the integrand the value that would make it continuous there. In fact you could take a continuous function on the interval [a,b] and change it at a countable number of points without...

Best.

I know plenty of dropkicks are both unis. That doesn't necessarily reflect on their 'prestige'.

oh sd...

I'm not one of those people who looks down upon other subjects, although many pure mathematicians DO look down on other sciences a bit. This is often on the basis that what constitutes proof in the sciences pales in comparison with the rigour of mathematical proof. A physicist/chemist/etc never...

This can be done without any integration :).