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All I listen to these days.

Think about proving the other direction - i.e. don't assume that p, q, r are vertices of an equilateral triangle.

I don't think that's sufficient for an iff proof. [EDIT: seanieg89 has addressed this already]

Haters gon' hate. Drongoski is one of the most talented and generous frequenters of the mathematics fora. If someone continuously asks questions, it's not so bizarre to offer them tutoring.

Hmm, I just noticed that it's 700mb...

For History/Memory I read 50 pages of The Fiftieth Gate. In trial got 20/20 for essay.

Absolutely - I thought you were strictly asking about majors. Personally, I preferred the first course MATH1151 to MATH1251 (second). Both are fantastic though. A nice introduction to the difficulty/rigour you can expect later.

Probably the two best "first year" subjects are FINS1613 (business finance) and ACTL1001 (introductory actuarial subject). Very indicative of major.

MX1, MX2 and Chem?

Yeah, it's definitely a good combination.

Not really - the actuarial major has I think 8 actuarial courses. The quant major has 2. Doing quant, you can't become an actuary...(unless you do actl/quant which a LOT of people are doing). Quant is math school and actl is business school - fundamentally different.

Well, I'm doing Finance/Quantitative Risk. To be perfectly honest, this is how it works: Every Tom/Dick/Larry who wants to get into the financial sector will hold a Commerce degree majoring in finance. Some lucky few will have this combined with Adv. Mathematics, a degree the financial sector...

Hey there. Commerce/Adv. Math is quite an interesting degree (thus far). I'm only in second year though, so I can't comment all that much. What majors are you considering? First year was genuinely very bludgy and you shouldn't have any issues maintaining a 70+ WAM. With an average amount of...

Hey there, sorry for the late reply. I actually don't have any preliminary papers unfortunately. When the time comes for HSC papers though, feel free to ask - I have millions. All the best.

It works in much the same way. Once again, you are interested in two letters out of four - arranging them gives 4P2. Now you need to arrange these two with the two you've already chosen. Treat it as if you haven't arranged anything yet - 4! * 4P2. Since you've actually arranged two already...

Personally, combinations make more intuitive sense to me. We want to find how many different 4 letter words can be made containing R and S (and subtract it from 360). Since we already know it contains these two letters, we need to choose 2 letters from the remaining 4 (i.e. 4C2). Then we...

\text{Too many unnecessary steps.} \,\, \text{Note that:} \\\\ x^{3}-x^{2}-x+1=x^{2}(x-1)-(x-1)\Leftrightarrow (x^{2}-1)(x-1) \,\, \text{then it follows that}\sum_{cyc}\alpha ^{3}=\boxed{1}.

Some very unthoughtful responses. Any means of equivalence will suffice. Make sure in your first line you write something like: "This is equivalent to showing that:" and you'll be perfectly fine. LHS-RHS is particularly useful for inequalities.

Real root.

All day.