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there is a perfect square screaming out. once you have that, it falls out nicely.

simplify (x+a)(x-b)(x+c)(x-d)...(x-z). "Life has real and imaginary parts. Therefore, life is complex."

don't mean to offend or pick on anyone, but you really should make the effort to go to the lectures. I admit that I didn't go to all my lectures, but in hindsight, I think I should have... Reason? The lecturers I know actually put some effort and thought into what they teach, even if they...

I am not sure what has been done in lectures so far, but it was just mainly complex numbers in the tutorial for week 2, and also for week 3. No-one likes to fail, and it is best avoided. Just keep up with each tutorial's work, and do the proper tutorial in each week. If you don't understand...

Damn. I'm being delusional again! Keypad: Taylor was a guy. Taylor series are approximations to a function using polynomials. The coefficient of $x^n$ is given by the nth derivative evaluated at 0, divided by n!...technically, what i just described was a Maclaurin series, which is a...

oh crap! have they taken it out? or was it never in the syllabus, and me just getting delusional again? I thought I remembered doing Taylor series in class.... didn't mean to scare you... anyway, then...since Taylors series is an alien concept... In short, e can be written down as an...

Free parking is available to motorbikes! Only at specific spots available to only motorbikes, though...but they are never full and you always get a spot.

Which book may this be? Is it Hardy's "A Mathematician's Apology"? for interested parties, 1729 is the smallest positive integer that can be written as a sum of two cubes two different ways, namely 1729 = 1 + 1728 = 1000 + 729.

dark_angel, it will do you no harm if you work through the question from the 1993 paper. Then buchanan's pdf file might make more sense. just by looking at buchanan's pdf file, it's hard to appreciate the simplicity and the ingenuity of the approach. It doesn't explain why one would consider...

Xayma, was the 1729 a legit question? or were you just quizzing? Ramanujan became a famous mathematician. This is amazing for someone who had no concept of proof in mathematics, yet conjectured many deep (now) theorems...

there are two answers: one answer is that it is the cab number which Hardy took for his visit to Ramanujan.... I'll leave the other (mathematical) one for the quizzer... Ramanujan was quite a mystery...

It all depends on what you know, and what you need it for. For exams, they would not ask you to simply prove the irrationality of e. They would guide you through it. This has been done before in previous 4-unit HSC exams, usually in question 7 or 8. There is no 'standard way' of proving...

most primes are odd, 2 being the only even prime. Note that 1 is not considered a prime. If an odd number were a sum of two primes, one would have to be 2, making the other number 2 less. The 2-less number is not always prime (eg. 11=2+9). This should make you change your conjecture. On...

i hope i'm not missing something....but i don't see how 15 can be written as a sum of two squares.... 1+1=2 1+4=5 1+9=10 4+4=8 4+9=13 9+9=18 hatty, i am not a legend.... I just have no life...

what does the : mean?? could you give an example of a simple situation, like the odds of a heads on a fair coin using this : symbol? the odds of getting 4 on a fair dice?

From what I can remember, you don't actually prove anything as such. Probably the biggest thing you 'prove' is DeMoivre's theorem. It is easy to prove when n is an integer (induction), but much harder if n is not an integer....first prove it when n is rational, then when n is...

my bad...thanks Affinity. I do mean a+ib as a zero. That is the definition of conjugate, but you can just remember that for complex numbers, the conjugate of a+ib is always a-ib.

There is a real mathematical definition of what a conjugate is. For what you need, though, it is enough to remember that the conjugate of a+ib is always a-ib. For those that are interested: for a complex number a+ib, there is an irreducible real polynomial which has a-ib as a zero. The...