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Well i'd be starting from 3rd year, so i assume either way i wont be doing it :p But yeah, i always take advanced maths when offered. As for stats, i dont mind it, i just never want to do it again. But like jm said, i do see its value to some areas. I'd take stats over applied any day if i had...

^^do you mean if n=k is true than n=k+1 is true?

10 - MATH2601 15 - MATH2130 23 - MATH1081 23 - COMP2041 24 - COMP2121 ghey

a3 + b3 = (a+b)(a2 - ab + b2) a3 - b3 = (a-b)(a2 + ab + b2) Negative when its the sum of cubes, positive when its difference of cubes

Chances are the people who posted in between his were deleted

Un = 52n+3n-1 divisible by 9 U1 = 52 + 3 - 1 = 27 = 3x9, so its true for n = 1 Assume its true for some integer n≥1 ie. Un = 52n+3n-1 = 9m for some integer m then Un+1 = 52(n+1)+3(n+1)-1 = 52n.52 + 3n + 3 - 1 = (9m - 3n + 1).25 + 3n + 2 (using the assumption) = 25.9m - 75n + 25 + 3n + 2 =...

Thanks for bumping a 4 year old thread to tell us that, champ

Avoid them!? They're the best ones, don't get me started on applied! :p

There is not a huge difference between the UNSW and USYD IT and compsci, however there is a difference to UTS. IT at usyd has a really high uai cut off and only offers 40 places, but its pretty similar to normal comp sci. I can't comment on UWS and MQ as I havent had too much to do with those...

jm and others, any idea about the difficulty and standard of pure maths at uow? I'm considering it

Well another way to get pi is using the circumference formula: C = pi*d, ie. pi = C/d so in the shapes they take C = perimeter, d = diameter. Thats how they get those values

Yes, you can put as many sides as you want. The more sides you put, the smaller the length of the sides becomes. As the amount of sides goes off to infinity the polygon actually becomes more and more like a circle. Edit: http://ganley.org/software/pi.html That shows graphically what happens

The area cant be infinity, if you're sticking something inside a circle that has finite area, then the thing you stick inside it must have area less than or equal to it. To get the value of pi, you inscribe an n sided polygon into a circle of radius 1 (the area of a circle of radius 1 is pi)...

In general, so long as all your steps are reversible its fine

Some random discrete ones: 1. Prove there are infinitely many primes 2. Prove is a = b (mod m) then gcd(a,m) = gcd(b,m) (note = means congruent here in the mod case) 3. Prove that if n is prime, then for all integers a and b, if n|ab then n|a or n|b 4. If a and n are integers, prove an-1 is...

Yes, but that constant has a particular value, which should be 3/sqrt(2) i think (correct me if wrong, havent done these before).

If you convert to standard units and do the same thing you'll find the answer is 0.02 m3/s which is the answer both Riviet and tristambrown got when you convert to mm3/s

Firstly E(g(X)) = E(E(g(X)|Y)) Proof: Let h(y) = E(g(X)|Y) E(E(g(X)|Y)) = E(h(y)) = int h(y)f(y) dy = int (int g(x)f(x|y) dx) f(y) dy = int int g(x)[f(x,y)/f(y)] f(y) dxdy = int int g(x)f(x,y) dxdy = E(g(X)) So var(X) = E(X2) - E(X)2 = E(E(X2|Y)) - E(E(X|Y))2 = E(var(X|Y) + E(X|Y)2) -...

If i recall correctly the proof of the first question is just a corollary of another theorem

Haha no responses for a few days :p Well, for X is a p*q matrix. prove that (X'X + a*I) is invertible for any positive a. Would you use that if det(X'X + a*I) = 0 then (-a) is an eigenvalue of X'X? So all eigenvalues are negative and thus det(X'X + a*I) =/= 0 for positive a.