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Hi again! Just dropping a message letting everyone know that the 2011 SUMS Puzzle Hunt starts next Monday! (26 Sep - to coincide with school holidays and Uni midterm break) Head over to our website at http://www.maths.usyd.edu.au/u/sums/puzzlehunt/2011/ to register a team. As usual, there are...

Hi everyone! I'm from Sydney Uni Maths Society (ΣUMS) and we're holding an online competition called the ΣUMS Puzzle Hunt. Those of you who like a bit of a mental challenge will enjoy this. You can form teams of up to 5 people for a chance to win prizes - with first place winning $300...

Hi everyone, Sydney Uni Maths Society (SUMS) is running a competition called the SUMS Puzzle Hunt, starting Monday (31st August). You can get into teams of up to 5 people for a chance to win hundreds of dollars worth of prizes - first place gets $300! Entry is FREE! There will be 20 puzzles...

Hi all. This thread is terribly out of date. I'm no longer in the business of private tutoring.

I don't believe you can have such a probability measure defined on the entire real number line which is uniform (which I suppose would reflect our intuitive understanding of 'at random'.) Suppose it did: Note that a requirement of being a probability measure in this scenario would be for the...

Does it mean, find the equation of the locus of R?

I don't think he was actually asking for a solution, more an interpretation. A diameter of any conic is a chord which passes through the centre (in this case, the origin). In this example you want to show that the midpoints of all chords PQ with gradient m lie on this particular diameter, given...

Or he could be working over the ring containing just {0}.

Well it is completely valid, though it seems a bit unnecessary, unless you were actually told to find the equation of the chord then sub the point in. Hint: note that cos(theta + pi) = - cos(theta) and sin(theta + pi) = -sin(theta) and the fact that the midpoint of any two points must lie of...

Just find the midpoint of P and Q :p.

I've done it plenty of times and received full marks. They're differentials. Plus, it makes integration by parts so much quicker and concise.

Q1. We shall do this by considering cylindrical shells of a small thickness, finding their volumes then summing to find the whole volume. For a typical point x between x=0 and x=2, consider the cylindrical shell generated by rotating the region between the curves from x to x + δx, for small...

milton: You can go one better and also say at least one of (n-1), n or (n+1) is divisible by 2, so the entire expression is divisible by 12.

I think that would only work if the acceleration is constant. It's been ages since I did physics, but equate the kinetic energy of the car with the elastic potential energy? I don't remember the formula for elastic potential energy though.

Another vote for Anaahhlysis.

I don't recall you being in my stats class last year Templar :p.

Sem 1: Metric Spaces (Adv) Rings, Fields and Galois Theory (Adv) Two 3rd Year Stats Adv units Maybe- Differential Equations and Biomaths Sem2: Measure Theory and Lebesgue Integration Adv Modules and Group Representations Adv Two other 3rd Year Stats Adv units Lagrangian and...

I found that HSC Physics was quite useless when learning uni physics. Ext2 Maths does help a lot, especially all the mechanics stuff.

You've hooked up at Olympiad camp Templar?

Re: BoS USyd Roll Call 2007! SeDaTeD B Science (Advanced Mathematics) III (Mathematics/ Statistics)