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This probably belongs in the extracurricular topics forum.

One of the advantages of doing the higher level courses is that you are much more likely to get lecturers as tutors. I think I only had one PhD student tutor the whole time I was at UNSW (and he was quite helpful, actually).

Well, I never claimed that it was the only solution. There are lots of theorems about writing numbers as the sum of squares, but I don't know anything about sums of cubes. Actually, I think the solution illustrates the fact that (1+2+3+...+n)^2=1^3+2^3+...+n^3 So any triangular number...

There are about a billion and one special functions like that. Logarithmic Integral -- from Wolfram MathWorld There is also a sine integral, cosine integral and an exponential integral, and so on.

100^100=100 x 100^99 = 100 x (100^33)^3 100 = 1+8+27+64 i think you can work it out from there.

Nothing, you've used a different trig identity, that's all. The answer according to BOB comes from using the identity cos(3A) = 4 cos^3(A) - 3 Cos (A). If you graph the two answers you will find that they (a most) differ by a constant. This happens a lot when doing calculus with trig functions.

You do what I would call enlightened trial and error: (1) Sketch both graphs on the same number plane to confirm that there is only one solution. (Also gives you some limitation on the size of x and y.) (2) Realize that the RHS of both equations is a whole number, which implies that x and y...

How many students want to do honours each year anyway? TBH, you don't want a supervisor who has lots of honours students, as they won't be able to help you much, and you'll be left to flounder on your own. Survivor, how competitive is it to get into honours in BABS anyway? (I get the...

Yep. Basically, PHYS111= physics without calculus, PHYS1121= physics with calculus. Since you have done all that calculus and applications of calculus in 4U, you should be fine.

If you did OK in 4 Unit Maths you should be able to cope with PHYS1121.

They used to say that it has 15% more content. I think it has the same content, just taught in a more theoretical manner.

Talk to someone in Student Central.

The main reason why you should do MATH1141 is because you learn more. If you're not a maths major or planning to do a substantial amount of maths later, I don't think it is really worth it. There are more Ds and HDs given out for 1141 compared to 1131, but you will have to work for them.

You need to do MATH1131 if you are a maths major. You shouldn't take MATH1031, as you won't be able to count both 1131 and 1031 towards your degree. In second semester, you do MATH1231. MATH1031 is for people doing majors like biology who are required to do some first year maths (I think...

I agree with you. The changes they were suggesting c.18 months ago weren't improvements at all. I think the best we can hope for from the national curriculum is that they leave it vague enough that NSW can continue with business as usual (at least, as far as the calculus based maths courses...

Until national curriculum is decided it is all up in the air.

I did PHYS1121 and MATH1081. I didn't particularly like PHYS, though it probably does help to have done it if you ever want to teach the mechanics section of 4U Maths. (I should add that it is quite possible that by the time you graduate they will have dropped mechanics from the 4U syllabus...

I have just checked Coroneous' Year 12 3 unit book, and he does rabbit on a bit about the signs of f(x_0) and f''(x_0), (it is on pp267-268 of the edition that I happen to have). I would like to draw your attention to the following quote (which is italicized in the original): "However...

Yes, Newton's method does not guarantee convergence to the closest root in all cases. But the idea is that if the initial guess is *close enough* to the root, and the root it not at a stationary point, the method will converge. (Unfortunately, it can be very hard to figure out how close close...

It is quite possible. You just have to keep checking.