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Bx is also an eigenvector, hence it is also in the eigenspace of lambda. What does this tell you about the form of Bx?

Presumably you are expanding around x=0? sqrt(1+x) = 1+1/2*x-1/8*x^2+1/16*x^3-5/128*x^4+7/256*x^5+... First, substitute in -9*x^2 where every you see an 'x' in the first series (this gives you the Taylor series for sqrt(1-9*x^2). Then multiply every term by x^2. And truncate, to give you...

Yeah, Sylvester's law of inertia. It's the same thing.

You remember quadratic forms from linear algebra?

I think you've made a mistake in the third line. lolokay's method is far more interesting - just make sure that you substitute for the limits of integration as well...

Apart from MATH3411 mentioned above, you could have a look at the 3rd year number theory course, Algebraic Techniques in Number theory. UNSW Handbook Course - Algebraic Techniques in Number Theory - MATH3521

You might also want to consider doing MATH3411 Information, codes and ciphers at some point (after Finite).

I think the idea with tutorial participation marks is that if the tutor likes you they give you good marks and if they don't like you then they don't. If they don't even know who you are, I guess you have a problem.

I assume that this is for a physics assigment? If so, a sufficiently accurate numerical approximation to the problem should suffice. The Airy function is defined as the solution to the DE y'' = xy. That equation you have is an alternate representation of the Airy function. In this case...

1) Yes, there is, but only if you do the higher version of a subject. 2) Nobody knows, because they make it up on an ad hoc basis. 3) No. This isn't the HSC. Do a subject if you think it is worthwhile doing, not because they play funny games with the scaling.

Re: "Bachelor of Science (Advanced Science) with major in blah" -- this could be real Yeah, and doing a double degree means that you can usually escape doing Gen Eds.

When you multiply an even function by an odd function, you get an odd function. You may wish to pause and consider the arithmetic of positive and negative numbers to realize why this is so.

For the next bit, show that if P(x) is an odd polynomial (presumably an odd polynomial is a polynomial consisting of odd powers of x), then it is an odd function. Then use what you have proved in part (i) about odd functions to show that if P(x) is an odd polynomial, then P(0)=0, hence, x...

Yeah, I think you can use the Cayley-Hamilton theorem to show something like that.

Re: "Bachelor of Science (Advanced Science) with major in blah" -- this could be real The problem with advanced science is that many of the people with "better" scientific ability don't do advanced science - they do double degrees. So it is a bit hard to market an elite course that doesn't...

Not all matrices have an inverse, so it can't be true in general. If the matrix A is a rotation matrix, i.e., it has the effect of rotating a vector through 2pi/3, however, you can see that A^2=A^-1.

OH, I should probably add that I have no idea how a fail will affect your WAM, but I am sure that it can do it no good.

OK, I'm a graduate too, so maybe I should comment. There is no WAM on your transcript or testamur. The transcript simply lists the subjects that you did and what marks and grades you got for them. WAM is something that the uni calculates for its own internal purposes, and different bits of...

The statistics done at school is horrible. And it seems to be taking over the world at the moment - just look at the suggested new syllabus. The main problem is that, however useful, relevant and abounding with real world applications statistics is, students can't do anything beyond...

I don't think there are any compulsory subjects as such, but you have to do a certain amount of first year maths - there are several courses to chose from, depending on your background - and a certain amount of Level I subjects from science schools. It should all be in the handbook.