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You're done with exams now, right?

That seems right but I don't really see how that constitutes a proof satisfying the 'iff' condition.

Yes.

I don't think that's entirely correct as it is because you assumed there that alpha and beta are real in order to have obtained your inequality (a-1)(b-1)>0.

I just like reading books and to be honest it really isn't that difficult to compute various things taught in Vector Calculus. It's very much like High School except it has Matrices in it in the case of the Hessian Matrix or the Jacobian Determinant as you said. Very mechanical processes. Take...

Well the coordinate of the vertex is trivially (-2,1) very much like the centre of a circle. And I don't get what you mean by the coordinate of the parabola? I don't see a locus anywhere here...

Can't wait to go to Uni!

Are you talking about Differential Geometry? I flicked through a book on it the other day and it really seems to be heavily reliant on Metric Spaces and more advanced Vector Calculus.

At the moment, leaning towards Analysis moreso anything else. Not really the Calculus-ish Analysis where it's just mindless computations for the most part, but I'm talking about deeper definitions, Series and nice integrals like the Gaussian Integral or the Sine Integral. It's strange, I like...

Maybe next term?

This.

I don't remember doing a Cambridge question on it, but I'm not surprised that it included the Folium in it. This is what I love most about the Cambridge book, much more sophisticated and clearly written by a Mathematician as opposed to MIF. Well the Double Integral is a little bit more...

I took a look at it earlier but he didn't let me keep it. You can find areas of cool parameterised curves like the Folium of Descartes using Double Integrals. Beforehand I actually had no idea how to find the area of such things. You can also prove that the are between a Hyperbola and its...

If it makes you feel better, I found your signature to be really funny. What games?

Carrotsticks, can you please bring your Uni stuff that is remotely relevant to elementary Mathematics for me to look at? But if I'm the only person who's interested, then never mind.

Sy123, to test your hypothesis you could have easily deduced a class of angles that could have been expressed in this form by having the cosine of an angle in a similar closed surd form, then using the Pythagorean Identity and equating it with 1 so we have two surdic expressions summing up to be...

In all honesty Drongoski, I think the whole idea of "Showing that you test 180 or else you lose marks" is very silly. It can very be easily seen and instead of deducting perfectly good students for it, the Examination Committee could simply include questions where 180 is indeed a solution, and...

\\ $Consider the polynomial $ P(x)=x^2+bx+c. $ Show that $ |x_i| < 1 $ if and only if $ |b| < 1+c < 2. \\\\ $ Extend this criterion to a cubic polynomial $ P(x)=x^3+bx^2+cx+d $ by showing that $ |x_i| < 1 $ if and only if $ |bd-c| < 1-d^2 $ and $ |b+d| < |1+c|

Your method works, but it doesn't exactly give a general equation. Suppose you wanted to calculate a similar condition but with gradient 2, then you would have to do that all over again whereas Carrotsticks' method has a general form where you simply substitute m=k for any real k.

As I said here.