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't Hooft goes through such a calculation in his lecture notes on general relativity. (Any other good account of GR will do something similar) http://www.phys.uu.nl/~thooft/lectures/genrel.pdf Hope that helps. If not, let us know.

Things that bad in Glasgow? With more and more people getting degrees in all kinds of subjects it does lower the reputation of "proper" degrees and makes job hunting harder. It also means that in order to stand out you need a postgraduate degree.

Last week I had a student ask about how to differentiate something like [math]\frac{x}{x^{2} + y^{2}}[/math] wrt [math]x[/math]. He was sure a log function should be there somewhere! This guy was a level 2 mathematics student!

To teach in a UK state funded secondary school, you will require on top of the BSc a PGCE. That is a Postgraduate Certificate in Education. In colleges and universities, there is no formal requirment as such but a PhD would be the norm. As for the rest of the world I have no idea.

Back to the original topic. Light is special because light cones are identical to causal cones. (In the geometric optics approximation within classical GR) Why I do not know.

For most of us it is a lot of hard work. I would not say that am particularly gifted in science or maths, just that I am willing to put in the effort in what are difficult subjects. There are those who for some reason are "gifted", but most of us are not.

hi pcgeek, I like your signiture. It is what I have been stressing to some of my mathematics colleagues! A little physics can be very useful.

I would call a course on Hilbert spaces "functional analysis". It is the infinite dimensional version of vector spaces and operators. It is fundamental in quantum physics.

I did see prof. Hawking at a conference at Imperial. I was not as close as Swanshot! He gave a talk on the second day of the conference, but I was unable to attend the second day and missed it.

Linear algebra = vector spaces and their operators.

I agree with everything that Severian said. (He talked about superspace formulation of supersymmetry, it is not the only way, but in some sence it is the best). Even more basically, supersymmetry is a non-trivial symmetry that a theory with both bosonic and fermionic degrees of freedom can possess. Wroughly it means that we can interchange the fermions with the bosons and vice versa leaving the theory unchanged. There is a lot of interesting mathematics that has been developed to deal with such theories. It goes under the general heading of supermathematics, I work on an area of this known as supermanifold theory.

Isn't this related to the notion of irreducible polynomials and Galois theory?

I agree with woelen, I don't think there is a definition of "simplify". However for your expression you could use the difference of two squares to cancel a y+z in the denominator.

Absolutely correct. In a "practical" situation I would use L'Hopital's rule, but for a rigid proof it may not be the best approach.

The problem with L'Hospital's rule is that it requres one to know what derivatives are and as such what limits are. It can be the case that you have a circular argument, one needs the derivative that depends on the limit you are trying to prove etc... So I would say be careful with L'Hospital's rule.

Equations only "look" complicated because of the notation used. Simple looking equations may hide very deep facts behind the notation. Part of mathematics is trying to find "better" notation so that things look "obvious". So really, you have to think about the notation used rather than the equations themselves.

If we take string theory as a serious candidate for a description of our world then we a forced to believe that extra dimensions exist. Technically, quantum string theory is inconsistant if it is not formulated in 26-d for bosonic strings and 10-d for superstrings. The reason is that these theories have a conformal anomaly in any other dimension and this spoils the quantum description. (It can also be understood as the no-ghost theorem and via BRST methods.)

I don't hate women at all. Just I know I will NEVER let one hurt me again.

I have been in a very similar situation. You can't trust women period. You are too young for this kind of shi*t. Forget her and have fun. Whatever you do don't do what I did, 4 year booze fuled hell.

I have now put a version of this package on my website. I have also included a notebook with some elementary examples and a short article about the package. It should be considered work in progress as I will continue to improve it. If anyone is interested that is...

I would avoid the term relativistic mass at all costs. Mass is a parameter in the Lagrangian that would correspond to the so called rest mass of a particle.

Woelen, you can think of it that way.

I was not sure exactly what the question was. Of course Atheist you are right. As light carries energy-momentum it will curve space-time.

True, you can set up coordinates that mean that locally the light rays are travelling in straight lines. Light rays can be though of as "mapping out" the curvature of space-time. This leads to the prediction that light is bent around a massive object. This was observed by Eddingtion in 1919. This effect is now known as gravitational lensing and is being used to try to detect dark matter, cosmic strings and other objects.

If you mean in a gravitation field then yes. According to general relativity, gravity is the bending of space-time. Light rays now do not move in straight lines but instead follow the anologue of a straight line known as a (null) geodesic.