Recent content by Jaunty

As far as job opportunities, it of course depends on what degree you have. If you get a bachelor's in astrophysics, then you have pretty much the same job opportunities as someone with a physics or math degree - most quantitative careers that aren't research/teaching focused. Some examples...

Yep! Although the events are not simultaneous in different frames, the different observers will always agree on what frame the events are simultaneous in. So the guy on the ground can observe the events to be simultaneous and the guy on the train can observe them not to be, but the guy on the...

As far as understanding the implications of GR and getting some intuition for what's going on, I don't think there's a better book than Exploring Black Holes by Taylor & Wheeler. It's written using high school mathematics for the most part (basic algebra and a tiny but of calculus) and provides...

Yes, a functional is a mapping with additional requirements (those of a function to scalars). A mapping that's not a function could be anything that takes one input element to more than one output element (eg. the graph f(x) = \pm \sqrt{x} would assign 2 to two values, \pm \sqrt{2}). Actually, a...

Yes, a tensor is mapping (an assignment of elements in one set to elements in another set). The rank will specify from what to what (eg. a (1,1) tensor can be thought of as a mapping from a vector to a dual vector, a dual vector to a vector, or a pair consisting of both a vector and a dual...

Oh weird, when I learned this notation (0,1) and (1,0) were flipped - (1,0) was a vector and (0,1) was a dual vector. Here's another way to explain why the dual of a dual vector is a vector (everything here will be finite-dimensional of course): Say we've got a vector v \in V, and a dual vector...

Oh, all it means is that of the many connections one could choose - many ways of transporting vectors between tangent spaces - you pick the one that makes the covariant derivative of the metric zero, \nabla_\rho g_{\mu \nu}=0. This is only a point worth making if you've already studied...

Eredir, You are absolutely correct that the solution to Einstein's field equations are a differentiable manifold M together with a pseudo-Riemannian metric (usually a (3,1) one). A priori, there is not much of a relation between the metric and the underlying manifold - mainly the manifold...

The excellent book Mathematical Physics by Hassani has a proof of the spectral decomposition theorem for finite-dimensional vector spaces. As a corollary, a normal operator (one that commutes with its adjoint - more general than simply Hermitian) has eigenvectors that span the space. To be...

Well, it depends on your background. The book Quantum Computer Science by Mermin is a good intro to the subject written for people with a CS background. Taking quantum mechanics classes certainly won't hurt (I would even recommend it!), but most of the material you'll see won't be very relevant...

Okay, you're just making a small mistake when you're turning index notation into matrix notation. You're right that X^{\mu}{}_{\nu}=\eta_{\nu \sigma}X^{\mu \sigma} Now since we're writing this in terms of indices, it doesn't matter which order you write \eta_{\nu \sigma} and X^{\mu \sigma}...

Hey Dragonfall, I'm also thinking about getting into quantum computing (theory), and as far as I can tell it's a smaller field than most (in terms of both people & funding). As it is, CS theory in general is rather underfunded as compared to most fields in physics. Barring some breakthrough...

As I mentioned, both classes will be very useful to you - take whichever one you prefer at the moment (ODEs are also a good choice btw). As for research in applied mathematics (and pure math as well), it's a huge field and your best bet is to just check your department's webpage for a list of...

Hi PieceOfPi, These are both really useful classes if you're planning on using a lot of applied math in your future - you should definitely take both eventually. I assume the CS class you're talking about is more of a programming course than a course on say complexity theory. If so, then I...