The need of having done a class "formally"
I'm (something like) a master student in Europe, now being in my first year and I have the following problem: Last semester I was attending lectures on QFT, but I haven't done the exam/assignments, since it was way too much for me that semester and...
We have been discussing this topic with my classmates recently, and I find it quite interesting, so I also want to ask you guys:
1. For how long can you study without taking a break?
2. How long are your breaks?
3. What do you do in the breaks?
If you're interested in hep-th, then you might consider: Cambridge, Oxford, Imperial College London, ETH Zurich, LMU Munich, University Utrecht. They all have very good reputation in hep-th and I think that all of them offer master's degrees in theoretical physics.
As to what your chances are...
I'm interested in doing my PhD in theoretical and mathematical physics - i.e. subjects like Quantum Field Theory, String Theory or Quantum Information Theory. My question is which universities in the US have really good programs in these areas?
It depends on whether you want to do theory or experiment.
If it's theory, then theoretical/mathematical physics would be the right field, with taking some additional math and computer science courses, like Functional analysis, Advanced Algorithms, Complexity theory, Coding Theory,...
In...
Aah, I see, the problem with my formula was that if I changed f, x_i would change too. Your picture, jtbell, explains it very well. Thank you very much for your time.
This is perfectly clear.
This is the critical point. Let's say that the heigth of the object is y_0, the focal length is f, and the distance from the focal point to the film is x_i (as in the first picture in http://www.inyourfacefotos.com/fstop.htm). Then by similarity of triangles the...
ooops, you're right of course, N is the inverse of the f-number.
Anyway, I still seem to misunderstand something. I found this 'derivation' of the equation, here: http://www.inyourfacefotos.com/fstop.htm , although I quite don't understand some of the steps there (even if it's elementary...
Well, it's actually in most of the books on photography, but it's never derived. They say, that when you change the aperture by a factor of sqrt(2), the intensity of light will change by factor 2.
I've been searching through the internet and some of my optics books, but nowhere was I able to find the derivation of the law for a camera lens, that the intensity of light that comes on the film or chip is proportional to \frac{D^2}{f^2}=N^2, where D is the aperture diameter, f the focal...
Has anyone done this?
I'm a physics major and I'd like to pursue a degree in mathematical physics. I guess that physics GRE is expected from me as a physics student, although actually I feel much more comfortable in math.
Do you think that it would be hard to make both? Would it make me...
Traditonally, it is about solving mathematical problems that arise in physics (and are too difficult to be left to the physicist :-) ) - like finding a solution to some PDE, making integral transforms, minimizing some functional,...
But it can also mean mathematically rigorous study of...
The answer is definitely Differential Geometry, especially when you want to do QFT, where it is widely used. It will also give you much insight in other subjects (apart from the obvious GR), like classical mechanics, electrodynamics, advanced QM,... it's everywhere.
Real analysis might be also...
I'm applying for a masters degree on an European university this year. I have an almost perfect GPA of 3.98, I took some pretty advanced classes and have two years of research experience, but the problem is with the letters of recommendation.
They require me to send one letter of...
yeah, but I'd like to know where exactly the points are, so the method I'm searching for should be using some kind of interpolation and then find the zeros.
Hi,
does anyone know of some nice root-finding method (preferable GSL :-)) for a data set - i.e. I have a set of 3D data (x,y,z) where z = f(x,y,) and I want to know where the zeros of f are. I guess, I could write it myself with some interpolation method, but just in case someone knows...
:rolleyes:
The ball was just an example. The objects that I'm working with are much complicated.
I'm not really sure if interpolation is what I'm searching for.
Well, let's say I have some 1000 points which form (or should form) a ball, for example. What I want to get is a nice, smooth 3D ball. Is that possible?
I have a set of 3D data (i.e. a large file where each row contains three spatial coordinates) and I'd like to get a nice, smooth 3D object out of it. The objects are not surfaces, so it's not just plotting a function (i.e. to every (x,y) there exists more than one z).
Does anyone have an...
I'm really stuck on this simple problem: Let X be a topological vector space and U, V are open sets in X. Prove that U+V is open.
It should be a direct consequence of the continuity of addition in topological vector spaces. But continuity states that the f^{-1}(V) is open whenever V is open...
Well, I don't know how about the OP, but I'm studying in Austria and we have a three year bachelor degrees here. After completing the bachelor degree you apply for a 2 year master degree (and after that you can apply for a 3 year Phd.).
As far as I know the usual bachelor degree in the US...
How do I transform a second-order PDE with constant coefficients into the canonical form?
I tried to solve this problem:
u_xx + 13u_yy + 14u_zz - 6u_xy + 6u_yz + 2u_xz -u_x +2u_y = 0
I wrote the bilinear form of the second order derivatives and diagonalized it. I found out that it is a...
Well, I tried both, but the problem is that I still miss some kind of inequality that I could use.
I mean - if I want to show the continuity for example - I have to show that:
\forall \varepsilon > 0 \quad \exists \delta >0 \quad \forall g \in C([a,b]) : \rho(f,g)<\delta \quad |\int^1_0...
This seems to be a very easy excercise, but I am completely stuck:
Prove that in C([0,1]) with the metric
\rho(f,g) = (\int_0^1|f(x)-g(x)|^2 dx)^{1/2}
a subset
A = \{f \in C([0,1]); \int_0^1 f(x) dx = 0\} is closed.
I tried to show that the complement of A is open - it could be...
Well I think you got the concept, but what you wrote is not allright.
L is a normal function which you encountered in multivariable calculus. It's a function from (R^3 x R^3 x R) to R. q is a function from R -> R^3 and so is q'.
The core of the chain rule is the fact, that the function is...
Well, q depends on t, but you don't know how, which makes it an independent variable.
Lets say that you have
L = q + q'
q = t^2 + 5t
q' = 2t + 5
Now you cannot write L(t) = t^2 + 7t + 5 but you have to write
L(t^2 + 5t, 2t + 5, t) = t^2 + 7t + 5
Makes more sense?
I think I now what you're asking, but it's just a mathematical and terminological question.
Consider this example:
f:Rx[-1,1]x[-1,1] -> R f(x,y,z) = y + z,
g1: R -> [-1,1] g1(x)= sin(x)
g2: R -> [-1,1] g2(x) = cos(x)
denote y =g1(x) and z = g2(x) , f(x,g1(x),g2(x)) = f(x,y,z);
Now...
Well, we are not using anything from the Lebesgue integration theory, we didn't even mention L^2 spaces.
Does that mean, that what we're learning ther is useless :smile: ?
I'm just taking Calculus 4 this semester, where part of it is also Fourier analysis.
When I was browsing a little bit about the subject I found out that there are several different approaches and so I'm a bit confused now.
So this is how I understand it, correct me if I'm wrong:
There...
:smile: Thanks, sometimes I just read to quickly.
The proof looks nice, but since I haven't taken any measure theory yet, I'm not sure about the details, but I'll try to catch that up.
Thanks once again.
I'm sorry, but I couldn't really follow your argument. I think you showed something else - namely that if f>0 (or f<0) almost everywhere then the integral can't be equal zero, which is a well-known fact.
But you skipped the case of f being oscilating (around zero) almost everywhere .
A function which is discontinuous everywhere can be Lebesgue integrable - for example the characteristic function of the rationals.
The problem of the characteristic function is that it is equal zero in every irrational point.
Is there a function f: R->R, such that:
\forall x \in \mathbb{R}: f(x) \neq 0 \wedge \forall a,b \in \mathbb{R}: \int_a^b f(x) dx = 0
I made this problem myself so I don't know, wheather it is easy to see or not. The integral is the Lebesgue integral.
I would say, that there should be...
I'm reading a book on electromagnetism and I am a bit confused about some things in Maxwells equations. This is what I don't like about many physics books: they are very wordy, but at the end you don't know what is an experimental fact, what is a "theorem", what is an assumption and so on...
I don't really understand what you mean, can you give an example?
To StatusX:
Can it be proven, that if f is not measurable, then the integral is not linear?
Basically, what I want to know is - I try to imagine that I'm in the position of Henri Lebesgue and I have to define a new kind of...
I have one more question about the Lebesgue integral:
What if we defined the Lebesgue integral like this:
Let X be a measurable space and f any nonnegative function from X to R.
Then the Lebesgue integral of f as \int_X f d\mu = sup(I_X) where I_X is the integral of a simple function...
integral more general than the Lebesgue integral?
The Lebesgue integral is defined for measurable functions. But isn't it possible to define a more general integral defined for a larger class of functions?
I guess that we would then loose some of the fine properties of the Lebesgue integral -...