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1. The need of having done a class formally

yeah, I have been doing it informally, i.e. nothing will show up on my transcript.
2. The need of having done a class formally

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...
3. Study breaks

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?
4. MSc in theoretical Physics

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...
5. Mathematica Theoretical and mathematical physics grad schools

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?
6. Physics Career in Quantum computation

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...
7. F-number and light intensity

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.
8. F-number and light intensity

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...
9. F-number and light intensity

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...
10. F-number and light intensity

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.
11. F-number and light intensity

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...
12. GRE in both Math and Physics

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...
13. Non-commutative geometry

Lie group = group + differentiable manifold, hence knowledge in both algebra and differential geometry is needed.
14. Mathematica Mathematical Physics

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...
15. Real Analysis vs Differential Geometry vs Topology

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...
16. Letters of recommendation (for the 100th time)

Yeah, I'm going to ask both. But anyway, what if the I don't get it from the supervisor? Will it look suspicious on the application?
17. Letters of recommendation (for the 100th time)

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...
18. Zeros in a data set

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.
19. Zeros in a data set

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...
20. Plotting 3D data

It's about 30x30x30 points, more or less.
21. Plotting 3D data

: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.
22. Plotting 3D data

yeah, but those objects are pretty crazy and really far away from spheres. what kind of averaging schemes do you mean?
23. Plotting 3D data

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?
24. Plotting 3D data

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...
25. Simple topological problem

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...
26. What are these functions called?

Is there any name for the functions for which |f(x+y)| \leq |f(x)| + |f(y)|?
27. Programs Doing Master degree in US

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...
28. Programs Doing Master degree in US

No, he's asking if he can apply for a master degree in the US when his bachelor degree took only 3 years (compared to 4 years in the US).
29. Canonical form of PDE

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...
30. Closed subset of a metric space

Of course :rolleyes: - a little modified Cauchy-Schwartz inequality is the key. I hate algebraic tricks :smile: Thanks for help
31. Closed subset of a metric space

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...
32. Closed subset of a metric space

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...
33. Explicit vs implicit time dependence in Lagrangian mechanics

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...
34. Explicit vs implicit time dependence in Lagrangian mechanics

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?
35. Explicit vs implicit time dependence in Lagrangian mechanics

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...
36. Fourier analysis

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: ?
37. Fourier analysis

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...
38. Is there a function, that

: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.
39. Is there a function, that

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 .
40. Is there a function, that

nobody knows?
41. Is there a function, that

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.
42. Is there a function, that

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...
43. Farady's law and div B = 0

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...
44. Lebesgue integral once again

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...
45. Lebesgue integral once again

The set IS measurable, the FUNCTION is not measurable. Thanks, this seems to be reasonable.
46. Lebesgue integral once again

Why shouldn't the supremum exist?
47. Lebesgue integral once again

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...
48. Integral more general then Lebesgue integral?

And what if we changed open sets in the definition of a measurable function to some more general sets? What would be wrong?
49. Integral more general then Lebesgue integral?

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 -...
50. Lebesgue measure

Thanks, that claryfies many things to me.