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    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...
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    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?
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    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?
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    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...
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    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...
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    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...
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    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...
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    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...
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    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...
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    What are these functions called?

    Is there any name for the functions for which |f(x+y)| \leq |f(x)| + |f(y)|?
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    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...
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    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...
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    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...
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    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...
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    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...
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    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...
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    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 -...
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    Lebesgue measure

    Hi, I'm just reading Rudin's Principles of mathematical analysis - the last chapter on Lebesgue integration and I am having a bit trouble understanding the motivation of the definition of Lebesgue measure. This is how I understand it: We want to measure sets in \mathds{R}^n so what we...
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    Lagrange equations with constraints

    When we seek the extreaml value of the functional \Phi(\gamma) = \int_{t_0}^{t_1} L(x(t),\dot{x}(t),t)dt where x can be taken from the entire E^n then we come to the well-known Lagrange equations. Now when we are given a constraint, that x \in M, where M is a differentiable manifold and when...
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    Proof of the implicit and inverse function theorems

    Today I revised my knowledge from multivariable calculus and I found that I couldn't remember the proofs of these two theorems. Then I looked in Rudin, and everything was clear. Except one thing, which probably made me forgot the proofs. There are two weird functions in these two proofs...
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    Plotting and modifying graphs

    Hi, I have to draw this kind of graphs on the computer: [Broken] [Broken].[/URL] I tryed to plot the graph of the function in mathematica, export it into .wmf file and then add some of...
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    Is the d'Alambert principle universal?

    In a lecture on classical mechanics, the professor derived a formula, which is a part of the D'Alambert principle: \nabla \Phi_{\alpha} \cdot \delta \vec{r} = 0 where \Phi_{\alpha} are the restraints. He derived it in a strange way from the Taylor's formula: \Phi_{\alpha} (\vec{r} + \delta...
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    Series problem

    hi, I found this problem in Rudin, and I just can't figure it out. It goes like this: Prove that the convergence of \sum a_n a_n \geq 0 implies the convergence of \sum \frac{\sqrt{a_n}}{n} I tried the comparison test, but that doesn't help because I don't know what the limit \lim_{n...
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    Math knowledge used in theoretical physics

    Hi, as usual in September I am deciding which courses to take. I am in the second year of my study and so far I am following the more theoretical path, later maybe with focus on quantum mechanics and quantum information proccessing. My question is: which math courses should I take this...
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    Two questions on electrostatics

    Hi, I'm a bit stuck with some things in electrostatics. My first problem: in my textbook, when they try to derivate the formula for the potential of a point charge: V(b) = - \int E.d\mathbf{l} = -\frac{q}{4 \pi \varepsilon_0} \int_\infty^b \frac{1}{r^3} \mathbf{r}.d \mathbf{l} they...
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    Inscribing square into parallelogram

    what is the necessary condition (if there is any) for inscribing a square into a parallelogram. In other words, what should the parallelogram be like - so that we can inscribe a square into it.
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    Mode of 1,1,2,2

    what is the mode (modus) of 1,1,2,2 I was checking the definition but it didn't count with two maximums. So is it 1,5 or both 1 and 2, or none of them?
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    Stieltjes integral

    Can you give me a simple real-life problem, where you need to use Stieltjes integral and can you show how you proceed in solving this kind of problems?
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    Pronunciation of Feynman

    pronunciation of "Feynman" How is the "ey" in "Feynman" pronounced: 1. "ei" like in the word "hey" 2. "ai" like in the word "hi" 3. neither of 1,2.
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    Length of coiled tape

    Imagine you have a tape wrapped around a coil (e.g. an audio magnetic tape or adhesive tape). The thickness of the tape is T and the radius of the coil is R. The task is to determine the dependence of the length of the coiled tape and the radius of the whole (coil + tape). (e.g. - if I know...