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    Proof of the Lindemann-Weierstrass Theorem

    I am wanting to find a good proof of the Lindemann-Weierstrass Theorem. Most importantly I need the part that states that eα is transcendental where α ≠ 0 is algebraic. What are good online resources or books for the proof? Thank-you.
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    Some remarks on complex numbers

    The complex numbers are a very important aspect of mathematics. They are utilized often in Analysis (obviously), Mathematical Physics, Algebra, and Number Theory (I am not certain about Geometry/Topology). There was a problem that was solved in the 19th century: Can one construct a square...
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    Determining a formula for a (sub)sequence

    The sequence is the set of n's where | ∑_{k=0}^{n} a_{k}z^{k} | is a local maximum in the sequence of the magnitudes of partial sums (the partial sums are complex valued).
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    Determining a formula for a (sub)sequence

    I currently have the first 125,256 terms of a sequence of natural numbers. I need to find a formula for any non-finite sub-sequence. Are there any good methods for obtaining such a formula? I can already say that it isn't a linear distribution, and I highly doubt it being polynomial (although...
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    Principal root of a complex number

    Thank-you. So it is how I though. As for the latter question, we can ignore that since I understand it now. Thank-you.
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    Solve a differential equation for the initial conditions,

    Edit: What (s)he was trying to state is that y = 0 is an equilibrium solution of the differential equation. What would this imply about the equation?
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    Principal root of a complex number

    Evaluate the integral of ∫\Gamma f(z) dz, where f(z) is the principal value of z1/2, and \Gamma consists of the sides of the quadrilateral with vertices at the pints 1, 4i, -9, and -16i, traversed once clockwise. I understand how to compute this for the most part. I'm just not 100% confident...
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    Principal root of a complex number

    Homework Statement I am doing a problem of a contour integral where the f(z) is z1/2. I can do most of it, but it asks specifically for the principal root. I have been having troubles finding definitively what the principal root is. Anyplace it appears online it is vague, my book doesn't...
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    Verify that the Stokes' theorem is true for the given vector field

    This is a problem from an old final exam in my Calc 3 class. My book is very bad at having examples for these types of problems, and my instructor only went over one or two. Help would be much appreciated. Homework Statement Verify that the Stokes' theorem is true for the vector field...
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    Need help understanding Lagrange multipliers at a more fundamental level.

    Nevermind. I understand now. I spent 2 seconds on the wikipedia page for it, and I finally had that "Oh my God. I get it." moment.
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    Need help understanding Lagrange multipliers at a more fundamental level.

    So, is the max and min found a max and min based on the constraint, and not a regular max/min of f(x,y) or f(x,y,z) ?
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    Need help understanding Lagrange multipliers at a more fundamental level.

    I understand that for Lagrange multipliers, ∇f = λ∇g And that you can use this to solve for extreme values. I have a set of questions because I don't understand these on a basic level. 1. How do you determine whether it is a max, min, or saddle point, especially when you only get one...
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    Use Lagrange multipliers to find the max & min

    Ah! Yes, I know this function. I just didn't know it's name. Thank-you for reminding me of it!
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    Use Lagrange multipliers to find the max & min

    I am sorry, but can you elaborate more on what a Hessian is? Currently we have only covered Lagrange multipliers.
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    Use Lagrange multipliers to find the max & min

    Homework Statement Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x,y) = exy; g(x,y) = x3 + y3 = 16 Homework Equations ∇f(x,y) = λ∇g(x,y) fx = λgx fy = λgy The Attempt at a Solution ∇f(x,y) = < yexy, xexy > ∇g(x,y) = <...
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    Programs What can one specialize in for a MS/PhD in Mathematics?

    I just remembered I am actually going to a University now so I can use their library! Yeah, I'm not used to having access to books in math/physics. My town library is a bit small, and usually have to use inter library loan to get books like these. Thanks for the reminder!
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    Programs What can one specialize in for a MS/PhD in Mathematics?

    Thank-you very much Espen :D That should help. When I get some spare money, I'll work on getting those books.
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    Programs What can one specialize in for a MS/PhD in Mathematics?

    I do not know what the areas of focus are for Mathematics. A link to an outside source would be amazing, but I do not know how to expand upon the question. I am primarily interested in Pure Mathematics though. I want to know if it's worth me going into mathematics (to see if I'll enjoy it in the...
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    Programs What can one specialize in for a MS/PhD in Mathematics?

    What is a list of areas of focus for Masters/PhD pursuers for Mathematics? What has the best future prospect for careers?
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    Genetic Modification of a Live Organism Is it Possible?

    Which is, once again, why I am here. I, as I have stated, have taken 2 biology courses (Biology 1 and AP biology). Thank you for the clerification though!
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    Genetic Modification of a Live Organism Is it Possible?

    What I'm wanting to do is modify the mitosis process slightly. After the DNA splits, I want the two new cells to produce telomerase to reextend the telomeres to prevent DNA degradation. This would require the ability to affect all cells to not have any "aging" at all. Just an idea =P
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    Genetic Modification of a Live Organism Is it Possible?

    Could you extract some cells and genetically engineer them for the specific purpose of changing the other cells? It would (theoretically) be immune to the immune system like cancer cells, but without the, well, cancer. The main thing I'm contemplating doing is when a certain gene/expression is...
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    Genetic Modification of a Live Organism Is it Possible?

    Don't viruses do something similar? I've only had the equivalent of 1 semester of college biology, so sorry if I ask any stupid questions. For example...if one were to use a genetically engineered virus to splice onto the dna, could one infect a majority of cells (80%+)?
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    Genetic Modification of a Live Organism Is it Possible?

    *** I know this is of questionable ethics, but I am asking a hypothetical *** If we had a human of adult age, let's say, age 20-30. Would it be possible to genetically modify all cells in the body and make the changes take effect in a realistic manner? If so what would be the limits and steps...
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    Programs Math & Computer Science Double Major - What Graduate Degree?

    It can't hurt to plan ahead. You can always change your future, but you can't change your past. This will help me choose what math/computer classes I want to take. I already have 18+ credit hours before starting college. I'm already doing 2nd year math courses. It's time for me to start thinking...
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    Programs Math & Computer Science Double Major - What Graduate Degree?

    Originally I hated trigonometry the most. Then I entered calculus 2 and began to love trig (it is so much like algebra). If the higher level statistics uses a lot of math theory, I might be more apt to try it. I'm wanting to stray a bit from discrete mathematics because I will be getting much...
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    Question: are there proportions in infinity?

    Yes, but it is still debated between many people (I personally am on the side of different sizes of infinity).
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    Schools AP tests for college credits?

    If your school didn't tell you about the AP exams...it fails, or you were absent/asleep when they told you. http://apcentral.collegeboard.com/apc/Controller.jpf Now you know something to tell your kids in the future: Take the exams.
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    Converting an Integral to a Rieman Sum

    I know I should know this, but how would one convert a typical integral into a Rieman Sum? ∫0n sinx + x dx for whatever n. for example.
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    Find symmetric equations for the line of intersection of the planes

    I assumed it because of how y and z cancel each other out. Plus i kinda knew that x held constant and y & z covers all integers =P (oops)
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