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    Probability problem: upper bounds on binomial CDF

    Homework Statement Hi all, just a quick question here - the setup is as follows: X is a random variable, X \sim \operatorname{Bin}(m,p) where p=2^{-\sqrt{\log n}}(\log n)^2 and m \geq 2^{\sqrt{\log n}}c for constants c, n (n "large" here). I wish to show that \mathbb{P}(X < c) \leq e^{-(\log...
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    Quick help finishing off a proof: extension of p-adic fields

    Homework Statement Let L_1/K,\,L_2/K be extensions of p-adic fields, at least one of which is Galois, with ramification indices e_1,\,e_2 . Suppose that (e_1,\,e_2) = 1 . Show that L_1 L_2/K has ramification index e_1 e_2. Homework Equations I have most of the proof done: I'm trying to show...
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    Bipartite graphs and isolated vertices

    Homework Statement Hello everyone, I am trying to determine the the threshold function p=p(n) for a random bipartite graph (see http://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model for a 'random graph': I am interested in the same idea, but for random bipartite graphs), such that...
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    Algorithm for computing conjugacy classes in subgroups of the GL(n,F_p) efficiently

    Homework Statement As the title says, I'm trying to find an efficient algorithm in order to write a program for computing conjugacy classes in subgroups of the general linear group GL(n,\mathbb{F}_p) (n x n matrices over a finite field of p elements, p prime) efficiently. In particular, I am...
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    Cts functions on [0,1] tending ptwise to 0 - convergence be uniform on an interval?

    Homework Statement As in the question - Suppose that f_n:[0,1] -> Reals is a sequence of continuous functions tending pointwise to 0. Must there be an interval on which f_n -> 0 uniformly? I have considered using the Weierstrass approximation theorem here, which states that we can find...
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    Efficient way to calculate a power of one polynomial mod another polynomial in GF(p)

    Hi all, I've been set some holiday work by my study director which is meant to be teaching us all about algorithms and a few other mathematical bits and bobs - unfortunately I've come unstuck on one of the bobs, and was hoping for some help! I've asked for help elsewhere but was given very...
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