Recent content by alyscia

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    Graduate Can the homotopy extension property fail on certain pairs of spaces?

    Can someone elaborate? Let I = [0,1], A = {0, 1, 1/2, 1/3, 1/4, \cdots}. Show that the homotopy extension property does not hold on the pair (I, A). Thanks in advance, A
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    Graduate Understanding Oiler's Approach to the Zetha Function: A Math Book Review

    For me, this is one of the most beautiful identities in number theory. I think a book by T. Apostol is very easy to follow, I think it's called introduction to analytic number theory. If you want to know more, I recommend it! :)
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    Graduate Understanding the Smash Product of Two Topological Spaces

    Hi all, I do realize that my previous thread on CW complexes was unanswered, so perhaps I am posting my questions to wrong section of this forum. If so, please direct me to the right forum. Otherwise, I am having some problems understanding the smash product of two topological spaces. If anyone...
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    Graduate Show that (A:B) = (A^f:B^f)(A_f:B_f) in Abelian Groups

    I think just chasing the index using the first isomorphism theorem is good enough.
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    Graduate Question on linear combinations of sines and cosine (complex analysis)

    Yes, look up Euler's formula. $e^{i\theta} = cos \theta + i sin \theta$.
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    Undergrad Laplace Transforms to solve non IVPs?

    I think you can. Just leave x'(0) to be an unknown, then you should have a function back that is in terms of T and x'(0). Then apply the fact that x(4) = 7 to find the value of x'(0) which gives you the full equation back. Laplace transforms, I think, solves exactly the same family of equations...
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    Find the general solution to this ODE (with generalization)

    I believe there is some existence & uniqueness theorem for ODEs that could tell you whether a solution is "general" or not.
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    Very clever complex inequality.

    let z = a+ bi and physically evaluate the modulus. Is this some homework question? I am not sure why this is in the analysis section.
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    High School Boolean Algebra: What Audio Engineering Majors at UMiami Need to Know

    http://en.wikipedia.org/wiki/Boolean_algebra_(logic )
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    Graduate Guide to CW Complexes and n-Cells

    I hope I am posting in the right section. I am having a lot of trouble understanding what exactly CW complexes look like. In particular, I am not sure of the definition of an n-cell (in terms of topology, not geometry), and the inductive step of building a CW complex (from X_{n-1} to X_n)...