Recent content by Mystic998

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    Troubleshooting Homework: Identifying and Addressing Mistakes

    Actually, I can't really see a problem. So...am I really just that rusty? What's the answer supposed to be?
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    Algebraic expressions - simplifying

    It shouldn't be too terrible. The obvious thing to note is that (b - a) = -(a - b), for example.
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    What is the cyclic subgroup order of GL(2,p^n) generated by the given matrix?

    It seems like you're going about the problem correctly except that obviously the splitting field won't be as described if the quadratic is reducible. Other than that, unless I'm forgetting something (which would hardly be surprising), what you're saying is completely true.
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    Solving A^7 Using Matrix Multiplication: A 3x3 Example

    In general. Well, for nonnegative integer exponents anyway.
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    Partial derivatives using definition

    The definition of the second partials is just the partial derivatives of the first partials. Why couldn't you just use the same method as before?
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    Fourier series via complex analysis

    Homework Statement Show that f is 2-pi periodic and analytic on the strip \vert Im(z) \vert < \eta, iff it has a Fourier expansion f(z) = \sum_{n = -\infty}^{\infty} a_{n}z^{n}, and that a_n = \frac{1}{2 \pi i} \int_{0}^{2\pi} e^{-inx}f(x) dx. Also, there's something about the lim sup of...
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    Power Series Homework Help: Exploring Equations and Solutions

    Well, it looks like you're trying to find the power series of ln(5 - x) by differentiating the series for 1/(5 - x) term by term. But ln(5 - x) is the integral of 1/(5 - x) (give or take a sign).
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    Proving Isomorphism and Galois Group Existence in Abstract Algebra Homework

    Oh, I meant for the intersection to be trivial. I'll think about what you said though.
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    Double integral with cos(x^n) term

    I think changing the order of integration is the way to go. You'll get an x^3 term in the integral with respect to x. Then it's easy.
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    Proving Isomorphism and Galois Group Existence in Abstract Algebra Homework

    Homework Statement Show that G is isomorphic to the Galois group of an irreducible polynomial of degree d iff is has a subgroup H of index d such that \bigcap_{\sigma \in G} \sigma H \sigma^{-1} = {1} .Homework Equations The Attempt at a Solution I know that if G acts transitively as a...
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    What are the properties of quartic polynomials with different cubic resolvents?

    Homework Statement I'm trying to come up with an example of a quartic polynomial over a field F which has a root in F, but whose splitting field isn't the same as its resolvent cubic. Homework Equations The Attempt at a Solution Well, I know the splitting field of the cubic...
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    Triple integral over a sphere in rectangular coordinates

    I think you need to rethink your bounds on that one...
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    Trisectible angles | divisibility

    Without additional assumptions on m and n, the implications aren't true...
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    Trisectible angles | divisibility

    Isn't your first question essentially, "Can you construct an integer multiple of a constructable angle?" Well...can you?
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