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    Numerical analysis

    Homework Statement Consider the equation y0 = Ly; y(0) = 1: **L = lamda** Verify that the solution to this equation is y(t) = e^(Lt). We want to solve this equation numerically to obtain an approximation to y(1). Consider the two following methods to approximate the solution to this...
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    Lagrange, cosets, indicies

    Homework Statement suppose that H and K are subgroups of a group G such that K is a proper subgroup of H which is a proper subgroup of G and suppose (H : K) and (G : H) are both finite. Then (G : K) is finite, and (G : K) = (G : H)(H : K). **that is to say that the proof must hold for...
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    Open sets

    Homework Statement how do you show a set is open in R^n? Homework Equations The Attempt at a Solution
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    Closure math problems

    Homework Statement 6) Prove or give a counter-example of the following statements (i) (interiorA)(closure) intersect interior(A(closure)): (ii) interior(A(closure)) intersect (interiorA(closure)): (iii) interior(A union B) = interiorA union interiorB: (iv) interior(A intersect B) =...
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    First isomorphism theorem

    Homework Statement can someone explain the 1st isomorphism theorem to me(in simple words) i really dont get it Homework Equations The Attempt at a Solution
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    Homomorphism help

    Homework Statement let R* be the group of nonzero real numbers under multiplication. then the determinant mapping A-> det(A) is a homomorphism from GL(2,R) to R*. the kernel of the determinant mapping is SL(2,R). i am suppose to show that this is a homomorphism but i have no idea where to...