# Search results

1. ### Numerical analysis

yes that is what i meant, sorry, working on this for a long time... kinda burnt out
2. ### 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...
3. ### Lagrange, cosets, indicies

|G| = g = mh = m(nk) = (mn)k. so that makes sense, but how do you relate that to the left cosets of K in G. or in other words, how do you relate that to the index of K in G. so does it suffice to state that a coset in H partitions H into |G| subsets? im just having difficulty seeing the...
4. ### 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...
5. ### Open sets

then there exists a neighborhood of x such that neighborhood of x is contained in the set
6. ### Open sets

a set is open if every point in the set is an interior point. now i know that but i am having difficulty proving it. (every point being an interior point that is)
7. ### Closure math problems

my mistake for the first one i meant to say write the closure (interior A) is a proper subset of the interior (closure A) i took A = [1,2] then the right side would equal [1,2] and the left would be (1,2). therefore the (closure (interior A)) is not a proper subset of the...
8. ### Open sets

im reading rudin's book: principles in mathematical analysis, ad we are talking about metric spaces, ie topology. so can you expand on you second approach to the problem please?
9. ### Open sets

Homework Statement how do you show a set is open in R^n? Homework Equations The Attempt at a Solution
10. ### 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) =...
11. ### First isomorphism theorem

can you specify G/K is isomorphic to I.
12. ### First isomorphism theorem

If G and H are groups and f is a homomorphism from G to H, then the kernel K of f is a normal subgroup of G, the image of f is a subgroup of H, and the quotient group G /K is isomorphic to the image of f.
13. ### 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
14. ### 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...