Recent content by TaliskerBA

Hey belated thanks for your help. Quite obvious in the end!

I was hoping someone could help me understand the equivalence between the definitions for functions to be continuous between topological spaces, ie: For X and Y topological spaces, and f:X-->Y a function, my notes don't prove why these definitions are equivalent (possibly because I'm missing...

Hey, just trying to get my head around the logic of this. I can see that if composition factors are cyclic then clearly the group is soluble, since there exists a subnormal series with abelian factors, but I am struggling to see how the converse holds. If a group is soluble, then it has a...

Sorry that'd be ab_{44} = a_{41}b_{14} + a_{42}b_{24} + a_{43}b_{34} + a_{44}b_{44}. So could you set u = (a_{41}/a_{44},a_{42}/a_{44}, a_{43}/a_{44})^{T} and v = (b_{14}/b_{44},b_{24}/b_{44}, b_{34}/b_{44})^{T}? I'm assuming we want to show the dot product is positive, but not sure of...

For the 1st bit it's the complement of P(-1<X<2) I think.

Homework Statement Prove that the proper orthochronous Lorentz group is a linear group. That is SOo(3, 1) = {a \in SO(3, 1) | (ae4, e4) < 0 } where (x,y) = x^T\etay for \eta = [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 -1] (sorry couldn't work out how to properly display a matrix). Homework...

Got there in the end. Here is the proof I used, I thought I'd post it as it was quite fun to prove in the end. I would also appreciate it if anyone can point out errors. Also, apologies for poor presentation I'm fairly new to Latex. Since q | F_{k} = 2^{2^{k}} + 1 \Leftrightarrow...

Let k\in\mathbb{N}, and q be a prime factor of F_{k}=2^{2^{k}}+1. Deduce that gcd(q-1,2^{k+1})=2^{k+1}. q|F_{k} \Rightarrow mq = 2^{2^{k}}+1 for some m\in\mathbb{N} 2^{2^{k}}=q-1+(m-1)q \Rightarrow 2^{2^{k}}=q-1 (mod q) 2^{k+1}|2^{2^{k}} since k+1\leq 2^{k}, \forall k\in...

Thanks very much for your help, I get it now. I'm sorry about bumping I didn't know it was against the rules. I won't do it again.

bump. Help!

Homework Statement For the system u' = v, v' = −u with initial conditions u(0) = 1 and v(0) = 0, find an approximate solution by performing 4 steps of Picard iteration. Compare the results with the actual solution.Homework Equations In general: y'= f(x,y), y(x0)= y0 y(x) = y(x0) + \int...

Ah what a stupid mistake to make. I did everything right apart from that bit. It doesn't matter if I use initial conditions x(0) = 2 or x(0) = 0.02 as when I use the latter I now get 0.01209 which is the correct answer. Thanks for your help that would have bugged me.

Homework Statement The displacement x (in metres) of a damped pendulum from the vertical satisfies x'' + x' + 10x = 0. The pendulum is displaced 2cm from the vertical and released so that its initial velocity is 0. Find the displacement of the pendulum to the other side at the end of its...

That is useful to know, but the notation in this example still claims that Pr(-47.7<X<49.4) = 0.95 which clearly doesn't work when n=1. My notes state that over many repetitions of sampling then 95% of intervals will include X, but what if all samples were of size n=1? Or are the samples sizes...

Should Say Intervals.. I'm tired... I am probably going wrong somewhere but I am running into problems with understanding this. My understanding of a 95% confidence interval is that in a sample of n the sample mean is 95% likely to be within 1.96 standard errors of the actual mean. I have a...