Recent content by cakesama

I've been thinking about this all day and couldn't come up with a solution! Also, I was working on some other questions as well and came to another problem that I couldn't finish because I couldn't explicitly define a homomorphism! If I can define a homomorphism, then things will start to...

I *think* I got it this time, If we define a nontrivial homomorphism theta from G to A_k, then the kernel of theta must be trivial since G is simple, and theta is nontrivial. So then by the 1st isomorphism theorem, the mapping from G to G' (G' is the image of G under this mapping) is an...

Another attempt using the hints: Question 1 following on from my first post, Now for a contradiction, suppose that G does not have a prime order p. case1 : G finite, |G|=n Then G=<x>, and there exists a d that divides |G|, so by the fundamental theorem of cyclic groups there is a cyclic...

Hi, it's my first time posting in this forum, so I'm sorry if I have done anything against the forum rules and please point it out to me. Currently revising group theory for an exam in a week's time, and these two practise questions I couldn't finish, so if anyone can push me towards the right...

so you expand to get this =\int{(\frac{1}{4}-\frac{1}{2}cos(2x)+\frac{1}{4}cos^2(2x))dx then its an integral of 3 terms, so you integrate the 3 terms separately did that help?

expand the expression in the integral, then you get the last term being cos sqaured

double angle formula?

At the moment it's definitely for fun, not sure if I'll try to get into it properly after I get my masters degree in maths. Guess I'll have to study some undergrad physics as well in my spare time, thanks for the reply~

I would start by saying: Suppose x is in B union (intersection of all A's) then that means, either x is in B or x is in the intersection of all A's sorry I haven't learned latex yet so I have to resort to just typing it all out and also in your setup, are you saying let x be an element...

for the first question let x be in the LHS expression and deduce that it's also in the RHS expression. the two questions use the same concept, but 2nd one is stronger - to prove the 2nd one you prove two inclusions, LHS is contained in RHS and RHS is contained in LHS. in the 1st one you only...

Hi I'm currently a postgraduate student doing pure maths, and I'm quite interested in self-studying astrophysics! If you do physics or know something that can be of help, could you please suggest me some reading materials? oh and I haven't studied physics after getting out of high...