Okay, I got it now. Thanks! There's another one I can't figure out.
Prove that every element of An is a product of n-cycles.
I always think of induction when I see a "for every element of such and such", but I don't think induction would be the right direction for this one. Instead, I would...
If σ is a k-cycle with k odd, prove that there is a cycle τ such that τ^2=σ.
I know that every cycle in Sn is the product of disjoint cycles as well as the product of transpositions; however, I'm not sure if using these facts would help me with this proof. Could anyone point me in the right...
Let N be a normal subgroup of a group G and let f:G→H be a homomorphism of groups such that the restriction of f to N is an isomorphism N≅H. Prove that G≅N×K, where K is the kernel of f.
I'm having trouble defining a function to prove this. Could anyone give me a start on this?
Right, it just sounds like trying the other way around would be a terrible idea. I'll try fitting both in, that seems to be my best bet. Anyways, thanks for the advice.
I'm actually required to take a semester of a course called "Intro to Analysis" and then I have the option of either Real Analysis or Complex for another semester. I could definitely take both, however I'm already taking a ton of courses as it is. The course description for Real Analysis says...
I'm about to start scheduling my courses for next year, and I have the option of taking either Real Analysis or Complex Analysis. I'm double majoring in Math and Physics, and I want to go to grad school to study either Applied Mathematics or Physics. I haven't taken any higher level math...