Recent content by polarbears

Hi, I'm a high school student that has completed my most of my under division in mathematics (Diff. Eq., Discrete math, single/multi variable calculus, linear alg, problem solving, and basic group theory stuff) and I'm now interested in Analysis. Can someone suggest an introductory book to...

So only way is by brute force?

Homework Statement Is the Cyclic Subgroup { (1), (123), (132)} normal in A_{4} (alternating group of 4) Homework Equations The Attempt at a Solution So I believe if I just check if gH=Hg for all g in A_4 that would be suffice to show that it is a normal subgroup, but that seems...

Homework Statement If H is a subgroup of G, show that g^{-1}Hg={g^{-1}hg \; h\in H is a subgroup for each g\in G Homework Equations The Attempt at a Solution I know I just have to check for closure and inverses, but the elements in this group g^{-1}hg with different h or with...

Wait so my answer wasn't right? or is it? How about this... The equivalence class of T are sets of all continuous functions mapping R to R which intersect f(x) at x = 4? But then I feel like that's just restating what the equivalence relationship is in the 1st place

I think I know how to approach it...check me if I'm right though check if its one-to-one and onto if it is one-to-one that implies if f(a)=f(b) then a=b

Been awhile and no response

Old thread but I think I'm still not done with this problem So I've establish that this is not an equivalence relationship in a non-abelian group, but it still works in an abelian group. So would the equivalence class be sets of elements in an Abelian group? I'm still trying to grasp this idea...

Alright--hehe yeah I was getting lazyUmm all functions that intersect this function at 4?

Homework Statement Identity if it is an equivalence relationship and describe the equivalence class. The relationship T on the set of continuous functions mapping R to R, where fTg iff f(4)=g(4) Homework Equations The Attempt at a Solution It is an equivalence relationship just...

Differential Equations -Laplace transforms OHHHH waitttt does the delta function just determine the bound of my intergral?

Homework Statement y''+y=\delta (t-2\pi )cos(t) y(0)=0,y'(0)=1 Homework Equations The Attempt at a Solution The left side is (s^2+1)Y(s)-1=RHS My problem is the fact that cosine is being multiplied by the delta function. I put it in the form of an intergral but I don't know...

thanks=)

Homework Statement y''+2y'+3y=sin(t)+\delta (t-3 \pi ) Homework Equations The Attempt at a Solution Left side is just Y(s)*(s^2+1)-1 But I don't know how to deal with the delta function, I made it into just an intergral but I don't know how to intergrate it.

Homework Statement Determine if the following is a group morphism. Find the kernel and the image if so. f:C_{2} \times C_{3} \rightarrow S_{3} where f(h^{r},k^{s})=(1,2)^{r} \circ (123)^{s} Homework Equations The Attempt at a Solution I'm stuck on the morphism part. So I know I...