Recent content by PiAreSquared

Ok, so first begin by letting m= p^{κ_{1}}_{1}...p^{κ_{r}}_{r} and n=p^{β_{1}}_{1}...p^{β_{r}}_{r}, where κ_{i},β_{i}≥ 0 \foralli. Then (m,n)= p^{δ_{1}}_{1}...p^{δ_{r}}_{r}, where δ_{i} = min{κ_{i},β_{i}}. Then use the fact that \Phi(w) = w∏^{i=1}_{r} (1-1/p_{i}), given that w =...

Yeah same here. I'm kinda worried about getting into a decent grad program now because of my scores.

I think I answered around 45-48 of them. So not too great :(

Haha right? My brain is demanding a break over the next few days.

Yeah same here dumbQuestion. The time restraint renders getting a good score almost impossible for me as I also suck at standardized tests. :(

Ha, well I envy your happiness as preparing for this exam has been nothing but exhausting and stressful for me! I made the foolish mistake of waiting until a couple weeks before the exam to even start reviewing, so my hopes aren't too high for my score. I'll just be glad once it is finally over...

Well I'm sure that other members will be much more equipped to answer your question, but it sounds to me like you just described the field of mathematical physics.

You really don't have to assume that S is non-empty, as you can easily prove this fact.

Masters before Phd in Mathematics --bad idea? Hi all, I am a senior at a regional campus of a large state university in the US. I have always thought that since I love math (and I do really love learning and doing math), that love of the subject would be enough to propel me through a PhD...

Maybe something with the Mandelbrot Set? If you have access to a computer and projector displaying one of the many YouTube videos pertaining to it would probably be pretty enticing and would attract at least a few students.

voko, I have a quick question about one of your previous posts on this thread. You said that "If S satisfies ST = I and T is linear, then S is automatically linear." I was wondering why that is true? I know that If a linear map is invertible, then its inverse is also linear. But for T to be...

Yeah that was my point of confusion. I could not figure out how S could be non-linear and still satisfy ST=I and TS=I. So I guess I just assumed that if T was invertible, then its inverse was by default linear, without realizing that it needed to be shown explicitly. Sorry for the confusion.

Well, he assumes that T is linear, and shows that ST = I and TS = I, but he then says that to complete the proof, it is necessary to show that S is linear. But if S is automatically linear if T is linear and ST = I, why then does he take the time to show explicitly that S is linear?

Hello, I have been working through Linear Algebra Done Right by Axler and I have a quick question about Linear Maps, and in particular, their inverses. My question arose while working through the following proof: A linear map is invertible iff it is bijective. My qualm is not with the...

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