Recent content by doubleaxel195

I'm getting a little confused about what exactly Sylow's first theorem says. On Wikipedia, it says that Sylow's First Theorem says "For any prime factor p with multiplicity n of the order of a finite group G, there exists a Sylow p-subgroup of G, of order p^n." Then in the section of the...

I am getting a little confused over the notations of Big O, Theta, and Omega. I am completely fine with the formal definitions. This is what is confusing me. A problem P has worst case time complexity O(f(n)) and Omega(g(n)). Does this mean that P has worst case time complexity Theta(h(n))...

Nevermind, I found this in the exercises of Ireland and Rosen on page 63. Just thought I would post where I found it in case anyone else needs to know.

Proposition: \sum_{i=0}^{p-1} (\frac{i^2+a}{p})=-1 for any odd prime p and any integer a. (I am referring to the Legendre Symbol). I was reading a paper where they claimed it was true for the a=1 case and referred to a source that I don't have immediate access to. So I was wondering if...

Just got accepted for SMALL's probability and number theory! :) I am probably going to accept. They want to know by Friday morning. Good luck to everyone else!

You should try to pick up Spivak's Calculus. It's accessible but in depth and rigorous at the same time. He motivates most of what he does including why definitions are the way they are.

I will let you guys know when I hear from them. Our response is due tonight. :/

Congrats l'Hôpital! Maybe...possibly I'll be seeing you over the summer? :) How long you have to decide to commit to SMALL?

I probably would have been so stressed out and freaked out if they called me on the spot! Where else are you applying? Or just Nebraska?

@l'Hôpital: Thanks. Why do you think you messed it up? Did you have a phone interview or something? I'm on the short-list for the Number Theory and Probability project. He wants us to read a few papers and write up what we think of the proofs, describe the paper, any related questions,and how we...

I too made the short list for SMALL :D I hope I actually get in too :/ Since this probably varies from school to school, does anyone know how many applicants some REU's get?

I'm just wondering if anyone has any advice on writing personal statements. Is there anything I should absolutely say or anything I should absolutely not say? What should the focus be? Should it go something like: why I like math, what kind of math I like, any relevant experiences with math I...

Thanks for your feedback. I guess I will just go with my formal statement of interest.

I want to say that an axiom is my unbounded love for math. but does that sound dumb? because my time on Earth is finite, so how can my love be unbounded? haha.

I would never do this for graduate school by the way...