Recent content by SeReNiTy

Is there no help?

Hello experts, I'm about to embark on a new line of research. Random Matrices as you might of guessed. Coming from a algebra/geometry background, I am looking for some simple papers along with some references you guys could give. I need to do a literature review in a few weeks, so please any...

Hey guys, I've been studying some number theory recently and have a question. We know if (a,n) = 1 then a^phi(n) is congruent to 1 (mod n) where phi(n) = euler's totient function Now my question is the totient function does not always return the smallest possible integer such that a^k is...

I got accepted to UCB, it seems that my reference letters played a huge role in determining my acceptance. GPA is not really a issue (mind you you better have a 3.9 +).

When i was at Monash University in Australia, all the cutting edge theory was done in the mathematics department. At UCB its different however...

It seems to me cutting edge theoretical physics these days are done my people with very strong mathematical background. So learn as much mathematics as you can.

I wasn't talking about elementary algebra.

Physics can be done in the algebraic setting.

Well done. If your a top student I will see you around the campus...

I have the same problem. It was because class work was too trivial. I just started studying books that were more interesting and got hooked on doing challenging problems that took days to solve, not seconds. Maybe all this martial arts can help but i don't see how it is different to a good...

So does anyone know of a proof using induction? The identity is also known as vandermonde's convolution \sum_{k=0}^{n}{a\choose k}{b \choose n-k}={a+b\choose n} Where a,b are real numbers. I already know of the proof using binomial theorem and the combinatorics counting argument, now...

I want to do it without using binomial theorem. So by induction, but my combinatorics is weak...

Can someone point me in the right direction with vandermonde's identity, I'm seeking a algebraic proof. essentially it its the sum of (a ,k)(b ,n-k) = (a+b ,n) when summed over k = 0 to n. Could someone right this out in latex since it is probably incomprehensible. I used (a ,k) to denote...

Your relationship is correct, although i don't like to call them the christoffel symbols, i prefer to use the term connection co-efficients since they rely on the second half of the levi-civita connection to calculate. your wijk = 1/2( g(ek,[ei,ej]) - g(ei,[ej,ek]) - g(ej, [ek,ei]) ) where...

There is no better introduction calculus text then calculus by spivak.