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 +).
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 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...
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...