Hi guys,
I'm a mathematician from Miami Florida working in paraquaternionic and symplectic differential geometry, but I come from a very extensive physics background, pretty much well-versed in all modern physics. But my favorite of all is probably the philosophy of mathematics and science as...
Can anyone explain or point me to a good resource to understand these operators? I'm trying to the understand determinants for skew symmetric matrices, more specifically the Moore determinant and it's polarization of mixed determinants. Can hone shed some light? I'm confused as to how the...
For a map between vector bundles (which commute with a certain Lie groups like Sl2R or GL2R), what does it mean exactly for a fiber to be multiplicity free?
Eplanations would be good, but examples would be even better. Thanks in advance, Gauss bless you!
CM
Let n <= m and G:=Gr(n,m) be the (real) Grassmanian manifold. I understand the topology of the simplest case, that of projective space, and am wondering if there is a way to interpret the topology of the G to similar to projective space, with the according generalizations needed.
If V^n is an...
Hi everyone. I'm trying to understand the step where they wrote
1/2 ∏1/(1+p^-3) =1/2 Ʃ(-1)^ord(k)/k^3
How can I see this? I know the Euler product formula, but it has a negative sign before the p^-3, where here we have a + sign.
Thanks for the help.
Let k[x,y,z,t] be the polynomial ring in four variables and let I=<x,y>, J=<z, x-t> be ideals of the ring.
I wanna show that IJ=I \cap J and one direction is trivial. But proving I \cap J \subset IJ has stumped me so far. Anyone have any ideas?
I know UC San Diego is good, Rothschild and Ebenfelt are there, but are there any other ones that stand out in these and related fields?
Thanks a bunch
Im applying to an REU in San Diego State where the focus will be Nonunique factorization theory but I'm clueless as to what this actually is. Does anybody know anything about this?
Lemma 13.2: Let X be a topological space. Suppose that C is a collection of open sets of X such that for each open set U of X and each x in U, there is an element c of C such that x\in c\subset U. Then C is a basis for the topology of X.
Proof: The first paragraph is trivial, it just shows...
my book on prime numbers has a line where it skims over a residue computation, and Im in dire need of clarification. It's rather simple, and I may very well be the one mistaken, but Im getting a extra factor of 1/2 in the residue whereas in the book it does not appear and apparently isn't a typo...
theory of Riemann zeta function question
analytically continuing the Riemann zeta function (RZF) using the gamma function leads to this identify:
n^{-s} \pi^{-s \over 2} \Gamma ({s \over 2}) = \int_0^{\infty} e^{-n^2 \pi x} x^{{s \over 2}-1} dx ________(1)
and from that we can build a...
I'm a bit confused as to how to calculate the 2nd chebyshev function.
I know \psi (x) = \sum_{p^k \le x} \ln p
but can someone show me how to expand it? Like, do I use for 2^k, 2, 4, 8, 16, 32... for all the p^k \le x, same with 3, and 4 and so on?
MW gives the example:
\psi (10) =...
I mean, according to my knowledge, Bertrand's postulate has already been proved, I've already read and understood one, but Paul Erdos, and a few other mathematicians have proved it using various methods. I just finished reading Ramanujan's proof. Its amazingly advanced, and really short. The...
\sum^{\infty}_{x=1} \frac{cos(14.1347 \ln (x))}{x^{a}} = 0
Is there a way to solve for a? I dont think so but maybe someone here will have an insight as to what to do..
Homework Statement
Solve the following inequality and express the solution set in interval notation.
http://www.webassign.net/www24/symImages/4/6/aaf987edafbf00c172f8cfaf01966c.gif
The Attempt at a Solution
I got most of the answer right, except the lower interval.
the answer is...
Homework Statement
sun, I dont know why Im stuggling with a simple freakin problem. Its not even for me its for my friend who's in college algebra, but for some reaon I cant get the correct answer.
{9 - 11i \over 6i}
The Attempt at a Solution
I multiplied by the conjugate twice and got...
x^3-7x^2-10x-8 = 0
what are the roots?? Sorry, Im horrible at doing these kinds of things, this is for another problem in my differential equations thread.
Its been so long since I did simple roots of a polynomial, I forgot how to do it LOL! and please, this homework is due tomorrow...
Find the eigenvalues and eigenfunctions for the given boundary-value problem.
{d \over dx}[x{dy \over dx}] + {\lambda \over x}{y} = 0, subject to y(1)=0, y'(e^\pi)=0
Find the eigenvalues and eigenfunctions for the given boundary-value problem.
{d \over dx}[{1 \over 3x^2+1}{dy...
can anyone find a solution without using a calculator??
This is the problem:
Find the positive interger k for which \sum \limits_{n=4}^k {1 \over \sqrt{n} + \sqrt{n+1}} = 10
Homework Statement
An open-top box can be formed from a rectangular piece of cardboard by cutting equal squares from the four corners and then folding up the four sections that stick out. For a particular-sized piece of cardboard, the same volume results whether squares of side one or...
number theory problem
For every prime p \ge 5, prove that p^2-1 is evenly divisible by 24(gives an integer answer).
Example: for p=5, {5^2-1 \over 24} = 1
General Info.
A Mathematician's Apology is a 1940 essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician. It is, however, a very individual view as Hardy's...
Ok so the problem:
2 trains are 100 miles apart traveling towards each other on the same track. Each train tavels at 10 miles per hour. A fly leaves the first train heading towards the second train the instant they are 100 miles apart. The fly travels at 30 miles per hour (relative to the...