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  1. camilus

    Anything actually physically infinite within the universe?

    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...
  2. camilus

    Pfaffian and determinants of skew symmetric matrices

    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...
  3. camilus

    Multiplicity free fibers in maps between vector bundles

    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
  4. camilus

    Where is the number theory section?

  5. camilus

    The Grassmanian manifold's topology

    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...
  6. camilus

    Zeta(3) and Euler's formula

    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.
  7. camilus

    Product and intersection of ideals of polynomial ring

    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?
  8. camilus

    Top grad programs in several complex variables and complex geometry?

    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
  9. camilus

    Nonunique factorization theory

    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?
  10. camilus

    Lemma 13.2 from Munkres

    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...
  11. camilus

    Residues over simple poles

    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...
  12. camilus

    Theory of RZF question

    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...
  13. camilus

    Chebyshev function help

    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) =...
  14. camilus

    Why doesnt Bertrand's postulate imply Legendre's conjecture?

    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...
  15. camilus

    Universe expanding faster than light

    I read it is possible for the universe to be expanding faster than the speed of light. What would be the implications of this?
  16. camilus

    Infinite series convergence

    \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..
  17. camilus

    College algebra question. inequalities interval

    Homework Statement Solve the following inequality and express the solution set in interval notation. The Attempt at a Solution I got most of the answer right, except the lower interval. the answer is...
  18. camilus

    Complex conjugate problem

    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...
  19. camilus

    Roots of a polynomial (simple!)

    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...
  20. camilus

    Differential Equations problems

    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...
  21. camilus

    DE problem: Dog chasing a rabbit" [Broken] Can anyone help me with this? Thanks.
  22. camilus

    Infinite series problem

    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
  23. camilus

    Cube volume

    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...
  24. camilus

    Number theory proof?

    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
  25. camilus

    Simple polynomial problem

    if the polynomial x^3+3x^2+9x+3 is a factor of x^4+4x^3+6Px^2+4Qx + R, what is R(P+Q)?
  26. camilus

    A Mathematician's Apology. great read

    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...
  27. camilus

    The fly and train math problem

    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...
  28. camilus

    Evaluate the sum

    Let d(n) denote the number of digits of n in its decimal representation. Evaluate the sum \sum\limits_{n=1}^\infty \frac{1}{d(n)!}