Recent content by Dmak

Hello I was reading through some research and I came across the proof of a lemma which I did not wholly understand. The problem statement is as follows: Let F be a non-degenerate non-symmetic bilinear form in V. Then there exists a basis in V with respect to which F has one of the following...

I've been studying both on my own for quite a while now both are very studyable subjects although you will probably find one more interesting than the other depending on your preference.

Hello, I'm an undergraduate math student planning on getting a Ph.D in math after I get my B.S. in pure math. I am wondering if a computer science minor really helps say, if you plan on going into Cryptography, or if it is more like what one teacher of mine put it, "if you have an advanced math...

The scalar product or dot product, allows you to tell if two vectors are orthogonal or perpendicular among other things. So if you can visualize that the vector (2, 3, 4)^{T} must be orthogonal to every point in the plane then the plane through the origin with normal vector (2, 3, 4)^{T}...

Well there is an invertible transformation for any reflection across a line through the origin.

Well you could first find out what the matrix representation of this linear transformation is. Are you familiar with these terms?

This would be a fine method: http://www.sosmath.com/diffeq/second/variation/variation.html essentially find two homogeneous solutions y_{1}, y_{2} then using those you can find a solution to the differentiall equation of the form, \phi(x) = y_{1}u_{1} + y_{2}u_{2} where u'_{1} =...

whoops what i meant was a particular solution of the form: y = x(A_{0} + A_{1}x)e^{xi} you have to derive the coefficients by evaluating L[y] and matching up the coefficients A_{0}, A_{1} with the right hand side of the equation ( xe^{ix} ) then you use the imaginary portion of this...

instead of looking at that equation you could try to look at an equivalent equation L[y] = y'' + y = xe^{ix}, where i = \sqrt{-1}. then since i is a particular root of the characteristic equation, y has a solution of the form y = x^{2}A_{0}e^{ix} from there it is easily shown that the...

Suppose B is singular then there exists a nonzero vector v such that Bv = 0 hence (AB)v = A(Bv) = A(0) = 0 but AB is nonsingular so v must equal zero. Similar situation for A as well.

Hello, I'm a math major and I'm wondering how much the university you attend as an undergraduate matters for acceptance into top graduate schools, any ideas?

haha thanks Gib_Z :p

yes but no need for spherical coordinates since its just the triple integral: SSS1dV = volume of sphere over the domain d = { (x,y,z): x^2 + y^2 + z^2 = 1 } ( sorry no latex )

First of all, I'm a second year pure mathematics major/computer science minor with a 4.0 math g.p.a. and a 3.878 overall g.p.a. I'm looking to go to graduate school right after I get my B.S. I am very studious and I am constantly studying. I've been asking all my professors about research...

divergence theorem: triple integral of the divergence of the vector field, in this case the divergence is just 1, so you're just essentially finding the volume of the sphere