I am wanting to find a good proof of the Lindemann-Weierstrass Theorem.
Most importantly I need the part that states that eα is transcendental where α ≠ 0 is algebraic.
What are good online resources or books for the proof?
Thank-you.
The complex numbers are a very important aspect of mathematics. They are utilized often in Analysis (obviously), Mathematical Physics, Algebra, and Number Theory (I am not certain about Geometry/Topology).
There was a problem that was solved in the 19th century: Can one construct a square...
The sequence is the set of n's where | ∑_{k=0}^{n} a_{k}z^{k} | is a local maximum in the sequence of the magnitudes of partial sums (the partial sums are complex valued).
I currently have the first 125,256 terms of a sequence of natural numbers. I need to find a formula for any non-finite sub-sequence.
Are there any good methods for obtaining such a formula? I can already say that it isn't a linear distribution, and I highly doubt it being polynomial (although...
Evaluate the integral of ∫\Gamma f(z) dz, where f(z) is the principal value of z1/2, and \Gamma consists of the sides of the quadrilateral with vertices at the pints 1, 4i, -9, and -16i, traversed once clockwise.
I understand how to compute this for the most part. I'm just not 100% confident...
Homework Statement
I am doing a problem of a contour integral where the f(z) is z1/2. I can do most of it, but it asks specifically for the principal root. I have been having troubles finding definitively what the principal root is. Anyplace it appears online it is vague, my book doesn't...
This is a problem from an old final exam in my Calc 3 class. My book is very bad at having examples for these types of problems, and my instructor only went over one or two. Help would be much appreciated.
Homework Statement
Verify that the Stokes' theorem is true for the vector field...
I understand that for Lagrange multipliers,
∇f = λ∇g
And that you can use this to solve for extreme values.
I have a set of questions because I don't understand these on a basic level.
1. How do you determine whether it is a max, min, or saddle point, especially when you only get one...
Homework Statement
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint.
f(x,y) = exy; g(x,y) = x3 + y3 = 16
Homework Equations
∇f(x,y) = λ∇g(x,y)
fx = λgx
fy = λgy
The Attempt at a Solution
∇f(x,y) = < yexy, xexy >
∇g(x,y) = <...