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.
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...
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) = <...
*** I know this is of questionable ethics, but I am asking a hypothetical ***
If we had a human of adult age, let's say, age 20-30. Would it be possible to genetically modify all cells in the body and make the changes take effect in a realistic manner? If so what would be the limits and steps...
Homework Statement
Find symmetric equations for the line of intersection of the planes
The planes:
5x - 2y - 2z = 1
4x + y + z = 6
Homework Equations
r = r0 + tv
x = x0 + at
y = y0 + bt
z = z0 + ct
The Attempt at a Solution
I have attempted this in many different manners and would like...
I am heading into my Freshman year in college. I know it's going to be far in the future, but I want to start brainstorming what my 5-10 year goal is. Any help is appreciated.
With these majors, I'm planning on getting a masters in Computer Science, but what should I do with the math degree...
I am currently attending IUPUI for a double major in Pure Mathematics and Computer & Information Science with a double minor in German and Physics. Overall this will take me 4 1/2 years and give me $38,000-$45,000 of debt.
1. I am wondering, which masters degree should I go for first? Math or...
Homework Statement
A boatman wants to cross a canal that is 3 km wide and wants to land at a point 2 km upstream from his starting point. The current in the canal flows at 3.5 km/h and the speed of his boat is 13 km/h.
(a) In what direction should he steer?
(b) How long will the trip take...
I've been programming c/c++ for a month or two, I have experience with Expression 2 (an in game programming language in Garrys Mod which is similar to VBasic), and 7 years experience with web development.
What I'm wanting to do now is begin learning Assembly language and how to compile it...
I'm planning on going into Physics and Mathematics.
Should I get a double major in:
1. Physics & Applied Mathematics
2. Physics & Pure Mathematics
- How would Applied/Pure affect my career?
What minor should I get?:
1. Computer Science
2. Chemistry
3. Other?
I am planning on...
#include <iostream>
#include <string>
using namespace std;
void str2hex(string str) {
int strlen = str.length(); // Assign the length of input/str to strlen
string hex[strlen]; // Initialize the Array hex with the length of the string
for (int x = 0; x <...
I am currently thinking about getting a double major with a combination of any of the following degrees:
Physics
Mathematics
Chemistry
German
And possibly (With less consideration):
Biochemistry
Molecular Chemistry
Software Engineering
Most recently I have thought about doubling...
I am currently trying to go between any two bases which are between and including base 2 to base 10. (i.e, base 10 to base 3, base 4 to base 6, etc...). Is there an equation or set of formulas for a one-step transition between the bases (or one-way method, rather than converting to base-10 then...
I am a high school senior who is new to these forums. So far, I have found them intriguing, but I do have a question that I have asked many of my teachers, but sadly, had no real response.
What are the basics of quantum physics? Basic concepts, theories, equations for example. I haven't been...
As my state (Indiana) has removed Astronomy from the curriculum, my school no longer offers it. I have taken AP Physics B and that is my best knowledge provided by the modern school system, so I apologize ahead of time for any low-level or simple questions.
I am wanting to know the equations...