/sci/ - Science & Math

>>5748493
>Man level
>Basic Algebra

http://mathworld.wolfram.com/PrimeDiophantineEquations.html

Can anyone find an instance where someone actually gave examples of the variables a...z for some prime-2 k?

What's a closed formula for the symmetric polynomial

<span class="math">p_n(x,y):=(x+y)^n-(x-y)^n[/spoiler]

with n being a natural number. I assume one would have to use the binomial expression for <span class="math">(x+y)^n[/spoiler] and trick around a bit.

ITT: We pose basic questions that too many people can't answer due to the "just accept that it's true" mentality and lack of rigor in high school and some undergraduate courses. I'll start. inb4 babby thread, criticisms for not using LaTeX, etc.

1. Show that a negative number multiplied by a negative number yields a positive number.

2. Show that x^0 = 1.

3. Show that 0! must equal 1.

4. Show that integrating 1/(x^2 + 1) will yield the tangent inverse function. Many calculus courses simply tell you to memorize this fact. Make sure you can do the same for all inverse trig functions.

5. Given that a vector X in Rn is orthogonal to ANY vector Y in Rn, show that X must be the zero vector.

>>4922840

Any odd times and odd is odd.

Zero times an odd is zero, i.e. it's odd. As we already know its even, we conclude that it's both even and odd (it has "dual parity").

As you get farther in you're mathematical career, you'll discover many oddities like that. It's fine to not know them now, but if you get too cocky too early you'll miss out on the chance to learn a lot.

>>4912312
>>4912312

Rush SigEp. Trust me on this.

Hey /sci/,

So I'm in the midst of what should be a simple undertaking, but things aren't working out for me, wondering if anyone may be able to shed some light on what's going wrong.

Basically I'm trying to solve Laplace's equation with an ADI scheme. I have a Fourier series solution for comparison, and the interior points of the ADI solution are coming out to be about half the value of the Fourier series ones. I have no idea why this is happening. What follows is my MATLAB code.

clear
x_0 = 0;
x_f = 1;
M = 100;
dx = (x_f-x_0)/M;
x = x_0 : dx : x_f;
x = x';
x1 = linspace(x_0,x_f,M);

y_0 = 0;
y_f = 1;
N = 100;
dy = (x_f-x_0)/N;
y = y_0 : dy : y_f;
y = y';
y1 = linspace(y_0,y_f,N);

t0=0;
tf=1;
Z=500;
dt=(tf-t0)/Z;
t=t0:dt:tf;
t1=linspace(t0,tf,Z);

[X,Y] = meshgrid(x,y);

Do you like determinants/want to use determinants?
Yes: http://www.amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X
No: http://www.amazon.com/Linear-Algebra-Right-Sheldon-Axler/dp/0387982582/

Do you like determinates/want to use determinates?
Yes: http://www.amazon.com/Linear-Algebra-Dover-Books-Mathematics/dp/048663518X
No: http://www.amazon.com/Linear-Algebra-Right-Sheldon-Axler/dp/0387982582/

Working over an old Algebra Midterm and I can't figure out how approach one of the questions on the class equation.
>Let G be a group with exactly 5 conjugacy class, of orders 1, 3, 6, 6, and 8. Prove that G=S₄ by using this outline: A) Find the orders of G and Z: The order of G = 24 and |Z(G)|=1
>B) Let P be a Sylow 3-subgroup of G, show that |N(P)|>3
>C)Show that G has a subgroup H of order 4 (by showing that N(P) contains a subgroup of order 6)
>D)Show the resulting homomorphism from G to S₄ is an isomorphism

Can someone give me a hint?