Teach me math

now I am genuinely interested if there's any research been done into the equation

ab=a + b

like what are the distribution of (a,b)

a=-(-a)

Derivative rules
1. Sum/ Difference Rule
>The derivative of a function is the sum of the derivative of it's components
ex. f(x) = x^2 + x + 2
f'(x) = 2x + 1 + 0

2. Power Rule
>For functions with a constant exponent, take the same number as the exponent, multiply the function by it, and subtract 1 from the exponent
ex. g(x) = x^4
g'(x) = 4*x^(4-1) = 4x^3

3. Chain Rule
>When you have a function with another function as the input, the derivative is the derivative of the outside function with the regular other function as it's input, multiplied by the derivative of the second function
ex. f(g(x))
dy/dx = [2(x^4)+1] * 4x^3
simplification of the above is trivial and left as an exercise for the reader

4. Constant Multiple Rule
>When a function has a constant in front of it, the constant can be pulled out and multiplied by the derivative of the remaining function
ex. j(x) = x^2 / 2
j'(x) = .5 [dx^2/dx] = .5 * 2x = x
This is largely useless in basic differentiation and makes it easier to fuck up distribution of negative signs, not recommended.

OK, sure. Let's start slow.

The topological index of an elliptic differential operator D between smooth vector bundles E and F on an n-dimensional compact manifold X is given by

ch(D)Td(X)[X],
in other words the value of the top dimensional component of the mixed cohomology class ch(D)Td(X) on the fundamental homology class of the manifold X. Here,

Td(X) is the Todd class of the complexified tangent bundle of X.
ch(D) is equal to φ−1(ch(d(p*E, p*F, σ(D))), where
φ is the Thom isomorphism from Hk(X, Q) to Hn + k(B(X)/S(X), Q)
B(X) is the unit ball bundle of the cotangent bundle of X, and S(X) is its boundary, and p is the projection to X.
ch is the Chern character from K-theory K(X) to the rational cohomology ring H(X, Q).
d(p*E, p*F, σ(D)) is the "difference element" of K(B(X)/S(X)) associated to two vector bundles p*E and p*F on B(X) and an isomorphism σ(D) between them on the subspace S(X).
σ(D) is the symbol of D
One can also define the topological index using only K theory (and this alternative definition is compatible in a certain sense with the Chern-character construction above). If X is a compact submanifold of a manifold Y then there is a pushforward (or "shriek") map from K(TX) to K(TY). The topological index of an element of K(TX) is defined to be the image of this operation with Y some Euclidean space, for which K(TY) can be naturally identified with the integers Z (as a consequence of Bott-periodicity). This map is independent of the embedding of X in Euclidean space. Now a differential operator as above naturally defines an element of K(TX), and the image in Z under this map "is" the topological index.

youtube.com/watch?v=wM8BREc3RYo

youtube.com/watch?v=_ON9fuVR9oA

youtube.com/watch?v=aw_VM_ZDeIo

mathsisfun.com/calculus/

There you go OP

have fun

but can i divide by zero?

t. person who doesn't do math

But what is moral and not?

He's right though, to a first approximation.
Problem solving is another aspect.

hyperbola

2/2=4 (mod 3)

I dont even know why i browse this board, i could barely finish the high school basic math course, i never had a teacher who taught me nor did i have the drive to learn it. Im gonna learn a trade and become a skilled labourer, only way out....