/sci/ - Science & Math

[Anonymous No.2042333]

I need math formulas and facts from the primary school to the university. Don't really need any examples - just the formulas if possible.

[Anonymous No.2042363]

There are no integers <span class="math">x,y,z \in Z \setminus \{0\}[/spoiler] which fit the equation <span class="math">x^n + y^n = z^n[/spoiler] for <span class="math">n \geq 3[/spoiler].

Pretty nifty formula. I needed that on a homework assignment in my last high school year.

[Anonymous No.2042471]

only one i have sorry

[Anonymous No.2042512]

>>2042363

It's n>2. L2Fermat'sLastTheorem noob.

[Anonymous No.2042520]

>>2042512
The set of natural number strictly greater than 2 is equal to the set of natural numbers greater than or equal to 3.

You're a complete idiot and very probable a troll.

[Anonymous No.2042523]

>>2042512
What that person typed is pretty much exactly the same, read it again.

[Anonymous No.2042531]

x:p:q = x.(q:p)

x^p.x^v = x^p+v

[Anonymous No.2042536]

>>2042471

Wish I could read it :< so small..got a larger file?

[Anonymous No.2042543]

Generalized Stokes theorem, it's very pretty:
<div class="math">\int_\Omega d\omega = \int_{\partial \Omega} \omega</div>
Cauchys theorem:
<div class="math">\int_\gamma f(z)dz = 0</div>
where <span class="math">\gamma[/spoiler] is a closed path, and f is analytic on its interior and on the path.

[Anonymous No.2042568]

>>2042363

Yeah. Except <span class="math"> n =4[/spoiler]. Also the more popular way of stating this is with n > 2.

[Pm No.2042586]

Mmmmmmmmh Cauchy-Schwartz

in Euclidian space Rn, heh

[Anonymous No.2042610]

Look up the fundamental theorems of calculus, arithmetic and algebra. Once you've got these and understand them fully, the rest of maths (roughly speaking) follows if you know your specific definitions within whatever field of maths you're working in.

[Anonymous No.2042623]

>>2042531
Oh lord, brackets if you're writing it inline please...
<span class="math">\frac{x}{(\frac{p}{q})}=\frac{xq}{p}\\
x^p\cdot x^q=x^{p+q}[/spoiler] is what I hope he means to write.

[Anonymous No.2042629]

Okay, it doesn't like line breaks... try again.
<span class="math">\frac{x}{(\frac{p}{q})}=\frac{xq}{p},
x^p\cdot x^q=x^{p+q}[/spoiler] is what I hope he means to write.

[Josef !!nUf2NflSAyw No.2042652]

Stokes' theorem! <span class="math">\int_{\mathcal M}\mathrm d\cdots[/spoiler] Oh wait, >>2042543, thanks ;D

[Josef !!nUf2NflSAyw No.2042663]

Curvature tensor constructed from the Christoffel symbols
<div class="math">{R^\tau}_{\alpha\gamma\beta} = \partial_\gamma \Gamma^\tau_{\beta\alpha}-\partial_\beta \Gamma^\tau_{\gamma\alpha} + \Gamma^\tau_{\gamma\mu} \Gamma^\mu_{\beta\alpha}-\Gamma^\tau_{\beta\mu}\Gamma^\mu_{\gamma\alpha}</div>
Christoffel symbols constructed from the metric:
<div class="math">\Gamma^\tau_{\mu\beta} = \frac{1}{2} g^{\alpha\tau}\left(\frac{\partial g_{\alpha\mu}}{\partial u^\beta}+\frac{\partial g_{\beta\alpha}}{\partial u^\mu}+\frac{\partial g_{\mu\beta}}{\partial u^\alpha}\right)</div>

[Josef !!nUf2NflSAyw No.2042670]

>>2042663
woops sign error
nevermind, they're fugly formulas anyway, but i had them in another file
Here, have Maxwell's equation instead. <span class="math">\mathrm d*\mathrm dA=\mathcal S[/spoiler]

[Anonymous No.2042678]

lol

[Anonymous No.2042684]

hsj

[Anonymous No.2042691]

trig 1

[Anonymous No.2042695]

trig 2

[Anonymous No.2042698]

calc 1

[Anonymous No.2042708]

<span class="math">s = \frac{D}{t}[/spoiler]
<span class="math">s[/spoiler] = speed
<span class="math">D[/spoiler] = distance
<span class="math">t[/spoiler] = time

<span class="math">a^2 + b^2 = c^2[/spoiler]

Pythagorean theorem:
The squared length of the hypotenuse of a right angled triangle is the sum of the adjacent length squared and opposite length squared.

[Anonymous No.2042709]

calc 2

[Anonymous No.2042715]

algebra

[Anonymous No.2042719]

random math

[Anonymous No.2042724]

moar random math

[Anonymous No.2042746]

more multiplication

[Anonymous No.2042750]

abstract math

[Anonymous No.2042981]

>>2042750

How is this abstract? 'Abstract' usually means the introduction or summary in scientific papers

[Anonymous No.2043045]

<span class="math">x^n - y^n = (x - y)\sum_{k = 0}^{n} x^{n - k} y^{k - 1}[/spoiler]

[Anonymous No.2043100]

>>2042981
Are you serious? Are you really not aware of the course called Abstract Algebra, and the fact that most of the mathematical proofs aren't intuitive and are therefore abstract?

For OP.

Try google=

[Anonymous No.2043117]

Sense, Undrips

[Anonymous No.2043123]

>>2042981
You might want to pick up a dictionary.

[Anonymous No.2043132]

Loathing

[Anonymous No.2043144]

I love you.

[Anonymous No.2043159]

Calculus Reference 1/2

[Anonymous No.2043162]

>>2043045
Forgot:

<span class="math"> n \in \mathbb{N}[/spoiler]

[Anonymous No.2043179]

>>2042663
Proper notation is better:
<div class="math">R(X,Y)Z = [\nabla_X , \nabla_Y ]Z - \nabla_{[X,Y]}Z </div>

[Anonymous No.2043185]

Calculus Reference 2/2

[Josef !!nUf2NflSAyw No.2043186]

>>2043179
Properer notation is betterer
<div class="math">\theta = \mathrm d\omega+\omega\wedge\omega</div>

[Josef !!nUf2NflSAyw No.2043198]

>>2043186
inb4 <span class="math">\theta = \mathrm d\omega+\frac12[\omega,\omega][/spoiler]

[Anonymous No.2043370]

Calculus 1 1/4

[Anonymous No.2043380]

2/4

[Anonymous No.2043402]

3/4 And I'm trying not to think of how stupid you are to not be able to google this stuff.

[Anonymous No.2043416]

4/4

[Anonymous No.2043472]

I'm trying to make a program in python 2.7 to calculate integrals, however I ran into some trouble.
I assume I need to use raw_input since the equation will contain a variable. How can I change the value of the variable in the equation, and since I used raw_input, how can I reassign values to the numbers in the equation?

[Anonymous No.2043473]

>>2043402
I do love you anon.

[Anonymous No.2043484]

>>2043472
1) specify your input language
2) write an interpreter

[Anonymous No.2043537]

Hm, found this thread still open. Why not revive it with the frobenius.

In finite fields with characteristic p (prime), ie <span class="math">F_q[/spoiler] with <span class="math">q = p^n[/spoiler] for some <span class="math">n \geq 1[/spoiler], the function <span class="math">x \mapsto x^p[/spoiler] is a field homomorphism, in particular we have the awesome formula
<div class="math">(x+y)^p = x^p + y^p</div> for all <span class="math">x,y \in F_q[/spoiler].
(You can easily use induction to generalize this for arbitrary natural powers of p, actually, you don't need a finite field, in fact, you don't even need a field in the first place, just a commutative unitary ring with characteristic p.)

[Anonymous No.2043572]

>>2043484
I really don't understand what you're saying, this is my first attempt at making a program.

[Anonymous No.2043575]

>>2043572
then solve a simpler problem, or use a different language

[Anonymous No.2043610]

>>2043572
Do it in two steps:

step one: read the function to integrate (and the limits of course) from the user and parse it so you can work with it. I don't think that's trivial or even possible for a beginner programmer, but you might have luck searching for a library/script like that which does exactly what you want. There's no shame in not reinventing the wheel every day..

step two: integrate the function, but not symbolically, since that's too hard. (Either that or you restrict yourself to sums of very simple to integrate functions)
Integrate numerically, that should be quite fun. If you know how the Riemann integral is constructed you should have no problem coding an algorithm which numerically calculates an integral.

Congratulations, you can now sum over uncountable index-sets. (Integration FUCK YEAH)

[Anonymous No.2043619]

>>2043610
In other words, write an interpreter.

[Anonymous No.2043623]

>>2043575
Can you just tell me how I can change the value of the variable in an equation.

[Anonymous No.2043626]

>>2043619
do you perhaps mean a "parser"?

I associate "interactive" with "interpreter", but I could be wrong.

Btw, we so stupid, couldn't he just eval? Does python have eval? I think it does!

Jesus Christ, how horrifying!

[Anonymous No.2043629]

>>2043623
give us example code or shut the fuck up. You obviously don't know the terminology well enough to be asking useful questions.
So give us your code and example user input so we see what you mean, or, alternatively, shut it.

[Anonymous No.2043649]

>>2043626
I assumed since he was contemplating "raw_input" that there would be user interaction, but that it not required for an interpreter.

interpreter = parser + translator
translator = domain language -> implementation language

convert integral into python = interpreter

[Anonymous No.2043655]

>>2043626
> use "eval"
> implying python natively handles numeric integration
oh my oh my

[Anonymous No.2043679]

>>2043629
let's say he enters 5x^3-4x
I just want to know how to give x a value so it can be calculated

and since I'm forced to use raw_input how do I turn my(after x has a value) string of numbers into something calculatable?

and yes, I was thinking of riemann integrals