BRAINLET GENERAL: Basic concepts in science only you don't

string theory

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>inter-universal Teichmüller theory

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>matrix multiplication

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Induction.

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>>9008839

THIS

I still can't tell the difference between rows and columns

>>9008839
An m*n matrix T is secretly a function with domain is the set of all vectors of length n, and codomain the set of all vectors of length m.
As a function it assigns the m-vector Tx to the n-vector x, i.e. [math]x \mapsto Tx[/math].

For example, the matrix [math] T = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6\end{pmatrix}[/math] assigns to each 3-vector [math]\begin{pmatrix} x \\ y \\ z\end{pmatrix}[/math] the 2-vector [math] \begin{pmatrix} x+2y+3z \\ 4x+5y+6z\end{pmatrix}[/math].
So e.g. the vector v=(42,0,-3) gets mapped to Tv=(42+0-9, 168+0-18) = (33,150).

Matrix multiplication then corresponds to function composition, i.e. for matrices [math]T_{m\times n}[/math] and [math]S_{n\times k}[/math] corresponding to the maps [math]v\mapsto Tv[/math] and [math]u\mapsto Su[/math], the matrix product TS maps [math]u \mapsto TSu[/math] which can be written as the composition [math]u \overset{S}{\mapsto } Su \overset{T}{\mapsto } TSu[/math].

I get vectors, but what exactly are tensors?

>>9008837

Hope this helps.

>https://www.youtube.com/watch?v=6HCz1tFqIcs

>>9008854
>secretly
secretly to engineers maybe

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vectors
transformation formulae

>>9008835
what an electron is
; (

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wtf is a vanishing cycle

>>9008862


Tensors are a generalization.
The skalar is a tensor with grade 0, you raise the grade of the tensor by adding base vectors to the number. So a vector is a tensor with grade 1 a matrix a 2 and so on.

>>9008854
hm, never heard it explained like this before. Is there anywhere I can read up more on this?

>>9008874

wow!

you must really be retarded

>>9008862
To give an informal description that lacks geometric intuition, just as vectors/vector fields let you assign an N-by-1 array to every point in N dimensional space, tensors are a generalization letting you assign N-by-N arrays etc to every point in a space.

Example application: Stress tensor. Think of the pressure applied to the faces of a tiny cube of material. You can have forces applied in the principal (x y z) directions orthogonal to cube faces, plus "shear" forces that deform the cube of material by rotating the faces' relative orientations by acting to each face (google an image of it). If you represent the these as a matrix with the forces orthogonal to faces in the diagonal and the ones parallel to the faces off the diagonal, you have a nice symmetric matrix. You can then use this to compute e.g. total amount of energy absorbed by a body under a certain combination of loading

>>9008839
There's not much to understand. For a regular joe it's just an overly complicated rule for multiplying two compatible vectors together.
Really the only two interesting things about it are that
1.) despite being so elaborate it's still transitive -
among same-sized square matrices anyway.
2.) the complex rules are not arbitrary. There are practical reasons for doing things the way they're done.
And that's about it. If you want to get good at that stuff, practice. But if you want to understand it, well, the above two points mostly cover it.

>>9008883
could shearing forces be modeled using affine transformations?

>>9008888
No.

>>9008881
Literally any linear algebra book that focuses on theory, rather than computation, will define matrices this way.
As >>9008872 points out, this way of thinking about matrices (i.e. as linear maps) is the norm among mathfags.

>>9008892
damn. i thought the points on a form shifting due to shearing stress could be calculated using an affine operator of some kind on each n-tuple of coordinates defining it.

>>9008888
Well, though not being an affine transform as far as I know per se, look up Mohr's circle as a way of eliminating the nondiagonal terms of the stress tensor locally by choosing an appropriate basis in standard engineering practice, which is of course implemented computationally through matrix multiplication.

>>9008841
>if any domino block falls, the next one falls also
>the first domino block falls
>therefore all domino blocks fall
Are you having trouble understanding the intuition on why induction works or is the problem in applying induction in practice?

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How to get laid

>>9008914
"ayy bb check this out"

*calculate all primes up to order n*

literally unbeatable

>>9008914
>go to the gym
>get healthy
>act with confidence
done
women are hardwired to go to the alpha male
if you look and act like a beefcake brawler, you then become the alpha
women are hardwired to scorn betas, as a beta cannot protect them and their children from predators, while the alpha can

simple straightforward shit, it's baffling that /r9k/ exists at all

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>>9008908
From the picture of Hume I'm guessing that he was making a joke.

>>9008924
>"ayy bb check this out"
>*calculate all primes up to order n*

>>9008835
Check out YouTube channel 3blue1brown and his "Essence of Linear Algebra" series.

Integral calculus.

>>9008839
>Redpill inc
http://eli.thegreenplace.net/2015/visualizing-matrix-multiplication-as-a-linear-combination/

This is how it really is anon, classes don't teach it though because they don't want to confuse brainlets

I can't read equations.

D'Alamabert's principle of virtual displacement

>>9008931
>he doesn't know the average /fit/izen

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>random variables

I didnt fucking die

>quantum path integrals
I am a fucking retard senpai

>>9008835
>eigenvalues/ eigenvectors
>hypothesis testing
>optimization

What does a determinant represent?

>>9010478
the volume of the image of the unit hypercube

>>9008893
it's pretty hard to break intuition. for most non math students in my school linear algebra is literally the last or second to last class they touch involving matrices

>>9010474
Eigenvalues are the values by with a vector is scaled, meaning it still spans itself only in bigger or smaller intervals.
An eigenvector is the vector corresponding to this value.

https://www.youtube.com/watch?v=PFDu9oVAE-g

Here faggot.

>>9010478
Dimensional Volume spanned by the basis of a matrix.

If 2x2 it's area.

>>9010488
I'm retarded.
The scaled vector is part of a nxm matrix.
In order for it to be considered an eigenvector it must stay on its span.
Watch the video.

>>9010460
>random variables
A random variable is a function from the sample space to the set of all possible values it can take.
For example, if the experiment is that we flip two coins, then the sample space is S = {Hh, Ht, Th, Tt}.
If we let X denote the random variable corresponding to the number of heads, then the set of values it can take is V = {0,1,2} and we can interpret X as a function [math]S \to V[/math] with X(Hh) = 2, X(Ht) = X(Th) = 1 and X(Tt) = 0.

Now if the coins are fair then each of the four experiment outcomes occurs with probability 1/4, which defines a probability distribution for X in the obvious way, i.e. P(X=0) = P(X=2) = 1/4, P(X=1) = 1/2. If the coins were weighted or the two flips were correlated (for whatever bizzare reason) then the probability distribution would be different, but the basic idea remains the same.

>>9010534
I still don't understand probability distributions.

Thanks for the help though

>>9008931
>>act with confidence
What does this mean?

DiffEq. All of it, I think. I'm not sure how I passed the class last semester but I retained nothing.

>>9008836
faggot

>>9010593
>probability distributions
Knowing the probability distribution for a random variable X helps you answer the question 'for each possible value [math]x \in V[/math] that X could take, what is the probability that X actually ends up taking that value?'
Using the same example, X is a discrete random variable taking the values {0,1,2}. Since X = 1 (for example) if and only if the two flips turn out to be either Ht ot Th, the probability that X is 1 should be the sum of the probability that the coins land Ht and the probability that the coins land Th. In this case we assume P(Ht) = P(Th) = 1/4 so the probability of having exactly one head, ie P(X = 1), is equal to P(Ht) + P(Th) = 1/2.

More precisely, the probability distribution for (discrete) X is a function [math]p_X: V \to \mathbb{R}[/math] that 'inherits' its values from the probabilities of the individual outcomes of S, in such a way that [math]x \mapsto p_X(x) = P(X = x) = \sum_{ s: X(s) = x } p_S(s)[/math].
The formula isn't pretty, but it makes perfect sense once you have a concrete example to show you how it works.

For continuous random variables you'll have to replace the sum with an integral, and at this point the definition gets more subtle. But unless you study measure-theoretic probability you won't need to care about these subtleties (though if you want to, you can look up the Lebesgue integral).

What are differentials?

>>9008835

The basic thing about a vector is that it's "two-things-all-at-once". Once you understand that, then you understand what a vector is.

It's a number, and a /direction/, bundled into the same thingy. This is commonly represented by a line segment with an arrow point at the end, which shows what direction the thingy points in. The longer the line, the "harder" it points in that direction.

Of course, in order to have a common sense of /direction/, we have to have some sort of standard space in which vectors are depicted. This is most commonly a two-dimensional space, or a three-dimensional space.

Vectors are commonly used in physics to depict forces acting upon a body, or a point, for discussion. See wiki and look up some exercises. Try drawing some problems! Then you'll get a feel for how vectors work.

>>9008862
The dual space of a vector space(over R) is the space of all linear maps V->R. If your vector space is over C then its dual will be the space of all linear maps from V->C. Every dual space is also its own vector space. Denote the dual of V by V*.

Tensors are multilinear maps of VxVx...VxV*xV*x...V*->R. By multilinear we mean linear in each argument. Example, f: VxV*->R. f(v,w)=r. Both f(av1+v2,w)=af(v1,w)+f(v2,w) and f(v,aw1+w2)=af(v,w1)+f(v,w2) are satisfied.

Say our vector space is R3. Its elements are column vectors with 3 components. The dual space is all row vectors with 3 components. The dual space elements, row vectors, are an example of tensors. A row vector multiplied by a column vector gives a real number. These are called type (0,1) tensors, they take 0 elements of the dual space and 1 element of the vector space, and spit out a real number.

Continuing with R3. The column vectors themselves are also tensors. Define v(v*)=v*(v)=r. So they are type (1,0) tensors.

We can write v*(v) as v_a v^a, where a is an index and we sum over all values of a. In our example above a=1,2,3. If we know how one of these vectors transforms, then the other must transform in the opposite way. See Chapter 2 of Schutz's general relativity.

addition

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>>9008835
Sequences and Series in Analysis

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>mitosis vs meiosis

>>9010715
cats have paws so cations are PAWSitive

>>9010478
We would like a way to assign a signed area(negative area is allowed) to linear maps from V to V. For this the key idea is the wedge product ∧ which when applied to basis vectors keeps track of orientation, and as we will see simplifies when setting the wedge space dimension equal to the vector space dimension.

Given a vector space V of dimension n we define the wedge product of vectors ∧ as being linear in both arguments and satisfying v∧v=0. This implies v∧w=-(w∧v). Call the space of these objects V∧2. Define V∧m analogously as the set of objects v1∧...∧vm. The dimension of V^m is (n m). Consider the n=2 case with m=2, then the only basis element is e1∧e2, since e1∧e1=0 and e2∧e2=0 and e2∧e1=-(e1∧e2).

Suppose we have a square matrix M:V->V. The map V∧m->V∧m defined by v1∧...∧vm->Mv1∧...∧Mvm is a linear map which we will call ∧(M). In the case when m=n, then V∧n is one dimensional and isomorphic to R. Thus ∧(M) is just multiplication by a constant. This constant is the determinant.

Example. V=R2. Consider M=(a b, c d). So Me1=ae1+ce2 and Me2=be1+de2. V∧2 has the basis e1∧e2. So the map ∧(M) sends e1∧e2 to Me1∧Me2 = (ae1+ce2)∧(be1+de2) = (ad - bc) e1∧e2. Thus the determinant of M is ad-bc.

The rule det(AB)=det(A)det(B) follows immediately from looking at the map ∧(AB) = ∧(A)∧(B) since these are one dimensional maps.

Also det(M)=0 immediately implies that we cannot find an inverse matrix, since V∧m is annihilated by ∧(M).

>>9010605
>What does this mean?
What did he mean by this?

>>9008835
What is it that you don't understand about theme? They're pretty simple senpai

>>9008841
Honestly though I don't understand induction. I don't understand how to apply it correctly, the examples always seem to have some odd form.

>>9008844
Column hold buildings up and are thus vertical. Rows are the other one.

>>9008835
Elementary probability and combinatorics. For some reason, my brain fries whenever I try anything of the sort.

How the fuck do particles work how can they not be in one place reeee

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>>9008835
Paradoxes in Set Theory & Logic.

Like the Russell's paradox.

>>9011006
We know how they work but I don't think anyone knows why they work like that

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>>9008839
you baiting r..right ?
we learn that shit in school

>>9008931
Lifting does not cure autism.
Its the main flaw of may fitizen.

>"you shouldn't care about what people think"
>the basis of ethics is caring about what other people think

I'm only insecure because I'm intelligent and ethical.

>>9008835
Literally anything past basic maths. Went for the humanities route in school. Psychology and Literature and ignored/forgotten the majority of basic science and anything past the most basic maths.

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>>9008835 >>9007252
Katy Perry: Is math related to science?
http://youtu.be/Orf8NkcIDig
http://youtu.be/OB4znOVsfnA

>>9008839
I learned that shit in high school and it was easy as fuck.

>>9008839
Is this a joke?

>>9010712
A sequence or series (a series is a type of sequence) can either diverge, converge, or infinitely oscillate. What's not to understand?

>>9008862
N-dimensional array of numbers. Its that simple. It can represent anthing.

>>9011128
Nit really, you can represent tensors that way, but that isn't the tensor per se. What happens if you change coordinates then?

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Magnetism

>>9008835
Its like a line pointing somewhere
A visual representation of basic algebra i guess. Multiple Dimensions added to it are just multiple factors.
Lets says you have a factory. Every cycle (represented by [x|-|-]) they produce 20 somethings (represented by [-|y|-]) and they spend 100$ (represented by [-|-|z]).
Im that case that vector is e:x=[1|20|-100]
Now you take that times the cycle and you have the different ressources.
I hope that is mathematical enough for /sci/

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>>9008882
>brainlet general
>must really be retarded

>>9008872
anyone who has ever taken a linear algeba class knows that, engineer or not.

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Is 115 iq enough to study applied math?

>>9011354
yes

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>>9008835

>>9011354
70 iq is pretty much enough for anything that isnt combinatorics

>>9010718
HOLY FUCK
Why didnt anyone tell me this two years ago i wouldve passed gen chem fuck

Anyone? >>9010691

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>covalent vs ionic bonding

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>>9011431

>>9010715
>>9011571
kek

reality

like, scientifically speaking, what IS reality? *smokes weed*

why do people discredit wildberger when we all know deep down he's right

>>9011431
>posting a rapist
you people need to check some privilege

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>>9008835
>writing complex proofs

>>9010691
Differential is a change in one thing with respect to another. So say you have distance on your y axis and time on x axis. A straight line going 45 degrees. Y=x

First order differential gives you velocity, the change in distance per unit time... Because this is constant gradient your velocity is constant also

If you then take the differential of velocity ( second order diff) you are looking at the change in velocity per unit time squared.... As the gradient is constant this will equal zero

Want to know how brainlet I am? everything in this thread I've never studied, tried, or learned before. I didn't have a deep interest in math before, because they never tried to help me understand only to obey, memorize, and finish test after test. I want to feel excited about Math instead of worried. But I don't know how and it's really hard.

wave functions and wave function collapse

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>>9013342
... actually, just functions. F. Wtf is F?

>>9013343
A really big list (possibly infinite) of pairs like (A, B). Every time it gets an A, it returns a B.

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>>9013346
I don't know what you mean

>>9013356
Imagine you have a bag of things, and imagine this bag has a big, capital letter A embroidered on it. We'll say that items in this bag are elements of the set A. Now imagine there's a second bag, with different items, labeled B. Now imagine there's an autistic kid called Francis that forms associations between objects - if you give him an item from bag A, he'll immediately run to bag B and pull out the item he's associated with the item you gave him. Francis is the function F.

>>9013356
a function f is a rule of assignment

If you have two sets, for every element in one of the sets, I can assign it an element from the other set. A function is this rule of assignment, where every element in the set gets assigned a single element of the other set.

A function is called surjective if every element in the "target" set gets hit by the function

A function is called injective if there are no elements in the target set that were assigned by function for more than 1 element

>>9011114
probably the [math]\epsilon[/math]-definition of convergence of sequences and cauchy sequences

>>9013393
>>9010712

consider a sequence of numbers. If you give me an upper and lower bound ([math]\epsilon[/math]), and I can find a term in the sequence from which every element is within that bound, then the sequence converges

>>9013356
A function is a really big dictionary. For each word in it, there's a meaning. Different words may have the same meaning ("satisfied" and "content"), but there are no repeated words (you won't find "happy" twice in it).

The words are the x and the meanings are the y. x goes in (word), y comes out (meaning). f(x) = y. Dictionary("happy") = "enjoying or characterized by well-being and contentment".


It's just that instead of using words, functions usually use numbers. Imagine that human beings all live to exactly 80 years of age. The function yearsLeftToLive takes in your current age and gives you how long you've got left to live.

yearsLeftToLive(age) = 80 - age.

Try different values for age to see why this makes sense.

>>9011063
Only brainlets listen to celebrities yap about topics they don't understand

>>9013143
Couldn't give two shits about it even if I tried. His lectures are good and that's all I care about

>>9008835
That is the shit that I 'just got'. For every vector section I got 100%. I thought it was because I was white and europeans score higher on spacial reasoning IQ tests.

>>9013387
>>9013389
>>9013399
I think you're just confusing him, guys...

I don't know the fucking multivariable calculus

>>9008854

Not LENGTH m,n

DIMENSION m,n

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I'm an atheist that doesn't understand the big bang theory. I know that the universe is visibly expanding but how can you extrapolate anything from that other than "it used to be smaller"

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>>9008835
Dawg... vectors are quanitified physical attributes.

>>9013532
That's a terrible description

>>9013511
Not necessarily smaller, more dense.

>>9013532
Pretty dumb.

The only accurate description of vectors is as elements of a vector space.

And what is that? Well, now read the definition of a vector space to find out.

>>9013330
It's ok anon, I used to feel the same way. It gets better.

>>9011091
>>9011087
>>9011038
>implying any of you actually understood what the fuck you were doing

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>>9013594
>simple transformations are difficult to understand

I don't understand integrals and derivatives.

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>this fucking thread

I can't believe people like this exist.

I did a maths degree and never got multiple integrals

I don't understand how you project functions onto each other. first time I heard about this was with fourier transforms, and how the fourier transform is just a projection of the function onto sine and cosine

people can be happy without knowledge

>>9013647
this person exists. math degrees are as much of a joke as engineering degrees

>>9008835
>>9008839
>>9008874
>>9010478

literally first week in linear algebra

>>9013639
Given a function [math]f : A \rightarrow \mathbb{R}[/math] (where [math]A \subseteq \mathbb{R}[/math]), and a point [math]x \in A[/math], the derivative of [math]f[/math] at point [math]x[/math] is defined as [math]f'(x) = \displaystyle\lim_{h \rightarrow 0} \frac{f(x + h) - f(x)}{h}[/math] if it exists. The derivative of [math]f[/math] is a function that maps [math]x \in A'[/math] to [math]f'(x)[/math], where [math]A'[/math] is the subset of [math]A[/math] of all points [math]x[/math] such that [math]f'(x)[/math] exists.
See, that wasn't too hard.

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>>9008835
systems of equations

>>9013738
I am unable to decipher the contents of your post.

I still have no clue why Cauchy's Theorem is actually true even though I know the proof.

>>9014039
https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

This is calculus for dummies.

>>9013639
integrals is a sum

derivatives the rate of change

>>9010715
>mitosis
every cell ever, one splits into two identical cells
>meiosis
germ line cells undergo meiosis in which they produce 4 genetically unique cells (sperm and egg cells)
As in the chromosomal information they have are a unique mix of paternal and maternal information
Inaccurate division during meiosis causes down syndrome and other complications

>>9013291
I don't think this is a good explanation. How are differentials typically written (symbolically)? Are differentials purely notational or are they elements of [math] \mathbb{R} [/math]? Do differentials obey the same rules as reals do under addition, subtraction, multiplication and division? You should answer these kind of questions in addition to your original answer.

>>9014048
I get this feeling a lot. Especially during my course in abstract algebra I could prove several things but was never able to explain the proofs in an intuitive layman way..

Green's Theorem, Stokes Theorem.
I've searched the internet to get the intuition behind, I can follow the explanation, but it just doesn't click to me. If you tell me to write those theorems down, I'll most probably write bullcrap.

>>9008844
>I still can't tell the difference between rows and columns
i can but i must admit i have to think harder which is which than id like to admit AHAHA

>>9014039
it's just a dummy trying to be smart

>>9010718
another approach:
cats are pussys thus cations are PUSSYtive

>>9014039
Which parts specifically do you find undecipherable?

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>>9008835
buoyancy!

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>>9008835

I don't understand how 1s and 0s can create something like this. Like, I genuinely don't get how stuff can be used with static electricity, to actually create moving images....

>>9013143
>sending lewd texts is rape

>>9014290
Take a physical optics course. You're preq will prob be electromagnetism and maybe quantum

>>9014228
To find the total variation of a quantity inside a region, you need only count how much comes in and out

Injective, bijective and surjective

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>>9014290

>>9014358
Well that explains it!

p-value

>>9008908
>he doesn't know the difference between mathematical induction and regular induction
Cerebrito

>>9014367
Integral of the standard Norma distribution to the right of the cutoff

>>9014290
https://youtu.be/IyUgHPs86XM?t=85
Great (as always) presentation by Carmack

>>9014342
Injective is the set of me to your mom.
Surjective is the set of your mom to me.
Bijective is you and a trap

trigonometric substitution
IT'S SO UNINTUITIVE.

magnets. Took physics 2 last semester, got an A in the course, still don't get that shit tho.

>>9014342
Do you mean you literally don't understand the terms or just can't remember which is which?

>>9014394
It's application. How do you determine a function is either one of the three?

>>9014387
Trigonometry is a meme

>inverse proportions

>>9014398
Alas I'm so long gone I can no longer comprehend the value of psychology,sociology,social work, I'm no longer afraid of death I can't comprehend it I can't remember people's names

>>9008874
I literally learned that in physics 101 if I'm not being baited just keep doing practice problems it can't possibly take you that long to figure it out.

>>9014342
This. Can never remember which one is which.

That said, I haven't spent too much time trying to learn it and apply it.

>>9014387
Trigonometric substitution is actually just u-substitution. Any analysis textbook details how and why it works, usually with a proof.

It just has to do with continuous functions. What happens when you make a continuous function go through a continuous function? That's right. Now, the trig functions are continuous aren't them? Well, there you go. Trig sub explained.

The only reason it gets its own name is because it is very useful and because unfortunately society has made the decision that even brainlets who don't understand analysis should learn calculus and therefore to not confuse the little 30 IQ brains of engineers with too much "nonsense" about continuous functions we just tell them "Oh, this is a formula. The trig sub formula. Just like the ones in your formula sheet, but better. Just learn it kids :D).

>>9014396
Given a function [math]f : A \rightarrow B[/math], to show it's...
Surjective: take any [math]b \in B[/math], show there has to be an [math]a \in A[/math] such that [math]f(a) = b[/math].
Injective: take any [math]a, a' \in A[/math] show that if [math]a \neq a'[/math] then [math]f(a) \neq f(a')[/math].
Bijective: do both.

>>9014272
>(where A⊆RA⊆R), and a point x∈Ax∈A,
Some of these runes are mysterious to me whats the big C with an underscore in it

>>9008835
Most of algebra and everything more difficult than that.

>>9014122
It's a perfectly good explanation for a 'brainlet general' thread. Stop trying to show how ((intelligent)) you are faggot.

>>9011571
shit, I read irony bolding

>>9011009
Let R be a set of sets that do not contain themselves.

Does R contain itself?

No -> R is a set that doesn't contain itself -> R contains itself (definition of R)

Yes -> R contains itself -> But R is defined to contain all the sets that do not contain themselves -> R doesn't contain itself.

>>9015051
do you not know how to read, brainlet?

>>9010534
I get it just it feels

unnatural

>>9015026
No its a shitty explanation. You are just stating facts without providing any brainlet friendly insights as to why things are the way they are.

I don't know the answers to my suggested questions. I think these are common questions on a brainlet level but you go ahead and wave my criticism of as tryhard intellectualism you fucking coward

>>9015107
>I don't know the answers to my suggested questions. I think these are common questions on a brainlet level but you go ahead and wave my criticism of as tryhard intellectualism you fucking coward
cringe

>>9014390
What's your background in physics?
Have you taken a full course on electromagnetism? Quantum physics?
Magnets were a nightmare for me, I'd like to help you.

A question for anyone that enjoys thinking:
If the magnetic forces don't do work, how come a magnet can lift a piece of Iron and make it gain potential energy, which means work has been done?

>>9014591
⊆ - is an improper subset of
{1, 2, 3} is an improper subset of {1, 2, 3}

∈ - belongs to / is a member of
2 is a member of {1, 2, 3}

>>9008876
Why do they do what they do?

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>>9009111
How?
It's just sums.
And areas under the curve. You can learn it graphically to understand the concept, and then use a table to learn the formulas and equations. EZPZ.

>>9010474
>Hypothesis testing
You mean the scientific method or the statistics portion?
>optimization
You mean in a process or in maths(by using differential equations?)

>>9011516
Doubt it.

>>9011571
Covalent is a homo relationship. Ionic is a hetero relationship.

>>9013330
You need to find passion for something you love, apparently that is not math.

>>9013639
Here it goes.
Do you understand position, velocity and acceleration?
If so, look at pic related

Imagine yourself jogging. You start from zero, but you accelerate constantly (like when you start jogging)
At first, your position is Zero, but you start moving, this means that you are gaining velocity, and to gain velocity means that you're accelerating.

The change in distance/time is Velocity. The change in velocity/time is acceleration.

This relationship is exaclty the same as woth Derivatives and Integrals.

The velocity is the derivative of the position, and the acceleration is the derivative of the velocity ( or the double derivative of the position)

And as it's counterpart.

Velocity is the integral of accelerstion, and position is the integral of velocity ( and the double integral of acceleration)

Hope this helps visualize it.

>>9014285
Like in physics?
Just the difference in density*gravity.

>>9013330
Pretty much this, I only browse /sci/ for the after-death theories

>>9015249
>If the magnetic forces don't do work
Questionably premise

Quantum computers

>>9013671
Actually you become more unhappy the more you "know"
Because you realize how dumb everyone and everything is

Fourier analysis. I've studied it more than once and I know how to use it but it's still magic to me. Explain like I just rolled out of the womb what the idea is why people use it to get cool data.

>>9008841
>>9010901
It's simple.
First you prove the initial case. (I)
Then you prove that if a condition happens for n-1, then it happens for n. (II)
Thus, because the 1st case is true (I), then its true for the second (II). Because it's true for the second, it's true for the third (II) and so on.

>>9010472
Idea is simple. You know that classically, a particle travels through the path that extremizes the action.
In QM, you know that particles can travel through classically forbidden paths.
Then, you assume that the probability of a particle going from A to B is a "sum over all possible paths" from A to B (i.e. a functional integral) with a weight associated with each path (similar to statistical physics where you had a weigth exp(-beta H) ), this weight basically being responsible for when E is high (classical limit), the weight goes to 1 for classical path and to zero elsewhere.
If you do the calculations, you can prove that this formalism yields the exact same results as standard QM iff the weight is exactly exp(iS), where S is the action.
The calculations are straightforward and almost magical. The fact that you get exactly iS is ridiculous in so many levels.

Afterwards, this formalism is pretty straightforward to be generalized for fiels instead of particles. Try reading Peskin's book.

>>9013330
i feel you mon

>>9017556
Tl:dr functions of the type exp(iwt) form a complete basis of functions

Basically, when you have a generic periodic function, you can write it as a sum over n of sin(nt*pi/T) and cos(nt*pi/T) (which are also periodic), where T is the period of that function.
Because exp(ix)=cos(x)+i sin(x), you can instead write it as a sum over n of exp(int*pi/T) (but this time, n goes from -infinity to infinity). This is basically expressing shit as sums of plane waves exp(iwt).
Afterwards, you can take the limit T->infinity and that takes you from a sum over n to an integral:
f(x)=int( f*(w) exp(iwt) dw)

Here, f*(w) has the role of the coeficient of the plane wave and is your fourier transform.
This function then illustrates (in a continuous manner) how the (infinite) coeficients associated with a frequency w change.

I.e., you take a function, take its fourier transform, and then if it has high values for an interval of frequencies, then the sum (integral) is dominated by those frequencies.

Note that this reduces to the standard definition by taking use of dirac deltas.

Hope that helps for now, im not near my computer so i cant do much
>>9017593
Oh and i mistyped "fields" here

>>9008835
>2 F grades last semester
>Intermediate micro and macro econ
Fuck How do I get better at studying? I wanna stop being a brainlet.

>>9010908
BUT WHICH IS N AND WHICH IS M IN NxM

>>9013330
look into the concepts for whatever you're studying. if an instructor doesn't provide you with a reason to be excited, then search for it on your own. read some books on general concepts or history in math or look online for "whys" so you become motivated to learn how to execute the actions to then know how

>>9018789
N is the vertical position and M is horizontal, because fuck your intuition.

>>9011134
Conservation of physics among frames of reference. http://galileo.phys.virginia.edu/classes/252/rel_el_mag.html

>>9013639

a derivative is the rate of change or the line tangent to the function. for an example, lets say that someone is driving a car. a regular straight line would be if they are consistent speed. this is not likely irl, they are accelerating and braking constantly in traffic (their line of speed is curving up and down). at some points they may be going 70mph, or 55mph. if you want to find the exact rate of speed they were at during a specific point in their travel you would take the derivative.

when you take a derivative of a function like f(x)=x^2+5
the derivative is (using most simple power rule)
f '(x)=2x
integrals are just doing the same thing backwards. the reason you see a + C at the end is because there is a constant you may not know the value of, like in the example i gave, if you were working backwards with only the f'(x) information how would you know that the original function has a +5? that is the C. keep in mind in other problems there may not be a value at all, but the constant of +0 would still be valid.

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Complex number, Argand plane, derivatives of complex numbers, limits and continuity, derivative and Cauchy Riemann conditions, analytic functions, integration in the complex plane, Cauchy's integral formula, infinite series for complex variables. Taylor series, Laurent series, residue theory, evaluation of integrals around indented contours. Linear vector spaces, matrices and determinants, eigenvalues and eigenvectors.

tldr please tell me what to expect I have to take this in two years oh god

>>9019338
>please tell me what to expect
probably something like
>Complex number, Argand plane, derivatives of complex numbers, limits and continuity, derivative and Cauchy Riemann conditions, analytic functions, integration in the complex plane, Cauchy's integral formula, infinite series for complex variables. Taylor series, Laurent series, residue theory, evaluation of integrals around indented contours. Linear vector spaces, matrices and determinants, eigenvalues and eigenvectors.

>>9019361
Yeah but in terms a retard who's only finished Freshman year can understand.

>>9019365
Well if you've finished freshman year you should already know:
>Complex number, Argand plane, Taylor series, Linear vector spaces, matrices and determinants, eigenvalues and eigenvectors.

the rest is basically just a minor difficultly increase from doing single variable calculus on a line to doing calculus in a plane

just read this or something

http://people.math.sc.edu/girardi/m7034/book/VisualComplexAnalysis-Needham.pdf

Still don't know why you can't derive an endpoint of a graph, or a value in a hybrid graph where 2 separate functions meet

>>9019409
You mean taking the derivative of a function at an end point right? I think it's because both the function and it's derivative have no value on one side of the point, basically that there isn't a limit value from both the pos and neg side of the points that are equivalent

>>9008835
calculus, category theory, any maths that require a lot of specific terms.

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>>9008864

im about to prank call this guy in 4 dimensions

>>9011128

so it's a set?

?????

??

????

>>9011134

the changing electric field fuckulates the farads

>>9008835

what the fuck is a newton series

how does this mean all polynomials can be expressed as a sum of binomial coefficient

I've never understood fully the role of the observer in regards to superposition, does it mean actual consciousness or does any interaction with a macroscopic system collapse a superposition?

>>9014418
please give me a quick rundown on rotation formulae

>>9020156
https://youtu.be/8ORLN_KwAgs?t=1m50s

differential k-forms

I mean, I can work with them, but it just seems like such a contrived meme, that I don't "get it".

Do you stop "getting" things in higher-than-freshman-level mathematics?

I'm starting to teach myself differential equations, but i think there's something i'm missing. it seems too simple of a concept i'm almost certain that i'm misunderstanding something

>>9008835
Tensors

Analytic continuation

>take calculus 3 for the 4th time
>get to the triple integrals section
>drop out

every. single. time.

>>9020517
remember her?
[math]f(x) = f(0) + f'(0)x + f''(0)x^2 + f^{(3)}(0)x^3 + \ldots[/math]
try not to gasp when you see how she looks now

>>9020465
no, you just need to work more with geometry. the first time I saw k-forms I was really fucking lost. over time and after doing more stuff in geometry and topology things start to fit together.

>>9008835
why is c the speed limit?

>>9020109
Yeah that's what I meant. Thanks for explaining it

>>9020541
because Einstein had a dream where he was running faster than the speed of light, and he turned around and he saw himself running right at him and got really spooked and woke up.

Ever since, it's been a taboo subject.

>be me
>Be talking to a qt Arab girl I met online
>show her my maths homework with a caption "man this sucks"
>she basically solves it for me
>she shows me her math homework and it's way more advanced
>mfw I haven't even taken chemistry yet and she's well versed in it
Jesus Christ I feel retarded. I'm just going to major in biology now

>>9020600
That's what my physics professor said too.

So if you run faster than light you can turn around and see yourself coming.
But if you run faster than sound you would be able to turn around and hear yourself coming.
Going faster than sound isn't impossible or the same as time travel.
What's the deal with light?

>>9008835

>moment generating functions
>math word problems that doesn't explicitly tell you what to do in a concise logical order that yields the right answer
>combinatorics

statistics is suffering sometimes

electricity.

>>9020632

1.
>moment generating functions
Literally a Laplace transform

2.
>math word problems that doesn't explicitly tell you what to do in a concise logical order that yields the right answer
That's a problem of unclear English, not unclear mathematics.

3.
>combinatorics
You're not being clear here so I'm going to chalk this up as a symptom of 2.

>>9020650
>Literally a Laplace transform

Wow, all this time and I never made the connection. But why does this stuff show up in my statistics course and not in my differential equations course?

>>9013678
yo me too, which school?

>>9014290
1s and 0s tell the computer which pixels to light up and which to color to light them with. that's why high resolution takes so much time to load, so many pixels

>>9008835
Calc 1

I understand the concept of product/ quotient rule and chain rule, its just taking derivatives of fractions and exponential as well as some logarithms that really screw me over.

Learning math for me is hard, Thank god all the math courses I took though were in community college, cost of retaking them in state/private schools would probably put me 6ft under.

>>9019338
Are you doing a pure math course or an applications course? Seems a bit weird that you'd have the latter subjects mixed in with complex analysis.

If it's complex analysis (with proofs, not just complex calculus), be prepared for the weirdest and unintuitive shit at first, then everything clicks and you notice that the complex numbers really are the best shit ever. The arguments in proofs and theorems are completely different to real analysis, in that they are more topological arguments, and everything just werks. (once differentiable implies infinitely differentiable, all contours integrate to 0, etc)

>>9020329
>bepiswithdrool.jpg

>>9008835
Solid geometry

>>9013330
Also, if history interests you at all, looking up info on the lives of famous mathematicians and gaining an understanding of just how revolutionary their ways of thinking were is a good way to help you become more interested.

>>9013643
>I can't believe people like this exist.
These people are fucking average/very near it.
You wouldn't believe the kinds of retards you'd find on the other end of the bell curve.

>>9021613
>looking up info on the lives of famous mathematicians
http://www-history.mcs.st-and.ac.uk/ has a lot of well-written/well-researched biographies

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>>9008835

First of all THIS.png

Second of all I can't pronounce the entire name of the molecule, of which the trival name is Titin.

>>9021501
It's some engineering math course.

>>9021716
:'(

>>9015026
>>9013291
>>9015117

t. Calc 1 kiddy who thought he had a chance to answer a question but realizes he doesn't know anything about the question that was asked

>>9008835
It's a DIRECTION AND A VALUE, where it's traveling on a grid and how fast. Internet infographic searching is your friend

>>9014290
https://www.youtube.com/watch?v=MzlK0OGpIRs

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>>9013511
I used to be an atheist too because I was tricked into believing you're either a dogmatic fundie or a cool rational independent atheist.

Neither, the creator iz u.

>>9018492
get your wallet out of their hands and get yourself to a free information platform

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>>9014390
>got an A
>still don't get that shit
education is magic

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>Einstein Field Equations

How the fuck do you learn how to use these without a class?

>>9008844
Columns starts is c so just think of cocks. Straight cocks

>>9022080
just kinda mentally masturbate more, play abstract vidya games

>>9008880
Not true in general. A vector is defined as an element of a vector space, which is a very broad definition. A tensor is defined as an element of a tensor product space, which is a special type of vector space. So a tensor is a special type of vector, not the other way around.

>>9014517
Wait, are you telling me people don't learn the general theorem in calc classes?

>>9011128
Only if you define a basis. Both vectors and tensors can be defined without a basis. The "big pile of numbers that transform correctly" understanding of tensors is a bit weak.

>>9021962
Oo la la somebody's getting laid in college

>>9022162
with "...that transform correctly" at least you emphasize the important part about tensors. saying this >>9011128 is totally misleading.

>>9022107
Uh, my cock is curved. Please check yout straight cock privilege

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Honestly, and don't make fun of me, but what the fuck is fire? I don't see how it fits into solid, gas, or liquid.

>>9022570
Privilege? I want a curved cock.

>>9023463
The flame is the same substance as the smoke. Everything glows when it gets hot enough. The flame is the smoke before it has cooled down enough to not glow.

>>9008839

ok ill bite, what is the determinant and inverse and diagonalization used for in major applications? the only one i can think of is the helix transform used by rosalind franklin to configure the x-ray images she attained form data points

>>9023518
Ever heard of eigenvalues?

>>9023518
dude linear algebra is used fucking everywhere
literally everywhere

I'm surprised to see /sci/ is just a LARPing science enthusiasts

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Would anyone please be able to tell me what that arrow is called?

Could not find it by googling

>>9024233
it means w is a vector
https://en.wikipedia.org/wiki/Vector_space#cite_note-1

>>9024245
Ah, I see. Thank you, I didn't realize.

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>>9008835
>vectors
>Newtonian mechanics
the latter isn't really that hard to learn but I'm a lazy piece of shit who would rather work with wires than throw rocks and calculate their speed

>tfw grade A pure math student
>can't understand hypothesis testing, t tests, chi-sq, fucking P VALUES and so on

Can someone give me a non-pleb explanation of these concepts?

>>9022080
you can just read a book, the equations have a lot of definitions behind them

>>9023756
Shouldn't be surprising at all desu

>>9023514
I finally see. Thanks, anon.

>>9021962
nice my dude we should smoke up sometime and i can show you my gems.

Maths, Physics.

I win "the most retarded" award

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Most of complex analysis
I know the bare basics of complex numbers, but once you get into residues and contour integrals, I'm lost.

Also, PDEs

>>9020630
maybe c is the speed of time. the speed at which events propagate?

>>9014364
it does though. it is that simple.

>>9008835
>entry level college physics :/

>>9014390
>>9022008
That's worrying

>>9010691
The speed at which your function changes.
For example f(x)=3x increases three steps in height for every step forward on the x-axis
The rate of height increase is thus 3 or f'(x)=3

Engineer here, I understand almost nothing that is taught in lectures. I have to sit down for a couple of hours and learn the material by myself, which usually results in pretty good grades. I'd blame the professors but there's a couple people in every lecture that seem to really get what is being taught.

BURGER HERE

I never learned my multiplication tables. I'm also learning disabled in the maths so it is what it is.

Can someone explain vaccination to me? I feel as though the high-school explanation is missing something.

>>9008835
Everything
t. EE Masters

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>>9008835
Factoring

can do everything but that thing in particular, and what surrounds it

how to get gf

>>9028573
It's when the rothschilds and bogdanoffs meet at bilderberg meetings to make a toxic cocktail to make more autistic kids to increase the 4chan user base and hence increase the effectiveness of their psyops of 4chan

Jk it's just getting your immune system to remember a certain pathogen so you can fight off the same pathogen much easier next time you meet it. You get injected with something to trigger an immune response, like antigens (biomolecules that the specific pathogen has) or a weakened (attenuated) version of the pathogen, or some other ways I forget. A T cell receives the antigen, either directly or by another leukocyte meeting the pathogen/part of the pathogen and presenting the antigen to the t cell via the majorhistocompatibility complex. This t cell then undergoes clonal expansion, and the longterm important products of this repeated division are the t memory cells which stay around for a fuck ton of time. You'll also get memory b lymphocytes that stay around for a fuck ton of time too. If you meet the same pathogen again, these t memory cells will undergo clonal expansion once they meet the antigen again to form (among others) t helper cells which activate the right b memory lymphocyte, which also undergoes clonal expansion to form b plasma cells which produce antibodies to help your body fight the pathogen by toxin detoxification, pathogen weakening by preventing the pathogen binding to your cells, and causing the pathogens agglutination which makes it shit at being a pathogen and also helps phagocytes phagocytose clumps of the pathogens easily.

>>9028566
Different styles of learning. Nothing wrong with that. A lot of people can only grasp a concept by doing it themselves.

>>9028925
B.E. yourself

>>9028566
well at least you're good at sucking cock and all, since you're an engineer. brainlets can't even suck a cock.

I still struggle to divide polynomials.

>>9008835
any math above basic calculous.

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>long division

>>9030033
I was cringing through this whole thread til I saw this. Are polynomials actually reasonably divisible if they don't have common roots?

>>9030568
I actually still don't know how the long division algorithm actually works, I know how to apply it, but I don't understand WHY it is.
I'm fine with the multiplication/addition algorithms, but the long division algorithm seems like magic to me.

I failed high school precalc, which means I'm now stuck doing a bad degree which I hate. Really wished I was smart enough to understand math and be in STEM, but I'm a failure.

I'm trying to read this thread, and it really is making me remember how much of a brainlet I am. Thanks /sci/.

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Addition and subtraction