/mg/ math general: Poppin' Wheelies Edition

[Anonymous No.10334233]

What are you studying today, /mg/?

https://en.wikipedia.org/wiki/Wheel_theory

Anton Setzer - Wheels
http://www.cs.swan.ac.uk/~csetzer/articles/wheel.pdf

Jesper Carlstrom - Wheels: On Division by Zero
http://www2.math.su.se/reports/2001/11/2001-11.pdf

Previous thread >>10322503

[Anonymous No.10334344]

[math]p[/math]-local groups.

[Anonymous No.10334371]

Second for algebraists are all scum and analysts are the most pure mathematicians, algebraists just toy with their pathetic little bullshit constructions like ittle bittle toddlers playing with their building blocks.

[Anonymous No.10334386]

>>10334335
grug need help

[Anonymous No.10334398]

>>10334371
Oh the bitterness. I get it, you don't like it when people make anal jokes.

[Anonymous No.10334405]

Threadly reminder to work with physicists.

[Anonymous No.10334417]

>>10334405
>expand ℏ as a power series
>erase higher order terms

Physics is mathematical blasphemy

[Anonymous No.10334449]

hey what does it mean for the tangent vector of another vector to be <0,0,0>

for example, if you take 5i+3j+2k and take the derivatives, you get <0,0,0> this will happen when none of these terms have t parameters

[Anonymous No.10334512]

>>10334449
It means that the curve defined by the single vector 5i + 3j + 2k is constant, i.e. it just sits still at the point 5i + 3j + 2k.
A tangent vector is the tangent to a curve, while a point is just a point. There's no movement, so the tangent (which is really the velocity) is zero.

[Anonymous No.10334519]

>>10334386
Construct an example. Try to think - how can I make a sequence of differentiable functions (ones with no corners) approach a function that has a corner?
They have to converge uniformly, but this isn't that hard to make happen for what you're trying to do.
Remember that the uniform limit of a sequence of continuous functions is always continuous, so your limit WILL be continuous (just not differentiable).

[Anonymous No.10334526]

>>10334417
You do know that's literally what the entire field of deformation quantization is based on, right? And you do know absolute units such as Kontsevich, Moyal and Fesodov helped shaped the field as a mathematical study, right?
I highly doubt you have any credentials/achievements that allow you to call whatever Kontsevich works on a "blasphemy". I doubt you even know what constitutes a "mathematical blasphemy" at all to be quite honest.

[Anonymous No.10334544]

>>10334233
I know this is just the thread talking about math but that wheel theory is genuinely interesting, I always thought devided by 0 is the most boring thing of all, but right now it is not then. what kind of algebra is that?

[Anonymous No.10334549]

>>10334519
I think I got it thanks to the help I recieved. Now I must consider the same space under [math]\displaystyle d(f,g) = \max_{a\leq x \leq b} |f(x)-g(x)|+ \max_{a\leq x \leq b} |f^{\prime}(x)-g^{\prime}(x)|[/math]. Apparently this metric makes the space complete, but this is what I need to show.

[Anonymous No.10334556]

>>10334544
>what kind of algebra is that?
Wheel theory?

[Anonymous No.10334561]

>>10334549
Ah, I remember that problem being quite annoying (though I had to do it for lipschitz functions, which is a slightly weaker condition than differentiable).
best of luck! typically you want to go at these directly, taking a cauchy sequence, looking at the function that is the pointwise limit of your cauchy sequence, and showing that the sequence converges to it for that metric.
see what you can do!

[Anonymous No.10334581]

I'm interested in self-learning maths but I often read that textbooks aren't enough, and without a teacher / mentor I won't really be able to make progress -- at least when it comes to proofs. I'm assuming most of the ppl here are studying math in college, but for others involved in self-study, what has been your experience?

[Anonymous No.10334653]

>>10334581
Just don't slow down!

[Anonymous No.10334762]

>>10334581
It'd be helpful if you gave a little of your background/where you are in life. What is your goal?

[Anonymous No.10334791]

>>10334581
Whoever tells you textbooks aren't enough have no idea what they are talking about. You'll only succeed in math if you can develop a good mathematical intuition, and if you have the capacity for that, then it doesn't matter how you learn it.

[Anonymous No.10334818]

Where can I find crypto books? More than just basic intro stuff. Focusing on theory rather than programming because I can't program and like math.

[Anonymous No.10334839]

>>10334818
I haven't read it but last thread someone recommended "arithemetic of elliptic curves" by Silverman.

[Anonymous No.10334842]

>>10334818
>I can't program
What's your excuse anon?
Learning is easy!

[Anonymous No.10334844]

>>10334842
Programming is useless in crypto since you would mostly rely on solid libraries to implement your crypto algorithms to avoid side channel attacks

[Anonymous No.10334852]

>>10334844
Someone writes the solid libraries. If you can write algorithms you can program.

[Anonymous No.10334859]

>>10334233
Algeo.
>>10334405
Physicists are super cute. They're especially cute when they say things like "what's the difference between a symmetric and a self-adjoint operator?".

[Anonymous No.10334860]

>>10334842
I've tried for five years and did not pick it up. I failed out of computer science into math. It's not easy

[Anonymous No.10334864]

>>10334860
What did you try?

[Anonymous No.10335364]

>>10334864
alcohol
a shitload of it
fuck hawthorne

[Anonymous No.10335389]

I found the part with the calligraphy

How excited are you for the return of quill and ink?

[Anonymous No.10335401]

>>10335389
haha
remind what force prevents me from phasing into super solids

[Anonymous No.10335429]

>>10335401
quasar ink

[Anonymous No.10335578]

dude superpermutations

[Anonymous No.10335702]

>>10335429
is this fucking /mg/?why the fuck am i posting here?
someone kill me

[Anonymous No.10335788]

>>10335702
refer to the universal scaling law discovered by rauscher

[Anonymous No.10336395]

>>10334818
HI sci

[Anonymous No.10336399]

>>10335702
Because the physics general is essentially never up.
But you could make the thread.

[Anonymous No.10336964]

Why does it matter if a matrix is invertible? What's the significance? I'm working my way through Elementary Linear Algebra by Anton and Rorres and have no idea why invertibility matters.

[Anonymous No.10336979]

>>10336964
its equivalent to the matrix being of full rank
an example could be the rows/columns represent vectors, and if it is invertible, the vectors form a basis for the whole space

[Anonymous No.10337015]

>>10336964
We like inverting things. The whole reason we can divide by nonzero real numbers is because they have a multiplicative inverse.
Invertibility can tell you when a system of equations described by a matrix has a solution.

[Anonymous No.10337058]

>>10336979
I'm a few chapters away from learning about ranks. Googling didn't really help with the significance behind ranks.
>>10337015
So if its not invertible, it has no solutions?

[Anonymous No.10337061]

can someone shine some intuition on the bounded linear transformation theorem?

[Anonymous No.10337073]

I have to pick two out of these facultative modules: algebra II, probability theory, crypthography, nonlinear programming, discrete programming, theory of algorithms. Which ones will be most useful, I have no idea which should I pick or avoid

[Anonymous No.10337077]

>>10337058
>So if its not invertible, it has no solutions?
For a square matrix there is always a solution when it is invertible. There may still be a solution if it is not invertible.
If you're solving the equation Ax=y for x then it only has a solution if y is in the column space of A. When A is invertible its column space is the whole space.
In a lot of contexts you might not have a specific y and be trying to derive a general solution (perhaps for a more complicated equation). If you know your matrices are invertible then you can just write this solution in terms of the inverse. ie x = A^-1y.

[Anonymous No.10337109]

>>10337061
>bounded linear transformation theorem
Which one? Hahn Banach?
>>10337073
Algebra 2.

[Anonymous No.10337126]

>>10337109
The one that goes:
Let [math]X[/math] be a normed linear space, [math]U\subseteq X[/math] a dense subset, and [math]Y[/math] a Banach space. If [math]T:U\to Y[/math] is bounded, then there exists a unique operator, [math]\hat{T}\in B(X,Y)[/math], such that [math]Tx = \hat{T}x[/math] for all [math]x\in U[/math] and [math]||\hat{T}|| = ||T||[/math].

[Anonymous No.10337152]

>>10337126
Imagine a is a point in Y. We take the open ball B(a, ε).Because the operator is bounded, the difference in value between two random points in X also in the ball is also bounded, and de facto a linear function of the radius. So if we take successively smaller balls around this point the maximum difference naturally grows smaller and we squeeze the values the operator can possibly give to a. Repeating this process on every point lets us continuously extend the originsl operator, and the new construction ends up also being linear.

[Anonymous No.10337161]

>>10337152
is this supposed to be a brainlet filter? thanks for the insight, I will have to think about it for a bit.

[Anonymous No.10337378]

>>10337126
bounded implies lipschitz implies uniformly continuous
uniformly continuous is determined on a dense set
done

[Anonymous No.10337454]

28 y.o. anon here taking discrete math for comp sci after not taking any math since high school. I need to simplify the expression as much as possible. Am I on the right track??

I think the last step is to figure out log3 of 81 and divide by 4?

[Anonymous No.10337462]

>>10337454
yes, that's correct. to what power must you raise 3 in order to get 81?

[Anonymous No.10337556]

How come no-one ever talks about Elie Cartan? Dude is pretty based.

[Anonymous No.10338230]

>>10337556
You guys don't thank Cartan every day for not having to memorize 3D vector calc theorems?
Embarasssing.

[Anonymous No.10338238]

>>10337161
Tbh anon this is fairly basic

[Anonymous No.10338240]

Why is there a new thread if the last one isn't even at 200 posts??

[Anonymous No.10338322]

>>10337378
this theorem, correct?

[Anonymous No.10338336]

>>10338230
>memorize 3D vector calc theorems
Quite sad if that's what Cartan is to you.

[Anonymous No.10338341]

>>10338322
or should [math]S[/math] be dense here?

[Anonymous No.10338348]

>>10337454
log_3(81)=log_3(9^2)=2*log_3(9)=2*2=4
=>4/4=1

[Anonymous No.10338382]

>>10338240
Autism.
>>10338336
Cartan is moving frames man to me, but I like to shitpost.

[Anonymous No.10338391]

>>10334233
bump

[Anonymous No.10338603]

>>10334526
not the guy you replied to but I hope you adding an anime image to your reply makes you seem like to last godforsaken asshole on earth

If I'd know you in RL I'd punch you for that, disregarding if your reply is right or wrong

[Anonymous No.10338609]

>>10334526
not the guy you replied to but I hope you know, adding an anime image to your post makes you seem like the most godforsaken asshole

If I'd know you in RL I'd punch you for that, not caring if your argument is right or wrong

[Anonymous No.10338616]

>>10334526
>the weaboo is an undercover physics poster
cringe

[Anonymous No.10338624]

is OP loss?

[Anonymous No.10338636]

>>10338609
Grow up.
>>10338616
>2018+1
>not an undercover econophysics poster
>>10338624
Now that I notices it, yes.

[Anonymous No.10338660]

Why does this work

[Anonymous No.10338925]

>>10338322
>>10338341
that theorem is what you want to use, remember that U dense implies U closure = X.

[Anonymous No.10339371]

>>10338609
>asshole
nice projection

[Anonymous No.10339801]

Autist here, would it be weird to email a professor who works in an area I'm interested in an ask for resources / general advice? I was told by another professor I know better that he was the guy to talk to, but it feels awkward just to cold email someone like that.

[Anonymous No.10339822]

>>10339801
>resources
You can always ask for book recs here, at your local library, or refer to the bibliography of another book you've read.
But no, it wouldn't be weird, as long as you ask properly.

[Anonymous No.10339823]

>>10339801
I don't think it's that weird as long as you're not asking for too much. Just tell him the other guy said to talk to him.

[Anonymous No.10339831]

>>10338322
S definitely needs to be dense

[Anonymous No.10339841]

>>10334581
>without a teacher / mentor I won't really be able to make progress -- at least when it comes to proofs
Bullshit. The only thing college gave me was the textbooks I learned from on my own.

All you need for mathematics is curiosity, creativity and ability to sit down and think for a long periods of time.

[Anonymous No.10339848]

>>10338238
Would you happen to have an example of this theorem being applied?

[Anonymous No.10339970]

tfw too lazy to do a PhD

[Anonymous No.10339976]

How do you define "operator". It's not just a function, is it?

[Anonymous No.10339991]

>>10339976
Yes it is. Generally we only call things that map from a set back into itself operators though, like taking the cardinality of a set wouldn't be called an operator in any situation I've encountered.

[Anonymous No.10340005]

>>10339991
Thanks for the clarity

[Anonymous No.10340063]

Find three positive integers x, y, and z that satisfy the given conditions.
The sum is 48, and the sum of the squares is a minimum.

can anyone help me with this?

[Anonymous No.10340068]

>>10340063
[math]\nabla f = \lambda \nabla g [/math]

[Anonymous No.10340071]

>>10340063
x=y=z=16

[Anonymous No.10340072]

>>10340063
What do you know about optimisation theory?

[Anonymous No.10340098]

>>10340071
[math] \checkmark [/math]

[Anonymous No.10340166]

>>10334233

today im studying topology and real analysis. zoo wee mama

[Anonymous No.10340220]

[Anonymous No.10340241]

>>10340220
Rudin is a meme.

[Anonymous No.10340570]

how do you find how many unique hands in 5 card poker. by unique I mean as long as there are the same cards in a hand its considered the same hand, it doesn't matter the order.

I know where different card orders do count as separate hands its 52!/47!

[Anonymous No.10340582]

>>10340570
Google combinations and permutations

[Anonymous No.10340584]

https://arxiv.org/pdf/1901.10363.pdf
>New critical exponent inequalities for percolation and the random cluster model
>Tom Hutchcroft
>(Submitted on 29 Jan 2019)

>We apply a variation on the methods of Duminil-Copin, Raoufi, and Tassion to establish a new differential inequality applying to both Bernoulli percolation and the Fortuin-Kasteleyn random cluster model. This differential inequality has a similar form to that derived for Bernoulli percolation by Menshikov but with the important difference that it describes the distribution of the volume of a cluster rather than of its radius. We apply this differential inequality to prove the following:
>The critical exponent inequalities [math] \gamma \leq \delta-1[/math] and [math] \Delta \leq \gamma +1[/math] hold for percolation and the random cluster model on any transitive graph. These inequalities are new even in the context of Bernoulli percolation on [math] \mathbb{Z}^d[/math], and are saturated in mean-field for Bernoulli percolation and for the random cluster model with [math]q \in [1,2)[/math].
>The volume of a cluster has an exponential tail in the entire subcritical phase of the random cluster model on any transitive graph. This proof also applies to infinite-range models, where the result is new even in the Euclidean setting.

[Anonymous No.10340589]

>>10340582
I did but im having trouble finding this specific example

[Anonymous No.10340609]

>>10337556
The Cartan model for [math]G[/math]-equivariant cohomology was fucking based.
http://www.math.toronto.edu/mein/research/enc.pdf
Can't do Wess-Zumino-Witten without it imo.
>>10340584
What I know is that in certain percolation/MBL models the critical exponent [math]\gamma \leq \frac{2}{d}[/math]. Since presumably for strongly-enough-correlated phenomena the conformal scaling relations don't necessarily hold, the paper may imply a similar inequality for the magnetic critical exponent [math]\Delta[/math].

[Anonymous No.10340972]

is Ahlfors or Needham's Visual Complex Analysis a better intro to the field?

[Anonymous No.10341001]

>>10340972
rudin's real and complex is the best intro to "the field."

[Anonymous No.10341005]

>>10340972
Read Ahlfors

[Hffghfftyf No.10341030]

T

[Anonymous No.10341038]

So does anyone in this thread actually understand the topics you guys talk about or do you all just memorize buzzwords?

[Anonymous No.10341053]

>>10340972
For an intro, definitely Needham. It will teach you all about the actual geometry of it all and is just a fantastic read, very informative and pleasant.
Now, Ahlfors is much more thorough and also has a geometric slant so, once you are more familiar with the subject or if you want to go deeper, it can be interesting.

[Anonymous No.10341082]

>>10334818
check out 'a mathematical introduction to cryptography'. silverman is one of the authors and it's pretty solid stuff (assuming you're looking for more of a math perspective.) if you're looking to go deep into stuff like elliptic curves, the canonical reference is the Silverman trilogy (rational points on elliptic curves, arithmetic of elliptic curves, advanced topics)

[Anonymous No.10341151]

Really struggling to grasp the answer to problem 1.20 in Casella Bergers statistical inference (pic related).

Using the stars and stipes technique, I get (12+7-1)C(7-1)=18C6 total combinations and (12-1)C(7-1)=11C6 combinations with at least one call each day.
Putting these together gives P=11/442=0.02489.

Somehow they arrived at 0.2285. Why doesn't the stars and stripes technique work for this problem? fuarrk

[Anonymous No.10341167]

>>10334233
KK-Fredholm operators in symplectic geometry

[Anonymous No.10341169]

>>10334526
based yukari poster, too bad you flirt with LQG, i could have loved you

[Anonymous No.10341170]

>>10334549
[math] \displaystyle
d(f,g) = \max_{a\leq x \leq b} |f(x)-g(x)|+ \max_{a \leq x \leq b} |f^{ \prime}(x)-g^{ \prime}(x)|
[/math]

[Anonymous No.10341194]

>>10334233
It's my first semester of topology! I'm excited to be honest because it is something that seemed interesting to me since my first year. I don't think I will pursue a masters or PhD in maths so for those of you that haven't done so, what do you do to keep your mind occupied with it?

[Anonymous No.10341228]

>>10341038
ask me anything about intro calculus

[Anonymous No.10341253]

[Anonymous No.10341281]

>AoC

[Anonymous No.10341283]

>>10341038
I do.

[Anonymous No.10341377]

Can the union of an open set and a not open set be open? (Notice that "not open" does not mean closed)

[Anonymous No.10341380]

>>10341377
Yes, just let the other set be contained in the open set. otherwise, still yeah, like make it look like an open set outside the open set but inside it make it all weird.

[Anonymous No.10341384]

>>10341377
it's even possible if you require X and Y to be disjoint. Just make X and Y' two intersecting open balls, and set Y = Y' - X. Note that Y is not open.

[Anonymous No.10341388]

>>10341038
i memorize the buzzwords

[Anonymous No.10341393]

I had a dream tonight where my hair started falling off and i was really scared. There were only smalls tripes of hair left on my head. Then i decided to shave it all off and looked in the mirror and saw grothendieck. Is that a good sign?

[Anonymous No.10341427]

>>10341253
>where え is the total number of primes
>え
Fucking weeaboos invading math

[Anonymous No.10341795]

>>10341082
There are no books anymore

[Anonymous No.10341856]

MA on analysis, algebra or stats? I'm interested in machine learning and AI

[Anonymous No.10341873]

What did they mean by this?

What does 2 or for that matter, 1 mean in an abelian group? Shouldn't it have been ring of characteristic non-two?

[Anonymous No.10341883]

>>10341873
Every group has a natural structure as a Z-module.

[Anonymous No.10341894]

>>10341883
Only abelian groups

[Anonymous No.10341900]

>>10341894
My bad.

[Anonymous No.10341909]

>>10336964
Remember that matrices represent linear mappings. A noninvertible map is one that loses information; you can't tell where you started from based on where you end up.

[Anonymous No.10342161]

>>10341281
>axiom of infinity

[Anonymous No.10342164]

>>10334371
All maths is great. Shut the fuck up.

[Anonymous No.10342182]

>>10341873
it's what you'd call the square root in a non-abelian group: h/2 = g means g+g=h

[Anonymous No.10342251]

Hi, I'm a second year student in mathematics from an avarage university. We learnt linear algebra for 2 semesters and we used some more advanced stuff (caylay-hamilton , quadratic forms, LU ...).
I would like to have a second look on linear algebra with a rigorous book not avoiding determinants (like "linear algebra done right" book).
Is "linear algebra" from hoffman a good choice? Any recomandations?

[Anonymous No.10342293]

>>10335578
Superpermutations are fucking awesome.
Do any anons here know of any mathematical literature about them?

[Anonymous No.10342334]

>>10337462
Just from memory, [math]\sqrt{81}=9=3^2[/math], so [math]3^{2*2}=81[/math], so [math]log_3{81}=4[/math].

[Anonymous No.10342339]

>>10342251
Hoffman and Cunt is recommended a lot.
And did your class actually use LADR? Man. That's depressing.

[Anonymous No.10342368]

Can someone help me again?
>Consider a smooth quartic curve [math]C\subset \mathbb P_{\mathbb C}^2[/math] and a line [math]L\not\subset C[/math]
>[math]L[/math] intersects [math]C[/math] in [math]4[/math] distinct points
>Place one point at infinity and consider the elliptic curve [math]E_L:Y^2Z=(X-x_1Z)(X-x_2Z)(X-x_3Z)[/math] through all 4 points.
>It's a smooth curve of genus [math]1[/math] and forms a double cover branched over the four points.
Now here is where I'm lost again:
>Consider subset [math]S(C)[/math] of [math]\mathbb (P^2_{\mathbb{C}})^\vee[/math] consisting of the closure of the locus of lines [math]L\subset \mathbb P^2[/math] such that the [math]j[/math]-invariant of [math]E_L[/math] is [math]0[/math].


Can someone walk me through that final point really slowly please?
>>10319184
>>10325159

[Anonymous No.10342380]

Is there any function that satisfies [eqn]f(x)=f'(x)[/eqn] except trivial examples like [math]f(x)=0[/math]?

[Anonymous No.10342412]

>>10342380
Uh e to the x?

[Anonymous No.10342428]

>>10342380
All functions that satisfy this (real linear differential) equation are of the shape [math]Ce^x[/math] where C is a real constant. Conversely, all those functions also satisfy the equation.

Tl;dr The functions that satisfy that are exactly the [math]Ce^x[/math] where C is a real constant

[Anonymous No.10342480]

>>10342339
Thanks for the recommendation. No we don't use books at my university, only notes from professors and sometimes handwritten notes (pic related).

[Anonymous No.10342505]

>>10342368
okay im considering S(C)
and then?

[Anonymous No.10342643]

>>10342380
That's a differential equation and the complete solution is c*e^x, your example is included with c=0.

[Anonymous No.10342648]

>>10342428
It kinda defeats the purpose of TLDR if it's as long as the main body of your post.

[Anonymous No.10342795]

I'm taking an undergrad topology course, and all the proofs feel circular. Like we're given a definition or a lemma, so if we want to prove something about that definition, we basically just said it fits the other part of the definition, and done.
Is this how more abstract math is? Or am I misunderstanding something greatly?

[Anonymous No.10342803]

>>10342795
Beating definitions until they give is the essential proof technique in point-set topology. But there are exceptions. Give it a few classes until Jordan Closed Curve, or Urysohn's, or intro to algebraic topology.

[Anonymous No.10342834]

>>10342795
The ideal theorems are characterizations; A if and only if B. Point set topology is comfy because it's filled with charactizations. E.g. there are like 10 different properties equivalent to compactness, so you can take any one of them as the definition.

[Anonymous No.10342835]

>>10342803
How should I practice "beating definitions"? Just talk with the professor with rote memorization? Feels more like an English major at this point.

[Anonymous No.10342886]

>>10342835
>Feels more like an English major at this point.
yup
shoulda done physics.

[Anonymous No.10342928]

>>10342835
There are essentially two techniques. You can transport the problems into a geometric scenario, develop an intuitive understanding of why the statement is true there, and then try carry it back into the original formal situation. Urysohn's lemma is a good example within topology, but its overall the most common technique in analysis. The problem is that sometimes the intuition is wrong, or it resists formalization.
Developing a "formal intuition" for how decontextualized statements imply other statements gives you a general grip on axiomatic systems that essentially lets you consistently work with anything. This usually happens in topology, projective geometry, analysis, category theory or set theory. You can try for that, too. It works consistently, but it doesn't really help with hard statements, or when you don't have that much to immediately work with.

[Anonymous No.10342966]

>>10342795
The problem with babby point-set topology is that everything you're describing is incredibly general. There's very few things you can say about something so abstract, so everything really just follows from definitions. The definitions are usually grounded in some intuition though. Eventually, you will get to the point where you do come across interesting statements like the other anon said.

It's like if I said: Let [math]f:\mathbb R\to \mathbb R[/math] be a function. What can I say about this function? Well, very little, but we can start nailing down the little "obvious" things. Like we can define its image, or we can define a set of representatives of each point in the image: [math]S:=\text{im}(f) / \sim[/math], where [math]\sim[/math] is the equivalence relation [math]a\sim b\iff f(a)=f(b)[/math]. Then we have a theorem that says every such function [math]f[/math] defines the following: [eqn]\mathbb R\twoheadrightarrow S\stackrel{\cong}{\to}\text{im}f\hookrightarrow \mathbb R[/eqn]

Where the first map is a surjection, the second a bijection and the third an injection. Everything here is very trivial, since we're working with an extremely general function, but we have still managed to 'factor' it into more digestible bits.

[Anonymous No.10343584]

>>10341169
>you flirt with LQG
But I don't? I've barely done any quantum gravity to begin with

[Anonymous No.10343675]

>>10341194
have fun with topology, it's so much fun

[Anonymous No.10343691]

>>10342795
is this your first proof based class? why are you taking topology without the context from analysis to make it meaningful?
topology should be the class you take to generalize everything your learned about metric spaces in intro analysis. it will just be confusing otherwise.
if you did take into analysis and you don't see why topology is great, meaningful, and makes perfect sense, then you didn't understand analysis very well.

[Anonymous No.10343692]

hey, no this is a silly question but here goes... how do I find the second question?

[Anonymous No.10343832]

>>10343691
Analysis wasn't a prerequisite here.

[Anonymous No.10343853]

>>10343832
it's not a prerequisite, it just doesn't make sense to take it beforehand
it's like taking differential equations before linear algebra. like, yes, you can do all of it. but it isn't going to make much sense.
are you at least talking about metric spaces? do you even have any idea of why we care about open sets being preserved under infinite union but only finite intersection?

[Anonymous No.10343885]

>>10343853
No.

[Anonymous No.10344261]

>>10343692
Solve h(t1)=25
Then calculate v(t1)

[Anonymous No.10344311]

Since there's no similar thread on Physics, I will post here.

I have been reviewing Newtonian physics. I am doing so because I want to understand physics in general. However my main goal is to understand quantum theory.

I have been checking some other responses on the internet and the focus as far as math goes is on lineal algebra, differential equations and complex numbers theory. Anything else I should be studying to understand the math which underlies the subject without hassles?

[Anonymous No.10344336]

>>10344311
just make sure your diffeq covers fourier series extensively

[Anonymous No.10344464]

>>10342368
bump (function)

[Anonymous No.10344986]

where can you buy used math books? I'm sick of using pdfs but I'm not handing over 150 dollars to fucking pearson

[Anonymous No.10344999]

>>10344986
Just print the pdf? Do you have access to a printer? They can be big but it's not expensive.

[Anonymous No.10345008]

>>10344311
To add to this >>10344336 I would brush up on special functions and the techniques surrounding them. You'll need them going forward and getting some practice with them will be helpful later on.

[Anonymous No.10345126]

I'm applying to an REU, and they want a statement of interest. I've never written something like that before, any advice?

[Anonymous No.10345156]

>>10345126
>I've never written something like that before, any advice?
>>>/adv/

[Anonymous No.10345162]

>>10345156
not him but adv is a joke board only newfags actually recommend it

[Anonymous No.10345184]

>>10344999
this

[Anonymous No.10345196]

>>10345126
Just write some stuff about how you're keen to get experience in research and to learn some mathematics beyond that offered in class

[Anonymous No.10345221]

>>10345162
>the appropriate board is bad so it's okay to shit up other boards with off-topic
>/pol/ is horrible, so it's okay to post IQ/race threads on /sci/
>/wsr/ is slow, so you can clearly make however many homework threads you want on /sci/
>/qa/ is disgustingly bad, and that's a free pass for meta threads on /sci/

[Anonymous No.10345228]

>>10345221
/qa/ is good though

[Anonymous No.10345397]

>>10345126
Well, what are you interested in lmao?

[Anonymous No.10345404]

What do I reply?

[Anonymous No.10345424]

>>10345404
That was physically painful to read.
But,
1-Something about completing her.
2-Something about having a sequence that converges to her.
3-Something about one-point compactifications.
4-Something about a loop that's not homotopic to the 0 loop around your heart
4-Something about Stone-Cech compactifications.

[Anonymous No.10345433]

>>10345424
first one was good, dunno how i didnt figure it out. I also have another chick im trying to woo with algebraic curves, told her with their power i could hack anything, but im only interested in hacking her heart. she replied:
>how would you hack your way into my heart?
What do i reply? Yes i know this is cringe but need to get laid pronto.

[Anonymous No.10345443]

Cramer was a fucking a joke and a brainlet why did he get his own rule?

[Anonymous No.10345451]

>>10345228
It isn't

[Anonymous No.10345487]

>>10345404
"My life without you is divided by zero"

[Anonymous No.10345488]

>For every real ε > 0, there exists a real δ > 0 such that for all real x, 0 < | x − p | < δ implies | f(x) − L | < ε.
wat

[Anonymous No.10345617]

>>10334417
The other day in astronomy class the teacher had a quotient and she wrote it as a Taylor expansion, shit was hysterical.

[Anonymous No.10345622]

>>10345487
Really nice, but somehow too basic.
If anon wants to get laid, he probably wants to impress her, as cringe as it sounds.

[Anonymous No.10345652]

>>10341151
I think the problem is that stars and stripes assumes that the calls are indistinguishable but they aren't in some sense.

Imagine a simpler version with only two days, and two people A and B making one call each. Then getting one call each day can happen two different ways: etiher A calls on day 1 and B on day two, or B on day 1 and A on day 2. Stars and bars only count one way of getting a call every day.

It's similar to those typical problems where you flip two coins -- there's a 50% chance of getting one head and one tail since all the equally likelly combinations are HH HT TH TT, half of which have exactly one head.

[Anonymous No.10345660]

>>10341151
What's your chance of not getting called on the first day?
If you didn't, what's the second.
Tl;dr you go exhausting the combinations and abridge the process with Pascal.

[Anonymous No.10345945]

What's the best textbook on functional analysis?

[Anonymous No.10345950]

>>10345945
>What's the best textbook on functional analysis?
anything but Rudin

[Anonymous No.10345953]

>>10345945
Lax.

[Anonymous No.10345966]

>>10345443
Does anyone even use Cramer's rule?

[Anonymous No.10346147]

>>10345945
Riesz & Sz-Nagi

[Anonymous No.10346162]

>12 hours until exam
>I finally understood proof of fundamental theorem of algebra

[Anonymous No.10346441]

>>10345945
I don't know anything about functional analysis books, but I'm having a good time with 'Principles of analysis' by Junghenn. It is a book on measure, lebesgue integration (differentiation and such, as in Stein-Shakarchi), functional analysis and applications (distributions, probability, analysis on locally compact groups and semigroups??). Check it out if you want.

[Anonymous No.10346556]

I was working on a program to generate groups based on a presentation but it turns out it's actually impossible in the general case and while the case of finite groups is solvable it's one of those bullshit CS things were they go "well we can certainly define this turning machine, so it's computable :^)".

[Anonymous No.10346577]

>>10346556
hold up apparently this is implemented in magma so maybe there's hope for an actual algorithm yet

[Anonymous No.10346583]

>>10346577
scratch that computational algebra is a nightmare I'm giving up

[Anonymous No.10346586]

>>10346556
>generate groups based on a presentation
You mean ennumerate their multiplication tables?

[Anonymous No.10346596]

>>10346586
well specifically I wanted expressions for all the elements in terms of the generators, but it turns out to be a lot fucking harder than I thought it would be because deciding if two words represent the same element is fucking uncomputable

[Anonymous No.10346742]

>>10346596
I ran into a problem like this while working on research, I think you want the Todd-Coxeter algorithm, which has an implementation in MAGMA i believe

[Anonymous No.10346767]

>>10345966
Yes its still used and learned.

[Anonymous No.10347007]

>>10334233
I'm taking a remedial math class at my second-rate college and it's going really good and I like it lots :)

[Anonymous No.10347068]

>>10342795
>Is this how more abstract math is?
Well yes and no. It is like that when you begin because, as >>10342966 said (he really nailed it), what you are describing is so general that there are few nontrivial theorems you can state.
Similarly, there are very few things you can say about groups or rings in general, which is why a first (or second..) abstract algebra class might feel dry. The goal of these classes is essentially to introduce a language, so you have to learn many new definitions and exercises will focus on examples and forming basic sentences with those words.
Be sure to spend that time understanding this new vocabulary and finding examples/counterexamples for all your definitions and propositions.
Once you are more comfortable with that language, you will be able to answer more interesting questions.

[Anonymous No.10347138]

>>10345966
It's useful if you need a closed-form expression for the solution. It's commonly used for inverting small matrices due to its simplicity and determinism (the result not being affected by the choice of a pivot column). You wouldn't use it for larger matrices because it's much slower than the alternatives.

[Anonymous No.10347225]

I've seen identities of the form A - B = kAB where A and B are elements of an algebra and k a scaler that may depend on A and B, an example is resolvents, is there a name for such a property or structure where difierince or sums are related to products in some way?

[Anonymous No.10347454]

>>>/vg/242759563

[Anonymous No.10347634]

How do I find the minimum and maximum values of expressions like [math]\sqrt{x-1} + \sqrt{4-x}[/math]? Is it possible to find the same for different powers (instead of the square root)?

[Anonymous No.10347672]

>>10347634
compute the zeros of the derivative
compute the values of function at those points, and also at the endpoints of domain
choose biggest and smallest number

[Anonymous No.10347839]

Every positive integer n allows exactly one solution to [math]n=m*2^p[/math] when m and p are both positive integers.

How would you generalize [math]f(x):=[/math] the value of p in the solution for x to all positive real numbers?

Bonus points if you could make your solution highlight properties of the special-case function. Bonus points if you could make your solution continuous. Bonus points if you could work on some calculus-related properties of your solution.

First anon to come up with something like f(x) = 0 for all non-integer values of x is actually retarded.

[Anonymous No.10347851]

>>10347839
Ilegible question.

[Anonymous No.10347873]

>>10341883
Posting with an avatar is against the rules.

[Anonymous No.10347908]

>>10347839
>>10347851
Note: I forgot to add m has to be an odd number.

[Anonymous No.10347964]

>>10347908
And p can be 0.

[Anonymous No.10348023]

>>10345433
Kill yourself pronto

[Anonymous No.10348027]

>>10348023
i was on the edge before but this has really sealed the deal for me

[Anonymous No.10348029]

>>10347839
Sounds like a job for the 2-adic norm. Any positive rational can be expressed as [math]x = \frac{a}{b} 2^p[/math]; the map [math]\phi (x) = \frac{1}{10^p}[/math] has the properties you mentioned when extended continuously to the reals

[Anonymous No.10348031]

>>10348029
Sorry should say [math]\phi (x) = \frac{1}{2^p}[/math]

[Anonymous No.10348046]

>>10345433
>how would you hack your way into my heart?
IMO drop this girl, like, what the fuck was she expecting you to say, "to do that I need access to some very important entry points, luckily I have just the tool to plug myself in"?

[Anonymous No.10348050]

>>10346147
>megaforce
>es

[Anonymous No.10348163]

>>10348046
Dude, anon's just trying to get laid.
Don't worry, he's self-aware.

[Anonymous No.10348312]

>>10347873
It's not avatarfagging, Remilia is just my entire reaction folder.

[Anonymous No.10348607]

Almost finished the first chapter of Hoffman and Kunze and there are almost no proofs just calculating
I also scrolled forward and looked at the later excercises and it seemed the same
Did I get roped into doing a memebook or something

[Anonymous No.10348651]

>>10348607
>read the 20 page intro to a 400 page book
>thinks it's time for anime_reaction_face.jpg
You've still been memed, because the latest edition of HK is nearly 50 years old, but you're also retarded.

[Anonymous No.10348660]

why is combinatorics so hard? with every other field I feel like I can understand the point, the theorems, and the main result for example, in real analysis: metric spaces->continuity->derivatives->integration->fundamental theorem of calculus
call me a brainlet, but combinatorics is just one big clusterfuck

[Anonymous No.10348673]

>>10348651
>I also scrolled forward and looked at the later excercises and it seemed the same

[Anonymous No.10348691]

>>10348660
because theorems in combinatorics actually state new facts, compared to babby's first analysis where everything is just trivial result of definitions

[Anonymous No.10348698]

>>10348607
It's undergraduate linear algebra, of course it's mostly evaluations.

[Anonymous No.10348704]

>>10348673
What's your point? All exercise sections contain computational exercises. They're there so you can actually learn how to do anything and don't walk around pretending like you know linear algebra when you can't diagonalize a matrix.

[Anonymous No.10348712]

Does this proof count, for all intents and purposes, as literal pornography?

[Anonymous No.10348753]

>>10348660
The point of combinatorics is:
>you have some shit you want to count
>you have some other shit that you already know how to count
>you find a bijection between them
The reason why combinatorics as a field is a big pile of problems is that the problems are the same thing as the theory. Every different set you learn how to count is something you can use to count another set later.

[Anonymous No.10348837]

I have four days to learn like 30 statistics theorems.

I learned one of the lengthiest yesterday and it was very difficult for me, spent like 2 hours on wikipedia and reading some papers to get the full idea, deconstruct it and them assemble again in my head.
I'm not used to learn purely theoretical things, how do I get through it?

[Anonymous No.10348862]

>>10348837
>statistics
>purely theoretical

[Anonymous No.10349048]

>>10348753
Remember that combinatorics also has extensive ties to discrete probability.
>>10348837
Just memorize them. There isn't time to learn the proofs, and only time to learn the intuition behind the main ones, so you have to do with formal applications.

[Anonymous No.10349084]

Been writing some code to generate cayley graphs, going good so far though coercing graphviz to layout things nicely is a pain the ass. I mean look at this shit. Only got cyclic graphs and direct products implemented so far, need to come up with a nice way to multiply permutations. Might just go for matrices.

[Anonymous No.10349091]

>>10349084
Some of them turn out nice. For example here's C10 as C5xC2

[Anonymous No.10349103]

>>10334233
>What are you studying today, /mg/?
Zorich - Mathematical Analysis I

[Anonymous No.10349108]

>>10348837
actual statistical theory has a lot of vocabulary you have to get used to, and is not as neatly packaged as fields like analysis and algebra. If you have a background in probability it should be easy enough to get used to but if you don't then you need to start from the basics and get familiar with the notation and vocabulary at a basic level. The following is a good sequence of topics:

1. Probability review: random variables, discrete and continuous distributions, densities, transformations of random variables and confidence intervals (as random intervals), characteristic functions. Theory of estimation of parameters, bias, MSE etc.
2. Formal hypothesis testing: intro to Neyman-Pearson framework, Neyman-Pearson's lemma on simple hypothesis testing, type I/II errors, power analysis, basic examples including hypotheses with the binomial distribution and the normal distribution (t-test, z-test), look into generalizations of the lemma in connection with UMPUs
3. Further hypothesis testing (skip if not relevant): More tests, non-parametric alternatives, ANOVA etc. the basic arsenal of any general science student
4. Further probability: Here is where the bulk of the theory is, learn about different modes of convergence: start only with convergence in probability and convergence in distribution and their relationships. Law of large numbers, Slutsky's theorem, central limit theorems and continuous mapping theorems. Apply this in the context of estimation, find consistent estimators etc.
5. Further estimation: Continue from (4), learn more kinds of properties of estimators. Fisher information and especially its relationship with UMVU and Cramer-Rao's bound
6. Linear models: Lots of theory that I forgot about but its just lots of linear algebra, but practical application is somewhat easy

[Anonymous No.10349109]

>>10345404
The secret is before she even replies the girl has already decided whether or not she is going to fuck you. Even if you said something retarded, if she is attracted to you she will respond positively. Imagine yourself sending a girl the same message she did as a chad. She feels the same way.

[Anonymous No.10349416]

>>10346596
There are some partial workarounds to the word problem, implemented in Sage I think

[Anonymous No.10349419]

>>10349084
What kind of code?

[Anonymous No.10349522]

>>10348607
Maybe read what the name of the first chapter is, bucko.

[Anonymous No.10349821]

>>10334233
I'm an engineer and I'd like to become mathematically mature. What do I do?
>>10341167
well I'll be damned. I'm interested in symplectic geometry. Any advice on getting into it as a dumb engineer?

I have a dumb engineer problem, I don't know if this is related to symplectic geometry or what. But let's say I have a 2d manifold? I think? which can be on a plane, cylinder or torus. At each point on the manifold? we have a positive real number. Now we have a thing on this manifold with a 2d position. This thing follows the gradient of the of the values on the manifold plus a vector. How can I find values for manifold such that certain properties are obeyed? For example if the vector is + x, the thing will translate along + x forever, and for -x the thing will translate as small a distance as possible along -x, and I want to be sure of this at all possible locations in the manifold. Another is if apply +x, then 0 for the vector it ends up in position a, then if I apply + x then 0, it ends up in position b, and if I repeat the process it ends up back at position a. I don't know if I've explained this right. Basically I have a mass which potential energy is determined by it's position on the manifold, which I apply a force to, and that experiences a damping force(doesn't matter what) and the above is my attempt at a first order approximation of it to get rid of the nasty dynamics. But hey if there's some stuff from symplectic geometry that let's me find potential energy values on a cylindrical manifold such that for any position on the manifold and for a range of positive values of force along y that the mass always settles into an oscillation about x with a constant period.

[Anonymous No.10349843]

>>10340609
The Cartan model was actually from Henri, Elie's son.
>>10349821
Fredholm operators are homotopically classified by K-theory via Atiyah-Janisch, so it's an alg-top object. KK-theory is a generalization of K-theory
through this perspective.
To answer your question, in symplectic geometry the Hamiltonian [math]H\in C^\infty(M)[/math] including the potential is first given on a symplectic manifold [math](M,\omega)[/math], then from which a Hamiltonian vector field [math]X_H\in TM[/math] satisfying [math]dH + \omega(X_H,\cdot) = 0[/math] is constructed. This vector field generates a flow [math]\gamma:\mathbb{R}\rightarrow M[/math] satisfying [math]\dot{\gamma} = X_H(\gamma)[/math] as physical trajectories.

[Anonymous No.10349876]

>>10349821
Is there a nice way to reason about if a trajectory has certain properties? Such as converging to a point from all points? And what if I don't know what exactly those trajectories should be in the first place? For example, I want to get to go from point A at x+ to point B at X- and then back by only pushing in -X and on a planar manifold. Once at point A or B with velocity=0, if any force with magnitude less than zero is applied it will converge back to the respective point.

[Anonymous No.10349994]

>>10334233
I'm done with the math section of the DAT for now, I have just spent the last 3 days going over the perceptual ability section, this key hole shit is making me wish I was doing math again.

also any of you anons, know any quick way to do the below divisions? can I just see significant figures or use the number or decimals on either the numerator or denominator to come to the answer quickly?
I find myself wasting precious time converting the decimals into whole numbers or powers of 10 and dividing it out that way, just wanted to know if anyone knew of a faster way

[Anonymous No.10350308]

>>10349994
what is this image about? look pretty cool but also pretty mind twisting.

[Anonymous No.10350438]

>>10350308
You have a three-dimensional object on the left, you want to find which picture on its right is a face.

[Anonymous No.10350459]

>>10349994
move the dot to the right on top and bottom until you're dividing by a whole number

[Anonymous No.10350462]

>>10350438
how is it called? what are the fractions for? is it the rotation u need to do get to a letter?

[Anonymous No.10350498]

What's the organic chemistry of mathematics?

[Anonymous No.10350502]

https://www.youtube.com/watch?v=Ly8sZ25qtkM
https://www.youtube.com/watch?v=b01Ueur_sFs
https://www.youtube.com/watch?v=uumb58hwNkQ
https://www.youtube.com/watch?v=Sx8WJ0Ne3SI

[Anonymous No.10350678]

>>10345660
Bruh, Pascal died in the 1970's.

[Anonymous No.10350718]

>>10350498
Linear algebra

[Anonymous No.10350774]

>an anonymous person emails your whole department attaching your entire posting history
what do you do, /mg/?

[Anonymous No.10350861]

>>10350774
Repent for all the nasty and kinky shit you've sent and try to find a new job.

[Anonymous No.10350863]

>>10350774
Tranfer immediatiely.
I don't care about anything I say now, but now I'm much smarter than I was when I was posting here on 4chan for the first time.
Nothing good could come from it.

[Anonymous No.10350866]

quick question, /mg/. Working my way into discrete math right now, and I just want to make sure I'm reading this right. if you're given A- (~B), then the effected area in area U is nothing, right? Because they cancel each other out.

[Anonymous No.10350882]

>>10350774
commit suicide

[Anonymous No.10350894]

>>10350774
Laugh at my shitposts from 10 years ago, then pic related

[Anonymous No.10350899]

>>10334233
Stochastic Portfolio Theory

[Anonymous No.10350918]

>>10350774
>implying my department would open the e-mail

[Anonymous No.10350920]

>>10350774
hope they don't ctrl-f "nig"

[Anonymous No.10351003]

>>10336964
Invertibility tells you a lot of information about a matrix A and the linear transformation whose standard matrix is A. Specifically, you get a series of statements that are equivalent to saying a matrix is invertible so once you know one is true/false you know they are all true/false.
It’s called the Fundamental Theorem of Invertible Matrices.

[Anonymous No.10351023]

The coordinate ring of the parabola is [math]k[x][/math] and of the hyperbola is [math]k[x,x^{-1}][/math] by simple computation. Let's assume for simplicity that we're looking at a unit circle, not ellipse. It's coordinate ring is [math]k[x,y]/(x^2+y^2-1)[/math] so every element can be written in the form [math]ay+f(x)[/math] with [math]f(x)\in k[x][/math] and [math]a\in k[/math], since the higher powers of [math]y[/math] get reduced to linear terms. How can I show that this ring is isomorphic to either of the other two?

It looks enticingly like [math]k[x][/math] but it is not a UFD...

[Anonymous No.10351049]

>>10351023
On second thought, is this correct?

Take [math]\phi :k[x,x^{-1}]\to k[x,y]/(x^2+y^2-1)[/math]
by [math]\;\;x\mapsto x+iy,\;\; x^{-1}\mapsto x-iy\;\;[/math] and extend linearly. By noticing [math]\frac12(x+x^{-1})\mapsto x[/math] and similar for [math]y[/math], we have that [math]\phi[/math] is surjective and injectivity is not hard to see, so it's an algebra isomorphism.

[Anonymous No.10351065]

>>10351023
>[math] k[x, x^{-1}][/math]
>not [math]k(x)[/math]
>>10351049
[math] \phi :k(x) \rightarrow k[x, y]/[(x+i3^{-1/2}y)(x-i3^{-1/2}y)-1][/math]

[Anonymous No.10351072]

>>10350774
I'm probably fine just on volume
No one important is going to take the time scroll through thousands of pages of random conversations across a decade to see if they can find the handful of times I said something shocking.

[Anonymous No.10351084]

>>10351072
>>10350920

[Anonymous No.10351087]

>>10351065
[math]k[x,x^{-1}]\subsetneq k(x)[/math], retard. Also the second reply literally says nothing

[Anonymous No.10351127]

>>10351087
>when anon complains you don't explicit things enough
[math] \phi : k[x, y]/[xy-1] \rightarrow k[x, y]/[(x+i3^{−1/2}y)(x−i3^{−1/2}y)−1][/math]

[Anonymous No.10351132]

>>10351127
are you that schizo poster?

[Anonymous No.10351137]

>>10351132
Which one?

[Anonymous No.10351415]

i failed math every year from 5th grade to 10th grade where i dropped out because i needed full time work.

Im 22 and being promoted to a supervisor position at a warehouse but if i want to keep the job i need a degree.

this fucking sucks guys

[Anonymous No.10351509]

>>10351415
Are you in the US? If so, find an adult education program and learn enough math to pass the GED. It will be a lot of work, but a lot of the math they teach you between grade 5 and grade 12 is redundant. Shouldn't be too bad.

[Anonymous No.10351573]

>>10351509
i have my GED. but they need a degree. any degree.

its $25 an hour starting job and maxes at 30

[Anonymous No.10351618]

http://www.kurims.kyoto-u.ac.jp/~motizuki/news-english.html
>2019-02-01
>(Papers) Revised version (list of revisions):
>Inter-universal Teichmuller Theory III: Canonical Splittings of the Log-theta-lattice.
>(Past and Current Research) Updated the webpage containing a report and related documents on discussions conducted at RIMS in March 2018 concerning IUTeich.

[Anonymous No.10351727]

>>10350774
better be a damn good reason for that

[Anonymous No.10351772]

>>10350459
been doing that, using exponents of 10, I guess I will stick with that.
>>10350308
what this anon said>>10350438

[Anonymous No.10351988]

>>10350774
I have literally nothing to hide

[Anonymous No.10352390]

>>10350498
>What's the organic chemistry of mathematics?
combinatorics

[Anonymous No.10352395]

>>10351772
>80% of /sci/ can't figure that puzzle out

[Anonymous No.10352398]

>>10352395
>>80% of /sci/ can't figure that puzzle out
Who are you quoting?

[Anonymous No.10352408]

>>10352398
What was so special about post >>80?

[Anonymous No.10352543]

I am going to stop casually playing video games... even visual novels.

[Anonymous No.10352573]

>>10349843
whoops meant to reply to you with >>10349876

[Anonymous No.10352759]

>>10352543
try quitting life first

[Anonymous No.10352935]

>>10334233
redpill me on gaussian function how sid he come up with that? did he just draw a symmetrical bell curve and derived its equation or something else?

[Anonymous No.10353198]

>>10352935
it's pretty obvious that e^(-x^2) has statistical significance...

[Anonymous No.10353344]

>>10352935
one way is to consider limit of something simple, for example coin toss n times

[Anonymous No.10353436]

Are you comfortable with part of your understanding of a concept being "a mystery"? Like there's always a "why" leading to deeper concepts?
I need maths for practical reasons so I'm okay with this feeling, but it's strange to just ignore black magic when it inevitably crops up.

[Anonymous No.10353465]

>mathsisfun.com

[Anonymous No.10353478]

>>10353198
>>10353344
u guys are saying like its very natural to perceive this. i am not able to think apart from it being symetrical. Do natural processes behave in such manner?

[Anonymous No.10353479]

Functional Analysis textbook?

[Anonymous No.10353550]

>>10353478
Central limit theorem.

If you take the sum of n independent random variables with the same probability distribution, as n grows, the probability distribution of the sum tends to the Gaussian distribution. Note that the underlying distribution doesn't matter so long as its variance is finite.

This was first postulated by de Moivre in 1733, based upon empirical results, and proven mathematically by Laplace in 1820.

For a numerical simulation, plot the binomial distribution (P(r)=C(n,r)/2^n, where C(n,r)=n!/(r!(n-r)!)) against the normal distribution P(r)=sqrt(2/(n*pi))*e^(-(2/n)*(r-n/2)^2) for 0<=r<=n. As n increases, the two distributions converge.

[Anonymous No.10353555]

>>10353479
See >>10345945

[Anonymous No.10353557]

>>10352935
Well, you need a function of one variable that is symmetrical around its center, is strictly decreasing after its center, is smooth, is always positive, and tends very fast to 0, as well as "feeling natural".

Natural candidates that you could think of are polynomials, rational functions, exponential/logarithmic functions, trigonometric functions. After some careful analysis, one notices that only exponentials have this property.

Now, to figure out the behaviour of the exponent, ie e^f(x), what f(x) could we have? Since it has to be symmetric, f must be an even function. Since it has to decay to 0 strictly, f must tend to - infinity strictly. This reduces the question to f(x) has to be an even polynomial-type function centred around 0. Natural candidates are either polynomials like -x^2 or -|x| or -(x^2+1)(x^2+3) or similar things that involve these expressions.

Now if you test -|x|, you see that f is not smooth at the top, so discard this. -x^2 is a good candidate, but so are -x^4 and -|x|^3.
So why not those? Well, the question is what "feels natural". If you have noticed, almost every equation appearing in real life stuff is either linear or quadratic (including things like ODEs, PDEs). Therefore, they are the two most natural candidates for something that models population naturally. Therefore -x^2 is the only one that makes sense.

[Anonymous No.10353560]

>>10353436
This is just something you have to learn to deal with at some point, especially once you start being expected to produce your own work. You're going to drown very quickly if you insist on trying to develop a deep understanding of every single thing you're told about. You'll spend all your time studying, get no work done, and still fall behind.

[Anonymous No.10353663]

>>10353557
>>10353550
Thanks it make sense now.

[Anonymous No.10353773]

>>10341281
>>10342161
finitist trash

[Anonymous No.10353976]

Help a brainlet. Why does pic related work? First we define V1 and V2 mod q but then we use those definitions when calculating mod p. Why can we do this?

[Anonymous No.10354194]

>>10353976
>Victor
Why is your book describing an imaginary person using the algorithm? Do algorithm books usually do this?

[Anonymous No.10354208]

>>10354194
>Why is your book describing an imaginary person using the algorithm? Do algorithm books usually do this?
Algorithm books are often memebooks. For example, cryptography books typically employ "Alice", "Bob" and "Eve".

[Anonymous No.10354227]

can anyone help me with double integrals in polar coordinates? I have the integral 0-9 0-9cos(theta) r dr d(theta)

im getting 9cos(theta)^2 / 2 evaluated from 0-9 which gives me 9pi/4 but its saying this is wrong

[Anonymous No.10354233]

>>10354227
fuck the first integral is suppose to be from 0-pi not 0-9

[Anonymous No.10354237]

>>10354233
it was a typo I still need help

[Anonymous No.10354251]

>>10354227
>>10354233
>>10354237
nvm I got it now

[Anonymous No.10354880]

>>10351137

> which one

heh

[Anonymous No.10354906]

why the fuck is it so difficult to get stochastic process sequences that converge weakly to anything other than a fucking brownian motion

[Anonymous No.10355122]

>when you can't tell if the author is using a slightly non-standard definition or you're just retarded

[Anonymous No.10355192]

mathlet here, what's it called when you're adding percentages to find a new percentage?
Example being if I have 16% chance of getting something and then I have a 14% chance, what is my exact chance of getting it?

[Anonymous No.10355195]

>>10334233
Why do pseuds absolutely refuse to accept any system that doesn't have division by zero?

[Anonymous No.10355207]

>>10355192
Conditional probability.
>>10355195
Having complete inverses is comfy.
But the stuff you give up diesn't really justify it.

[Anonymous No.10355208]

>>10355207
thanks so much

[Anonymous No.10355243]

>>10355195
They don't understand what division is and think its the multiplication-version of subtraction.

[Anonymous No.10355331]

>>10355243
Hur-dur Newton what a fag.
I learnt about that stuff when I was like 10 and somehow he is considered more intelligent?

[Anonymous No.10355384]

>>10355331
Newton didn't live in an era with abstract algebra. They didn't even have a proper description of the reals, they were just larping that they existed

[Anonymous No.10355408]

[Anonymous No.10355413]

tell me about calculus on manifolds

[Anonymous No.10355437]

can anyone help me with this?

f(x,y)=9-x^2-y^2

Find D_u f(1,2),where u=cosθi+sinθj ,for θ=-π/4

[Anonymous No.10355447]

>>10355437
Use polar coordinates dummy

[Anonymous No.10355452]

>>10355447
okay so that would be 9-r^2 over the integral 0 to -pi/4?

[Anonymous No.10355458]

>>10355452
>integral
You're calculating the directional derivative, idiot.

[Anonymous No.10355464]

>>10355458
man im spent right now give me a break

[Anonymous No.10355579]

>>10355413
just let spivak do it

[Anonymous No.10355712]

>[math]M[/math] is a skew-symmetric square matrix with coefficients -1, 0 or 1
>[math]\mathbf P[/math] is the set of all column matrices with nonnegative coordinates and sum of coordinates equals 1
>Define binary relation over [math]\mathbf P[/math] with [math]P\;\leqslant\;Q \qquad\Leftrightarrow\qquad P^\top\,M\,Q \;\leqslant\; 0[/math]
>Is [math]\leqslant[/math] a preorder? A partial order?
Any idea? I can only do reflexivity.

[Anonymous No.10355721]

even /sci/ how's you perceptual ability?

[Anonymous No.10355724]

>>10355721
derp.
forgot to add
rank the internal angles from smallest to largest

[Anonymous No.10355906]

Is it too late at age 23 to go for a masters in financial mathematics? I read 2 years for ChemEng, which I have fallen out of interest in, and 1 year of business which made me fall in love with finance. Math was not my strongest subject but I have a real thirst for it now. Im in Sweden so changing programs isn't as much of a deal as it seems in the US.

[Anonymous No.10355921]

>>10334526
>deformation quantization
What's the road map for learning about this?

[Anonymous No.10355958]

>>10355192
> if I have 16% chance of getting something and then I have a 14% chance, what is my exact chance of getting it?
What do you mean by "then"?
If you have a 0.16 probability of A, and a 0.14 probability of B given that A already occurred (conditional probability), then P(A and B)=P(A)*P(B|A)=0.16*0.14=0.0224.
If there are two mutually-exclusive ways of getting something, A and B, then the probability of getting it one way or the other is P(A or B)=P(A)+P(B)=0.16+0.14=0.30.
If you get two attempts, A and B, the probability that at least one of them succeeds is one minus the probability that both fail, P(A or B)=1-(1-P(A))*(1-P(B))=1-0.84*0.86=1-0.7224=0.2776.

[Anonymous No.10355990]

>>10355413
It sucks.
>>10355721
That's a happy merchant.

[Anonymous No.10356183]

>>10334233
>https://en.wikipedia.org/wiki/Wheel_theory

Did CS majors just reinvent complex infinity for no good reason?

[Anonymous No.10356884]

>>10344311
functional analysis kreyszig, He explain schrodinger quantum field equation in last chapters