/mg/

[Anonymous No.12081118]

Math, generally
>locking space into place with fixed distance triangle crystals
edition

Talk maths

[Anonymous No.12081125]

>Zariski topology

[Anonymous No.12081144]

Time is running out. I'm starting to doubt whether or not I'm going to make it.

[Anonymous No.12081159]

This seems really retarded, but I need to tell someone

I am going to be doing a maths degree at a good uni, and I literally don't know anything about maths. It's in the UK so there's no introductionary classes or any of that shit. I went for an interview and a visit like a few months ago, and was completely gobsmacked at the intelligence level of some one the people that were there too. I just did some research and found out that for each position at the mathematics department, they reject like 10 people that they were interested in. So I've been selected over 10 really intelligent people

I'm starting in like 20 days, really depressed.

It's a long story, but I by chance managed to fall upwards into this position. Got really lucky

How fucked am I? Literally want to kms right now

[Anonymous No.12081204]

>>12081159
I'm not sure I follow. Are you talking about undergrad studies?
Didn't you do some math in high school?

[Anonymous No.12081209]

>>12081159
>How fucked am I? Literally want to kms right now
I seriously hope you are not 24 yet.

[Anonymous No.12081228]

>>12081159
By the way, for my interview at the university, they got me to do some maths on a whiteboard in from of some people at the department. It just so happens that I specifically read about the 3 problems they asked me about in the train in the way there. After these three problems, they said this was sufficient. I asked some person who seemed autistic there and he said he was given like ten problems. So I literally lucked out

They told me that I did the maths good, even though I have zero idea what the fuck was going on. I just could remember the solutions from reading them on the train. They asked me to explain verbally what I was doing, and I just mumbled nonsense...

They asked me why I like maths, and I just reguritated some shit I read from the internet about how great maths is.

I literally didn't expect them to actually give me an offer to study there. I don't know why I even turned up. God, I'm such a retard

[Anonymous No.12081240]

>>12081209
>I seriously hope you are not 24 yet.

What?

[Anonymous No.12081275]

>>12081240

[\bottom No.12081284]

https://youtu.be/Ysp7P4wW-zE

[Anonymous No.12081305]

>>12081204
I dropped out of high school

Re did my A levels privately, because of covid there was no exams, so my predicted grades from my tutor were used instead. My predicted grades from my tutor were very high for whatever reason

[Anonymous No.12081352]

>>12081305
Well, then you just have to catch up on high school math, it's not such a big deal.
Go to Khan Academy or something.

[Anonymous No.12081354]

>>12081159
Firstly, don't compare yourself to others. Secondly, don't worry too much. UK math is easy in comparison with e.g. Germany, except if you're at Cambridge or Memeford. Even then it's a lot less work in comparison with most universities on the continent.

[Anonymous No.12081407]

>>12077813
Hey if you're in this thread I posted a lazy comment about how you can just look up the contour integral for the Lerch transcendent because I was tired, but if you want a solution I'm more awake this time around:
I'll let [math]I(a)[/math] be the integral which converges for [math]a>0[/math] and first we substitute [math]x=y^2[/math] to get
[math]I(a)=\int^\infty_0x^{-\frac32}e^{-nx-a/x}dx=2\int^\infty_0\frac{dy}{y^2}e^{-ny^2-a/y^2}[/math]
Now notice that if
[math]J=\int^\infty_0e^{-ny^2-a/y^2}dy[/math]
then
[math]I(a)=-2\frac{d}{da}\int^\infty_0e^{-ny^2-a/y^2}dy=-2\frac{dJ}{da}[/math]
Next make the substitution [math]u=\sqrt{n}y[/math] and define [math]b=\sqrt{na}[/math] (I'm assuming [math]n[/math] was intended to be an integer here but it's not a problem as long as it isn't negative or anything):
[math]J=\frac{1}{\sqrt{n}}\int^\infty_0e^{-(u^2+b^2/u^2)}du[/math]
Differentiate [math]J[/math] with respect to [math]b[/math] now, and you'll see that you get the suggestive
[math]\frac{dJ}{db}=-\frac{2b}{\sqrt{n}}\int^\infty_0e^{-(u^2+b^2/u^2)}\frac{du}{u^2}[/math]
and on substitution of [math]u=b/v[/math] you'll see that
[math]\frac{dJ}{db}=-\frac{2b}{\sqrt{n}}\int^\infty_0e^{-(v^2+b^2/v^2)}dv=-2bJ[/math]
where the minus sign comes from swapping the limits; it follows immediately that [math]J=Ce^{-2b}[/math] but if [math]b=0[/math] the integral is just half a Gaussian, so [math]C=\frac12\sqrt\pi[/math] and recalling the differential equation for [math]I(a)[/math] in terms of [math]J[/math] we obtain
[math]I(a)=\sqrt{\frac{\pi}{a}}e^{-\sqrt{2na}}[/math]
which is your integral dealt with.
I've tried to get my signs right but if I have bungled a sign, just follow the general method because this stuff pretty much always works for integrals of this type. Let me know if that helped out.

[Anonymous No.12081443]

>>12081407
Shit sorry, I should check this more carefully, I meant to write
[math]I(a)=\sqrt{\frac{\pi}{a}}e^{-2\sqrt{na}}[/math]
but wrote the 2 under the square root sign instead. It's fairly obvious though if you've already obtained [math]J[/math] that this is just a typo

[Anonymous No.12081454]

>>12081348
Those texts seemed ok
The precalc book by Stewart is pretty alright
The one in the /sqt/ is xboxhueg but should be fine I think?

I actually did Apostol mostly after precalc but it should work for Spivak

[Anonymous No.12081507]

>>12081407
>>12081443
And people say integration can't be beautiful.

[Anonymous No.12081515]

Is baby rudin a hard book? I saw another anon in the last thread say it would take a semester to finish the first 7 chapters after an intro to proofs course. Can I learn proofs whilst working through baby rudin?

[Anonymous No.12081562]

>>12081407
also
[math]J'(b)=-2J[/math]
the [math]b[/math] clearly cancels out
Hopefully no more typos, but you get the idea and basically the method I posted is right and you can check it if you're sick of my typos lol
>>12081507
would look a whole lot better if I wrote it up without those typos though

[Anonymous No.12081601]

>>12081515
You should at least know how to do proofs before trying baby Rudin.

[Anonymous No.12081618]

>>12081562
>basically the method I posted is right
kek
Based proof by intimidation poster

[Anonymous No.12081633]

>>12081601
Should I read Velleman first and then do Rudin?

[Anonymous No.12081737]

>>12081159
F

[Anonymous No.12081739]

>>12081618
I'm not trying to just insist I'm right for no reason, I just know how this sort of integral works. I make copies of all the problems I solve in certain fields and I just copied and pasted one for this type of integral here but made a couple of typos, that's all.
>>12081507
also thanks, appreciated (although it's just a standard technique)

[Anonymous No.12081823]

Name my band, /mg/.

[Anonymous No.12081863]

>>12081118
Another one for you fags.

[Anonymous No.12081893]

>>12081159
>>12081228
Haha fucking awesome bro good job man

[Anonymous No.12081913]

>>12081228
Just say the uni u aren't gonna get doxxed lol

[Anonymous No.12081924]

>>12081913
You will doxx me

[Anonymous No.12081944]

>>12081924
How the fuck could I doxx you? There are not only countless maths departments, the undergraduate programs all have like a minimum of 50 autists indistinguishable from you. Even if I could dox you what would I do with the information?

[Anonymous No.12081945]

>>12081823
Abstract nonces

[Anonymous No.12081973]

>>12081823
Niggas with magnitude

[Anonymous No.12081980]

>>12081633
bump

[Anonymous No.12082171]

>>12081973
Kek

[Anonymous No.12082177]

>>12081407
Bro I swear one day you've got to make a post where you don't need to correct like 50 fucking things in it, you post more corrections to your own posts than anything else.
You also forgot the factor of [math]1/\sqrt{n}[/math] in [math]C[/math] but yeah having followed it through myself it does work and I like this way of solving it.

[Anonymous No.12082414]

>>12081228
>I just reguritated some shit I read from the internet about how great maths is.

God fucking damn it, I wish you kids wouldn't do this. It creates a hostile work environment.

[Anonymous No.12082489]

>>12081633
I think most people here never read a proof book
Rather they learned while learning some "easier" subject

[Anonymous No.12082548]

Any good resources for learning trig? I have to take a physics class, and it all uses trig which I never learned. Or, would it be wiser to drop the class and take it later? I'm a geology major, and it's just a 101 class but I'm kind of a brainlet when it comes to math, although I'm trying to overcome my issues.

[Anonymous No.12082565]

>>12082548
This should be mandatory reading for all /mg/ posters without a maths bsc.

https://archive.uea.ac.uk/jtm/contents.htm

[Anonymous No.12082571]

>>12081932
What would make it based to you

[Anonymous No.12082863]

>>12082565
Gonna bookmark this, thanks!

[Anonymous No.12083115]

Just wanted to say that >>12081129 is a lame-wad

>>12081507
>and people say integration can't be beautiful.
That hurt my eyes to skim, beautiful my rear end

>>12081515
My uni did Baby Rudin after an intro to analysis course, and we only did chapters 2-4 and 7

>>12082565
What about posters with a ba?

[Anonymous No.12083128]

>>12081515
just try it. honestly i dont see why a math inclined high schooler couldnt read rudin

[Anonymous No.12083159]

>>12083128
I see lots of reasons.

[Anonymous No.12083276]

FUCK

[Anonymous No.12083779]

>>12081515
Why read Rudin when you have other introductory analysis books which are much more suited for self-learning?

[fuck racism No.12083935]

>>12083276
>No. Determinant
Is this one word sentence style really necessary

[Anonymous No.12084254]

Is this true: The intersection of n+1 n-speres has either 1, 2, or infinite points

[Anonymous No.12084259]

Given I have a circle of unknown radius, a viewer standing known height above it, and able to see at maximum a known distance (along the circumference) to the horizon, can I compute the circumference? No other knowns, just height and arcwise max viewline

[Anonymous No.12084336]

>>12083935
Yes. Succinct

[Anonymous No.12084346]

>>12084254
I swear this is not the first time you're asking this question. And yes, it's true.
Intersection of 2 n-spheres is either a point, empty or 1 n-1 -sphere.
So by induction you're done.

[Anonymous No.12084351]

>>12081118
Can someone give me a help here?

Let [math]ỹ=ỹ(x)[/math] be a continuously differentiable function and consider the family of functions
[math]y(x)=ỹ(x)+C,\ x\in\mathbb{R},[/math] where [math]C[/math] is any real parameter. Suppose those functions satisfy a
same differential equation of the form [math]\frac{dy}{dx}=f(x,y),[/math] where [math]f:\mathbb{R^2}\rightarrow\mathbb{R}[/math]. Show that [math]f=f(x,y)[/math] is independent from the variable [math]y[/math]

[Anonymous No.12084353]

I am CS student taking course in discrete math this semester. I am learning from Rosen's Discrete Math with Applications book. i really enjoy the mathematical material but not so much the applications part which bloats the book and I find distracts away from the math. Is there another more succinct book that covers discrete math in a more straight forward manner? My only goal for this class is to learn how to read and write proofs so I can understand math at a higher level.

[Anonymous No.12084379]

>>12081863
C is the only one in the image

[Anonymous No.12084455]

Need help with Kindergarten math.

How is (1 i) an Eigenvector of M?

I multiplied the vectors and got (-1, i), which is not the same as -i(1 i) (as the Eigenvalue given implies).

[Anonymous No.12084485]

>>12084351
dy/dx = f = derivative of y'
C disappears
y' is a function of x, so its derivative is a function of only x (or constant)

[Anonymous No.12084492]

>>12084455
You multiplied wrong, it's matrix multiplication, the multiple is(-i,1) because the first slot is 0*1+i*-1 = -i and second slot is 1*1+i*0=1, (-i,1) (which is an eigenvector)

[Anonymous No.12084499]

>>12084351
If you take some [math]x \in \mathbb{R}[/math] and then you check the value of [math]\frac{dy}{dx}[/math] for all the functions y in your family, it must always be the same.
but then [math]y(x)[/math] takes any possible value as y varies throughout the family of functions. And [math]f(x,y)[/math] must remain constant.
Therefore f is independent from the variable y.

[Anonymous No.12084506]

>>12084346
How do you prove that the intersection can be 1 n-1 sphere? I can visualize it in 3D but how about higher? I don't remember asking before but I may have or it may have been someone else

[Anonymous No.12084549]

>>12084492
Okay but if you now take (-i, 1) and multiply it by -i (since -i is the Eigenvalue, as it says in the pic) you get (-1, -i). How is this in the same direction as (-i, 1)?

[Anonymous No.12084551]

>>12084549
also is this not the right way to input into wa?

[Anonymous No.12084564]

>>12084549
Well, it is because you just got one vector from multiplying the other one by a scalar.
That's literally the definition of "being in the same direction".

You're just confused by the whole thing because your geometrical intuition fails to apprehend geometry over complex numbers, but there's nothing wrong here.

[Anonymous No.12084620]

>>12084564
I understand now thanks

[Anonymous No.12084681]

Abbott's book on real analysis has metric spaces near the very end. Is this a big problem? I saw that Rudin's book on RA has metric spaces in the second chapter

[Anonymous No.12084714]

>>12084681
You idiot, not all books are the same, some of them chose different orders to present their contents, is Apostol's calculus bad because he introduces integrals before derivatives and limits?

[Anonymous No.12084718]

>>12084506
Ok so you have 2 n-spheres. Spheres are symmetric, so you can assume the bigger one is centered at 0 and the other one lies on the x axis.
So you have two equations like
x_1^2 + .... + x_n+1^2 = R^2
(x_1- p_1)^2 + x_2^2 + ... + x_n+1^2 = r^2
This has a unique solution for x_1 unless p_1 = 0, and gives you the n-1-sphere.

[Anonymous No.12084787]

>>12084714
Integrals before limits?
How do they approach it?

[Anonymous No.12084946]

Brainlet here, please bear with me.

I have a function f(x) that goes to 0 quite quickly as x increases. How can I make "quite quickly" convincing mathematically? What's a good way to quantify the speed of convergence?

[Anonymous No.12084965]

>>12084946
Show that [math]\forall \epsilon >0, \ |f(x) - 0| < \epsilon[/math].

[Anonymous No.12084972]

>>12084946

Compare it to known functions that go to zero (like x^{-k}, e^{-x}, e^{-x^2}...), either asymptotically or in absolute value. Can you give an upperbound of the form above?

[Anonymous No.12084980]

>>12084965
my function is not a constant 0 function, unfortunately

>>12084972
that makes sense, thanks. what does asymptotically mean in this case?

[Anonymous No.12084999]

>>12084980

asymptotically here means the ratio between your function and one of those functions tends to a non-zero constant as x tends to infinity. It's stronger than giving an upperbound for the absolute value, of course

[Anonymous No.12085067]

>>12081144
fuggen checked, don't give up frogposter

[Anonymous No.12085097]

>>12083276
dude one of the entries is literally greater than 1 it's clearly not normalized

[Anonymous No.12085117]

>>12083276
effect on (1,0,0)
definitely not rotation

[Anonymous No.12085620]

Would transition have saved her?

[Anonymous No.12085667]

Does anybody know whether the set of modulated Cauchy sequences

[math] \langle x, \alpha\rangle\ :\ {\mathbb Q}^{\mathbb N}\times{\mathbb N}^{\mathbb Q} [/math]

[math] \forall (i, j > \alpha(\epsilon)).\ |\,x_i - x_j\,| < \epsilon [/math]

has any algebraic properties (is it a nice ring or something)
(possibly after equipping it with the standard equality relation)

[Anonymous No.12085814]

>>12085620
Might've saved that hairline

[Anonymous No.12086513]

Preparing for a putnam like competition and looking for practice problems. Can anybody recommend stuff? I can usually smoke questions 1 and 2 on a putnam and I have mixed success on 3s and 4s. Occasionally I snag a 5 or a 6 but it's very rare.

[Anonymous No.12086517]

>>12084980
Look up big oh notation

[Anonymous No.12086524]

>>12085667
No

[Anonymous No.12086527]

>>12086513
Michael Penn does at least one Putnam problem a day and uploads them to YouTube.

[Anonymous No.12086529]

>>12086527
Michael Penn is a sick cunt and I watch his stuff already but thanks for the rec.

[Anonymous No.12086703]

>>12081118
I am learning Linear Algebra and Abstract Algebra with focus on Vector Calculus in parallel.
An angle is a geometric concept of how inclined one thing is onto another. Like sides of triangles.

While reading sections of dot product in a linear algebra book, the author mentions angle as angle between two vectors. Although I can relate but I have a feeling that angle is just interpretation or specialization of something more abstract which I would find in Abstract Algebra books. I haven't looked into it (again) but I believe there was no such thing. Any Abstract algebra guy can help here? What is angle?

[Anonymous No.12086818]

>>12084946
Limit of Rate of change of y wrt x reaches infinity as dx reaches 0 and y reaches 0.

[Anonymous No.12086822]

>>12085097
X1*X2+Y1*Y2+Z1*Z2 /= 0

[Anonymous No.12086826]

I thought this was /sqt/ absentmindedly scrolling past these terrible posts, good god /mg/ has fallen so far so fast. Stop fucking posting if you have nothing to say you fucking retarded summerfags

[Anonymous No.12086864]

>>12086703
Abstract algebra isn't really concerned with stuff such as angles. At least not as far as I know.

I guess the best way to do give a definition of an angle (in the context of a vector space) would be as equivalence classes of pairs of normed vectors, with two pairs being equivalent if one can be obtained from the other through rotation.

Then if you have a norm you can define a measure of the angles and work from there.

I know that in complex geometry they care about conformal maps that preserve angles, but I'm really not sure that angles have a role to play beyond the definition/caracterisation of what a conformal map is.

To be quite honest, angle isn't a word I've heard much since my early undergraduate years.

[Anonymous No.12086935]

Say you have a given surface Z(x,y), and x and y are restrained to the Naturals >=1. The question is the following: Does Z generate all the Naturals, and if not is there a finite or infinite amount of numbers not generated by Z.? Remember x and y are natural >=1.

Some surfaces are very easy of course. For example Z=2x. That generates all even numbers, so not all , and there are an infinite number of odds it will skip. Z=2x+1, is the opposite, all the odds but no evens or 1. Z=4xy is multiples of multiples of 4.

But what about when they get more complicated? Is there some kind of standard mapping or technique you can apply to tell? What type of proofs would you use for such? Take Z=2xy+x+y for example. I know it doesn't generate all Naturals, for example, there is no Natural solution for Z=5, or Z=8. but are there an infinite such values?

[Anonymous No.12086971]

>>12086935
That's basically the whole question behind number theory: "does my equation have integer/natural solutions ?"

Now you're asking about the specific case of surfaces, but even this is very far from obvious.

[Anonymous No.12087010]

>>12086971
Yeah I guess that is sort of a general statement of the field. Still even relatively simple surfaces can get out of hand very quickly, and I would think my ability or the ability in general to say generate counter examples would be more obvious. Another example that sounds like it should be very easy but is hard: the same way i can take a reciprocal, or inverse, or transpose, or rotate, you would think there is some easy way to take any surface, put it through a process, and spit out the numerical "reflection against the naturals or integers" that is, a surface made of all the values not on the first and not containing any of the values on the first.

[Anonymous No.12087081]

>>12087010
I think Daniel Loughran adresses questions ressembling your "how many natural numbers are generated by my equation Z = f(x,y)".
Check this article for instance : https://arxiv.org/abs/1310.6219
He's trying to count the number of varieties in a family that contain a rational point, which is a generalization of counting the number of equations in a family that have a rational point, which would answer your question.
He does it in a much more general and abstract way so maybe it's not as hard for simple cases such as concrete and simple surfaces. Also he looks for solutions in a number field, not in [math] \mathbb{Z}[/math], let alone in [math]\mathbb{N}[/math]

[Anonymous No.12087093]

>>12087081
hey thanks, will take a look

[Anonymous No.12087128]

>>12087081
wow, took a look, nice paper, tried to sift through to find related material, but it's out of my league. I'm getting 5 or 10% here and there. I'm familiar with many of the terms he uses, but in no way have the command of the info the way he is using it. It wold take me hours to decode even a few lines of his work. good stuff though, wish I could understand it at reading speed. maybe if I had majored or continued in math instead of science.

[Anonymous No.12087257]

>>12087128
Don't worry, I don't get the details either.
Unless you really specialize in the field, you can't read such an article and understand everything quickly.

I was just researching potential topics for a PhD and found this guy. It felt like a possibility because my master's degree was about arithmetical geometry and the lab were I've been accepted is more about algebraic and probabilistic number theory, so I was wondering if I could find some sort of middle ground.

[Anonymous No.12087345]

>>12084714
damn wtf are you so mad for. idk, some things make more sense when explained one way than another.

[Anonymous No.12087369]

>>12084787
Partitions and upper/lower sums. Rudin uses a similar approach, as does Spivak. Limits are unnecessary. The limit of the Riemann sum approach is stupefying and provides no generality.

[Anonymous No.12087489]

>>12086524

[Anonymous No.12087502]

>>12086826
This
Only a handful of posts actually containing any mathematical content. At least half of you should stop posting.

[Anonymous No.12087505]

>>12087369
Alright, I somehow thouht you needed limits at some point, or at least limsup and/or liminf.
Maybe I was confused with something else, or I just learned it in a different way.

[Anonymous No.12087510]

haha, remember that time when some moron tried to disguise his statistical physics research as a problem with ants walking on a grid
really made me lel, what a retard

[Anonymous No.12087518]

Still amazed by the fact that over 99% of groups of order less than 2000 are of order 1024.

[Anonymous No.12087544]

I love learning, but I'm concerned about living in a low income area.

My home got burglarized last week and it made me wonder if studying without applying myself is really the best thing.

I really enjoy the purity of learning without purpose, but I feel doomed to have to enter the world at large to avoid it eventually, literally, kicking my door in.

[Anonymous No.12087548]

>>12087544
If anyone kicks your door in, just urge them not to disturb your circles

[Anonymous No.12087595]

>>12087544
black lives matter, chud

[Anonymous No.12087652]

>>12087544
why not both?

[Anonymous No.12087653]

>>12087544
Get a degree
>>12087518
2^10
10 is a weird number

[Anonymous No.12087658]

>>12084946
Everything is quick in the eyes of infinity so you just need to specify a quantity or relation of quantities

[Anonymous No.12087669]

>>12087518
Well 2^11 > 2000 so it could maybe be the highest order you could fit as many symmetries (somehow related to the powers of 2) under the order of 2000.

[Anonymous No.12087673]

>>12087653
>>12087669
yeah I know it's because it's a power of 2, but still that's fucking weird.

[Anonymous No.12087678]

>studying and passing advanced math courses is possible
>for the life of me cant grasp basic physics and I'll probably fail the exam
reeeeeee

[Anonymous No.12087743]

>>12087678
that's weird

There's nothing complicated about python I can think of. Maybe you just don't remember syntax

Also, I don't know of any major that both has advanced math courses as well as python - what are you doing?

[Anonymous No.12087841]

Guys I've been studying category theory for 2 weeks now and the gender dysphoria still hasn't kicked in. Should I be worried?

[Anonymous No.12087853]

>>12087841
You might be using the wrong book. You're using categories for the working mathematician, right?
The mental illness won't appear otherwise.

[Anonymous No.12087881]

Thoughts on this Korean CSAT question?

[Anonymous No.12088015]

>>12087743
Anon are you meming or having a stroke

[Anonymous No.12088043]

>>12084714
My uni recommends Apostol and then teaches derivatives first anyways
What a pain

[Anonymous No.12088061]

>>12087544
Grad school + postdocs = 15ish years of renting in low-income, left-leaning neighborhoods

Hope your butthole is ready

[Anonymous No.12088072]

>>12086703
Depending on the book they usually introduce the notion of an inner product space then using that they introduce the notion of an angle between two vectors using said product

[Anomynous No.12088377]

Is there a way to calculate the largest rectangle that can be inscribed in a circle of 1580 pixels, given a fixed 7 / 5 ratio of width to length?

[Anomynous No.12088393]

>>12088377
Scratch that I'm dumb

[math]x^2 + (1.4x)^2 = 1580^2[/math]

[Anomynous No.12088427]

>>12088393
math is power

[Anonymous No.12088501]

>>12088427
Indeed.

[Anonymous No.12088506]

>>12081159
>want to kms right now
nooooo don't, UK still uses miles a lot

[Anonymous No.12088510]

>>12086703
>What is angle?
underrated question

[Anonymous No.12088533]

>>12086703
>What is angle?
parameter of the exponential map [math]\mathbb{R} \cong \mathfrak{so}(2) \to \text{SO}(2)[/math]

[Anonymous No.12088535]

http://nautil.us/issue/89/the-dark-side/why-mathematicians-should-stop-naming-things-after-each-other

>Stop naming things after men

[Anonymous No.12088536]

>>12088535
Cope.

[Anonymous No.12088570]

>>12088535
>Laura Ball is a journalist-in-residence at the Kavli Institute for Theoretical Physics
so uh, why is she talking about math?

[Anonymous No.12088572]

>>12088570
Women need complain about everything

[Anonymous No.12088576]

>>12088572
Ironic.

[Anonymous No.12088603]

>>12081275
Anon, please elaborate. Don't just post alarming shit. I'm 26 and considering masters -> potentially phd. I definitely don't have the mental clarity and ability to learn that I did in my younger years, but it's still possible.

[Anonymous No.12088612]

>>12088603
Should we tell him?

[Anonymous No.12088619]

>>12088603
It's a le epic reddit meme xDDD

[Anonymous No.12088655]

>>12088603
don't listen to him, just do what you want

[Anonymous No.12088743]

>>12081118
Hello my dear very smart mathfag friends.

I have a question that might be interesting for some here.

For my numerical analysis homework I was tasked with finding the Lagrange interpolation polynomial for the heaviside step function:
[eqn]u (x) = \begin{cases}1 & x \geq 0\\0 & x < 0\end{cases}[/eqn]

On nodes [math]-1<-1/2<-1/3<0<1/3<1/2<1[/math]

The thing is, I made 2 matlab programs to find the polynomial, the first using the symbolic math package and the second using vectors in order to speed computations up.

The symbolic one resulted in a function very different from the heavyside step function whilst the non symbolic one resulted in something very close to it.

Interestingly, if in the symbolic code, I go from a 6 degree polynomial to a 100 degree polynomial then the approximation is actually very good, looks almost exactly like the fourier series of a square wave, but changing the degree for the non symbolic code changes it like in picrel


Why is this?

[Anonymous No.12088746]

>>12088743
Symbolic result

[Anonymous No.12088749]

>>12088743
>numerical analysis
not math.

[Anonymous No.12088752]

>>12088746
bug probably
>>12088749
dilate

[Anonymous No.12088758]

>>12088752
>dilate
says the CS tranny

[Anonymous No.12088759]

>>12088746

[Anonymous No.12088760]

https://youtu.be/ZYyORDIIGiU


Surface area is equaled to this

[Anonymous No.12088764]

>>12088758
go draw some commutative category arrows tranny

[Anonymous No.12088770]

>>12088764
It's called commutative diagram, and it's real math done by real mathematicians, something I wouldn't excpect some faggot in programming socks to understand.

[Anonymous No.12088776]

>>12088749
>A very big and important branch of math isn't math
Dunce.
Numerical analysis is the literal sweetspot between pure and applied math, I'm proving theorems and running code in the same class, it's like a dream come true.

>>12088759
>>12088752
You would say it's a bug?
But increasing the degree does make for a better approximation. And I computed the 6 degree interpolation polynomial by hand and the result is exactly what I get with my code

[Anonymous No.12088779]

>>12088776
>branch of math
said who?
>applied "math"
not math.

[Anonymous No.12088780]

>>12088770
>IT'S MA'TH! I SWEAR!

[Anonymous No.12088785]

>>12088780
>typing code is math

[Anonymous No.12088787]

>>12081354
>UK math is easy in comparison with e.g. Germany, except if you're at Cambridge or Memeford. Even then it's a lot less work in comparison with most universities on the continent
What a bunch of horseshit. Oxbridge is superior than any other university in Europe for mathematics, by any metric you want. Also the guy your replied to made up the whole story (I know who he is and that he is trolling) - you can't 'get lucky' here since you'd at least have to pass A level maths, further maths and do step exams.

[Anonymous No.12088788]

>>12088770
>>12088785
no one cares about your arrows and diagrams but other category trannies and undergrads

[Anonymous No.12088789]

>>12088770
>and it's real math done by real mathematicians, i swear!!

[Anonymous No.12088795]

>>12088779
>>12088788

[Anonymous No.12088797]

>>12088788
if by category traniies" you men all algebraic geometers, algebraic topologists, logicians, algebraists, etc... then yes.

[Anonymous No.12088804]

>>12088797
algebra is worthless

[Anonymous No.12088805]

>>12088804
enjoying highschool, faggot?

[Anonymous No.12088806]

>>12088535
Once you get to the advanced levels of any field, terminology being "accessible" doesn't really matter, but being precise does.

Areas like philosophy and law actually suffer in my opinion when they overload common words with uncommon meanings, or descend into weird disambiguations that depend on suffixes.

For example, in philosophy there's "contractarianism" and "contractualism", and trying to remember which is the general term and which refers to a specific theory drives me nuts. (If "contractualism" were just known as "Scanlon's theory" it would be a lot easier.)

Naming things after their creator is actually super-helpful because it's really easy to disambiguate, helps situate things historically, and once you're at that level there often isn't a single unique word or phrase that can easily encapsulate the idea anyways and isn't easily confused with something else.

[Anonymous No.12088808]

>>12088779
Purists are major cringe bro.

The love for math, pure or applied, should bring us all together. There are countless fascinating things to study on both subfields.

[Anonymous No.12088809]

>>12088805
Quite so.

[Anonymous No.12088812]

>>12088809
figured.

[Anonymous No.12088816]

>>12088806
That or just keep naming properties "normal" and hope for the best.

[Anonymous No.12088817]

>>12088797
>>12088805
>>12088809
>>12088812
I know: Group theory gets used in quantum mechanics and elsewhere in physics, but the group theory used is trivial. E.g., never hear of Sylow's theorem, the Jordan-Holder theorem, the Feit and Thompson work on simple groups, etc. For group representations,you need to know very little about group theory to do group representations (I wrote my undergrad honors paper in it). Heck, I wrote a paper on multidimensional, distribution-free hypothesis tests based on groups of measure-preserving transformations, and the group theory needed was trivial. Similarly for the use of group theory in ergodic theory, ODE, and integer linear programming. Groups are nice, but really need to know only about 10 pages of the basics and can pick it up in an hour whenever need it. Or, you want group theory to attack Rubik's cube?

Yes, Hamming used some finite field theory in error correcting codes: Now that work and a dime won't cover a 10 cent cup of coffee. Instead, coding theory has moved on. Yes, yes, I know, from A. Wiles we finally have a proof of Fermat's last theorem; other than Wiles, who made any money with that?

Algebraic geometry is building expensive houses on-spec that stand empty too long. There's just no significant promise of return on investment there, or elsewhere in abstract algebra. E.g., the US NSA pushed hard on finite field theory for years before RSA showed that they had been wasting their time.

US mathematics' long, disastrous, self-destructive love affair with algebra, algebraic geometry, algebraic topology, algebraic number theory has been a major contributor to shrinking Federal research grants to mathematics, shrinking departments, mathematicians who'd swap their Ph.D. for an electrician's license, and the technology world putting mathematics on the back burner if not in the trash. Can cover nearly all abstract algebra in 1 word: Useless.

[Anonymous No.12088822]

>>12088808
>bro like, both are good and you should listen to both sides
sounds like you're really fun at parties

[Anonymous No.12088830]

>>12088817
What areas do you like then?

[Anonymous No.12088832]

>>12088822
Not what I'm saying.
There are very interesting things to learn from both subfields, even if you prefer one over the other dissing the other is childish

[Anonymous No.12088838]

>>12088817
TL;DR
who gives a shit about applications?

[Anonymous No.12088842]

>>12088743
>>12088746
Can someone pls try to help with this?

[Anonymous No.12088849]

>>12088842
debug your code or figure out what the symbolic shit is doing, now you should go to /sqt/

[Anonymous No.12088952]

on suicide watch

[Anonymous No.12088963]

>>12088952
Can you prove the irreducibility of the cyclotomic polynomials without appealing to analysis?

[Anonymous No.12088969]

>>12088838
There's nothing wrong with applied math.

[Anonymous No.12088989]

>>12088849
Hmm should see what symbolic is doing

[Anonymous No.12089037]

I wish my teachers pushed step papers more
when I was applying 5 years ago, I massively overestimated m'local redbrick, thought the cambridge MA was a meme and couldn't be bothered to do an extra exam just for oxford
At least I spent that summer beating dark souls

[Anonymous No.12089044]

Not a mathematician, just researching schizophrenia. Can someone tell me just how wrong this is? Is it like some mathematical technicality, or does it seem like the work of a madman?

https://vixra.org/abs/1906.0236

[Anonymous No.12089050]

>>12089044
Tooker, like Galois or Grothendieck, is rejected by the mathematicians of his time, but he will be aclaimed after his death. Such is the life of the genius.

[Anonymous No.12089069]

I somehow have made it into year 3 of a maths major with 0 knowledge of maths

[Anonymous No.12089098]

>>12089050
Grothendieck was offered a fields medal by the mathematicians of his time.

Galois got himself killed in a duel before most mathematicians of his time had time to even hear about him.

What are you talking about?

[Anonymous No.12089103]

>>12089044
>>12089044
>Can someone tell me just how wrong this is?
it's so wrong that even taking the time to explain why it's wrong indicates that it's not as wrong as it actually is

[Anonymous No.12089106]

>>12089103
this sentence makes no sense

[Anonymous No.12089110]

>>12089106
neither does tooker's paper tbqh

[Anonymous No.12089116]

>>12089050
Galois and Grothendieck were both unanimously considered once in a lifetime geniuses, though.

[Anonymous No.12089127]

>>12089098
>>12089116
I was being ironic you fucking autists.

[Anonymous No.12089137]

>>12089127
>Merely pretending

[Anonymous No.12089176]

Is there any theorem about the eigenvalues of perturbations of a fixed symmetric and positive semidefinite matrix?

[Anonymous No.12089214]

>>12089044
Doesn't seem very consistent.

[Anonymous No.12089234]

How do I actually learn math?
I'm working through Apostol and some of the proof exercises are making me frustrated, and skipping them feels wrong.
It feels like I never had a chance.

[Anonymous No.12089235]

>>12088743
are you sure the code is correct?

[Anonymous No.12089236]

>>12089176
https://en.wikipedia.org/wiki/Eigenvalue_perturbation

[Anonymous No.12089237]

>>12089234
>How do I actually learn math?
Doing lots of it.

[Anonymous No.12089241]

>>12089234
this is not a subject with linear progress
there will be walls you have to bash your head through, and times where your fly through content
calculus is only a pie of the mathematical pie

[Anonymous No.12089245]

>>12089241
>pie of
piece of

[Anonymous No.12089255]

>>12089241
>>12089245
shut the fuck up faggot

[Anonymous No.12089284]

>>12089176
I'm absolutely certain there are such theorems.
Especially since e.g. eigenvalues of random matrices and stuff like that are well studied.
If I can guess behind your motivations, note that a good way to deal with noise on symmetric matrices is to work with their roots, e.g.
https://en.wikipedia.org/wiki/Kalman_filter#Square_root_form

[Anonymous No.12089319]

>>12089284
Made for black cock

[Anonymous No.12089331]

>>12089255
This.

[Anonymous No.12089349]

https://www.youtube.com/watch?v=qAnjmha_Elo

/mg/ could never!

[Anonymous No.12089353]

>>12089319
Kill yourself

[Anonymous No.12089374]

>>12089349
When is he going to run out of problems?

[Anonymous No.12089421]

>>12089319
zoomers are so mentally ill they think this is a funny meme. you're probably asian but still

[Anonymous No.12089425]

>zoomers are so mentally ill they think this is a funny meme. you're probably asian but still

[Anonymous No.12089429]

>>12089374
When he becomes too senile to continue. He seems to be genuinely autistic (based).

[Anonymous No.12089430]

>>12089421
>>12089425
or a good old poo in loo or muzzie

[Anonymous No.12089432]

>or a good old poo in loo or muzzie

[Anonymous No.12089435]

/mg/ used to be good, along with the rest of the internet, before you ruined it shitskin zoomer

[Anonymous No.12089436]

>>12089429
Now that you mention it, he does seem like he has some form of unironic autism.

[Anonymous No.12089440]

>/mg/ used to be good, along with the rest of the internet, before you ruined it shitskin zoomer

[Anonymous No.12089442]

epic chapotranny wojaks

[Anonymous No.12089448]

>epic chapotranny wojaks

[Anonymous No.12089452]

all the good /mg/ posters are long gone, you now post with zoomer wojak spammers

[Anonymous No.12089468]

>giving attention to the chapotranny

[Anonymous No.12089472]

Are there any contexts where the trichotomy law does not hold?

[Anonymous No.12089498]

>>12089234
Hello fellow brainlet
I just do the ones I find neat and do the rote ones my uni gives me

[Anonymous No.12089503]

>>12089472
its more of a feature of certain binary relations
so in settings where the binary relation R is not defined for some x,y (xRy and yRx are both false)

[Anonymous No.12089518]

>>12089503
Makes sense. Thanks.

[Anonymous No.12090056]

>>12089235
Yeah, as I said the polynomial it produces for very high degrees are a very good aproximation of the heaviside function.

[Anonymous No.12090074]

Retard engineer here, I'm interested in learning more math, but it's been like 5 years out of college and I only think I'm strong on is the basics of calc 1 and 2. Should I start over from calculus on, or is there another topic I should start from? Any textbooks/online courses I should look into?

[Anonymous No.12090079]

>>12090074
If you're interested in more pure math, you could try getting into abstract algebra. It requires no math beyond basic arithmetic and a sense of mathematical maturity. Pinter's book is a great introduction and extremely cheap, since it's Dover.

[Anonymous No.12090089]

>>12090079
By "sense of mathematical maturity", do you mean the ability to read proofs or generate them yourself, or something else?

[Anonymous No.12090102]

>>12090089
Both.

[Anonymous No.12090175]

>>12090074
>>12090079
pinter is a great introduction to abstract algebra. i had a course on group theory from michael artins algebra, and a few days ago i got pinters abstract algebra to review, and it is amazing. artins algebra is fucking god awfully written; good problems though

[Anonymous No.12090207]

>>12089440
i luv how you react to my quote by opening your mouth just like when you succ me kok

[Anonymous No.12090256]

>>12081118
threadly reminder to ignore physicists

[Anonymous No.12090273]

>>12090256
I really don't care much for physics, lads.

[Anonymous No.12090360]

set theory is cool

[Anonymous No.12090390]

>>12090256
Sounds like classic cope
Why are people so insecure about their life choices

[Anonymous No.12090519]

Getting ideas off paper and into proof form really stinks sometimes. What I can jot down with a few equations, graphs, or diagrams, or explain to someone verbally is 10x faster than having to convert that into writing and latex code.

[Anonymous No.12090527]

I'm putting my revised proof of the Twin prime conjecture to paper and its grueling even though the explanation isn't that complicated. I don't wanna! lol, I just want to tell people verbally. haha.

[Anonymous No.12090644]

>>12090527
undergrad, have learnt a little latex this summer. is hard :(

[Anonymous No.12090659]

>>12090644
It does make nice output, but i never learned it when I was in school; it was still becoming more widespread. I still don't have it memorized at all, but can work with it using tools. There are tons of resources and it's easy to copy paste code. 2 keys I find very helpful are 1 just to have a template file to get each paper going, and 2 this website here: it lets you input visually and then spits out the code you can paste into the program. it's so helpful if you haven't seen it.

https://www.codecogs.com/latex/eqneditor.php

[Anonymous No.12090972]

>me back when i was 15 years old
>master undergrad level math easily
>do moderately well on olympiad

>me now at 38
>trying to get back into math
>struggle with simple stuff
>head hurts, feel tired
>no attention span
>end up drinking alcohol to cope

[Anonymous No.12090976]

>>12090972
stop drinking you faggot

[Anonymous No.12090979]

>>12090390
It’s technically (relative) brainlet cope as physicists are smarter than mathematicians

[Anonymous No.12090987]

>>12090976
yes i'm trying. i started drinking to make things bearable at home but now that i'm finally divorced thank god i can stop. but i've just built a habit.

[Anonymous No.12090992]

Guys I want to be a mining engineer

[Anonymous No.12090993]

>>12090972
When I was younger I could easily do well and concentrate even without getting enough sleep. Now I'm like you unless I get roughly 8 hours of sleep and caffeine doesn't really help. Maybe it's as simple as that for you as well?

[Anonymous No.12091002]

>>12090993
i'm considering taking modafinil or adderall. ever tried stimulants of this sort?

[Anonymous No.12091013]

>>12091002
No, I know nothing about that sort of thing. I still recommend good sleeping habits.

[Anonymous No.12091258]

wtf why did noone tell me artinian rings were so cool

[Anonymous No.12091282]

>>12090972
at what point in math did you resume after such a long absence?

[Anonymous No.12091315]

>>12081284
great video!!

[Anonymous No.12091418]

>>12091282
well is started with calculus and when i got to laplace's equations the slowing down began but i managed to get the questions done

then in vector calculus i got to tensors and that's when the real struggle started.

[Anonymous No.12091565]

>>12091258
Noetherian rings > Artinian rings

[Anonymous No.12091570]

>>12091258
Artinian rings are yet another example of how boys make better girls.

>>12091565
No.

[Anonymous No.12091667]

>>12081144
we're all going to make it anon.

[Anonymous No.12091726]

>>12091667
Cohn is the best measure theory book.

[Anonymous No.12091804]

[Anonymous No.12091834]

I used to be like "woah Euler's identity is cool"
Then I was like "it's not that cool, the formula seems obvious from the definition of sin and cos"
Now I'm like "wait a minute, how exactly does pi come into it? Isn't our value of pi a consequence of the Euclidean metric?"

Can anyone explain the connection between exp, sin, cos, and the Euclidean metric?

[Anonymous No.12091846]

>>12090519
It only means that it was not as clear as you thought, it happens all the time

[Anonymous No.12091856]

>>12091667
>Rudin- Analysis in R^n

Did whoever make this even use Baby Rudin? Baby Rudin has two chapters on multivariable. The only good things about it are his proofs of the inverse and implicit function theorem. His chapter on differential forms is terrible. To do analysis in R^n properly you want to do Munkres Analysis on Manifolds, or just go straight to a book like Smooth Manifolds by Lee.

[Anonymous No.12091857]

>I just noticed that the City University of New York shortens to CUNY.

[Anonymous No.12091881]

>>12091834
[math]\exp(it)[/math] can be defined as the unique solution of the initial problem [math]z' = iz[/math], [math]z(0) = 1[/math]. one can easily see that this equation describes arc length parametrization of the unit circle in [math]\mathbb{C}[/math]. [math]\pi[/math] is simply the value for which [math]z(\pi) = -1[/math]. if you write [math]z(t) = x(t) + iy(t)[/math], then the pair of real-valued functions [math](x,y)[/math] satisfies the ODE [math]x' = -y, y' =x[/math], [math]x(0) = 1, y(0) = 0[/math]. so does the pair [math](\cos t,\sin t)[/math], therefore they must be equal.

[Anonymous No.12091890]

>>12091881
Does arc length depend on the metric being used?

[Anonymous No.12091924]

>>12081118
Hey, I'm an EE, also took a while lot of math classes, both pure and applied.

I'm split between doing my master's/phd in either systems and signals (EE) or computational mathematics (applied math)

Which one should I pick and why?

[Anonymous No.12091940]

>>12083276
Obviously not you fucking dunce.
The FIRST entry is greater than 1 lmao

[Anonymous No.12091952]

>>12091924
do the signals and systems.

the time to be general is undergrad. the time to specialize is graduate school. EE will lead to good jobs and it's not putting a ceiling on your math curiousity. at the graduate level you can go as deep as you want

[Anonymous No.12091995]

>>12091952
>EE will lead to good jobs
it didn't get me a job.

[Anonymous No.12092006]

>>12091952
Wont computational mathematics lead to a good job also?
There's a lot of stuff for finance, data analysis, etc.

[Anonymous No.12092044]

>>12092006
it can. but you need a plan to sell it. nobody is hiring "mathematicians", rather you need to sell how your math skills benefit them

with an EE the expectation is more set.
don't get me wrong, you can be successful with math, but if you are on the edge EE is a safer path

>>12091995
> he can't get employment being more educated than 90% of the population

cry more

[Anonymous No.12092133]

>>12091856

[Anonymous No.12092151]

>>12086517
>Big oh
Hot

[Anonymous No.12092365]

>>12092044
This is a good point. Definitely did not expect to hear something like this in this thread lol.
Ty very much

[Anonymous No.12092478]

>>12091890
I'd say the fact that you look at exp is the artifact of working in the Euclidean norm, and that's why it's connected.
You have that
[math] t\mapsto \exp(it) = \sin(t) + i \cos(t) [/math]
defines a rotation (metric preserving continuous motion) in exactly that metric space in which a full circle of it has length 2pi.
We find exp interesting because it has that property and a fallout from that is that it has nice values along special points in R^2 where sin becomes 0.

If you take exp for granted, then generally, if [math] J^3 = j^2\, J [/math] in an module with j invertible, the exp-expansion will give you
[math] \exp(z\,J) = E + \dfrac{\sinh(z\,j)}{j} J + \dfrac{\cosh(z\,j)-1}{j^2} J^2 [/math]
where E is the unit in the space, and that doesn't really depend on j squaring to -1.
It's just that 2·cosh is the symmetrized exp by definition.

You can look at different p-norms, I suppose the astroid gives you "2pi equals 6"
https://en.wikipedia.org/wiki/Astroid
and then the parametrization will be
[math] t\mapsto \sin(t)^p + i \cos(t)^p [/math]

but that won't make for a nice Lie-group embedding.

[Anonymous No.12092624]

>>12091846
Somewhat. They say if you really want to know something, teach it to someone else. It's that difference between knowing it yourself and teaching it to another.

[Anonymous No.12092683]

How can I get a*cocoa + b*shea + c*tallow + d*coconut + e*butter as close as possible to the target?
with a, b, c, d, and e some variables from 0 to 1.

[Anonymous No.12092853]

>>12092683
nvm, got it via Data -> Statistics > Regression with force intercept to 0.
apparently a=0.316, b=0.400, c=0.078, d=0.232, e=0.061.

[Anonymous No.12092956]

>>12091667
>proof based linear algebra
>Strang
Fucking what

[Anonymous No.12093258]

>>12091834
Euler's identity is mindblowing until you actually understand what it means. Cauchy's residue theorem is the real 10/10 complex analysis result.

[Anonymous No.12093910]

My prelims start tomorrow anons, wish me luck.

[Anonymous No.12093930]

>>12091856
I've given an almost exhaustive list of Advanced Calc and Analysis/Calculus on Manifolds books probably a half dozen times already. Munkres is not the only text for this, and it's not at all a good idea to just jump into Lee's Smooth Manifolds without Advanced Calc and Topology, which Lee btw states as prereqs for his book.
>>12092133
This is one of the better intermediate texts for Advanced Calc, a very nice mix of proofs and interesting computational exercises, good exposition, correct statements of the key theorems, and a nice chapter on Calc of Variations at the end. The only thing it's really lacking is more of the topology and diff geo in munkres and loomis&sternberg. But, if you don't even know multi you shouldn't really be attempting those books if you haven't done Rudin and aren't planning on using something like the Hubbard book.

[Anonymous No.12094119]

is the set of Z twice as big as the set of N?

[Anonymous No.12094250]

>>12094119
No, since [math]0 \notin \mathbb{N}[/math]

[Anonymous No.12094352]

I conjecture: For any sets [math] A, B, C\subseteq (X,d)[/math] we have the inequality
[math] diam((A \ cup B) \setminus C)
\leq diam((B \cup C) \setminus A) + diam((C \cup A) \setminus B).

[Anonymous No.12094356]

>>12094352
[math] diam((A \ cup B) \setminus C)
\leq diam((B \cup C) \setminus A) + diam((C \cup A) \setminus B)[/math]

[Anonymous No.12094363]

>>12088506
Fuck off cunt

[Anonymous No.12094373]

>>12094250
sci = big brained

[Anonymous No.12094421]

>>12094363
kys

[Anonymous No.12094424]

Is there a cohomological analog for the Hurewicz theorem? For homology, one can interpret the first group as the abelinisation of the fundamental group. Is there some similar interpretation for the first cohomology group? (for spaces and not groups)

[Anonymous No.12094438]

>>12094352
>>12094356
Consider [math]X=\mathbb{R}[/math] and the sets [math]A=[1, \infty), B=[0, \infty), C=\emptyset.[/math]

[Anonymous No.12094442]

>>12094356
Consider the case where A={1,2}, B={3,4},C={2,3}, and d(x,y) = |x-y|.

[Anonymous No.12094469]

ok, got that improved and more complete version of the Twin Prime proof into latex. probably take me another day or 2 to review and revise it, then I'll post it up.

[Anonymous No.12094526]

>>12090972
>>>struggle with simple stuff
>>head hurts, feel tired
>>no attention span
like me after 24

[Anonymous No.12094584]

>>12088806
> ...helps situate things historically
Was reading Penrose's Road to Reality book. Pretty much every time he introduces an eponym he includes a footnote explaining why it's historically inappropriate.

[Anonymous No.12094598]

>>12094438
>>12094442
Can you find counterexamples with pairwise disjoint sets?

[Anonymous No.12094605]

>>12091315
there's gonna be (at least) 2 more, ending with the example of the Grothendieck topos who's images are all directed graphs (https://ncatlab.org/nlab/show/Quiv)), the truth object of which is the presheaf in pic related

[Anonymous No.12094651]

>>12081118
Starting analysis 3 next semester.
Wanna do a review of analysis 1 and 2 before starting the new semester.
What should I focus on?

[Anonymous No.12094659]

>>12094651
what is analysis 3 ?

[Anonymous No.12094664]

>>12094598
No.

[Anonymous No.12094704]

>>12081159
>>12081228
I'm gonna cut the bullshit. Get a copy of Algebraic Geometry by Hartshorne. Do ALL the exercises. You have two weeks. If you don't have that much knowledge it will be pretty hard but if you dedicate a couple hours a day it should be doable. If you fail or find it too hard I'd probably cancel the major enrollment. You're gonna be in for a world of hurt.

[Anonymous No.12094742]

>>12094704
This is a joke right? Can anyone who isn't this anon confirm that this is a joke?

[Anonymous No.12094744]

>>12094742
why would this be a joke? I did all my Hartshorne exercises in the first semester, I thought everybody did that

[Anonymous No.12094758]

>>12094744
Yeah but one semester is way more time than 2 weeks.

[Anonymous No.12094763]

>>12094424
judging by the fact that topologists are obsessed with dual stuff, I think that if coHurewicz theorem existed it would have been already discovered

[Anonymous No.12094766]

>>12094758
im kidding of course its a joke

[Anonymous No.12094793]

>>12094763
Yes, it could be. To be more precise, I have a situation where I have spaces X and Y, and a surjective homomorphism from the fundamental group of X to that of Y, and the kernel of this interests me. The arguments in a paper show that X -> Y is actually a covering space and they construct a space whose fundamental group this kernel happens to be. They then show the existence of an isomorphism between the first homology group of this "kernel space" and a certain module they are interested in. The claim is that nice things happen if the first homology group of the kernel with coefficients in a ring R is trivial, and the proof follows from their construction and Hurewicz. I have the dual setting but I just can't think of a similar nice interpretation of the first cohomology group of the corresponding "kernel space" here.

[Anonymous No.12094808]

>>12094704
> Algebra fag shilling his useless field.

[Anonymous No.12094832]

>>12094808
>useless

[Anonymous No.12095226]

>>12094659
Multivar I think.
1 and 2 covered rudin chapters 1 thru 7

whats truly important there?

[Anonymous No.12095251]

https://arxiv.org/search/math?searchtype=author&query=Euler%2C+L

[Anonymous No.12095346]

>>12095226
Generalized Stokes' theorem

[Anonymous No.12095394]

Are any of you guys interested in the psychology of mathematics and thought, as in what actually occurs on a neural/regional level in the brain when you do math? I have been thinking about it for a while and want to discuss it over the coming months. I think it's a worthwhile endeavor because doing math is one thing, but upgrading your processors to do math even better is another layer. Also, knowing how math is computed by neurons gives insight into efficient pathways and is interesting to compare to computer computation methods.

One example here is how visualizations of numbers can make base placement easier for addition/subtraction, while adders in computers are purely unit based afaik

[Anonymous No.12095471]

>>12095394
The psychology of mathematical thought and the neurology of mathematical thought are two separate fields.
Getting fit and enough sleep will optimize both much more efficiently than whatever you're proposing.

[Anonymous No.12095492]

>>12095394

I agree with what this guy >>12095471 said, but that's not to say I don't find it a worthwhile endeavour of interesting to talk about.
Other things is being around people who want to do something similar as you, and having tutors.
Assuming all other bullet points optimized (e.g. I think not bein tired when you try to do math will be 100 times more important than any other trick), what do you think would help?
Can you specify your goals a little more?

[Anonymous No.12095501]

I'm basically at the crossroads of my life. I have 3.5 years left in the uni and I need to pick between normal and a math intensive major, communications or DSP/ML.

To be honest I'v never "excelled" or been that interested in mathematics. I'v always done the bare minimum from entrance exams to the tests. I'v never been confident in my mathematical abilities even though I aced the entrance exams, got into somewhat selective university and did my calculus. I'v seen people who are crazy good, savants even and I'm not one of them.

Is there a way to test my abilities before I make a mistake and commit myself into a major I can't excel in? Something that if I were to understand I'd know my head is good enough for DSP/ML/stats. Inverse is fine too, something that if I fail to understand I'd know I wasn't going to make it.

I guess I'm looking for some sort of sign or confirmation. I don't want to struggle just to second guess myself, I want to know I can do it.

[Anonymous No.12095506]

>>12095501
Also, since my major has been EE it hasn't been that math heavy. I'v done signals, fouriers, calculus, some matrix bullshit and probably forgot most of them. There's a steep curve ahead of me and I don't know if I can climb it

[Anonymous No.12095543]

>>12094598
Yes, if you let C be empty. Otherwise no.

[Anonymous No.12095546]

>>12095492
I think it has to do with memory. Storing and operating on concepts is done in working memory

ANother relevant aspect is which type of sensation is used. Visual is more cumbersome than pure abstraction. It's a really diverse topic but thats why I wanna leave it open for discussion over time

>>12095471
>psychology/neurology different
Unclamp for the love of god

>fit and enough sleep
Von Neumann

[Anonymous No.12095609]

>>12087881
Easy compared to the MO gold medals you need as a non-black non-hispanic American to guarantee admissions to top unis.

[Anonymous No.12095662]

Is statistics considered math or just math adjacent?

[Anonymous No.12095670]

>>12095662
the younger brother that tried to get in with the scientist gang and is now just used for their dirty work

[Summer<3 !A4jsQTgi.Q No.12095779]

What’re some fun problems?

[Anonymous No.12095788]

>>12095662
I recently stumbled upon this nLab page article, which kind of argues against this point
https://ncatlab.org/nlab/show/Is+probability+theory+a+branch+of+mathematics%3F

(This is btw. not a very canon nLab type article, as you can see in the forum discussion, but they also want more people to write there.)
It's by Michael Hardy, the guy who - I'd not be surprised - it seems wrote about 1% of all math Wikipedia content, plusminus, over the last decade
https://en.wikipedia.org/wiki/User:Michael_Hardy

The text makes the case that probability theory/statistics/stochastic is more like physics, a field that uses math. I'm not sure if I agree, but mostly just because I'm not sure what math is or can be. But I think it's a fair case.

I personally don't feel like decision theory is a branch of math (not more than physics is), nor do I think that e.g. Bayes rule is a "theorem" about probability.
It certainly is a theorem in the Kolmogorov axiomatization of probability, but we should confused that with the thing itself - there's many dozens of probability theoretical paradoxes still around (assinging priors, differences of modeling in objects vs. subjective Bayesianism, etc)

[Summer<3 !A4jsQTgi.Q No.12095792]

>>12095788
I studied this in college statistics, it’s very fun and real.

[Anonymous No.12095834]

>>12095779

[Anonymous No.12095858]

>>12095834
I don't get the quesiton. They have one cup, then they do somehting and then they end up with one cup again.
>How much wine did each dwarf have
Well one cup, as it says there.

[Anonymous No.12095864]

>>12095858
Ah, nevermind, I suppose the idea is to merge all wine they have as soon as they receive it and "how much did they have" doesn't mean at the start but at the moment right after receiving. Without time spec, it's a bit vague.

[Anonymous No.12096223]

>>12095501
Help

[Anonymous No.12096651]

Tips for not losing my skills in math? Any sites where I have access to a shit ton of problems for practice?

[Anonymous No.12096680]

>TFW finally getting the hang of proofs
Analysis is kind of fun, lads.

[Anonymous No.12096705]

>>12096651
What topic(s)?

[Anonymous No.12096907]

>>12096651
I don't understand this question. You're either still in school learning, or you're working a job applying all the concepts you learned.

[Anonymous No.12097150]

So if we lived in some sort of curved space, could we experimentally verify this by measuring the ratio of a radius to a circumference on a circle to be not quite pi?
I don't know geometry on manifolds well enough but if I imagine a nonflat 2D manifold in 3D space and draw a circle with the subspace metric, the ratio of the circumference and the length of a straight line in the manifold going from the center to the boundary may not be pi.
Does this effect translate to a more accurate description of "curved space"?

[Anonymous No.12097279]

>>12097150
Maybe, but the fact that things fall down is a better hint that the model is a good one. The curvature of spacetime is, in this theory, the source of gravity. Think of a 2d graph where the horizontal axis is space (say with the center of the earth in the middle) and the vertical axis is time. The fact that an apple that you let fall moves towards the 0 vertically as it moves up through time horizontally is the curvature that's being modeled.
Geodesics are curved w.r.t. an ambient view

[Anonymous No.12097406]

>>12095394
>Are any of you guys interested in the psychology of mathematics and thought, as in what actually occurs on a neural/regional level in the brain when you do math?
the same as dreaming, fantasizing about categories and relations and made up fanfictions

[Anonymous No.12097810]

>>12096907
Something has gone terribly wrong.

[Anonymous No.12097901]

>>12081118
New:
>>12097896