/sci/ - Science & Math

How about you guess which number I'm thinking of instead.

yifferential equations

second for functional analysis and combinatorics
also rolling to decide what I study next:
0 or 1 complex dynamics
2 or 3 ramsey theory
4 or 5 nonlinear analysis
6 or 7 atiyah-macdonald
8 or 9 lie theory and/or differential galois theory
dubs and I don't study anything all summer

Should I order some algebra socks for winter?

>>11877650
Enjoy your summer

>>11877650
>meme subject
>meme subject
>important stuff
>important stuff
>important stuff and meme subject
Anon, you set yourself up for failure.

>>11877629
-3736372938374738287263839392726269282736372827303927271626484282736372728737374673839311020395584874820101928474757483901010o2847474.474838301383741038i

>>11877629
56
Lower or higher?

>>11877613
Erich Kähler
Yes I reverse searched

>0-4 I self study
>5-9 work on what my supervisor wants me to work on
>dubs i watch anime all day
>trips+ i kms

>>11877677
Lower

>>11877691
Bleach

>>11877613
>No elliptic curves guy

>>11877715
rip

>>11877654
yuh
>>11877647
very based

>[math]CAT(k)[/math] spaces

>>11877692
Umm, sweaty, [math]\mathbb{C}[/math] isn't an poset.

>>11877729
>>11877713
>>11877691
>>11877654
>>11877650
>>11877647
>>11877629
Kill yourselves.

>>11877729
What would be the best algebra colours? I was thinking about Springer's yellow and white or black, or maybe black and white because of the blackboard in my office.

>>11877747
blood red like the color of your face after someone chucks a brick at it for being a faggot.

>>11877756
Sadly that has not yet happened to me.

>>11877747
Black and white are the "professional" options, but if you find springer socks get them immediately. And tell me where I can get them

>>11877785
I must ask you if you are perhaps also a friend of /fa/gs, that is, free abelian groups. You seem to be a person of good taste.

racah-wigner algebra based

>>11877801
>ph*sics
your kind ain't welcome round these parts

>>11877801
Based on what?

>>11877803
they’re smarter than you, objectively.

>>11877810
I hate everyone smarter than me

>>11877813
Very few people are smarter than me and I admire them usually. You should let go of ressentiment

>>11877785
https://www.ebay.co.uk/itm/Ladies-And-Mens-Over-The-Knee-Thigh-High-118-118-Referee-Sox-Socks-Fancy-Dress/331529538747?hash=item4d30b34cbb:g:aG8AAOSwU-pXt22- Found the Springer socks.

>>11877650
>complex dynamics
based, complex dynamics is great

bros... i hate all of you...

>>11877855
Why?

Bros... I love all of you...

>>11877855
>>11877860
this is about as funny as doing PDEs

/mg/, now that many of us are working remotely / from home, how have you adjusted your setup to stay productive and communicate mathematics?
I recently loaned out a good drawing tablet from my university and it's a godsend. Taking notes and presenting mathematics over Zoom calls is incredibly easy and interactive now. Like it way better than Beamer presentations for informal talks, discussions, or teaching. My handwriting is also much better on it than it is on a whiteboard. Since I'm left handed I always have to be careful not to smudge what I write, with this the thing doesn't even detect my hand sitting on it, just the nub of the pen. Highly recommend looking into if your department has them.
Any other tips you have for doing math efficiently at home?

>>11877868
>how have you adjusted your setup to stay productive and communicate mathematics?
I didn't. I lost all my productivity and have hardly managed to do anything since March.

>>11877796
While I have never spent time with free abelian groups, I can appreciate what they do and have a respect for them

>>11877879
Well maybe you should consider a drawing tablet then.
What's your environment like? I would be horribly unproductive without some of the small changes I've made to keep myself moving. Not that I'm at full efficiency. But maybe we can recommend little shifts you can make which would help out. That's why I made the post to begin with.

>>11877796
>muh Z-modules

Is type theory for transexuals as well?

>>11877927
"foundations" topics get meme'd on here because undergrads want to study them before having done any serious math (commutative diagrams look cool)

>>11877937
>irl friend who loves reddit and facebook math groups starts laughing hysterically at his phone, and then shows me what he's looking at
>it's the fucking undergrad category theorist wojak meme

Am I the only one who feel weird when studying math because I might not be able to get into a PhD program and all of this will be wasted years spent on useless wanking.

>>11877946
No

>>11877883
I see you are a thinking person.

>>11877894
I have one, but I have no use for it. I live in a small student flat and it's so horribly hot inside at the moment, and simultaneously raining a lot, so it's not as easily fixed as just by going outside. I don't know. I'll just stop complaining.

>>11877898
Wow you knew.

>>11877946
I doubt it's that hard to get into a PhD program.

>>11877946
If your goal is to "get into a phd program" and not to simply learn as much math as you can, then you should start to feel a lot weirder. Concentrate on what matters.

>>11877952
>I doubt it's that hard to get into a PhD program.
I mean, make it into academia and all that stuff, not just get a PhD.
>>11877957
It is, but learning math doesn't pay the bills

>>11877952
>I doubt it's that hard to get into a PhD program.
are you saying this as a phd student or as a filthy undergrad

>>11877959
Then it may be a bit challenging.

>>11877964
PhD student.

>>11877952
>I doubt it's that hard to get into a PhD program.
It is if you didn't go to undergrad. I got in the 94th percentile on the GRE math subject test and the 98th on the general GRE. But I have no recs, internships, GPA, or degree. I've been a wagie for 6 years and studying math on the side, I took my GREs last October but couldn't get into anywhere for this fall. Wtf bros. What are some good but easy to get into grad schools? In America preferably but if I have to move I will. I don't want to wage anymore.

I've been working on a research project for a while now which involves some curve fitting to laser scan data.

For my application only circle segment (positive or negative radicand) can be used. the segments must also be continuous. the segments derivatives must also be continuous.

The quick dumb method I've been using so far is to generate circles using 3 points. If the circle is shit I half the domain of the circle and create two circles instead. I get some tiny ass circles but this does an okay job.... nope. This does not make my derivatives consistent between segments.

Next I tried creating circles using two points and a derivative and even two derivatives and one point. Both did better in terms of keeping the derivatives between my segments continuous but did much worse on matching my data.

Is there a way to create circles with two points and two derivatives?

>>11877975
>degree
Bro, I...
I'm not sure what you're expecting. At least do an online degree or something.

>>11877975
I literally have no idea what GRE is. However, I can say something. If I did, then so can anyone.

>>11877977
did anybody get any of that?

>>11877975
>no undergrad degree
Uh sweaty, what subjects do you actually know haha?

>>11877975
This is 100% bait

>>11877977
>Is there a way to create circles with two points and two derivatives?
https://math.stackexchange.com/questions/191486/find-the-center-of-circle-given-two-tangent-lines-and-two-points?noredirect=1&lq=1
>>11877991
Not really.

When are we going to finally have conferences in person again?

I miss talking to girls

>>11877996
>This is 100% bait
Mathematically speaking, how do I make my (You) bait more believable?

>>11878005
shut up simp

>>11878009
study actual autistic retards that unintentionally create terrible threads/discourse. go from there

>>11878009
You should've claimed that you did a math bachelors up until your junior/senior year, started doing drugs, dropped out, got better, and can't get into a master's program because you don't actually have a bachelors.
"My life sucks because drugs but now I'm clean" is such a weird cliche, but I've seen it extremely often here, so I've started somehow assuming it's true.

>>11877959
It's a risk to take. Do your best to pick up technical skills along the way that make you useful for engineering / software in case you need it. If you haven't taken some computer science like Data Structures or an intermediate course in algorithms, do it.

>>11877977
I recommend looking into "splines," I think that's more what you'd be looking for. Maybe not, but if not I guess the link Remiposter gave you is helpful.

Why are category theorists so cute?

So I have this matrix [math]\operatorname{diag}(by+cz, ax+cz, ax+by)[/math] and I want to factorize it so that I get all the a,b,c in one matrix A and x,y,z in another matrix X.
In the end I want [math]\operatorname{diag}(by+cz, ax+cz, ax+by) = A*X[/math] or [math]X*A[/math].
Anyone have any ideas on what to do? I don't know if it's even possible...

>>11878069
Pure category theorists are pretty toxic (both cis and trans) by my experience, but other abstract non-sensers are nice. Handsome too.

>>11878049
sadly I'm only interested in homosexuality groups and gay stuff like that

>>11878069
>>11878097
>>11878127
zoomers trannies/faggots ruined the internet

>>11878134
all me btw

>>11878134
>zoomers
How are they related?

What are all the [math]K_n(\mathbb{Z})[/math] that we know?

>>11878141
dilate

>>11878150
Instead of just posting random meme words, how about you give an actual answer?

>>11878161
dilate zoomertranny

>>11878164
Thanks.

>>11878004
This is pretty close to what I'm currently doing but it doesn't confirm that the circle passes through both points. Still this is an improvement thank you!

>>11878057
Splines are great for this. I previously used cubic beziers curves but eventually realized our application needs circles :( . We are limited by some vendor software I'm not interested in updating.

The cubic beziers curves were so great.... rip

>>11878127
Well get interested in something else then.

>>11878174
Rip. Well this doesn't sound to me like it's anything more than a slightly tricky calculus problem to set up and find the formula for, if you need circles.

Can't be bothered finishing undergrad, gonna just drop out and study the rest in my own time then do a masters on the open uni

>>11878225
Ok. Bye. Fucking moron.

>>11878206
well uh how about no

>>11878254
I'm not asking you to do anything. I'm giving you advice. If you don't want to take it, fine by me.
Imagine whining about the risks of studying mathematics but being unwilling to minimize the risk.

>>11878272
what an awful fucking post

>>11877613
>Elliptic curves

>>11877715
Sorry I'm late.

Does someone have this meme that is an edit of a Trump tweet and goes like this
>Ambitious young teenager goes to university [blablabla] becomes a category theorist. Many such cases!

>>11878289
What's so awful about it? Uncomfortable truths?

>>11878233
someone woke up on the wrong side this morning

>>11878335

>>11878358
My bed only has one side. But it is muggy. So yes, I am grumpy and unproductive.

>>11878352
yes

>>11878127
I don't really like computer science either, but pplied maths done by mathematicians is fun and you should give it an actual try. Tomography and Radon transforms is pretty neat.

>>11878396
>Tomography
what

>>11878396
Is Fourier analysis the highest form of applied math?

>>11878439
Highest? It's the most beautiful, if that's what you mean.

>>11878423
Fire beams at object. Beams come different at the other side. Use beam data to reconstruct what objects look like.
Computerized tomography. Applied maths.
>>11878439
No.

>>11878439
>your pic
how can you prove that the average of a semi-circle is 0.8?

>>11878460
The area of a circle is pi r^2.
The area of a semi-circle is pi r^2/2.
If a rectangle has base equal to the diameter of a semicircle and same area, you can compute the height from that.
High school stuff.

>>11878464
It's not 08 btw, it's pi/4.

>>11878471
.8 is a good enough approximation
t.engineer

>>11878439
>Is Fourier analysis the highest form of applied math?
No, it isn't even particular interesting.
Mostly it is just a tool to investigate actually interesting Problems.

>>11878363
thx anon

>>11878503
like what

http://web.mit.edu/18.06/www/videos.shtml

>>11878504

>>11878503
Here's your (You).

>>11878396
>Tomography and Radon transforms is pretty neat.
I actually had a course on CT last semester, it is actually really fucking interesting how much, quite heavy, analysis you need to study these types of Problems.

If somebody ever asks you what the point of Sobolev spaces of fractional order is, you can tell them that they literally saved lives...

>>11878515
See e.g. what >>11878396 talks about. To reconstruct a CT scan one technique (which is not actually used) is a formula which gives a straight up analytic formula for the solution, that involves the Fourier transformation quite heavily. Another use is in signal processing or image processing where there are various techniques based on Fourier methods.

>>11878523
>Here's your (You).
Thanks you. I never thought that I would get two (You)s for stating something so obvious.

>>11878503
>No, it isn't even particularly interesting
It's easily one of the most interesting pieces of mathematics in existence. How can you possibly say this? How many fucking function spaces does the Fourier transform extend to? On how many mathematical objects does a Fourier transform exist? How else would you even consider transforming between the discrete and the compact? How incredible is the fucking convergence? What about the Poisson summation formula? What about trivializing large classes of ODE and PDE?
How can anyone possibly say this, without having absolutely no clue what the Fourier transform does?

>>11878517
Based and strangpilled. How I learned Linear Algebra the first time.

All cyclic groups are abelian, but not all abelian groups are cyclic.

>>11878536
It is still a tool, I do not get what your point is.
Sure, it is a *cool* tool, but on its own it is just an oddity and if not for its ability to transform problems into other problems, nobody would really care about it...

>>11878544
R-really?

>>11878565
Yes.

>>11878544
That is as trivial as saying all squares are rectangles, but not all rectangles are squares

All fields are rings, but not all rings are fields

>>11878573
Oh no...

>>11878593
N-no!

>>11878593
R-really?

>>11878593
she's so fucking smug

>>11878600
Yes

Okay. Fuck you anime posters. At least all groups are commutative.

>>11878607
delete this before they find out

Every field is an integral domain, but not every integral domain is a field.

>>11878606
w..w-Wow!

>>11878613
FUCK YOU! STOP POSTING LIES!

Every differentiable function is weakly differentiable.

This post was made by Analysis gang.

>>11878607
>At least all groups are commutative.
Explain [math]GL_n(K), \forall n\geq2[/math].

>>11878613
Now you're just lying to me. IT CAN"T BE

>>11878623
T-that's not a group... at least not a group I'm part of! Algebra trannies rekt.

Every differentiable function is continuous, but not every continuous function is differentiable (at even a single point).

Another high quality post made by Analysis gang.

Every Hadamard manifold is a CAT(0) space, but not every CAT(0) space is a Hadamard manifold.

J'adore le mathématiques!

>>11878636
Ich liebe Mathematik (Analysis).

14 is the product of 2 and 7 in two different ways, but not every product of 2 and 7 can be written in two different ways

>>11878640
Watashi wa sugaku ga daisuki desu.

>>11878629
It's closed under multiplication, has an identity element ([math]I_n[/math]), is associative, and has an element such that [math]AA^{-1}=I_n[/math].
Sounds like a group to me.

>>11878655
It's not abelian tho.

Every integer is a number, but not every number is an integer.

>>11878517
>>11878539
Strang a shit, his books a shit

>>11878656
Exactly. See: >>11878607.

>>11878607
coomooter detected

>>11878517
nice

>>11878655
>Sounds like a group to me.
Lol.
That has nothing to do with a group. My group of friends has no identity and if one of them ever multiplies their child will not be part of it.
Also nobody wants to associate with us.

Get rekt.

1<2, but not 2<1

Every scheme is infallible, but not every variety is a scheme.

the joke died 146 posts ago

[math]1+1=2, but \ 1+1=0 \ mod(2)[/math]

The joke died 146 posts ago, but it was never funny.

>>11878680
Did it, though?

>>11878685
0=2 mod 2

>>11878688
149th post best post

>>11878688
Miss you killed the general

>>11878721
The general is dead but not all dead threads are generals.

>>11878396
applied maths/=CSfag retardation

>>11878741
What if I told you that CS is applied math?

>>11878752
CS is applied math but not all applied math is CS

Consider a Banach space [math]V[/math] with a (continuous) dual [math]V^*[/math] and the bidual [math]V^{**}[/math].

Take a continuous functional [math]f \in V^{**}[/math] and consider [math]\ker(f) \subseteq V^{*}[/math]. Is this kernel weak* closed?

I can't show this if the given [math]f[/math] is not obtained from some [math]x \in V[/math]. I don't know how to prove that it cannot be continuous either.

>>11878763

>>11878763
A-anon, the preimage of a closed set (i.e. [math]\{ 0 \}[/math]) by a continuous function is always closed.
This is like, ultra babby general topology.

>>11878775
I mean closed in the weak* topology of the pair [math]\sigma(V,V^*)[/math] though

>>11878786
Oh.
In that case, probably no. The closed unit ball is compact in the weak* topology, and if the weak* topoloy coincides with the weak one, we have that the closed unit ball is compact in the weak topology.
This means that your space is reflexive.
If it's not reflexive, then, by the definition of the weak*-topology, there's some linear functional on V^* which isn't continuous for the weak*-topology. Then, the preimage of some closed set isn't closed. I think you might then be able to do some bullshit trickery to show that, if the preimage of every singleton is closed, then functional is continuous, so that, for some singleton, it isn't. But the preimages singletons are translations of each other, so the kernel isn't closed either.

>>11878822
>if it's not reflexive
*If the weak and weak* topologies don't coindie.

>>11878685
1+1=2 either way

>>11878518
Made for cumming inside.

>>11878909
Her, me or both?

>>11878930
Yes.

>>11878676
Cebolinha!

Am I brainlet if I enjoy 3B1B's channel?

>>11878991
Yes, but only because you've asked this question at least twice

>>11879000
Checked.

am I a brainlet if I enjoy Insights into Mathematics's channel?

>am I a brainlet
Yes.

>>11878991
I like it and I'm a brainlet, but not all who likes him are brainlets

>>11878991
There's a high probability that you are a brainlet if you require 3B1B to understand freshman mathematics

>>11879091
Exposure can only get one so far

generally speaking dy/dx = tanx is true right?

>>11879091
>you require 3B1B to understand freshman mathematics
Where did I say or imply that?

>>11879103
For what other reason are you watching videos intended for mexicans, pajeets, zoomer highschool students and remedial math community college retards?
>>11879096
You know what really helps me with math and science? Thinking about things outside on a nice day. I sit in my chair and just sort of mull things over, maybe draw in my notebook a bit. If I need to recall something but can't quite come up with the theorem, formula, image, I open one of my hundreds of reference texts from my favorite authors past and present and find the section dealing with the topic. Maybe work a few exercises, look up some similar problems on stackexchange, check wikipedia if I need a very fast and dirty explanation or set of sources to draw from, even plot something in mathematica. Then I just go back to sitting. Sometimes I even think about it while cooking or in the shower, on a walk, at the gym. This is how I deal with the kinds of things that 3B1B brings down from his mountain for great oceans of retarded human sludge that watch his videos.

How can one civilization be some based?

>>11879159
this triangle is valid

>>11879159

Pythagoras never talked about lengths. He would just btfo you by saying there's no such thing as a quadrance of -1 and stop your retarded argument right there.

>>11879192
>Thinking about things outside on a nice day. I sit in my chair and just sort of mull things over, maybe draw in my notebook a bit.
I usually just pace around a small area.
Being spoonfed intuition is nice on occasion, tho. Very comfy.

>>11879249
>being spoonfed
that's what stackexchange, /mg/, and your professor(s) are for anon.

Figures you'd crawl out of sepia you lil shit

>>11879253
>your professor(s)
not all of us are liberals anon

>>11879192
Not him but the random tidbits of math are fun, the animations are neat and he has a nice voice

>>11879253
>your professor(s)
A professor of mine literally played a 3b1b video during a class tho.
>an undergrad class?
No.

>>11879309

>A professor of mine literally played a 3b1b video during a class tho.

americans literally pay for this

>>11879318
Cope.
America has the best universities in the world.

>>11879394

Best universities maybe for professors and administration. American students are cucked cattle lmao

>>11879450
Is that why we siphon all of the top international talent?

>>11879309
>grad students needing 3B1B to grok their course material
L O L

Is a vector just a point in space?

>>11879484
a vector is a point in a vector space, or a little arrow. These descriptions are equivalent up to isomorphism.

>>11879490
I should add that this is really only sensible in the context of finite dimensional vectors, though.

>>11879484
https://math.stackexchange.com/questions/645672/what-is-the-difference-between-a-point-and-a-vector

>>11879450
>>11879471
America is like a genie. If you're careful and know what you want, and are good enough, it can make your wildest dreams reality. But if you're stupid and just enter it without thinking, it can crush your soul beyond repair. But for most people you'll just end up with a mediocre wish that got warped by the system; though, now and days it seems more and more people are ending up in the "crushed soul" category.

>>11879480
The video wasn't about course material tho, the subject just had applications to the subject in the video.
It's like a differential geometry professor just playing a shitty video about general relativity because applications and pretty animations.

Also, grok makes me think of reddit for some reason. Do you use reddit?

>>11879498
>>11879490
So a vector describes the change from one point to another and is presented the same way as a point when it starts from the origin. What is a vector space though, and if you want to express something like water flow with vectors do they have to correspond to some time scale?

>>11879517
>Do you use reddit?

>>11879484
you can't add points

>>11879517
>do you use reddit
Not for 6-7 years now. Are you sure you aren’t extremely mad? You seem very mad that I called your pre-school panacea brainlet fuel. Do you like the guy’s effeminate affected “teaching voice” and infantilizing little cartoon characters he adds in? I don’t personally, it makes me want to split open his skull with a tire iron.

>>11879541
>are you mad
No, not particularly.

>>11879541
Take your meds.

Can you all help a CSfag out? I want to learn more math, but am not really sure where to start. The highest courses I took in undergrad were Calculus III and Linear Algebra. After I brush up on those, where should I go?

>>11879550
>>11879556
are you positive that you aren't mad that you've been exposed for enjoying content for children made by a retarded charlatan "educator"? Its ok to be mad, completely normal human behavior when you are injured or wronged in some way by another person. I get mad too sometimes, not about this kind of thing though, because I don't have an emotional attachment to explainer videos made by retarded charlatans for highschool students.

>>11879562
Intro to proofs and algebra.

>>11879602
Recommended books?

>>11879532
A point is an element of an affine space generated by the action of a vector space over itself. I.e you start with a vector space and think that the vectors are just marlers to distinguish points that change whenever you fix a basis. But yea a point is still a vector fundamentaly

>>11879621
>Proof
https://www.amazon.com/gp/product/0521675995/ref=ox_sc_saved_title_10?smid=ATVPDKIKX0DER&psc=1
>Algebra
https://www.amazon.com/dp/0486474178/ref=sr_1_1?crid=2M81HMLVLF25R&dchild=1&keywords=pinter+algebra&qid=1594178680&s=books&sprefix=Pinter+al%2Cstripbooks%2C172&sr=1-1

>>11877816

>>11879763

>>11879653
Is finishing Velleman and then moving straight on to Lang's Algebra viable?

>>11879805
Probably not. That book assumes a ton of knowledge and leaves a lot of filling in the blanks to the reader. That being said, you can always find a PDF online and see if you think it's worth your time. If you're looking for something more rigorous than Pinter, I would recommend Basic Algebra I and II by Jacobson (https://www.amazon.com/dp/0486471896).).

>>11879484
Hello, I have a little book full of silly questions like these (I mean no offense) and I want to post and see if I messed up something in my notes:

You generally can't add points, and if you substract them you get a geometric vector (you get a notion of a beginning and an end point),
Vectors have a notion of norm/length, points don't (substracting the origin from a point A, say, gives you the geometric vector OA still),
As such, vectors can be equipollent, points can't,
In LA considering points as vectors is mostly fine apparently (?),
This doesn't work with vector fields and such (? again)

>>11879484
A vector is just an array of numbers

>>11879159
Actually do some math guys, there are literally whole areas of math concerned with nontrivial spheres of radius 0.

>>11880018
most based explanation so far
also tensors are just arrays of numbers

I did my undergrad a couple of years ago at a top 10 math program in the US. I got very good grades. But I was not looking to pursue grad school at that point so my studies were not very focused.

I only did
>2 semesters of proof based calc + linalg
>2 semesters of algebra
>2 semesters of real analysis
>1 semester complex analysis
>1 semester probability theory
>1 semester topology
>1 semester representation theory
>1 semester differential manifolds
>1 semester grad level analysis
>In CS dept, 1 semester discrete math and 1 semester grad level ML

I failed to build much of a relationship with professors and never did research. I'm working in industry now but am planning on going back to school–is there any path towards a PhD in math?

>>11879484
A vector is just a set

>>11880013
I think part of the part of the confusion is from using elements of [math]\mathbb{R}^n[/math] as both points and as vectors. I usually default to the abstract definition of vector as being an element of a vector space, so this discussion ends there for me. Does it satisfy these axioms?
But at the same time I do think we shouldn't be so careless in treating points and vectors the same.

What do you recommend to a phys undergrad who wants do go into something like chaos theory and non linear dynamics?

Calculus of variatios?

>>11880018
No, you can encode a vector as an array of numbers.

>CS homo
>get interested in reading articles
>go to arxiv
>filter CS
>pure garbage and Chinese garbage
>use math filter
>many nice CS papers

What gives?

>>11880049
Sets don't have internal structures. Or do they?

>>11880053
Oh I do so too but at the level these confusions happen I'm not sure how much it would help. I should have mentioned it tough. And yeah, I do think the mixup comes from what you said.
This isn't even getting into matrices and >>11880018. "A vector is a 1xn matrix" but then matrices of a certain size are vectors, etc

>>11880069
Vectors don't either. Vector spaces, however...

>>11879484
a vector is just an idea

This Applied Category Theory (ACT) talk series is going on this week, so the channel they made has 10 new videos a day

https://www.youtube.com/channel/UC1Kxtc6DOexi4JT-t57Ey9g/videos

I'll start my day having a look at

https://youtu.be/fDWcX8akYMI

>>11880048
apply to masters programs, with those stats you will probably get in to a decent one

>>11879567
This guy sounds mad as hell

>>11880123
Are there any decent masters programs in pure math? I thought people only got masters in math as part of their PhD

It's true that [math]\mathbb{C} \oplus \mathbb{C} \cong \mathbb{C} \otimes_{\mathbb{R}}\mathbb{C}[/math], an isomorphism is [math](1,0) \mapsto \frac{1}{2}(1\otimes1 + i\otimes i)[/math], [math] (0,1) \to \frac{1}{2}(1\otimes1 - i\otimes i)[/math]. Is this isomorphism natural in some sense, or arbitrary?

>>11879550
>>11879541
>>11879567
You know what really helps me cool down? Thinking about things outside on a nice day. I sit in my chair and just sort of mull things over, maybe draw Grant's face in my notebook a bit. If I need to recall something but can't quite come up with the theorem, formula, image, I open one of my hundreds of specialized math findom playlists Grant has sent me. Maybe watch a few videos, look up some similar problems on Mathologer, check wikipedia if I need a very fast and dirty explanation or set of sources to draw from, even plot something in desmos. Then I just go back to fapping. Sometimes I even fap thinking about it while cooking or in the shower, on a walk, at the gym. This is how I deal with the overwhelming anger I feel at some random anon.

>>11880146
Generally, promising math undergrads apply to PhD programs. Since you've been out of college for a few years and have no research, it will probably be tough for you to get straight in to a worthwhile PhD program though (although it still might be worth it to shoot your shot). Yes, there are terminal math masters programs at some AMS Group I universities: UIUC, UNC Chapel Hill just off the top of my head. I recommend going through the AMS Group I lists and checking whether or not they offer a masters program.
http://www.ams.org/profession/data/annual-survey/group_i_public
http://www.ams.org/profession/data/annual-survey/group_i_private

>>11880252
In the UK we have the open uni which has a popular maths masters course. Maybe there are virtual/part-time alternatives in the US so you can study while you work? Also, one could look into the possibility of a PhD by published work.

>>11880055
What is calculus of variations, really?

>>11880243
Mathologer is based tho

>>11880317
He gives me this obnoxious homosexual vibe. His content is okay, I guess, good effort.

>>11880314
it's the study of extrema of functions defined on infinite dimensional spaces. usually the space is something like space of all paths connecting two points, space of all surfaces with prescribed boundary etc. and the function is an integral representing some kind of energy.

>>11880055
Sounds good.
Max-Planck in Göttingen researches this, look into it.

>>11880306
how hard is it to get into this program? does it have good outcomes for moving on to decent PhD programs?

>>11880322
I randomly found a channel called CHALK and that's the vibe I got as well. Like look at this https://youtu.be/-m_pvcrURGc

I still kinda like him tho.

>>11880239
2+2=2*2=4
That's litteraly why

>>11880465
I'm not asking why are they isomorphic, I'm asking whether the isomorphism is natural

I did a module that covered topological spaces this year (is that a pun?)
What is the connection between these and "topology" specifically the pop math stuff like coffee mug = donut?

>>11880474
What do you mean by natural? Natural like in category theory? If so sorry but I don't understand

>>11880476
your question reads kind of like "what's the connection between topological spaces and topology"

>>11880476
The mug/donut thing comes from homotopy. You usually see that in an algebraic topology course.

>>11880479
more like natural in a naive sense
[math]\mathbb{C} \cong \mathbb{R}^2[/math] in many ways, but [math]a+bi \mapsto (a,b)[/math] is the obvious identification. so I want to know if the formula I've written is supposed to be "obvious" like that and/or is an instance of some more general concept, or if it's just random. basically my question is why did the author of the lecture notes that I'm reading didn't just say "they have the same dimension so they're isomorphic", but wrote the formula.

>>11880243
absolutely seething

>>11880480
Yeah thats what I'm trying to ask.
I know what "a topology" is, but not how that connects to topology

>>11880505
I've literally answered your question

>>11880517
Yeah thanks, was just replying to the other reply

>>11880505
Open sets measure closeness of points. I assume you know that you get the circle by glueing the end points of the unit interval together. f we take a suitable nbd of 0, it will not contain any point that is very close to 1 because 0 and 1 are "far" away from each other. After we glue them together, any nbd of this 0=1 point will contain both a point that was very close to 0 and a point that was very close to 1.

>>11880505
well, donuts into mugs and shit are continuous deformations (whatever that means) and clearly "continuous" is a very important word here. the formalism of topological spaces (open and closed sets) just happens to be the most convenient way to rigorously study the concept of continuity. but yeah, this applies to literally any subfield of analysis or geometry, general topology is always the underlying framework whenever there's a notion of continuity present.

Does a restriction of a model cause the removal of things from its universe, or do they become simply unprovable due to that restriction?

>>11880497
Yes, this can be explained by the chinese remainder lemma:
[eqn]\mathbb C \otimes_{\mathbb R} \mathbb C \simeq \mathbb C \otimes_{\mathbb R}\frac{\mathbb R[x]}{(x^2+1)} \simeq \frac{\mathbb C[x]}{(x^2+1)} \simeq \frac{\mathbb C[x]}{(x+i)} \oplus \frac{\mathbb C[x]}{(x-i)} \simeq \mathbb C \oplus \mathbb C[/eqn]
More generally, using the same argument, you can prove that, given a finite Galois extension [math]F/E[/math], there exists an isomorphism
[eqn]F \otimes_{E} F = \bigoplus_{\sigma \in \mathrm{Gal}(F/E)} F[/eqn]
compatible with the action of the Galois group on both sides

>>11880547
I should add that the Galois group acts on the right factor on the LHS and by permuting the coordinates on the right

>>11880531
Is that the same as adding {0,1} to our topology?
As unions of open sets are open, any point in an open set containing 0 (so "close" to 0) should also be in an open containing 1 (therefore "close" to 1)

More generally, when topologists are "gluing" spaces together, are they just adding the union of the gluing points to the topology?

explain what a cohomology is to someone who dropped out of 5th grade

>>11880556
if you look at any small portion of the stairs they're perfectly normal, but they don't piece together to form one big stairs. cohomology measures this phenomenon - whether local stuff comes from global stuff or not.

>>11880556
No
>>11880561
Explanations like this are borderline worthless imo, never benefited from a slogan like this (went to a lot of "le popularize math" events at local college for grade school students as a kid)

>>11880561
okay thanks

>>11880561
this is the correct picture

>>11878552
It's an extraordinarily well behaved and generalizable unitary operator of Hilbert spaces... How can you possibly think people don't care about such things? The whole field of Harmonic Analysis is tied to the idea.

>>11880561
>>11880572
Damn, that's a great explanation.
>>11880556
More precisely, cohomology (and homology) measures the failure of things to come back to themselves when they travel around loops. As a consequence, it is a way of telling how many holes something has.

>>11880114
>applied category theory
the state of "pure" math

Is [math]\mathbb{R}^2 \setminus (\{ (0,0) \} \cup \{ (1/n, 0) : n\in \mathbb{N}\})[/math] homeomorphic to [math]\mathbb{R}^2 \setminus \{ (n, 0) : n\in \mathbb{N}\}[/math]?

>>11880709
circle inversion ?

>>11880709
Yes, treat [math]\mathbb{R}^2[/math] as [math]\mathbb{C}[/math], then consider the map [math]z \mapsto 1/z[/math]. Basically this >>11880719

>>11880709
>>11880719
>>11880727
Yeah I realized this is trivially true if you view R^2 as a sphere with a point removed. What I actually wanted to ask was whether[math]\mathbb{R}^2 \setminus (\{ (\pm 1, 0) \} \cup \{ (\pm(1 - 1/n), 0) : n\in \mathbb{N}\})[/math] is homeomorphic to [math]\mathbb{R}^2 \setminus (\{ (1, 0) \} \cup \{ ((1 - 1/n), 0) : n\in \mathbb{N}\})[/math]
where a_n = -1 + 1/n
b_n = -a_n.
The same trick doesn't seem to work anymore.

>>11880789
The first one is homeomorphic to [math]\mathbb{C} - \mathbb{Z}[/math] and the second one to [math]\mathbb{C} - \mathbb{N}[/math]. There is probably a spiralling homeomorphism between these two, but I'm not going to write it out for you.

>>11880799
There definitely is a spiraling homeomorphism between the two space you've mentioned. However, I don't believe that the first one is homeomorphic to C-Z. Why do you think it is?

>>11880804
Because I'm retarded.

>>11880808
The situation is different this time because we know the homeomorphism cannot come from a homeomorphism of the plane because such a homeomorphism would send limit points to limit points and thus the cardinality of limit points would not be preserved.

>>11880813
of the sphere*, not the plane

>>11880789
apply two inversion to the first space and one inversion to the second space. this gives two copies of R^2 with *discrete* sets of points removed which are obviously homeomorphic

>>11880828
>apply two inversion to the first space and one inversion to the second space
Can you explain what you mean by that?

>>11880828
>>11880832
Sorry for the second space I understand what you mean, yeah it's homeomorphic to R^2 with a discrete set of points removed. But I don't understand how the first one is as well. Can you explain how you apply the two inversions for the first space?

>>11880828
Surely if you're simply applying inversions to the whole of R^2 that doesn't work for the reason I explained in the post above (the homeomorphism can't come from a homeomorphism of the sphere). Are you applying it only to some components of the space? How does that even work?

>>11880834
inversion centered at (1,0) and then inversion centered at (-1,0) makes the sequence not Cauchy, but maybe I'm wrong I'm just thinking out loud

>>11880844
There are initially two sequences converging to two different points. After applying one inversion you have one sequence converging to infinity (hence discrete) and another sequence still converging to some other point.
After applying another inversion the roles are reversed. You cannot get rid of one convergent sequence by simply applying inversions.
In general, looking at the whole sphere (1 point compactification) there will always be two convergent sequences.

>>11880789
nvm figured it out

>>11881032
Holy based.

>his department's logo is a möbius strip

>>11881114
>Möbius strip
>Klein bottle
>Gabriel's horn
>Koch snowflake
>Mandelbrot set

>>11881120
>Gabriel's horn
you forgot alexander sphere

>>11878991
>>11879091
What if I started watching his channel my sophomore year in high school and it helped me cultivate an interest in math?

>>11880036
Sauce?

This thread is literally just an array of numbers if you think about it

>>11881120
>Riemann Sphere

>>11881172
>Riemann surfaces

>>11881166
checked

[math]\nu[/math]

Algebra exam in an hour, lads.

Algebra exam in four minutes, lads.

>>11881253
>>11881389
I hope you fail.

>>11880317
he is very based

set of numbered numbers

>>11881404
[math]\{ n_k\ |\ k, n\in \mathbb{C}\}[/math] the set of complexly numbered complex numbers.

We need a new thread. This thread hit bump limit.

>>11881438
No it didn't and make it yourself.

Whats the difference between a mathematical *methods* textbook/course or a regular math textbook/course

>>11881495
Methods courses give you a whole year worth of stuff in a few weeks without actually teaching you anything. But that is exactly what it promises. You learn that there are methods.

>>11881552
So like learning the rules for solving things but not understanding the foundations/reasons behind the rules? Just more highschool maths

>>11881398
May I ask why?

>>11881585
I got myself some easy credits by doing my theoretical physics minor basically just by choosing these methods courses, and yes. There are some proofs in the material, but it is still mostly just listing results or giving some definitions.

>didn't do any of baby rudin's exercises

Why am I retarded?

>>11880317
Is Mathologer is the only based popsci channel?

>>11881601
>based
On what, may I ask?

>>11881601
>based

>>11881600
Why wouldn't you be retarded?

>>11881637
Reason of sufficient principle.

Currently on a graduate numerics track with focus on physics applications.

Should I continue or should I switch to machine learning? Feels like ML is where all the jobs are and nobody cares about modeling and simulations.
What kind of math is even involved in machine learning?

>>11881649
Complicated Hilbert spaces

>>11881649
It's comp sci so you only need addition

>>11881649
Legends say that the entirety of machine learning is numerical methods in linear algebra and some bayesian shit on the side.

>>11881651
>complicated
I think you were looking for the word "complex".

>>11881660

>>11878304
ayyy, you made it

>>11881666
begone satan

>>11880252
Really appreciate the advice

Love Noetherian rings, lads.

>>11881649
You can get enough machine learning praxis to get a job for companies in ML on your own, if that's your goal - especially if you got a solid math background like that.
Just do stuff now, try tools out and learn what works and why on the side.

>>11881684
Why do you love them more than?
Remotely related:
Rant about non-commuative coordinate rings

https://youtu.be/sX2VmeVSw_U

>>11881899
Because they're the foundation of algebraic geometry.

>>11881910
I've though of the chain condition as a size-limiting restriction and then you get Hilbert's so and so theorems in those cases as a gift, but is there a concise characterization saying if you have *algebraic set or generalization thereof*, then you're guaranteed that the object is Noetherian?
I.e. what's the most general AG "space" for which the ring on them is indeed Noetherian, as you seem to suggest?

>>11881922
Why did that whale just eat that poor bird?

>>11881933
Because being a carnivore = being a killer.

>>11877941
Based. Those Facebook math groups are actually funny

>>11877941
Based.

>>11878607
But anon... The group of real n by n matrices form under the operation of multiplication is not a commutative group

>>11881126
>Alexander sphere

>>11882182
[math]GL_1(\mathbb{R})[/math] is abelian.

fresh >>11882271

>>11880317
He absolutely is.