/sci/ - Science & Math

Clifford algebras are 8 dimensional vector algebras where space and volume are dimensions too, without linear ordering.

>>11940745
>Elliptic curves

Reposting this from /sqt/.
If anyone actually knows please tell me.

>>11939247
no I'm just asking: B(H) is the Banach space of bounded operators on a Hilbert space with the usual norm. what's its (continuous) dual space B(H)*? I can only find information about the preduals of B(H) and not anything about duals, not sure if I'm missing something

Should I study topology or combinatorics to complement algebra? I've heard topology isn't very proof heavy which is a turnoff but combinatorics sounds like the least fun thing imaginable.

>>11940809
topology, algebra is the proofs

>>11940809
Combinatorics is fun.

the flesh eaters haven't even taken over new york yet

>>11940840

>>11940809
there are a few things in algebra that require combinatorial thinking. Likewise, combinatorics greatly improves your problem solving abilities which you probably need. I'd recommend doing combinatorics over topology.

>>11940870
Based Kafkaposter.

>>11940809
>I've heard topology isn't very proof heavy
Then you were lied to

I have a master's in ME. I want to get another master's in math.

What do you anons think? Waste of time?

>>11940957
>Waste of time?
No, except you're into making money now.

>>11940961
True, I would be foregoing income

>>11940957
>Waste of time?
No.

>>11940795
why do zoomers think spamming their memes in generals is funny? happens on other boards too

>>11941157
*in the first post of generals

>>11941157
Because people keep calling it 'based', although it might just be a same fag who has nothing better to do.

>>11941276
>might
lmoa

>>11941276
>>11941285

>>11941157
Gen Xer here, I find the 'elliptic curves' guy pretty damn funny.

>>11941353
Based and Xpilled.

>>11941157
>once a slow thread
>spamming

>>11941477
How can I beat procrastination, guys? I really wanna turn my life around, but I'm too lazy...

>>11941485
You need to be insanely obsessed with what you do. If it's not like a drug to you it's not the best fit.

>>11941537
what if i'm not obsessed with anything
does this mean i was born for mediocrity

>>11941547
Yes, you're a normal person with no true goal or ambition. Work, consume, reproduce, and die.

>>11940795
BASED

>>11941551
i may not be obsessed with anything but i have enough discipline to study things i like such as japanese language so thats fine. being recognized is impossible unless you have been learning something since you were a kid

>>11941559
>being recognized is impossible unless you have been learning something since you were a kid
Yeah, because Tao has been learning Random Matrix Theory since he was a kid, am I right?

>>11940892
based redditor

>>11941559
incredible cope

>Treat [math]\frac{dy}{dx}[/math] like a fraction.

>>11941577
whats it like being this much of a retard

>>11941621
It's not easy, man.

>>11941621
You tell me, you're worse.

>>11941559
>being recognized is impossible unless you have been learning something since you were a kid
https://www.quantamagazine.org/a-path-less-taken-to-the-peak-of-the-math-world-20170627/
https://en.wikipedia.org/wiki/Edward_Witten#Early_life_and_education
http://www.wisdom.weizmann.ac.il/~vova/First-steps_2007.pdf

>>11941640
Good links, but that guy is baiting.

>>11941640
>https://www.quantamagazine.org/a-path-less-taken-to-the-peak-of-the-math-world-20170627/
He majored in physics kek, that's practically the same area as math.

>>11941684
Math is axiomatic; physics is not.

>>11941706
Physics is axiomatic, you need to assume the existence of God, otherwise nothing would make sense.

>>11940745
Do you mind quitting the subtracted meme?

Am I a retard for not being able to get through this. I can't remember the proofs or know how to do most of the problems and get the theory. I switched to linear algebra step-by-step by Singh but i'm stil struggling with it. I heard Strang or Shilov have good texts too as well as the MIT opencourseware thing but idk, having trouble making a decision.

>>11941759
Shilov or Axler would be my choices.
Strang's book is largely computational based, so I can't recommend it if your goal is to learn about LA from a mathematical perspective rather than an applied one.

>>11941767
Would Shilov be fine on its own, since Axler doesnt teach determinants or is it necessary to read both?

>>11941757
Why don't you create the next one like you do with the /sqt/?

>>11941795
Axler teaches determinants, but only in the ens, Shillov is not as good as Axler, the only other books on the same level are Hoffman and Kostrikin.

>>11941795
>Axler doesnt teach determinants
How did this meme start?

>>11941801
>>11941818
Why does he avoid them until the end?

>>11941841
Read the preface.

>>11932387
Hello, I'm an engy student. I think murricans take Calculus and such in HS, where they just learn methods and algorithms and stuff.
My math courses for engineering also went into a lot of proofs, but the problems weren't about proving stuff, for the most part, and we probably skimmed over some important results from a math major perspective.
This did lead to some funny stuff, like how an "Intro to Math" course that dealt with some geometry from a LA standpoint recommended Hoffman and Kunze as a course book.
>>11932423
>To improve critical thinking and problem solving.
I'm not quite sure that's how it works but hey. I did them because I found them neat, and to slack off on other work.

>>11941841
Because they are unmotivated, and because while they become useful later they are extraneous for a beginner.

>>11941759
What was your problem with it? And what are you studying for?
Personally I didn't like Strang because it was slightly meandering and nonrigorous. Shilov scared me off introducing determinants right off the bat, but that may be me being a coward.
>>11941841
He goes a bit into it in the book
Theres also https://www.maa.org/programs/maa-awards/writing-awards/down-with-determinants if you can understand it

>>11941841
Determinants are usually the second to last thing you'll learn in any introductory LA course.

What if current foundations of Mathematics are inconsistent?
https://www.youtube.com/watch?v=O45LaFsaqMA&t=1386

In this talk Voevodsky argues that because we can't prove that mathematics is consistent we should think about how to deal with inconsistency instead of just naively hoping for consistency. In standard set theory an inconsistency (a statement that is both true and false) leads to everything being true. He talks about some kind of type theory where this is not the case, and where moreover we can algorithmically check for inconsistency.

What is this kind of type theory and why is this the case? In the type theory I have been exposed to it does not work this way. What is the algorithm?

>>11934374
they are games though, why wouldnt they be

>>11941870
Idk what it was, I just read through a chapter and couldnt do any proof exercises.And some of the questions didnt have solutions that I could verify anything I had down. Now that I think of it I probably was reading it not like a textbook and just reading over things I didnt understand.

Going into EE. Have done a bit of LA like cramers rule and solving determinants but now I want to become a LA god and get really good at the subject.

>>11941767
>>11941801
>>11941818
>>11941849
>>11941869
>>11941870
Thanks for the advice

>>11941901
Cheers, lad. You really can't get better than Axler for what you're looking for. It's a very good book.

>>11941901
>Going into EE
Check your syllabus and stuff if you can. Some of the books people will recommend here may not suit you

>>11941922
Are determinants really that hard to justify? I mean, the determinant of an n by n matrix represents the volume of the cube [0,1]^n when transformed under the aforementioned matrix. Is that really so unintuitive?

>>11941980
I don't think it's really easy to see that without a bunch of linear algebra knowledge first though. Like how do you justify that without talking about eigenvectors/values?

>>11940807
>what's its (continuous) dual space B(H)*?
Well if you read my post you would have noticed that Wikipedia already answered your question. All Hilbert spaces are reflexive and therefore their continuous dual is (isomorphic to) H itself. If you don't see why this should be the case then you should study them again because it's a pretty basic result.

>>11942034
B(H) is not a Hilbert space

>>11942054
I fucked up the syntax in my post so I'll spoonfeed you instead. If H is a Hilbert space, then thanks to the Riesz representation theorem H and H* are isomorphic. Therefore (H*)* = H* = H where equalities are to be taken as isomorphisms.

>>11942060
Yes and B(H) is not a Hilbert space so literally none of what you said applies to the question that was asked.

>>11942064
At this point we're having a severe misunderstanding on what you mean by B(H) or I'm getting trolled hard. If by B(H) you mean the space of bounded operators AKA continuous, linear functions from H to R or C then H and B(H) are isomorphic.

>>11942069
An operator maps from H to H and not from H to C.

>>11942073
This is why you specify the codomain when defining those objects.

Perkele I am depressed

>>11941880
I don't see where you got the abstract you quoted from.
I have a coarse idea of Voevodsky's ideas and I don't really this sort-of paraconsistency proposal as you describe it there.

Is math hard or am I just retarded
It make my brain sleepy so quickly
:{

>>11942326
You're not retarded, you're probably average, and there are plenty of average people triumphing in math.

>>11942330
I just wish I had more capacity. I do like 3 pages of textbook and my brain gets math'd out for the rest of the day. I used to be like 1 page a week so it's progress. But I just wish I could do more without getting tired

are there any vector value functions where integral of f . dr is'nt path dependent but f isnt a conservative vector field?

>>11940807
I suspect [math]B(H)^*[/math] might have no nice description, it looks like "contains all kinds of stuff, can't be explained in simpler terms" situation. Some thoughts:
1) From the fact that trace-class operators form a predual of B(H), you get that the trace-class operators (with their special norm) can be isometrically embedded into [math]B(H)^*[/math].
2) Let [math]H = L^2[0, 1][/math], and [math]B[0,1][/math] denotes the bounded continuous functions on [0,1], with the supremum norm. For any [math]\phi \in B[0,1][/math] you can define [math]M_\phi (f) = \phi \cdot f[/math]. Then
[eqn] B[0,1] \ni \phi \mapsto M_\phi \in B(H)[/eqn]
is an isometric embedding. This lets you embed isometrically [math]B[0,1]^*[/math] into [math]B(H)^*[/math].

>>11942312
what's the problem finnfag

Some topics to study for the quarantine mood.
https://en.wikipedia.org/wiki/Corona_theorem
https://en.wikipedia.org/wiki/Corona_set
https://en.wikipedia.org/wiki/Corona_algebra

G'day, /mg/

>>11942394
I believe it is in their genes.

>>11942403
I would prefer rona over corona so I could go back to my chamber, but thanks.

>>11940804
The latex thing here explodes when you have a forced line break in the middle of the code. Putting those extra spaces allows you to choose where your line breaks happen and then you can prevent it from occurring in the middle of your favourite command.

Is there a name for this expression?

>>11942394
im just tired and i doubt my purpose, i am overworked and a slave in a devil planet

>>11942447
no its in your genes

>>11942453
To be fair, it is probably in the genes of everyone from the eastern side of Germany, but the statistics make me believe it is particularly strong among Finns. Anyhow, what is this thing that turned you into an empty shell searching for a purpose to go on? What level are you on?

>>11942466
im on level 2.5, mostly its just general drudgery and pessimism that is easy to handle panged by regret and loss from missing the past, but there is genuine anxiety and uncertainty if my life path is correct

but in the end ill still follow this path because i have nothing better to do. im probably just tired.

>>11942470
I meant bachelor/master/phd/wageslavery, but yeah, I feel you. The uncertainty is horrible and really keeps you awake in the darkness of the night everlasting.
>but in the end ill still follow this path because i have nothing better to do. im probably just tired.
Can you take a few days off? If the weather is nice, go swim in a lake for example. I just had one of my comrades drop out because he burned himself out. Don't be him.

>>11942488
im pre-bachelor, out of highschool been neet now im studying for college. im juggling studying math, studying german, learning coding, and trying to make money and research various life stuff

i would go outside but i cant exactly because my city has an average iq of 95 and it makes me paranoid. i think im just gonna succumb to the numb until i get my work done

>>11942488
im unsure if its the "right path" specifically today because i was getting annoyed at my studies today, ive never felt annoyed with math before when i would do it recreationally and for pleasure but im pounding it hard lately and learning about jordan forms seems really stupid at the moment.

>>11942494
Unless you think you want to become a translator, I would suggest you don't make German your main thing. Either do it in your own time or take the language courses offered by the uni you end up in. Coding and maths can be combined to give you a major and a minor in both ways, so that could be an option. If you feel like you would like to do research or otherwise feel like maths is your "the thing", then that would be a natural choice, but I don't know how hard it will be to get a "real" job after that. Regardless, there's the nice thing about being a European that you pay hardly anything for the uni, and so you will not ruin your whole life by making the wrong choice in the beginning, and you could of course switch after getting your bachelor's degree. The beginning will be a bit dry. You want to become a carpenter and make all sorts of fancy things, but first you need to learn how to properly use the tools (like those Jordan forms). After that you get to do art. That's my thought flow opinion on this. Agree or disagree, hopefully it helps to spark at least some ideas where to take your life (before grave).

>>11942541
the reason im learning german is because im an amerifat and i want to go to uni in germany for the free tuition
i agree with you, i know i have to learn the hard parts before i can do art. im just being a weakling i guess. sometimes i worry that i wont ever get to that level though. that ill always be hindered by my inclination towards intuition and away from rigor. ive made progress, but sometimes i feel defeatist

>>11942555
Oh, I thought you were a mongol because of the perkele. First the rigorous stuff, then the intuition. Learn German and make it to a nice uni, I will make sure I succeed in my stuff and then get myself an office in the very same place and recruit you into my gang. The best of luck with your efforts, anon.

>>11942574

>>11942585
Exactly.

I have two questions for you guys:
- are you aware of any good blogs at an undergraduate level?
- what material would you suggest for learning type theory (for use in mathematics, not PLs)

>ive made progress, but sometimes i feel defeatist

>>11940795
Can I have a quick rundown.
Also, is 0.999... exactly equal to 1, or just equal?

>>11940745
Next semester I'll be doing linear programming, I am going in for a treat?

>>11941759
In my experience going thru a simple computational book like Strang's first and then doing Shilov is the best way.

>>11942494
Still better than hanavesi-city probably. Have you considered avoin-yliopisto?

>>11942628
i live in america. we have a lot of black people here

>>11942617
>exactly equal to 1, or just equal?
same thing

>>11942541
>nice thing about being a European
You think you're better than me because you don't pay for your college, huh europoor? No wonder you people don't have a Harvard, an MIT or a Princeton.

>>11942574
>A place to hire /mg/ homotopists
Holy fucking based

>>11942649
>we have a lot of black people here
And?

>>11942847
have you ever met a black person?

>>11942838
That is precisely what my post says. Well read, anon.

>>11942845
We will be the next Bourbaki. We will be the better Bourbaki. We will make the old Bourbaki seem like Bourbaka.

>>11942083
Lmao retard B(H) is pretty standard notation
>>11942069
Also an operaror is not a linear functional.

>>11942911
[math]B(H)[/math] isn't just pretty standard, I genuinely don't think I've ever seen anyone use anything else.
Unless you count [math]L(X)[/math], but that's for operators on Banach spaces.

>>11942864
>Bourbaki
Not a person

>>11942857
I am a black person...

>>11942929
do you live in finland?

>>11942939
No, I live in the greatest european country: France

>>11942918
Then you should try more than a single book.

>>11942963
Nice non-example.

if you want to learn real mathematics, come to the math deparment when the sun is set and say you "came to see infinity"

>>11943006
Anyone can see infinity, but you can never be the man who KNEW infinity.

>>11943006
>>11943013
i am the man who knows the chain rule

did you prove that theorem yet son?

>>11943006
are you going to give thenm drugs

>>11943103
You're glowing.

>>11942597
bump

>>11943113
>Blogs
https://www.youtube.com/watch?v=WWgZr_jredo
>Type theory
Okay loser

https://www.youtube.com/watch?v=ccY25Cb3im0
top tier studying music

>>11941797
Sure thing.

>>11941759
>>11942623
my recommendation is dont waste your time struggling through a book for computational linear algebra, just watch the mit ocw lectures. it's not like you need to get it all down. you just benefit from strong familiarity with all the vocabulary and techniques before you start reading a real book or watching axler's lecture videos (which are also great)

>>11942963
What's your point? B(X, X) is essentially always abbreviated B(X).

>>11940745
Let [math](X,A) [/math] be a pair of topological spaces that is 0-connected (that is every path-component of X contains a point that belongs to A). Is [math]H_0(X,A) = 0 [/math]?

Any good math news site out there?

>>11943290
[math]H_0 (A) \rightarrow H_0 (X)[/math] is clearly surjective, so just apply the long exact sequence to get the result.

>>11942951
Since Janurary 31st of this year that is

Prof just recommended this by saying that is should be in everyone's reading. Is it really that good?

What are you supposed to write in a welcome letter to new postgrad students? I was given the honour to do that, but I have no idea what to tell them. The example they sent me was very cringy
>omg i like totally love chemistry <3
>this place is so beautiful <3

>>11943346
It has an extensive, titilating description of the Cox-Zucker machine, written by the fantastic mister Cox himself.

>>11943347
tell them to fight the system using free thinking science

>>11943290
ok. what about n-connected pairs, does the n-th homology group vanish?

>>11943346
>Unknown book
>Recommended by unknown professor
>Who teaches in an unknown university
Geez, I wonder if it's as good as the classics of the area that everyone recommends.

>>11940745
How the fuck am i supposed to solve this integral? It's wizard tier. Probably the teacher that wrote this stole the answer from sbd else

>>11943347
Be honest and tell them the legitimate reasons why you enjoy being at the university. Also congratulate them for their (presumably) hard work getting this far. Maybe point out resources to get help (maybe even give your contact info).

>>11943463
Using the famous "maple" technique

>>11943504
are you trying to troll me or what? develop

>>11943509
>are you trying to troll me or what?

>>11943465
Thanks! I'll do something like that.

>>11943550
Don't forget to add a picture of an /mg/ approved anime girl.

>>11943592
If I treat my career as a magic girl anime, I can then justify including a photo myself like they require. Remember, we are all magical here.

>>11941980
They’re a function of the columns of the matrix representing the operator, mentioning the thing about volume means nothing to most people including math majors.

>>11942864
>We will be the next Bourbaki. We will be the better Bourbaki. We will make the old Bourbaki seem like Bourbaka.
Heh.
>>11942574
>First the rigorous stuff, then the intuition
Do people really do this? I guess I'm small brained

>>11942597
yeah but i can't remember them
i think the guy that made napkin has one

>>11943463
The integral for the x and z component are obiously 0. For the y component, first notice that
[math]\frac{\partial}{\partial y}\left(r'^2+y^2-2yr'cos(\theta')sin(\theta')\right)^{-1/2}=\frac{(\vec{r}-\vec{r}')_y}{2|\vec{r}-\vec{r}'|^3}[/math] and use Leibniz rule to take the derivative out, the integral over [math]r'[/math] becomes easier, I know it can be donde by substitution and whatever but I don't want to do it lol.

>>11943866
>but I don't want to do it lol.
Based.

>>11942864
>We will be the next Bourbaki. We will be the better Bourbaki. We will make the old Bourbaki seem like Bourbaka.
you gave me a chuckle sir thank you

>>11943274
Yes, its the other retard who says B(X) is not standard or popular at least.

>>11943899
[math]B(X)[/math] is popular for Banach spaces, yes.
[math]B(H)[/math] is still golden standard for Hilbert spaces, and I still haven't seen any examples otherwise.

>>11943809
At least I do that. When I try to get the intuition for stuff, I find it useful to know what I am actually trying to fit into the big picture.

>>11943895
You are most welcome. And feel free to leave your application if you want to join the elite club.

Is it true that math majors live in poverty?

>>11944023
No, it's almost impossible to be jobless if you're a PhD.

>>11944023
Math majors among the highest earners, so no.

>>11943895
kill yourself

>>11944100
No.

>>11944118
Then at least go back

>>11944123
To?

>>11943809
>Do people really do this? I guess I'm small brained
I always thought that people grasp the formalism and the intuition simultaneously as part of a single learning process. You'll pick up some broad intuition from the author's summary in the beginning of the text, but properly going through the formalism solidifies it.

>>11944152

>>11944157
>>11944157
Oh yeah, good point.
Any book suggestions for that one?

>>11942597
This blog is good for both questions: https://xenaproject.wordpress.com/

>>11943346
I wouldn't read it cover to cover but found it a decent secondary reference.

>>11942322
I write it, that was my understanding of the talk. I was half asleep and he's not a great speaker though so it could be wrong.

>>11943866
i think it's
[math]\frac{\partial}{\partial y}\left(r'^2+y^2-2yr'cos(\theta')sin(\theta')\right)^{-1/2}=\frac{2(\vec{r}-\vec{r}')_y}{|\vec{r}-\vec{r}'|^3}[/math]
i still dont see why is that derivative useful tho

>>11944190
You are right
>i still dont see why is that derivative useful tho
You can take the derivative out of the integral and I believe the integral becomes easier.

Holy based.

>>11944205
oh so take the d/dz out of the whole triple integral? thanks bro

>>11941611
Does that mwan Im supposed to divide it then?

The journals of my field are all owned by the kikes at Elsvier. How do I fuck them from the inside?

>>11944167
Never mind.

>>11944272
What uni? How did they cheat?

>>11944272
Lmao what a fagglord.

>>11944312
send them papers generated by neural networks, this will slow down their process at least

>>11944386
Rutgers

>>11944272
>mixed discipline, suitable for biochem, do a different course if you are majoring in math version of calc 1
wew

>>11944312
send them machine learning papers this will set back the quality of research they publish by decades.

There's a guy at Stanford doing a lecture series on modern algebraic geometry here: https://www.youtube.com/channel/UCy3u23mZE4TyW88yr6JLx9A/videos
Anyone watching along?
He has a textbook as well, which from what I've read so far is great.

>>11944563
Based

>>11944272

do american universities REALLY? pathetic that a professor needs to handhold this hard a grown up student

How would I fare if I started a bachelor's in math at 23-24 years old

>>11944593
About as well as how much work and effort you put into it.

>>11944593
Acqurie Principles of Mathematical Analysis by Walter Rudin, Linear Algebra by Hoffman and Kunze, Calculus by Michael Spivak. Attempt all of the problems in the first two chapters of these books. If you can solve them correctly without significant amounts of help in a timely manner you should fare just fine. Alternatively you could pay for an iq test with a professional psychiatrist but this is not very informative as you may very well score high on sub-tests that aren't as useful for mathematics. If your plan is to publish research consider that you will be competing with younger and smarter people for very small amounts of research funding and scarce positions in academia. If it is just to pick up skills for industry or a related field then there's no problem at all. Math undergrads require marginally higher intelligence than other STEM majors.

>>11944577
Vakil didn't write The Rising Sea for some anon on a mongolian fishing forum to call him "a guy"

>>11944593
>24
Anon, I... I'm sorry. At that age your brain will have degraded so badly you can hardly walk or even breathe.

>>11944607
S-sorry

>>11944598
This is unequivocally true but no one wants to hear it.

>>11944642
In all seriousness you should read The Rising Sea if you want to into algebraic geometry. They're an excellent resource

>>11944661
I'm taking a course that uses it, following Ravi's lectures.

>>11944668
Good - don't fall for the Hartshorne meme. Vakil and Stacks are all you need

>>11944653
I think something along the lines of >>11944606 fits your post more really.

To that guy, those are a bit slanted on difficutly though.

>>11944712
Not really.

>>11944729
It is though, average people will eventually get filtered. It's not just a question of effort and time spent on the subject (and that carries a lot of weight as well)

>>11944787
Average people don't major in math.

>>11944796
Maybe, but some might try, like that anon

>>11944272
>am i excited to catch those cheaters? you bet your ass i am.
>these cheater have not only deeply insulted and hurt and dissapointed and disturbed me, but they have made the math135 experince a bit worse for everyone

>>11944610
How does it feel to be almost 30 without publications, ho?

Which do you think will be solved first, RH or GRH?

>>11944391
>>11944835
t. cheating asian

>>11944915
The former will be solved within the next 50 years.

>>11944272
Beyond based, is there anywhere I can watch these cheaters seethe?

>>11944938
>>>11944915 (You)
>The former will be solved within the next 50 years.
Hey no fair that's my prediction

>>11944915
RH will be proven false in the next 20 years by a vast computational effort and at least one number theorist will commit suicide as a result.

>>11945146
inb4 Jonathan Tooker

>>11944832
The fail rate from the very scant info i’ve found in higher math courses is quite low. Once you pass the brainlet filters you will probably graduate. The real limiting factor is brilliance and the feasibility of whatever research you’re interested. You cannot control either of these things, hence its worth mentioning that if you desire a life of solving difficult pure math questions you probably have a much lower chance of success than just finishing a bachelors.

>>11944940
Here's the thread: https://www.removeddit.com/r/rutgers/comments/g9f57x/126_of_us_are_caught/fot9yil/..
Safe to say that this prof is gigabased.

>>11945189
Which courses are the 'branlet filters'?

>>11945360

>>11945209
lmao holy fuckin BASED

>>11945378
It gets better. Some students started a petition to get him fired after the incident.
https://www.change.org/p/robert-barchi-have-dr-joseph-guadagni-removed-or-censored?recruiter=1083814491&utm_source=share_petition&utm_medium=copylink&utm_campaign=tap_basic_share

>>11945390
l m a o

What's the symbol for "once it reaches, move on to the next instruction"?
Say I've got code thats a loop of
while x < 47
x + 1
obviously there's a implied if else loop where else is just "stop and move on", but how does one write it in a purely mathematical form to move on?

>>11944272
instead of teaching your students, you are out to get them, what does that say about you as a person? i bet you live in your parents basement while your mother asks if you find a girl yet (or guy for that matter). the reason these kids probably have to cheat is because of your inability to teach. instead of putting in all this effort to catch cheaters, you should try putting some effort into losing weight, that double chin isnt a good look you know. this quarantine has given everyone lots if extra time and you choose to go after these kids, instead with all this extra time you could lose all that extra weight so the ground doesnt shake while you walk. lets hope you finally move out of your mothers basement and lose that weight, im rooting for you dr. g.

>>11945420
lol

/gmmg/

>>11944860
I publish if I publish. It's only a side product of being paid to do what I want to do.

If someone likes Morse(-Bott) theory
>Morse-Bott Theory on posets and an homological Lusternik-Schnirelmann Theorem
https://arxiv.org/pdf/2007.13565.pdf
A survey on
>Identities in group rings, enveloping algebras and Poisson algebras
https://arxiv.org/pdf/2007.12767.pdf
H-hentai!
>Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds
https://arxiv.org/pdf/2007.13365.pdf

Have a nice day!

>>11945539
Morning, lad.

Hey guys, how can I describe finding the nearest power of ten to some number in a formula without using the english language? No set notation allowed - just babby tier symbols and the floor/ceiling notation.

>>11945396
>>11945390
>>11945378
>>11945209
>>11944940
>>11944386
>>11944391
>>11944401
>>11944588
>>11945420

>>11945576
Based as fuck.

>>11945575
Just floor(log10(x)) dude, it's not hard.

>>11940745
>boards of canada
My man

>>11945576
big man makes the mathlets seethe, 135 is for the chemists, cs and physics students
based

Somebody explain to me how godel incompleteness works

>>11945913
I would but I can't give a full explanation

>>11945933
Based.

>>11945933
Ha

But seriously how the fuck is it possible for mafs to be self referential, how do you go about to encoding that?

what does the "E" in E-theory stand for?

I'm starting a math/physics prep semester at my university in a couple of weeks but I really can't grasp inverse proportionality.
As dumb as it probably sounds, I "get" the idea of halving = quadrupling in my head but just can't put it to paper once squaring and fractions come into the mix.
If anyone here struggled with it, do you have any resources that helped?

>>11946051
Excellent
It's an extension of Gauss' Theorema Egregium

>>11946051
eminem

>>11946051
Einhängung. Notice how there are suspensions involved. That's also why the Freudenthal map is denoted by E.

>>11946064
its just the inverse square rule bro.
Take a square and divide it once on both plains = 4 squares
4 squares divided is 16 squares (4^2)
16 is 16^2
What exactly are you struggling with past that? Also prep semester? What other stuff are you doing? Is prep semester only for those who didnt complete all their high school studies?

>>11946156
It's for people who didn't qualify for their desired undergrad study
I'm also struggling with rearranging the subjects of formulas quite a lot

>>11946064
1/2= 0.5
1/2^2 = 0.5*0.5 = 1/4 = 0.25
How many 0.25s go into 1?
4

So athiests, if God isn't real how do you fit 0.25 4s into 1?

>>11946234
0.25 + 0.25 + 0.25 + 0.25 = 0.100
plenty of room for more 0.25's

>>11944272
https://www.reddit.com/r/rutgers/comments/9o55st/why_is_calc_135_so_unnecessarily_hard/

Is Dr G infamous or something?

>>11946320
it just looks like he and his students are ribbiters
a lot of universities have 'that course', some people find it difficult then oral tradition ensures the next year of students look for holes and pitfalls to get trapped in

>>11946337
wdym holes and pitfalls to get trapped in?

>>11946278
>0.25 + 0.25 + 0.25 + 0.25 = 0.100
Idiot
It's 0.25 + 0.25 + 0.25 + 0.25 = 0.8,20

[math]\frac{\partial V}{\partial t}+\frac{1}{2} \sigma ^2 S ^2 \frac{\partial ^2 V}{\partial S ^ 2}+rS \frac{\partial V}{\partial S} - r V = 0[/math]

>>11946228
Oh yeah I get that, it's in relation to dividing / squaring / rearranging subjects in a formula where I end up confused.
I'm not very familiar with proper math language as I just picked it back up this week after dropping it in high school so I hope I make at least a bit of sense.

I can't remember which level the dynamical systems people were in these threads, but there seems to be a post-doc position available in Australia for similar minded people! http://careers.pageuppeople.com/533/caw/en/job/559664/postdoctoral-research-associate

>>11945539
>I publish if I publish. It's only a side product of being paid to do what I want to do.
HOLY BASED

>>11946562
Based Rinposter.

>>11946533
>number theory
>dynamical systems
extremely based

>>11946533
oh shit, if only the timing were right for me

>>11946562
Thanks.

>>11946591
>>11946640
Remember that you may have future with those things!

Having some trouble understanding Stoke's Theorem, any good resources I can use to study up on it?

>>11946687
do you have any questions in particular?

>>11946690
I'm taking a class on vectors and a big part of it is using Stoke's Theorem, particularly for finding work done by a force along a curve. I'm having trouble figuring out what the bounds are and how to use it when I have intersecting shapes.

>>11946707
can you give a concrete problem you're having trouble with? I don't know any good resources, but I can try to help

>>11946731
Ok, the problem I'm trying to solve is:

Let F(x, y, z)=<xy, z^2, zy^2> and C be the curve of intersection between the sphere x^2+y^2+z^2=9 and the cylinder x^2+y^2=4 with z≥0. Find a double integral that computes work done by the force F along the curve C using Stoke's Theorem. C is traversed clockwise when viewed from above.

It's my understanding that Stoke's Theorem applies when traversing counterclockwise, so the end result will be negative, which means negative work is done. However, I'm confused as to how to figure out what the surface is and what my bounds will be.

>>11946748
>what surface is it
Can't you use the circle given by [math]z = \sqrt{5}[/math], [math]x^2 + y^2 = 4[/math]?

>>11946779
*[math]x^2+y^2 \leq 4[/math].
Which reminds me that I should use disk instead of circle.

>>11946748
the curve is something like pic related, just intersection of sphere and cylinder. more precisely, we can plug [math]x^2 + y^2 = 4[/math] into the sphere to get [math]4 + z^2 = 9[/math] so [math]z = \sqrt{5}[/math], because the cylinder is assumed to be in the upper half-space. therefore the intersection is a circle with radius [math]2[/math] lying in the horizontal [math]z=\sqrt{5}[/math] plane. they tell us that the parametrization is clockwise from above, one such parametrization is
[eqn]
\gamma(t) = (-2\cos t,2\sin t,\sqrt{5}), \quad t \in [0,2pi]
[/eqn]
now you can easily compute the work by usual line integral. but they want you to use Stokes' theorem, I'll explain in next post.

Is there a single field of math that Lie theory can't be connected to?

>>11946799
Logic is about truth, lot lies.

>>11946779
I assumed so, but I wasn't sure if it was the "footprint" of the sphere or if it relied on the cylinder, too.
>>11946792
Thank you, especially for the picture, that helps a lot. What did you use to model that?

>>11946805
kek

>>11946748
>>11946792
to use Stokes', you need a surface [math]S[/math] with boundary [math]C[/math]. one choice is to use the disc [math]x^2 + y^2 \leq 4, z = \sqrt{5}[/math]. one parametrization is
[eqn]
\varphi(u,v) = (-u\cos v,\sin v, \sqrt{5}), \quad u \in [0,2], v\in[0,2\pi]
[/eqn]
you just need to make sure it's oriented properly. i.e. if you compute the normal vector from the cross product and apply the right hand rule, you should get the orientation of [math]C[/math] you were given. I'm not gonna do that for you, but if you get the opposite orientation, you can for example swap the [math]u,v[/math] parameters. by Stokes' theorem, the work done is
[eqn]
\int_C F = \int_S \text{curl}\, F
[/eqn]

>>11946812
You might find this to be of use.
https://www.monroecc.edu/faculty/paulseeburger/calcnsf/CalcPlot3D/

>>11946812
I made the picture by googling "sphere cylinder intersection"

0! = 1

>>11946831
>>11946831
should be [math](-u\cos v,u \sin v,\sqrt{5})[/math], forgot u in the y-component

>>11946839
[math]n!=n(n-1)(n-2)...(2)(1) \\ n!=(n)*(n-1)! \\ 1!=1*(1-1)! \Rightarrow 0!=1[/math]

>>11946852
[eqn]0! = 0*(0-1)! \\
1 = 0*(-1)!\\
(-1)! = \frac{1}{0}[/eqn]

>>11946857
[math]0 \notin \mathbb{N}[/math]

>>11946831
That makes sense. Thank you for your help.
>>11946832
I very much do, much appreciated.
>>11946835
lmao, well still, thanks for the picture.

>>11946857

>>11946862
if your function is not well-defined and continuous across all the complex numbers it's shit

*continuously differentiable

>>11946902
[math]\Pi(z)=\int _0 ^{\infty} \exp(-t) t^z \ dt, z \in \mathbb{C}[/math]

>>11946831
So I found the normal vector and the curl of F, but if I use Stokes' theorem I'll end up with a surface integral, right? Can I change that into a line integral or is there a way to use Stokes' Theorem and end up with a line integral? For this problem, I need a double integral, but it can't be a surface integral.

>>11946958
Surface integrals are double integrals tho.

>>11943818
You're right, and it's pretty updated too. Thanks!
>>11944170
Oh that's interesting, gotta follow up on it. Thank you.
>>11943127
idiot

>>11946963
I understand that, but the problem I'm trying to solve says to "Find a double integral (not a surface integral)".

>>11946971
I realize now I didn't put that in my post earlier (>>11946748), my bad.

>>11946971
Maybe you just need to get it in explicit form as a double integral?
[math]\int _{r = 0}^{2} \int _{\theta = 0}^{2 \pi} [thingeridoo ~ here] ~ d \theta ~ dr[/math]?

>>11946993
I have to assume that's what it means, I don't see how you could get a double integral using Stokes' Theorem without doing that.

>>11944023
It's true. I'm only making 40k a year and half of that is stolen from me via taxes.

>>11946562
Toesucker Rin is a slut!

prove that for T in L(V),
dim v = null t + range t

make it elegant, or die!

>>11942448
idk, I'd maybe call it the radius of the subset but i don't really do topology or anything, I just drew a picture and that was the intuition I got.

>>11947370
[math]T : V / ker ~ T \rightarrow im ~ V[/math] is an isomorphism, so [math]dim ~ V - dim ~ ker ~ T = dim ~ V / ker ~ T = dim ~ im ~ T[/math] .

>>11947370
For any [math]T[/math], there is a short exact sequence [math]0 \to \text{ker}(T) \to V \to \text{im}(T) \to 0[/math]. Since vector spaces are projective, the sequence splits and we obtain [math]V \cong \ker (T) \oplus \text{im}(T)[/math], from which the claim follows.

>>11947426
>dimV−dimkerT=dimV/kerT
you need to show this

>>11947439
Take whatever base for [math]ker ~ T[/math] and prolong it to a base [math]B[/math] for [math]V[/math]. The map [math]T: V \rightarrow V / ker ~ V[/math] maps [math]B[/math] onto a spanning set. For [math]v \in ker T[/math], [math]T(v) = 0[/math], but for [math]v \notin ker ~ T[/math] we have that [math]T(v) \neq 0[/math]. This implies that [math]T(B) - \{ 0 \}[/math] is a base.

>>11947458
Actually, it doesn't, my bad.
Fuck, I didn't wanna use the explicit definition of the quotient.

>>11947432
Based Megumiposter.

>>11945209

First thing: I don't know much about order theory, but if I have a totally ordered (or something like that) set X with the same cardinality as R, does that mean that there exists a bijection from X to R which preserves the orders? (This would probably be an isomorphism)
Second: If (X,d) is a metric space then we have an order on X x X where
(x,y) <= (x',y') if d(x,y) <= d(x',y').
This would be a sense of x is closer to y than x' is to y'. How could this be axiomatized?

>>11947370
>>11947370
1. [math]T = \pi[/math] is a projection ([math]\pi^2 = \pi[/math]). then [math]v = (v - \pi v) + \pi v[/math] gives [math]V =\ker \pi \oplus \text{im } \pi[/math].

2. [math]T[/math] is not projection. then [math]T[/math] is at least "conjugated" to some projection [math]T = f^{-1} \circ \pi \circ g[/math] where [math]f,g[/math] are isomorphisms. it follows [math]\dim \ker T = \dim \ker \pi[/math] and [math]\dim \text{im } T = \dim \text{im } \pi[/math] and use 1.

>>11947506
No. Take [math]R+R[/math] or whatever.
BTW you've now completely exhausted my knowledge of ordinals.

>>11947504

>>11947370
>extend a basis of null T to V
>the extended bases under T span Tv
>if they were linearly dependent, some nonzero coefficient sum of them could equal 0
>thus T of a nonzero coefficient sum of the extended bases is in null T
>arriving at contradiction

>>11947571
>uses a basis
>elegant

>>11947577
Yes.

>>11947577
>prove that the cardinality of bases for different vector spaces does this
>don't use bases btw, that's inelegant
>also you can't use common sense results about dimension

Guys don't let an anime tranny win this...

>>11947522
Do you mean 2 copies of R? Isnt the order not antisymmetric then? (1_A <= 1_B <= 1_A)

I remember how big of a deal it was in forst semester LA that we proved the existence of a basis not judt for finite dimensional, but arbitrary bector spaces. I can mot recall having seen a single usage of an infinite basis though?

>>11947583
>>also you can't use common sense results about dimension
but dim ker T + dim range T = dim V **is** a common sense result about dimension. it's literally the same thing as dim V/W = dim V - dim W.

>>11947588
Cope

>>11947590
No bro, basic ordinal arithmetic. Cardinality doesn't classify well-ordered sets.

>>11947606
In what way is it common sense?

>>11947606
If you look at it that way anon's proof is the only one someone has already posted, because Meguminfag's proof uses the version of rank-nullity for short exact sequences of free modules.

>>11947620
I forgot to point out the issue with the conjugation proof:
It doesn't prove anything until he actually shows that the maps exist.
>isn't it trivial
It's trivial if you use rank-nullity and the fact that dimension classifies vector spaces up to isomorphism, yes.

>>11947620
Megu fag is using Noether and splitting. Then he gets the isomorphism and uses the fact that dimension commutes with direct sum.

>>11947649
Prove that the map splits without using a base.

>>11947651
Any module over a semisimple ring is projective, fields are semisimple. A short exact sequence with a projective module as the third/fourth (however you want to count them) one splits. No need to touch the basis in order to have it split.

>>11947690
WORKING WITH DIRECT SUM DECOMPOSITIONS INSTEAD OF BASES DOESN'T CHANGE LITERALLY ANYTHING

>>11940795
based

>>11947748
it's more elegant

>>11947759
It isn't.

Algebra was a mistake.

>>11947773
you have a shit taste, anon

>>11947759
direct sum spaces of dim 1 are bases

>>11947782
Anon, I'll tell you a secret.
You can associate to any vector space base a unique direct sum decomposition, and you can associate to a decomposition an equivalence class of bases.

>>11947805
so ?

now that the show is over, and a BASIC victory has been achieved,
>>11947815

imagine cheating on an undergrad calculus class lmao