/mg/ - maths general

[Anonymous No.11428737]

weekend edition
Previous: >>11419925

[Anonymous No.11428768]

>Differential geometry

[Anonymous No.11428770]

>>11428768
Funny guy.
What's your favorite book on DG?

[Anonymous No.11428771]

>>11428768
>Algebraic topology

[Anonymous No.11428776]

Threadly reminder to work with physicists.

[Anonymous No.11428784]

>>11428737
https://www.amazon.com/Math-Olympian-Richard-Hoshino/dp/1460258738

Does anyone know where I can get that book online? It's not on libgen.

[Anonymous No.11428785]

>>11428770
Lang's "Fundamentals of differential geometry"

[Anonymous No.11428789]

>>11428770
He probably doesn't even know any DG

[Anonymous No.11428795]

>>11428737
>very high level majors
Mathematics
Physics
Philosophy (Analytical)
Music (Classical)
>high level majors
Medicine
Engineering
Chemistry
Biology
Applied Mathematics
>mid tier majors
Computer Science
Arts
Law
Languages
Political sciences
>low tier majors
The rest

[Anonymous No.11428807]

>>11428795
Bump applied math up to S tier.

[Anonymous No.11428814]

>triangle? oh, you mean 2-simplex.

[Anonymous No.11428823]

>>11428776
Threadly reminder that if you start math at 21, you'll never make it into the academy, believe me I tried, don't waste your time on a useless major if you're past your prime already.

[Anonymous No.11428830]

>>11428823
seeing everyone in the thread berated you for your shitty opinion last time, why would you post it again? desperate for attention? get the fuck off 4chan you idiot.

[Anonymous No.11428831]

>>11428785
>Lang's "Fundamentals of differential geometry"
Lang is a meme.

[Anonymous No.11428832]

>>11428830
Based.

[Anonymous No.11428834]

>>11428823
Threadly reminder that if you're this anon, you'll never make into the academy.

[Anonymous No.11428835]

>>11428830
I fell for your trap, I just don't want to let others fall for it as well. Also, I don't give a fuck about deluded people berating me, they're trapped in an illusion and can't even realize that.

[Anonymous No.11428838]

>>11428835
no one cares, doomer. go be nihilistic somewhere else.

[Anonymous No.11428877]

>Hmm yes, your application is promising but I have one more question for you. Prove that [math]\mathbb{Q}[/math] is flat, but not projective, as a [math]\mathbb{Z}[/math]-module.

[Anonymous No.11428879]

>>11428823
based doomer taking physpammer down a notch

[Anonymous No.11428887]

>>11428877
Wait, No I -

[Anonymous No.11428891]

For learning group theory, do you think it is better to learn all the definitions and theorems first then introduce examples, or introduce examples and motivate the definition and theorems. That is in the former, for example, learn all about subgroups, alternating groups, cosets, etc. first then talk about [math]\mathbb{Z}_{n}[/math], etc. I guess in essence is boils to down to learning it top-down or bottom-up.

[Anonymous No.11428897]

>>11428891
like, you teaching a class or self learning?

If you're teaching a class, realize that your just on stage fapping about as most of the brains watching you just wont catch onto what you're doing

if your self studying, always start by memorizing definitions

[Anonymous No.11428906]

>>11428897
i took algebra a long time ago and have virtually forgot it all so i'm looking to catch up in the most efficient way. think i like the top-down approach.

[Anonymous No.11428954]

>>11428891
No you won't properly understand the definitions and theorems without practice. This is true not just for Group Theory but all of math. You need to do examples and problems as you go along.

[Anonymous No.11428981]

>>11428897
>memorizing
No, that's the worst advice possible, you shouldn't memorize anything, you should first UNDERSTAND then do exercises to fixate that understanding in your head.

[Anonymous No.11429059]

>>11428981
This.

[Anonymous No.11429065]

Thoughts on 3Blue1Brown?

[Anonymous No.11429071]

>>11429065
Pretty sure everyone likes him here.

[Anonymous No.11429082]

>what if I put these two structures in the same object
>and ask for them to be compatible
How come so many absolutely excellent and extremely important constructions in maths are literally this?
>Lie groups
>topological vector spaces/groups
>Kahler manifolds
>algebras
>Sasakian manifolds

[Anonymous No.11429084]

>>11429065
he's a fucking fraud

[Anonymous No.11429094]

>>11429082
god intended it that way

[Anonymous No.11429100]

>>11429082
You know nothing about Kahler Manifolds you pseud

[Anonymous No.11429107]

>>11428823
Dont people start graduate studies at that age? Not to mention many people starting bachelor studies at that age?

The only way you may be unable to study at 21 before you brain has even full developed is that you are actually retarded or arent putting in the effort.

[Anonymous No.11429108]

>>11429100
do you?

[Anonymous No.11429109]

noob question but can anyone describe to me the difference between euclidean spacetime and flat spacetime?

[Anonymous No.11429120]

>>11429107
>Dont people start graduate studies at that age?
Yes, that's the common age to start graduation, the problem is that I started undergraduation at that age, I was full of hope at the time, then life gave me the biggest punch I could receive. At least it opened my eyes to reality.

[Anonymous No.11429128]

>>11429108
Yes. It's PhD level, no wonder you don't know what it is.

[Anonymous No.11429129]

>>11429082
>name a very vague general idea
>wow look this vague general idea comes up so often

[Anonymous No.11429132]

>>11429120
depends where you live, what your degree mark was, what you expected, how you approached things and what you applied for. massively variable

[Anonymous No.11429133]

>>11429128
then elaborate?

[Anonymous No.11429140]

>>11429109
A cylinder is flat, but it's not euclidean. Same with the flat torus.

[Anonymous No.11429143]

>>11429100
>not also correcting me on Sasakian manifolds
Confirmed for knowing nothing.

[Anonymous No.11429153]

>>11429132
I'm talking about mathematics here, I'm saying this from experience, abandon all hopes and dreams of becoming an academic if you start undergraduation after 20. Unless of course you are a genius.

[Anonymous No.11429156]

how do we get the stupid anime posters banned?

[Anonymous No.11429158]

>>11429133
Grab a book

[Anonymous No.11429163]

>>11429153
Why? Whats stopping you? Its literally one to two years older than the normal starting age for university.


Perhaps you arent ready for unuversity level maths and need a stronger foundation from studying precalc etc.

[Anonymous No.11429178]

>>11428737
Somebody in one of my electives is arguing that 0i = i and I’m going to have a fucking aneurysm. I already regret taking this course, I don’t event need it. It’s filled to the fucking brim with pseuds and it’s going to push me to suicide. Discussions are mandatory. I am becoming a more pretentious person just by attending this course.

[Anonymous No.11429179]

>>11429156
Math is inherently anime.

[Anonymous No.11429182]

>>11429178
https://en.wikipedia.org/wiki/Zero-product_property

[Anonymous No.11429185]

>>11429153
my friend was offered a PhD in something relates to maths that escapes my memory at age 26 before his undergrad graduation with dogshit (Cs and Ds) grades and near zero attendance/commitment at a respectable science uni because he showed the right attitude with regards to his approach to programming, so fuck off

i was offered one involving exploring the topology of extremal black holes in 2D spacetime, which I refused (although I had excellent grades, just preferred to accept another job)

[Anonymous No.11429187]

>>11429178
the worse they do, the better you do. remember that and excel.

[Anonymous No.11429198]

Is a course on graph theory/combinatorics worth taking?

[Anonymous No.11429201]

>>11429163
Jesus, perhaps you'll understand if I share my tragic story here:
>Be me
>Be happy 18 year old about to start math college in the third best university in the country
>Full of hopes and dreams
>First day of college
>'hum, it's awesome'
>One month in
>'those professors are terrible, all I do is procrastinate all day, I'm fucked'
>No friends
>Isolated in class
>Low grades on the first tests
>'it's ok, it's just because of my procrastination, I'll get better results next tests'
>Keeps procrastinating
>Low grades again
>Fails all classes except for one
>Depression
>Drops college
>Becomes a NEET for three years, spends all day playing videogame, watching anime and wasting time in the internet
>Forgets entirely about calculus and anything learned at college
>Asks on /sci/ if late starters can succeed in the academy
>Everyone is supernice and supportive
>'I can't keep living like that, I need to change, I need to go back'
>Now 21, goes back to math college again
>'new start, hell yeah, this time I'm gonna make it'
>Procrastination
>Depression
>'at least now I made some friends and I'm getting better grades this time around'
>2 years passes, I'm doing fine, nothing special
>See all my 18 year old friends getting ahead of me
>Some of them already been called to a masters
>Some of them will end college in three years
>Some of them will end it in the normal 4 years
>Takes me 5 years to finish it
>No one gave me a single compliment during my time there
>No professor gave a single fuck about me there
>They all wanted to advise my younger friends
>No job
>Not accepted for a PhD or a masters
>Starts living in subhuman conditions on a 5m room in my aunt's apartment
>All my friends are already progressing in their careers, they might become academics pretty soon
Understand now? I was blinded to the harsh reality, there's nothing stopping me? EVERY FUCKING PROFESSOR IS STOPPING ME. No one gives a fuck about some late starter with average grades, I tried, it's over now.

[Anonymous No.11429204]

>>11429158
looks like you're the pseud here

[Anonymous No.11429211]

>>11429201
haha lol I felt like you once before but then again I was diagnosed with legit schizophrenia (in remission)

It seems the majority of your problems are mental health related.

The issue with professors is possibly an attitude thing on your part and maybe not seeing prof enough to be friendly. Also generally profs dont give a fuck about undergrads because they are essentially cattle on a manufacturing line. New cohort every year, some stand out which they may 'collect', the rest are deposited out the other end with *graduate* branded on their sides.

[Anonymous No.11429213]

>>11429201
>spends all day playing videogame, watching anime
Here's where you went wrong.

[Anonymous No.11429220]

>"Keeps procrastinating"
>" EVERY FUCKING PROFESSOR IS STOPPING ME. No one gives a fuck about some late starter with average grades, I tried, it's over now."
unironically kys.

[Anonymous No.11429226]

>>11429201
I also started at 21, also went through depression and mental health issues. Finished in 4 years and started my masters at 26 (took a gap year cause I did not know where to go).

I thought it would be a new happier chapter of my life. Wrong. Fucked up my first semester, entirely. I had a good rapport with a professor, only to fail their class. I put a lot of work, but circumstances fucked me over. I feel like I have lost my one opportunity to get a Ph.d position now.

Life is tough, man. I totally understand what you mean.

[Anonymous No.11429232]

>>11429201
>EVERY FUCKING PROFESSOR IS STOPPING ME
>"procrastination"
you deserve no sympathy and evidently you're receiving none

[Anonymous No.11429237]

>>11429156
>how do we get the stupid anime posters banned?
What have you tried?

[Anonymous No.11429239]

New rule: if you have mental health problems/illness, stop complaining about being bad at maths

Get treatment and come back when you arent mentally disabled

[Anonymous No.11429244]

[Anonymous No.11429246]

>>11429239
Riemann had mental problems and was a top 5 mathematician of all time.

[Anonymous No.11429248]

>>11429244
In what world are Banach spaces, Lie algebras/groups, complex analysis, and differential topology freshmen topics?

[Anonymous No.11429251]

>>11429211
>legit schizophrenia
Must be terrible, I have a disease as well, I'm addicted to the internet, i can't concentrate much in my studies, sometimes I feel like it was a miracle that I finished college, though it took me a year more than the average person.
>>11429226
At least you finished it in 4 years. That's society's trick, they make you believe you can achieve anything you want if you work hard enough, but what about us? We worked, we tried, when are our dreams becoming true? Now I finally have the answer: Never. We were doomed from the start, we would never make it from the start, but society makes you believe you will, it's only when you experience all those defeats that you can really see the truth, this world is so cruel, it crushed me like an ant and funniest thing is that no one gives a fuck except some anonymous people on an imageboard.

[Anonymous No.11429255]

>>11429251
idiot

[Anonymous No.11429258]

>>11429246
The Chad Euler
>explored fundamental mathematical truths, daring to make statements about the complex plane in a dangerous time
>"Read Euler, read Euler, he is the master of us all."
>"Euler is the only mathematician to have two numbers named after him"

The Virgin Riemann
>time isn't straight lol

[Anonymous No.11429266]

>>11429258
Reminder that the e was discovered and computed by Jacob Bernoulli.

[Anonymous No.11429268]

>>11429198
sure
it's fun, at the very least (the whole course is basically a bunch of little puzzles)
you may not use graph theory very often again unless you're in CS but knowing a teensy bit of basic combinatorics is helpful fairly often, no matter what you do

[Anonymous No.11429270]

>>11429251
>I have a disease as well, I'm addicted to the internet
you don't "have" shit, you're just a manchild

[Anonymous No.11429274]

>>11429251
To fix internet addiction, just go offline. I mean, don't go online at all, all day. It is much easier to not be online than to be online and not procrastinate.
With regards to your future, I suggest you aim to get a job. Then when you got a job, you can do your masters one class at a time for the first few classes, then go full time to finish it. Doing it part-time should help you concentrate better and ease off on the pressure.

[Anonymous No.11429278]

>>11429266
The Virgin Bernoulli
>"He is said to have had a bad relationship with his father"
>"He later gave in to his father's wish and studied business"

in all seriousness i respect his fortitude

[Anonymous No.11429286]

>>11429251
you have to be intelligent. count yourself lucky you worked hard and didn't end up with a career lugging boxes, cretin.

[Anonymous No.11429291]

>>11429274
>just go offline
I appreciate you trying to help, but the problem is much deeper than that, you think telling a drug addict or an alcoholic to 'just stop' will help them? I try to go offline, I try to concentrate, but it's too hard.

[Anonymous No.11429292]

>>11429291
you can solve the problem by not existing anymore.

[Anonymous No.11429297]

>>11429291
The internet is not drugs or alcohol.

[Anonymous No.11429300]

>dunning kruger anime retarded procrastinates at uni and blames proffs and lack of self discipline
yikes

[Anonymous No.11429304]

>>11429300
This.

[Anonymous No.11429308]

>>11429258
It's shitty but I don't care.
I'm kinda proud of how the head fits, tho.

[Anonymous No.11429317]

>>11429291
Internet and Maths:
1) Get rid of internet
1.1) Delete online accounts
1.2) Maintain essential contacts via text (dumbphone not smartphone)
1.3) If email is required use email only phone or public library access
1.4) Buy some books for maths and study materials (pen and paper and scientific calculator)

Health:
2) Get a gym membership
2.1) Do cardio and learn to strength train
2.1.1) Get a gym routine and stick to it
2.2) Fix your sleep and diet
3) Go to a doctor for mental health if it persists
3.1) Avoid psychiatric drugs if possible
3.2) Fix diet, sleep, exercise, routine, goals

Social life:
4) Join some in-person social group, society, or hobby club, etc
4.1) Attend social 'situations' at least twice a week.
4.2) You are probably socially awkward
4.3) Avoid anime trash weebs who will bring you down and/or keep you down

Finances:
5) Idk your situation
5.1) Dont buy shit you cant afford
5.1.1) Buying includes continuous spending not just discrete amazon orders or gambling


This is generally it

[Anonymous No.11429323]

>>11429317
>dumbphone not smartphone
excellent way to mark yourself as socially undesirable. sad but true

[Anonymous No.11429333]

>>11429323
>mark yourself as socially undesirable

Literally who thinks this except superficial retards?

[Anonymous No.11429336]

>>11429317
Why do we hate anime, again?

[Anonymous No.11429341]

>>11429336
common trend of terrible posts linked to anime avataring.

[Anonymous No.11429342]

>>11429336
>Why do we hate anime, again?
It's just the redditors complaining about it

[Anonymous No.11429346]

>>11429336
Dont hate the anime, hate the crab bucket small world weeb

[Anonymous No.11429351]

>>11429336
it's the posters who post anime, not anime itself.

[Anonymous No.11429362]

>>11429336
Which anime is even close to a cinematic masterpiece like Godfather? Which manga is even close to a literary classic like War and Peace? It's the worst form of art, the creators are not worried about quality, only about sales.

[Anonymous No.11429368]

>>11429362
>Which anime is even close to a cinematic masterpiece like Godfather?
The End of Evangelion
>Which manga is even close to a literary classic like War and Peace?
Berserk

[Anonymous No.11429413]

what are a good pool of infinite groups to reference for examples?

[Anonymous No.11429439]

>>11429362
>which anime
Sur-vi-val gaaaames!
>which manga
When all creatures die, they go to a place called Mu.

[Anonymous No.11429441]

>>11429413
the real numbers
the rationals
the complexes
the reals within in any bounded set
god
void

[Anonymous No.11429445]

>>11429413
[math]\mathbb{R}[/math]

[Anonymous No.11429449]

>>11429441
>god is an infinite group
Hum, interesting take

[Anonymous No.11429456]

>>11429336
dumb weeb

[Anonymous No.11429457]

Is there anything a Lebesgue measure can't do?

[Anonymous No.11429461]

>>11429457
it cant be your girlfriend
what is a lebesgue measure btw?

[Anonymous No.11429462]

>>11429456
Mathematics is inherently anime.

[Anonymous No.11429469]

>>11429462
It really is
>Mathematicans have power levels
>You can increase your power level by training
>Each field has its own final bosses to topple

[Anonymous No.11429477]

>>11429461
A way to measure any subset on Euclidean space.

[Anonymous No.11429485]

>>11429469
>some math problems are so difficult, rivals will team up to take the problem down
kino

[Anonymous No.11429487]

>>11429477
what kind of measurement are you taking? why does it inherently have to do with geometry? is R considered euclidean? im confused

[Anonymous No.11429494]

>>11429082
There's like 4 simultaneous structures on Kahler-folds.
>>11429109
Euclidean means the metric is [math]\delta_{ij}[/math] while flat geometry has vanishing curvature. The Euclidean metric condition is much stronger.
>>11429457
It can't do integration on infinite-dimensional spaces for one.

[Anonymous No.11429512]

>>11429494
Oops I meant hyperKahlers. Kahlers have 3

[Anonymous No.11429516]

>>11429512
Yah, but you can derive the third one from two of them.

[Anonymous No.11429519]

>>11429516
No.

[Anonymous No.11429522]

>>11429519
>what is [math]g(u, v)= \omega ( u, Jv)[/math]

[Anonymous No.11429531]

>>11429084
>>11429071
the duality of man

[Anonymous No.11429532]

what about a linear map that transforms an intergral into like, a super integeral???

[Anonymous No.11429538]

>>11429522
>what is a Kahler potential

[Anonymous No.11429543]

>>11429538
I never said you *could only* describe a Kahler manifold in terms of two compatible structures, you autist.

[Anonymous No.11429546]

>>11429543
Nice backtrack.

[Anonymous No.11429551]

>>11429546
If you'll claim I did say it, at least point me where, faggot.

[Anonymous No.11429552]

>>11428795
>music is S tier, engineering and chemistry aren't
Terrible list, you should kill yourself for making it.

[Anonymous No.11429555]

>>11429552
chemistry should be S tier but engineers tend to be retards ime.

[Anonymous No.11429562]

>>11429552
Music is the greatest manifestation of human expression.

[Anonymous No.11429567]

>>11429555
depends on the engineering. there are many different disciplines of it, just like CS.

[Anonymous No.11429568]

i like how if you have 3 parts of a triangle you can find the other 3 parts

[Anonymous No.11429576]

>>11429568
Not at all, if you jnownthe measure of three sides, you can't find their angles

[Anonymous No.11429580]

>>11429576
are you sure

[Anonymous No.11429585]

>>11429580
I am sure

[Anonymous No.11429587]

>>11429585
canu explain

[Anonymous No.11429589]

>>11429587
Grab a book

[Anonymous No.11429590]

>>11429589
ok got one whats next

[Anonymous No.11429592]

>>11429589
im gonna shoot you

[Anonymous No.11429599]

>>11429590
Is it a geometry book

[Anonymous No.11429602]

>>11429562
So is the arts, its a mid tier major for you though.

[Anonymous No.11429605]

>>11429576
What if you use the cosine theorem tho?

[Anonymous No.11429606]

>>11429599
hold the fuck up, you said nothing about a geometry book

[Anonymous No.11429608]

>>11429602
Art has already reached its full potential, all there is in modern art is trash.

[Anonymous No.11429611]

>>11429606
It should have been understood without saying

[Anonymous No.11429618]

>>11429608
>Modern art is tras-

[Anonymous No.11429620]

>>11429611
you're the kinda guy who says a theorem is true without stating the assumptions ahead of the conjecture

[Anonymous No.11429644]

>>11428737
Is there a math stream? I want to set on a long as collection of math videos as I go to sleep tonight.

[Anonymous No.11429656]

>>11429644
https://www.youtube.com/watch?v=1LwkljjLBns
https://www.youtube.com/watch?v=cp6eudDomRY
https://www.youtube.com/watch?v=r_KqR5tBekQ

[Anonymous No.11429673]

>>11429620
thank you for your Psychology session, how much should I pay you, Doctor Bullshit?

[Anonymous No.11429675]

>>11429608
Classical Music has already reached it's full potential, all there is in modern classic music is trash.

[Anonymous No.11429677]

god damn'it i didn't think i'd have to learn category theory to do topology. god help me.

[Anonymous No.11429680]

>>11429675
If you knew anything about classical music you'd know that's not true.

[Anonymous No.11429686]

>>11429680
If you knew anything about art, you'd know that's not true.

[Anonymous No.11429771]

>>11429686
Oh, yeah? Then tell me more about modern art? Nowadays art is nothing but trash, son. Cinema, literature, music, poetry, all evolved, but art followed the opposite path.

[Anonymous No.11429774]

>>11429673
$17

[Anonymous No.11429777]

>>11429677
It’s inescapable.

[Anonymous No.11429788]

>>11429677
Category Theory permeates all math and physics these days.

[Anonymous No.11429803]

>>11429777
>>11429788
Digits of truth.

[Anonymous No.11429805]

>>11428737
>Dank math
I want to strangle you.

[Anonymous No.11429831]

Hey abstract algebra guys. I'm learning about Rings and I'm investigating an interesting example in my book. Suppose you're calculating the product of two very large integers, say [math]a[/math] and [math]b[/math]. You can split the calculation into, say, k parts as [math]a \equiv a_i \space mod \space n_i[/math] and [math]b \equiv b_i \space mod \space n_i[/math] for a set of pairwise coprimes [math]n_i[/math]. Then, the ith equivalences can be multiplied independently, and a clever use of the Chinese Remainder Theorem can solve the system mod [math]N = \Pi_{i=1}^{k}n_i[/math] for your intended product.

The way wikipedia describes this process, is performing the operation in each [math]\mathbb{Z}/n_i\mathbb{Z}[/math] then "applying the isomorphism from left to right" with that isomorphism being [math]\mathbb {Z} /N\mathbb {Z} \cong \mathbb {Z} /n_{1}\mathbb {Z} \times \cdots \times \mathbb {Z} /n_{k}\mathbb {Z}[/math].

What exactly does this mean, "applying the isomorphism from left to right"?

[Anonymous No.11429838]

>>11429831
Holy fuck my math tags.

Sorry, that's each [math]\mathbb{Z}/n_i\mathbb{Z}[/math], then "applying the isomorphism from left to right" with the isomorphism being [math]\mathbb {Z} /N\mathbb {Z} \cong \mathbb {Z} /n_{1}\mathbb {Z} \times \cdots \times \mathbb {Z} /n_{k}\mathbb {Z}[/math]

[Anonymous No.11429840]

>>11429831
At least link to the wikipedia page.

[Anonymous No.11429842]

>>11429838
Jesus fuck, tex preview is lying

[Anonymous No.11429845]

>>11429771
Oh, yeah? Then tell me more about modern classical music? Nowadays classical music is nothing but trash, son. Cinema, literature, art, poetry, all evolved, but classical music followed the opposite path.

[Anonymous No.11429846]

>>11429840
My bad, it's here https://en.wikipedia.org/wiki/Chinese_remainder_theorem#Theorem_statement

[Anonymous No.11429847]

>>11429244
Kinda hilarious how everything after Maxwell in freshman year is of no use to anyone

[Anonymous No.11429849]

>>11429831
>>11429846
The wikipedia page says from the right to the left.
Anyhow, it just means inverting the isomorphism and then applying it.

[Anonymous No.11429856]

>>11429831
Delete this fucking retarded post you just fucked up the entire thread for mobile users you pos

[Anonymous No.11429857]

>>11429856
>giving a shit about mobile users
OH NO NO NO

[Anonymous No.11429858]

>>11429856
Blame the preview, it showed everything correctly

[Anonymous No.11429862]

>>11429845
You're retarded.

[Anonymous No.11429864]

[math]Delete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you posDelete this fucking retarded post you just fucked up the entire thread for mobile users you pos[/math]

[Anonymous No.11429865]

>>11429856
Phoneposters belong back on r*ddit.

[Anonymous No.11429869]

>>11429849
Oh I see what's going on. This is to say that a multi-modular computation broken up into the pieces (right) is the inverted ring (left).

>>11429864
based

[Anonymous No.11429873]

>>11429864
Ok, now THIS is based.

[Anonymous No.11429875]

Realistically speaking, which famous mathematicians would've browsed /mg/?

[Anonymous No.11429876]

>>11429875
Only the autistic ones. Newton for sure

[Anonymous No.11429883]

>>11429831
I guess what I'm asking is, how is the chinese remainder theorem isomorphic to the direct product of these equivalence classes?

[Anonymous No.11429886]

>>11429864
REEEEE SON OF A BIIIIIITCH

[Anonymous No.11429906]

>>11429862
I'm not retarded, I'm just showing you how stupid your argument is. You can replace whatever form of art you're shit talking with any other form of art and both arguments will be equally valid as both arguments aren't valid at all. You can't state a certain medium of art is better then another medium of art without being subjective, because art is subjective. That's why it's fucking autistic to put one form of art above another when ranking them.

[Anonymous No.11429971]

>>11429906
Jeebus christ, yes you are fucking retarded, I'm pretty sure now that you used this red flag 'art is subjective', you have any idea how many books have been written on what is art? Why are you talking about shit you have no idea about as if you're an expert? What do you know about the current classical music or art community? You're assuming I'm clueless like you, but right now you're the only one showing lack of knowledge and stating retarded things as if they're equivalent. For starters, go read Tolstoy's take on art, then you can come back here to discuss this subject again.

[Anonymous No.11430042]

>>11429875
Definitely Euler

[Anonymous No.11430054]

>>11429971
Notice not a single objective argument for why classical music is better then art.

[Anonymous No.11430061]

>>11429201
>you can't possibly succeed if you start late!!!!
>yeah i just procrastinated and played video games all day

[Anonymous No.11430067]

>>11429248
literally any competent student is doing at least 2 or 3 of these in freshman year
what are you wasting your time with?

[Anonymous No.11430077]

>>11430067
I went to public schools in the US, which set you up for doing calc 1 in freshman year college... Where are the schools who are actually teaching students at this level?

[Anonymous No.11430082]

>>11428823
cope

[Anonymous No.11430099]

>>11430077
He's LARPing. At best, you'll be taking vector calc your freshmen year at college, assuming you did AB/BC senior year of highschool. No freshmen, at least not many, is learning about Banach spaces.

[Anonymous No.11430112]

>>11429248
Imagine being new enough to respond seriously to Verbitskyposting

[Anonymous No.11430592]

>>11429248
bro we did this is kindergarten lol

[Anonymous No.11430673]

laplace more like lashit

[Anonymous No.11430704]

> [..] is how it had been proven in 4 or more dimensions, but it took longer to prove for three dimensions! As for why it was harder for three.. It has to do with how we exist in three dimensions! There are ways to force it for four dimension and higher, but N=3 involves our reality, and that means a lot more conditions.

Yeah yeah.

[Anonymous No.11430946]

>>11430112
>>11429248
You mean there are freshmen who are NOT familiar with those?
LOL

[Anonymous No.11431001]

>>11429201
maybe you're not putting enough effort or maybe you just don't have what it takes to be a mathematician. but it's NOT because you're 21 instead of 18. nobody gives a shit about that.

[Anonymous No.11431011]

>>11429494
>Euclidean means the metric is δijδij while flat geometry has vanishing curvature. The Euclidean metric condition is much stronger.
vanishing curvature implies existence of coordinates where the metric is delta_ij

[Anonymous No.11431035]

>>11429201
>He didn't figure out in the first semester that Professors are not there to actually help but to just dance on a strange for 3 hours a week and hand out assignments/tests and report grades

The primary lesson one should take away from college is that is that college is a scam. Nearly everything you do in a college you can do for yourself. And Lecture is especially useless with mathematics. I stopped attending classes in ODEs when I realized I got more sitting down and working from the book for an hour then I did from listening to some frothing fat fuck from non-English speaking country #23 with an atrocious accent. Showed up for the tests, Bs became As and unless attendance was mandatory, showed up for Day 1, test days and finals day (that's ignoring the brief pop in to drop off homework every now when it was due then dipped out) and repeated with every other math course until I got my Bachelors of Science in Math. Math professors are a waste of your time and your tuition money.

[Anonymous No.11431054]

>>11431035
Maybe for an idiot like you. People like us who don't have so much difficulty with learning on the go use these interactive moments as an opportunity to network.

[Anonymous No.11431072]

>>11431001
>what it takes to be a mathematician.
Yeah? And what does it take to be a mathematician? You don't even know, you're trapped in an illusion, you delude yourself just as I did long ago. I'll tell you what it takes: either you start early or you're a genius. Otherwise you can forget about building a career in the academy. No one cares about age? Heh, what a joke, you've no idea how harsh things really are in reality.
>>11431035
I used to think like that too, until I got friends that didn't read a single book but were still getting As, then I asked them how they study and they said 'I just pay attention to the classes'. That's what it means to be a genius, that's what talent is, those people don't need books or hours of study, all they need is a professor explaining things for 2 hours so they can retain it in their brains.

[Anonymous No.11431130]

>>11431072
Oh yeah, that's a baseline. That's not because of age. There were plenty of undergrads at your school who needed tons of time to study and understand things, they weren't A students, never got attention from profs, and didn't make it in the grad school process despite being 18 when they started.
It's not about being a "genius" per se but to make it very far you do need a propensity and intuition for math. I do think that those are learned things, but it's a question of how quickly you are able to learn it.
I think if you're 40 it's harder to pick that up but there is very little difference between 18 and 21.

[Anonymous No.11431153]

>>11429244
>Americans think this is special
This isn't even enough to become a schoolteacher in Europe

[Anonymous No.11431158]

>>11431072
>No one cares about age? Heh, what a joke, you've no idea how harsh things really are in reality.
I didn't give a shit about math in high school. I entered university at 20 (in my country 19-20 is the normal age for this). For two years I was a total slacker, I studied just enough to pass mandatory classes. I didn't take my studies seriously at all until I was 22, that's when I actually began doing mathematics. I got my master's in geometry at 25 and I'm currently in second year phd. Joke's on you man. You don't have what it takes to be a mathematician because you're retarded. How do I know ? Because you unironically believe that all your problems come from the fact that you started at 21 and not at 18. LMAO

[Anonymous No.11431215]

Is Poincare the most important figure in topology?

[Anonymous No.11431224]

>>11431130
I'm 23, you think it's not too late for me yet?

[Anonymous No.11431227]

>>11431224
Dude, Euler only pooped on prime number days as a baby. If you haven't started doing that kind of math as an infant, you will never make it

[Anonymous No.11431236]

>>11431224
What do you mean by "late?" Where are you starting from? Where do you want to get? What do you need to live and be in school at the same time?
Ask yourself these questions and figure out if you can devote yourself to it.

[Anonymous No.11431297]

>>11431236
>Where are you starting from?
I know calculus I, II and III
I know LA, but forgot somethings
I know basic Python
>Where do you want to get?
I wanna teach in university and do research
>What do you need to live and be in school at the same time?
I don't understand that question, I don't need to work rn if that's what you mean
>Ask yourself these questions and figure out if you can devote yourself to it.
Can I make it?

[Anonymous No.11431321]

Which kind of math should I study if I want to apply it to computational biology?

[Anonymous No.11431393]

Mathematicians should never be allowed to name anything.

[Anonymous No.11431429]

>>11431321
ODEs

[Anonymous No.11431435]

>>11431393
LOLOLOL
Is this guy on weed? A set can't be closed and open at the same time kek

[Anonymous No.11431440]

>>11431393
>clopen

[Anonymous No.11431452]

>>11431435
Put some more effort into your bait.

[Anonymous No.11431459]

>>11431452
>Bait
Retard

[Anonymous No.11431463]

>>11431435
Cringe.

[Anonymous No.11431623]

>>11431614

[Anonymous No.11431633]

>>11429656
based

[Anonymous No.11431639]

>>11431215
no. the circle is the most important figure

[Anonymous No.11431640]

>>11431011
Locally. Euclidean is flat globally

[Anonymous No.11431654]

>>11431640
the distinction between "flat" and "euclidean" then lies only in the topology

[Anonymous No.11431668]

>>11431654
>only

[Anonymous No.11431680]

>>11431623
Any average IQ can succeed in all fields of math with enough effort. There's just one field that is literally impossible for people with an IQ below 140 at the very least: Combinatorics.

[Anonymous No.11431681]

>>11431640
>Euclidean is flat globally
>>11431654
Not really, maybe. I wouldn't be surprised if [math]R^4[/math] with a nonstandard smooth structure admitted a flat metric, and then it wouldn't be appropriate to call it Euclidean.

[Anonymous No.11431693]

>>11431072
>Heh, what a joke

[Anonymous No.11431761]

>>11431681
Nevermind. I think Cheeger-Gromoll Splitting gives an obstruction.

[Anonymous No.11431775]

Just how exactly is category theory used in physics?

[Anonymous No.11431778]

>>11431775
Dunno

[Anonymous No.11431785]

>>11431778
Call remilia poster here, he might know

[Anonymous No.11431789]

>>11431785
>>11431775
I think algebraic quantum field theory uses categories.
Also quantum topos theory.

[Anonymous No.11431791]

>>11431785
Ok I have him on my pager

[Anonymous No.11431795]

How do you get the universal property definition of adjunction from this? A priori (\epsilon_d)_* is not a surjection right??

[Anonymous No.11431800]

>>11431789
>algebraic quantum field theory
That shit real???

[Anonymous No.11431808]

>>11431795
It is a surjection but I don't see why I should be a bijection. I want to prove that \epsilon_d \colon FGd \to d is a terminal object in the category F \downarrow d. I see that every morphism Fc \to d factors through FGd (by sujectivity of (\epsilon_d)_*)

[Anonymous No.11431810]

>>11431800
https://ncatlab.org/nlab/show/AQFT

[Anonymous No.11431819]

>>11431680
>combinatorics
>proof by example
literally anti-math

[Anonymous No.11431836]

>>11429082
That’s not how it goes. You start from concrete objects that are interesting and then you abstract away their properties (eg. group structure, manifold structure, etc.)
People did not begin by defining groups on the one hand, manifolds on the other and then go «wait, what if we combined those ?»

[Anonymous No.11431838]

>>11429128
I have a PhD and I know nothing about Kahler manifolds

[Anonymous No.11431847]

>>11431838
Of course you don't, your field is probably not related to complex geometry, simplectic geometry or algebraic geometry.

[Anonymous No.11431850]

>>11431836
Another thing is that many abstract structures are too broad by themselves to have any interesting structure theory (eg. groups, topological spaces, rings).
You need to add some properties to say nontrivial things. Because all humans can do is count and do linear algebra, the properties we add are finiteness (either actual finiteness, or compactness) and linearity assumptions of some sort.

[Anonymous No.11431866]

>>11428823
Started uni at 20. I will be graduating with my PhD later this year (I'll be 31).

[Anonymous No.11431875]

>>11431866
Can't you read, I said 21, I started at 21 and it was too late already.

[Anonymous No.11431877]

>>11431866
Did you do a master's?

[Anonymous No.11431901]

https://mathoverflow.net/questions/3591/mathematicians-who-were-late-learners-list

[Anonymous No.11431915]

>>11431877
Yes. 3 year bachelor + 2 year masters + 3 year PhD. I also did some independent study while working full time. NEETing around at school sure is a lot better than honest work.

[Anonymous No.11431921]

>>11431915
3 years of bachelor? You finished it faster than most people, the regular time is 4 years, therefore you must be some kind of prodigy.

[Anonymous No.11431934]

>>11431921
>you must be some kind of prodigy.

[Anonymous No.11431936]

>>11431921
No I am actually a lazy idiot. 3 years for a bachelor degree is the norm in Europe.

[Anonymous No.11431956]

>>11431901
I got my BA/MA at 28. Went back to school at 24. It really wasn't that bad at all, biggest problem was that my social life was non existent.

[Anonymous No.11431957]

My pager started beeping, what's up?

[Anonymous No.11431960]

>>11431956
>problem

[Anonymous No.11431984]

>>11431957
someone made me feel inferior on the internet.

destroy them

[Anonymous No.11431987]

>>11431984
Who?

[Anonymous No.11432000]

>>11431956
What is a BA/MA?

[Anonymous No.11432002]

>>11432000
Bachelors of arts

[Anonymous No.11432004]

>>11431957
There you are, answer this now >>11431775

[Anonymous No.11432006]

>>11432000
Bachelor of Arts/Master of Arts

My uni didn't offer a BA/BS distinction for math like other unis

[Anonymous No.11432012]

>>11431957

[Anonymous No.11432017]

>>11432004
>>11431775
Fuck if I know lmao.
Doesn't Quantum Topos theory count? It's category theory and physics, isn't it?

[Anonymous No.11432044]

>>11432017
Aren't you a physicist?

[Anonymous No.11432079]

>>11431775
Right, so I was flipping through a paper, and apparently, you want a realist version of quantum mechanics, and because of locality, you want sheaves, but instead of open sets it needs to be von Neumann Algebras. So you have a category of von Neumann algebras in which given von Neumann algebras represent contexts(i.e. this electron, that electron, these two electrons) and the morphisms are inclusions.
I'm basically baiting someone into correcting me.
>>11432044
Not really.

[Anonymous No.11432083]

>>11432079
What are you, then?

[Anonymous No.11432085]

Imagine studying mathematics and looking down on anime.

Guide how to succeed:
1) Get a routine and a schedule. This includes work AND relaxation.
2) Start doing stuff even if you don't know what you are doing. Learn by doing.
3) Don't waste your time or money on thots.

[Anonymous No.11432100]

>>11432085
Math is inherently anime.

[Anonymous No.11432102]

>>11432083
Your father.

[Anonymous No.11432112]

>>11432085
>but do waste your time on screen-thots

[Anonymous No.11432125]

>>11432085
have sex

[Anonymous No.11432153]

>>11429201
you're a fucking retard, all you do is procrastinate all day, watch chinese cartoons and play vidya
That's why you failed, not cause you're 21 but cause you're a lazy deadbeat loser

[Anonymous No.11432160]

>>11432112
This but unironically.

[Anonymous No.11432208]

>>11432079
What is your opinion on this post >>11429201 remiliabro

[Anonymous No.11432210]

Anime should be watched in moderation.

[Anonymous No.11432265]

>>11432079
Good effort, but what you've said doesn't illustrate why category theory would be useful in QM; you've just modeled the observables with von Neumann algebras in which, over a fixed system, no reference to any categorical structure is required.
When the system starts to evolve in (space)time, we can define an operator net as a functor [math](\mathcal{R},\coprod)\rightarrow ({\bf vNA},\bigotimes)[/math] from the category of open sets on spacetime with inclusions into the category of von Neumann algebras. Locality is then the condition that only spacelike inclusions leads to an algebra embedding, otherwise the the algebra in the image splits into direct sums. Now this [math]still[/math] doesn't illustrate why category theory is useful (though it does organize the data of an operator net neatly); people had been working with local operator nets of observables as foundations of QFT for decades without reference to category theory. This is Haag-Kastler's non-perturbative QFT.
What [math]does[/math] demonstrate the usefulness of categories, however, is when we consider [math]{\bf vNA} = {\bf vNA}^2[/math] as a 2-category, with bimodules [math]M: A\rightarrow B[/math] as 2-morphisms. The reason for this is that QM is modeled by [math]representations[/math] of von Neumann algebras and not the algebras themselves, and the representation spaces, as algebra modules, induces a [math]{\bf unitary ~Morita~ equivalence}[/math] between the algebras aside from the usual algebra isomorphisms. Theories defined on Morita equivalent local nets are unitarily equivalent, hence we must consider something like [math]\pi_0 {\bf Rep}_{\mathbb{C}}({\bf vNA}^2)[/math] if we want to properly characterize QFT/QM theories

[Anonymous No.11432270]

>of the arts
oh no...

[Anonymous No.11432316]

>>11432265
Can you also explain the daseinisation thing?
I've tried to read Heidegger once, so seeing the word just gives me Vietnam flashbacks.

[Anonymous No.11432323]

>>11432316
What is Remilia dreaming about?

[Anonymous No.11432355]

>>11429153
Who do i get the feeling that you're projecting your own retardation and uselessness onto others?

[Anonymous No.11432363]

>>11432355
Because he's projecting his retardation and uselessness onto others.

[Anonymous No.11432389]

>>11432355
Because you're in denial and trapped in society's illusion.

[Anonymous No.11432392]

>>11432363
>Because he's projecting his retardation and uselessness onto others.
I'm not a "he".

[Anonymous No.11432395]

why calculus has to be so difficult :( linear algebra is much easier i think

[Anonymous No.11432398]

>>11431224
Yes, end yourseld and fuck off you miserable worthless waste of a human being, you retarded little weasel.

[Anonymous No.11432403]

>>11431224
Yes, end yourself and fuck off you miserable worthless waste of a human being, you retarded little weasel.

[Anonymous No.11432410]

>>11432392
Trannies are still not women, delusional faggot.

[Anonymous No.11432417]

>>11432410
Trans rights matter.

[Anonymous No.11432418]

>>11431035
Lol imagine getting jewed by the kikes so hard that you pay exorbitant amounts of money for college.
Get shot amerimutt.

[Anonymous No.11432427]

is it possible to define a quotient space with respect to multiple equivalence relations simultaneously?

[Anonymous No.11432430]

>>11432427
>is it possible to define a quotient space with respect to multiple equivalence relations simultaneously?
What have you tried?

[Anonymous No.11432432]

>>11432410
>Trannies
Why the transphobia?

[Anonymous No.11432438]

>>11432160
Ayy that white ass bitch couldda solve that cray asss integral faster and easier by integrating by damn parts yoo that lil honkey ass bitch is retarded bro lmao we gon fucc her up with ma cousin jamal

[Anonymous No.11432450]

>>11432430
that's not an answer to my question

[Anonymous No.11432467]

>>11432427
You can take the smallest relation which includes all of your relations and take the quotient with respect to it.

[Anonymous No.11432474]

>>11432395
>He doesn't know about Axler, Hoffman, Halmos and Roman
Oh nonono

[Anonymous No.11432479]

>>11432467
does this yield any unique properties or is it just still a run of the mill quotient space? how about topologically speaking?

[Anonymous No.11432500]

>>11432479
If you're quotienting out a bunch of subspaces, you just quotient them out in sucession (not necessarily the union).
If you're quotienting out a group action, you're just summing the group actions and quotienting them out.
If you're doing both, it gets weird, but a retarded sort of weird.

[Anonymous No.11432502]

>>11432474
>>He doesn't know about Axler, Hoffman, Halmos and Roman
Axler is a meme.

[Anonymous No.11432509]

>>11432474
i'm very rubbish at math. I just got into taylor sequences and i'm scared anon :(

Well i'm done with algebra at uni for this year so there is a good chance i'll not be educated about these guys you 're refering too

i'll keep the names tho.. i'm not in mood of studying things outside the uni but you never know what may happen tommorow.

Jesus you really have to love math to dig it.
Btw i'm on the second whisky

[Anonymous No.11432515]

>>11432502
Why do we hate Axler, again?

[Anonymous No.11432524]

>>11432500
cool, thanks

[Anonymous No.11432551]

>>11432515
Because he goes against the status quo, people like that will always be hated

[Anonymous No.11432558]

>>11432392
>tranny
>useless
>delusional
Checks out. You should try an hero.

[Anonymous No.11432564]

Will he ever admit he made a mistake?

[Anonymous No.11432568]

>>11432316
>daseinisation
Sweetie I don't even know how to pronounce it.

[Anonymous No.11432582]

>>11432551
If people didn't challenge the status quo, Cantor would've never created set theory, one of the most important fields of mathematics.

[Anonymous No.11432593]

complex analysis

[Anonymous No.11432605]

>>11432593

[Anonymous No.11432623]

>>11432605
baste

[Anonymous No.11432629]

>>11432593
>>11432605
Is there still research being done in Complex Analysis or is it a dead field made obsolete with the discovery of Several Complex Variables?

[Anonymous No.11432644]

>11429201
Bro you sound like a huge faggot.

[Anonymous No.11432656]

mgpill me on non-galoisian galois theory

[Anonymous No.11432657]

>>11432629
Yes

[Anonymous No.11432658]

>>11431072
> Not realizing a lot of niggas flex and lie about how much the study.

[Anonymous No.11432662]

>>11432657
That doesn't really answer

[Anonymous No.11432670]

>oh look a math thread
>never mind it's just weebs shitposting memes

[Anonymous No.11432674]

>>11432670
First time on 4chan(nel)?

[Anonymous No.11432690]

>>11431035
EXACTLY HOW I DID THINGS BASED AND REDPILLED

[Anonymous No.11432783]

Why is it that whenever this thread approaches the 300 replies limit it becomes very slow? Then when someone create another one it gets like 100 posts in thirty minutes

[Anonymous No.11432797]

I am confused by this picture representation that the Fourier coefficients provide the best approximation to a function [math]f[/math]. If we know that [math]S_n(f)[/math] converges to [math]f[/math] by taking linear combinations of the orthogonal projection of [math]f[/math] onto our basis of trig polynomials, then how does this sum reach our function, as it appears from the picture that [math]f[/math] lies outisde the span?

[Anonymous No.11432798]

>>11432515
The only thing that Axler does is avoiding determinants so he can prove classical results (for example about eigenvalues of linear operators) without matrices. So the characteristic polynomial isn't written using the determinant. This means, linear algebra is a coordinate-free theory and Mr. Axler want LA taught that way. Anyways he fails because he proves spectral theorem using matrices and that implies a basis is being chosen, what he avoided from the start.

[Anonymous No.11432832]

>>11432797
>best approximation

[Anonymous No.11432862]

>>11432783
because the shit posters and de-railers get bored after around 100 posts

[Anonymous No.11432865]

>>11432798
>Anyways he fails because he proves spectral theorem using matrices and that implies a basis is being chosen, what he avoided from the start.
Shut the fuck up

[Anonymous No.11432867]

>>11432865
cope

[Anonymous No.11432870]

Why is measure theory so ubiquitous in upper level maths?

[Anonymous No.11432886]

>>11432870
Mathematicians don't know how to use rulers

[Anonymous No.11432896]

logic isn't math

[Anonymous No.11432902]

Logic is math.

[Anonymous No.11432906]

Logic is and isn't math.

[Anonymous No.11432911]

Logic is math or logic isn't math.

[Anonymous No.11432916]

Both math and logic are subsets of computer science

[Anonymous No.11432926]

>>11432916
>Both math and logic are subsets of computer science
Subcategories, actually.

[Anonymous No.11433113]

>>11432797
For any finite [math]N[/math] you will have a bit [math]f - S_N(f)[/math] of [math]f[/math] that is orthogonal to [math]S_N(f)[/math] and not contained in [math]S_N(f)[/math]; however, each new Fourier coefficient is orthogonal to any of the previous ones and we don't "waste" our time in the subspace that we have already spanned. In this sense it is the most efficient way to approximate [math]f[/math]; the limit [math]S_N(f)\rightarrow f[/math] is rather quick depending on how regular [math]f[/math] is.

[Anonymous No.11433233]

>>11429864
o i am laffin

[Anonymous No.11433343]

>>11428784
Don't read it it's a shitty book

[Anonymous No.11433598]

>>11432798
So Axler Bad
then who good???

[Anonymous No.11433747]

>>11433343
Why?

[Anonymous No.11433749]

>>11433598
You low IQ are so easily manipulated through internet posts, I doubt you'd even be able to do the exercises on Axler.